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string | Question_type
string | Referenced_file(s)
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string | expert_annotation
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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Next we pad and center the data so that the centre of the Airy disk-like envelope of the fringes is in the centre of a larger two-dimensional array of size $2 0 4 8 \\times 2 0 4 8$ . To find the correct pixel to center to we first smooth the image with a wide (50 pixel) Gaussian kernel, then select the pixel with highest signal value. The Gaussian filtering smooths the fringes creating an image corresponding approximately to the Airy disk. Without the filtering the peak pixel selected would be affected by the fringe position and the photon noise, rather than the envelope. Off-sets of the Airy disk from the image center lead to phase slopes across the u,v apertures. To calculate the coherent power between the apertures, we make use of the van Cittert–Zernike theorem that the coherence and the image intensity are related by a Fourier transform. We therefore compute the two-dimensional Fourier transform of the padded CCD frame using the FFT algorithm. Amplitude and phase images of an example Fourier transform are shown in Figure 5. Distinct peaks can be seen in the FFT corresponding to each vector baseline defined by the aperture separations in the mask.
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5
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Yes
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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I. INTRODUCTION We consider the measurement of the ALBA synchrotron electron beam size and shape using optical interferometry with aperture masks. Monitoring the emittance of the electron beam is important for optimal operation of the synchrotron light source, and potentially for future improved performance and real-time adjustments. There are a number of methods to monitor the size of the electron beam, including: (i) LOCO, which is a guiding magnetic lattice analysis incorporating the beam position monitors, (ii) X-ray pinholes (Elleaume et al 1995), and (iii) Synchrotron Radiation Interferometry (SRI). Herein, we consider optical SRI, which can be done in real time without affecting the main beam. Previous measurements using SRI at ALBA have involved a two hole Young’s slit configuration, with rotation of the mask in subsequent measurements to determine the two dimensional size of the electron beam, assuming a Gaussian profile (Torino & Iriso 2016; Torino & Iriso 2015). Such a two hole experiment is standard in synchrotron light sources (Mitsuhasi 2012; Kube 2007), and has been implemented at large particle accelerators, including the LHC (Butti et al. 2022). Four hole square masks have been considered for instantaneous two dimensional size characaterization, but such a square mask has redundant spacings which can lead to decoherence, and require a correction for variation of illumination across the mask (Masaki & Takano 2003; Novokshonov et al. 2017; see Section VI). Non-redundant masks have been used in synchrotron X-ray interferometry, but only for linear (one dimensional grazing incidence) masks (Skopintsev et al. 2014).
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
|
By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
|
Carilli_2024.pdf
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Gaussian random noise is then added to the complex visibilities at the rms level of $\\sim 1 0 \\%$ of the visibility amplitudes, and a second test was done with $1 \\%$ rms noise. Since the noise is incorporated in the complex visibilities, it affects both phase and amplitude. In each case, a series of 30 measurement sets with independent noise (changing ’setseed’ parameter), are generated to imitate the 30 frames taken in our measured time series. We employ ’UVMODELFIT’ in CASA to then fit for the source amplitude, major axis, minor axis, and major axis position angle. Starting guesses are given that are close to, but not identical with, the model parameters (within $2 0 \\%$ ), although the results are insensitive to the starting guesses (within reason). We first run uvmodelfit on the data with no noise, and recover the expected model parameters to better than $1 0 ^ { - 3 }$ precision. These low level differences arise from numerical pixelization. Figure 32 shows the results for the two simulation ’time series’, and Table IV lists the values for the mean and rms/root(30). Also listed are the results from the measurements in Nikolic et al. (2024), and the input model. Two results are of note.
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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VIII. ERROR ANALYSIS A. Photon Noise Floor We have tens of millions of CCD counts per image, and hence the errors from photon counting statistics are low. To obtain a rough estimate, we perform two calculations. First, the number of photons contributing to a visibility is roughly the sum in the uv-aperture divided by the number of pixels in the uv-aperture (the finite size of the uv-aperture is due to a convolution in the uv-plane by the Fourier transform of the ’primary beam’, i.e. the Airy disk, and hence the uv-pixels are not independent). Typically, the visibility amplitudes integrated over the 7-pixel uv-aperture radius, are order $6 \\times 1 0 ^ { 7 }$ , implying about $3 . 8 \\times 1 0 ^ { 5 }$ counts. The fractional error from photon counting is then $1 / \\mathrm { r o o t } ( 3 . 8 \\times 1 0 ^ { 5 } ) = 0 . 1 6 \\%$ . Second, we sum over similar 7-pixel radius apertures in regions of the uv-plane with no signal, and get a mean value of $\\sim 1 . 5 \\times 1 0 ^ { 5 }$ , which, relative to the typical visibility-aperture values of $6 \\times 1 0 ^ { 7 }$ implies an error of $\\sim 0 . 2 5 \\%$
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
|
By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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$$ where, $\\star$ denotes a complex conjugation. The process of calibration determines these complex voltage gain factors. In general, calibration of interferometers can be done with one or more bright sources (‘calibrators’), whose visibilities are accurately known (Thomson, Moran, Swenson 2023). Equation (2) is then inverted to derive the complex voltage gains, $G _ { a } ( \\nu )$ (Schwab1980, Schwab1981, Readhead & Wilkinson 1978; Cornwell & Wilkinson 1981). If these gains are stable over the calibration cycle time, they can then be applied to the visibility measurements of the target source, to obtain the true source visibilities, and hence the source brightness distribution via a Fourier transform. In the case of SRI at ALBA, we have employed self-calibration assuming a Gaussian shape for the synchrotron source, the details of which are presented in the parallel paper (Nikolic et al. 2024). Our process has considered only the gain amplitudes, corresponding to the square root of the flux through an aperture (recall, power $\\propto$ voltage2), dictated by the illumination pattern across the mask. We do not consider the visibility phases. Future work will consider full phase and amplitude self-calibration to constrain more complex source geometries. Closure phase is a quantity defined early in the history of astronomical interferometry, as a measurement of the properties of the source brightness distribution that is robust to element-based phase corruptions (Jennison 1958). Closure phase is the sum of three visibility phases measured cyclically on three interferometer baseline vectors forming a closed triangle, i.e., closure phase is the argument of the bispectrum $=$ product of three complex visbilities in a closed triad of elements:
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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Figure 16 shows the center pixel locations derived using Airy disk centering for the 3-hole and 5-hole data. The X values are the same. But the Y values differ by 5 pixels. The largest departures from zero closure phase for the 5-hole data all involve baseline 0-2, which is the $1 6 \\mathrm { m m }$ vertical baseline (X direction in edf file which implies a narrow fringe in Y direction). This baseline is also in the 3-hole data, and it is the baseline with fringe length oriented horizontally, which might lead to the largest deviation in the case of a change in north-south centering of the fringe pattern on the CCD. Figure 17 shows the resulting phase image without any centering. The offset of the image center from the CCD field center leads to a complete phase wrap across the uv-apertures. This compares to Figure 5, where only small phase gradients are seen after centering. B. U,V aperture radius: 3-9pix coherence and closure phases We consider the radius of the size of the aperture in the u,v plane used to derive the amplitudes and phases of the visibilities. Figure 18 shows a cut throught the center of the amplitude distribution of the u,v image. The hatched area shows the 7-pixel radius. This radius goes down to the 6% point of the ’uv-beam’. Averaging beyond 9 pixels just adds noise, and beyond 10 pixel radius gets overlap between uv-measurements eg. 2-3 and 0-1.
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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Figure 13 shows the closure phases for all ten triads in the uv-sampling, and the values are listed in Table III. All the closure phases are stable (RMS variations $\\leq 0 . 7 ^ { o }$ ), and all the values are close to zero, typically $\\leq 1 ^ { o }$ . The only triads with closure phases of about $2 ^ { o }$ involve the baseline 0-2. This is the vertical baseline of $1 6 \\mathrm { m m }$ length, and hence has a fringe that projects (lengthwise) in the horizontal direction. The origin of closures phases that appear to be very small, but statistically different from zero, is under investigation. For the present, we conclude the closure phases are $< 2 ^ { o }$ . Closure phase is a measure of source symmetry. X-ray pin-hole measurements imply that the beam is Gaussian in shape to high accuracy (Elleaume et al. 1995). A closure phase close to zero is typically assumed to imply a source that is point-symmetric in the image plane (a closure phase $\\leq 2 ^ { o }$ implies brightness asymmetries $\\leq 1 \\%$ of the total flux, for a well resolved source), as would be the case for an elliptical Gaussian. However, the fact that the source is only marginally resolved (Section III), can also lead to small closure phases, regardless of source structure on scales much smaller than the resolution. A simple test using uv-data for a very complex source that is only marginally resolved, shows that for closed triads composed of baselines with coherences $\\ge 7 0 \\%$ , the closure phase is $< 2 ^ { o }$ . In this case, even small, but statistically non-zero, closure phases provide information on source structure.
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
|
Carilli_2024.pdf
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To check if some of the decoherence of 3 ms vs 1 ms data could be caused by changing gain solutions in the joint fitting process, in Figure 25 we show the illumination values for the 5-holes derived from 1 ms vs. 3 ms data from the source fitting procedure. The illumination is defined as $\\mathrm { G a i n ^ { 2 } }$ , which converts the voltage gain from the fitting procedure into photon counts (ie. power vs. voltage). We then divide the 3 ms counts by 3, for a comparison to 1ms data (ie. counts/millisecond). Figure 25 shows that the derived illuminations are the same to within 2%, at worst, which would not explain the 5% to $1 0 \\%$ larger coherences for 1!ms data. In Section VII we consider the effect of averaging time on all the data, including 2-hole and 3-hole measurements. E. Bias subtraction We have calculated the off-source mean counts and rms for data using 2, 3, and 5-hole data, and for 1mÀú s to 3 ms averaging, and for 3 mm and 5 mm holes. The off-source mean ranged from 3.43 to 3.97 counts per pixel, with an rms scatter of 5 counts in all cases. We have adopted the mean value of 3.7 counts per pixel for the bias for all analyses. The bias appears to be independent of hole size, number of holes, and integration time, suggesting that the bias is
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augmentation
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Yes
| 0
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expert
|
How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
|
Carilli_2024.pdf
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Table I also lists the gains derived after image averaging, with and without Airy disk centering. In this case, the gains are essentially unchanged (within $1 \\%$ ), relative to the mean from the time series (row 1). This similarity for gain results from data that clearly involved decoherence of the visibilities themselves lends confidence that the derived illumination correction (the ’gains’), are correct. Table: Caption: TABLE I. Gains derived from the self-calibration process for a 5-hole mask. Body: <html><body><table><tr><td>G0</td><td>G1</td><td>G2</td><td>G3</td><td>G4</td><td>σ/cells p</td><td>n</td></tr><tr><td>Mean of best-fits in time series 7.35 RMS in time series 0.067</td><td>8.43 0.045</td><td>8.40</td><td>9.37 0.029 0.027 0.034</td><td>9.11 4.88</td><td>74.66 0.9</td><td>0.66 0.42 0.13</td></tr><tr><td>Sum of 3O frames with no centering 7.45</td><td>8.50</td><td>8.47</td><td>9.35</td><td>9.15</td><td>49.1</td><td>0.22 0.15</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Sum of 30 frames with Airy centering 7.41</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td></td><td>8.45</td><td>8.50</td><td>9.37</td><td>9.13</td><td>68.8</td><td>0.37 0.58</td></tr><tr><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></table></body></html> Table: Caption: Body: <html><body><table><tr><td>Baseline</td><td>5-hole Coherence</td><td>RMS</td><td>3-hole Coherence</td><td>RMS</td><td>No Center Airy Center</td><td></td></tr><tr><td>0-1</td><td>0.793</td><td>0.0030</td><td>0.816</td><td>0.0050</td><td>0.67</td><td>0.75</td></tr><tr><td>0-2</td><td>0.972</td><td>0.0079</td><td>0.989</td><td>0.0088</td><td>0.74</td><td>0.93</td></tr><tr><td>0-3</td><td>0.945</td><td>0.0130</td><td></td><td></td><td>0.70</td><td>0.90</td></tr><tr><td>0-4</td><td>0.840</td><td>0.0089</td><td></td><td></td><td>0.67</td><td>0.80</td></tr><tr><td>1-2</td><td>0.645</td><td>0.0048</td><td>0.691</td><td>0.0073</td><td>0.42</td><td>0.61</td></tr><tr><td>1-3</td><td>0.875</td><td>0.0056</td><td></td><td></td><td>0.66</td><td>0.84</td></tr><tr><td>1-4</td><td>0.993</td><td>0.0030</td><td></td><td></td><td>0.90</td><td>0.97</td></tr><tr><td>2-3</td><td>0.933</td><td>0.0014</td><td></td><td></td><td>0.87</td><td>0.91</td></tr><tr><td>2-4</td><td>0.734</td><td>0.0028</td><td></td><td></td><td>0.59</td><td>0.70</td></tr><tr><td>3-4</td><td>0.938</td><td>0.0023</td><td></td><td></td><td>0.86</td><td>0.92</td></tr></table></body></html> TABLE II. Column 2 and 3: mean coherences and RMS scatter for the time series of measurements for the 10 baselines in the 5-hole mask, after Airy centering. Column 4 and 5 lists the same for the 3-hole data. Column 6 lists the coherence derived by first summing all of the frames together, then doing the Fourier transform, without any image centering. Column 7 lists the same but after Airy disk centering. D. Visibility and Closure Phases
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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First, the $1 \\%$ rms noise on the visibilities results in fitted quantities (amplitude, bmaj, bmin, pa), that are consistent with the model parameters, to within the scatter. Also, the rms scatter for the fit paramaters are of similar magnitude as those found for the real data. Second, the $1 0 \\%$ rms visibility noise leads to $\\sim 1 0 \\times$ higher scatter in the fitting results. Moreover, the minor axis fitting shows a skewed distribution toward values higher than the input model (ie. 21 points above the model line, and 9 below). We suspect that this skewness arises due to a Poisson-like bias when fitting for a positive definite quantity, when the errors become significant compared to the value itself. This skewness is not seen in the $1 \\%$ error analysis. C. Systematic Errors We investigate the effect of systematic errors using real data for visibility amplitudes from the ALBA 5-hole data. Two simple tests are performed: adjust the amplitudes systematically low by 5%, and high by 5%, then run the Gaussian fitting routine in Nikolic et al. (2024). The fitted source size for the 5% low amplitudes increases by $6 . 4 \\%$ , while the size decreases by 6.9% for the 5% high amplitudes. This is qualitatively consistent with the expected increase in source size for lower coherences, and vice versa. Quantitatively, for small offsets, the source size appears to be roughly linear with systematic offset for the visibility amplitudes. However, the fitting routine includes a joint fit for the gains of each hole. These gains also change slightly with systematic errors, with up to 2% lower gains for lower amplitudes, and similarly higher gains for higher amplitudes.
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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B. Processing Errors: Gaussian Random Approximation Beyond photon statistics, there are a number of processing steps that affect the resulting coherences, and hence the fit to the source size, including: uv-aperture size, bias subtraction, image centering, and others. In this section, we perform modeling of the uv-data to get an estimate of what level of errors in the coherences could lead to the measured scatter in the final results, assuming a Gaussian random distribution for the various errors over time. Systematic errors with time are considered below. While not strictly rigorous (the modeling does not include effects related to eg. the edges of the CCD or bias subtraction), this uv-model approach does provide a rough estimate of the summed level of error likely in the ALBA data, as well as how such errors may affect the final results. Table: Caption: Body: <html><body><table><tr><td></td><td>Amplitude</td><td>Major Axis microns</td><td>microns</td><td>Minor Axis Position Angle degrees</td></tr><tr><td>Data Fit</td><td></td><td>59.6 ± 0.1</td><td>23.8 ± 0.5</td><td>15.9 ± 0.2</td></tr><tr><td>Model</td><td>357.70</td><td>60</td><td>24</td><td>16</td></tr><tr><td>1% errors</td><td>357.59±0.26</td><td>59.87 ± 0.11</td><td>23.77±0.22</td><td>15.83 ± 0.14</td></tr><tr><td>10% errors</td><td>359.79 ± 2.33</td><td>60.02 ± 1.01</td><td>27.71 ± 1.58</td><td>17.49 ± 1.61</td></tr></table></body></html> TABLE IV. Error analysis from modeling. The first row lists the measurements from Nikolic et al. (2024) We start by creating a FITS image of a Gaussian model with the shape of the ALBA electron beam, for which we adopt a dispersion of $6 0 \\mu \\mathrm { m } \\times 2 4 \\mu \\mathrm { m }$ , and major axis position angle $= + 1 6 ^ { o }$ CCW from the horizontal. This model image is converted into arcseconds using the distance between the mask and the synchrotron source (15.05 m). We also generate a configuration file corresponding to the 5-hole mask used in our experiments, with baselines and hole size scaled to get uv-coordinates in wavelengths. A uv-data measurement set is then generated from the model and the configuration using the CASA task ’SIMOBSERVE’, resulting in a 10 visibility measurement set with the proper uv-baseline distribution, primary beam size, and model visibilities (complex coherences).
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
|
Carilli_2024.pdf
|
One curious result is the close correlation between the decoherence of the two redundant baselines with time, as can be seen in Figure 29 and Figure 28. Some correlation is expected, since the phase fluctations at hole 5 are common to both baselines. But we are surprised by the degree of correlation. Perhaps vibrations of optical components might be more susceptible to such close correlation as opposed to laboratory ’seeing’ ? Further experiments are required to understand the origin of visibility phase fluctuations in the SRI measurements. We conclude that redundant sampling of the visibilities leads to decoherence at the level $\\sim 5 \\%$ , with a comparable magnitude for the scatter for the time series. A 5% decoherence is comparable to that seen comparing 1 ms vs. 3 ms time averaging of interferograms (Figure 22), and likewise the larger rms scatter of the time series is similar to that seen comparing 1 ms and 3 ms averaging. A 5% decoherence for a redundantly sampled baseline would be caused by a $\\sim 2 0 ^ { o }$ phase difference between the two redundant visibilities. These results necessitate the use of a non-redundant mask to avoid decoherence caused by hole-based phase perturbations due to eg. turbulence in the lab atmosphere or vibration of optical components (Torino & Iriso 2015). Likewise, a filled-aperture imaging system will display image smearing due to these phase perturbations.
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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In most cases, we employ non-redundant masks. A non-redundant aperture mask has a hole geometry such that each interferometric baseline, or separation between holes, is sampled uniquely in the Fourier domain (herein, called, the u,v plane), by a single pair of holes (Bucher & Haniff 1993; Labeyrie 1996). Non-redundant masks are extensively used in astronomical interferometric imaging, in situations where the interferometric phases may be corrupted by atmospheric turbulence, or other phenomena that may be idiosyncratic to a given aperture (often referred to as ’element based phase errors’). In such cases, redundant sampling of a u,v point by multiple baselines with different phase errors would lead to decoherence of the summed fringes in the image (focal) plane. Similarly, a full aperture (ie. no mask), which has very many redundant baselines, will show blurring of the image due to this ’seeing’ caused by phase structure across the aperture. Our 5-hole mask is an adaptation of Gonzales-Mejia (2011) non-redundant array, with the five holes selected to maximize the longer baselines, given the source is only marginally resolved. The full 6-hole mask includes a square for the four corner holes, leading to two redundant baselines (horizontal 16 mm 2-5 and 0-1; vertical 16 mm 1-5 and 0-2). These will be used for testing of the effects of redundant sampling in Section VI.
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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We explore radii of 3, 5, 7, and 9 pixels, considering coherences and closure phases. Figure 19 shows the closure phases versus the u,v aperture radius. The closure phase values tend toward smaller values with increasing aperture size. The RMS scatter decreases substantially with aperture size until 7pix radius. Figure 20 shows the coherences for different u,v aperture radii. The coherences vary slightly, typically less than $2 \\%$ . The RMS of the coherences are relatively flat, or slightly declining, to 7 pixel radius, with a few then increasing at 9 pixels. C. 3 mm vs 5 mm coherences We consider the affect of the size of the hole in the non-redundant mask on coherence and closure phase. Figure 21 shows the coherence for a 5-hole mask with $3 \\mathrm { m m }$ and 5 mm holes. The 5 mm data fall consistently below the equal coherence line, implying lower coherence by typically 5% to $1 0 \\%$ . Also shown is the RMS for the coherence time series. The RMS scatter for the 5 mm holes is higher, more than a factor two higher in some cases. Lower coherence for larger holes may indicate phase gradients across holes. A hole phase gradient is like a pointing error which implies mismatched primary beams in the image plane and may lead to decoherence.
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augmentation
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Yes
| 0
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expert
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How does Carilli’s interferometric method measure beam size?
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By analyzing fringe visibilities from synchrotron light passing through a non-redundant aperture mask and fitting them to a Gaussian source model.
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Reasoning
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Carilli_2024.pdf
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A multi-hole, non-redundant mask and subsequent Fourier imaging analysis, including deconvolution of the point response function (Fourier transform of the u,v sampling), and self-calibration in both phase and amplitude, could be implemented to determine more complex electron beam distributions, without strict a priori model assumptions. The process could parallel the ‘hybrid mapping’ process employed in astronomical Very Long Baseline Interferometry, which includes self-calibration and some form of deconvolution (see Pearson & Readhead 1984). A requirement of such a process is the need for more measurements (visibilities) than degrees of freedom in the source. For example, a double Gaussian would have 10 degrees of freedom = position (2) and shape (3) of each Gaussian. We have generated a template for a 7-hole non-redundant mask based on the aperture mask used on the James Webb Space Telescope that fills the light footprint on the mask (Sivarmakarishnan et al. 2024). The full complex gain self-calibration of amplitudes and phases also represent a precise wavefront sensor, where the phases correspond to the photon pathlength through the optical system. More generally, characterizing the shape of intense light sources other than synchrotron sources may be possible with this technique, such as in inertial fusion reactors, where the driving lasers need to be highly focused shaped, and the shape of plasma EUV light sources in photo-lithography.
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augmentation
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Yes
| 0
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
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5.3. Flux measurement The detector position optimal for the measurement of the channeled particle flux is the channeling plateau for the inner bar and the background position for the external one. In this position, the CpFM 1 bar intercepts the whole channeled beam while the CpFM 2 bar measures only the background. If both the channels have equal efficiency, a more accurate flux measurement is possible in this location since the background signal can be subtracted from the channeled beam signal on event by event basis. During the commissioning of the detector, both CpFM channels were tested in their own channeling plateau positions to compare the results of the flux measurement while both bars intercept the whole channeled beam. In Fig. 9(a) the linear scan profile performed in October 2016 with $2 7 0 \\ { \\mathrm { G e V } }$ protons is shown. It is a similar plot as the one shown in Fig. 8(b), but in this case the amplitude value is divided by the calibration factor, as found in Section 4 and expressed in mV/proton, to display the number of channeled protons extracted per turn. In Fig. 9(b) the distributions of number of protons related to the channeling plateau regions of CpFM 1 and CpFM 2 are shown. No event selection has been performed since a pedestal event is caused either by the physical absence of channeled particles or by the inefficiency of the detector. In fact, the absence of channeled particles could be connected to orbit instabilities, beam halo dynamics or to the inefficiency of the crystal-extraction system, with the latter under study by the CpFM detector. The inefficiency of the detector is already taken into account by the calibration factors. In Fig. 9(b) pedestal events are much more abundant in the CpFM 1 distribution than in the CpFM 2 distribution. In this case the pedestal events are mostly due to the inefficiency of the CpFM 1 bar, a factor of 3 worse than the efficiency of the CpFM 2 bar. Indeed, when the number of extracted particles is low $\\left( < ~ 6 \\right)$ , the CpFM 1 cannot discriminate extracted protons by the electronic noise. Both the channels count in average approximately the same number of protons per turn (on average about 137 protons/turn); the slight difference being due to the saturation of the electronics which occurs for the two channels at a different number of protons per pulse and with different percentages $1 \\%$ of the entries for CpFM 1, $1 0 \\%$ for CpFM2). In order to validate these results the flux extracted from the halo beam was estimated by the Beam Current Transformer (BCTDC [8]) installed in the SPS. BCTDC integrates the beam current along an SPS revolution $( 2 3 ~ \\mu s )$ measuring the total charge circulating in the machine. The time derivative of the BCTDC corresponds to the total particle flux leaving the machine; since the crystal acts as a primary target in the machine, the beam intensity variation can be assumed to be mainly caused by it and hence corresponding to the flux detected by the CpFM. This is an approximation as other minor losses can occur in the machine. With the typical fluxes extracted by the crystal $( 1 0 ^ { 5 } - 1 0 ^ { 7 } { \\bf p } / s )$ BCTDC measurements are only reliable when averaged over time intervals of several seconds. The extracted flux estimated by the BCTDC in the time interval related to Fig. 9(b) is $1 7 9 \\pm 4 2$ protons per turn. This value has to be considered in good agreement with the values of the flux measured by CpFM 1 and CpFM 2 remembering that the BCTDC measurement represents the upper limit estimation of the crystal-extracted flux.
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1
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Yes
| 0
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
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5. Commissioning and operations In this section the most common operations in which the detector is involved are described. During the commissioning phase they were also used to validate the functionality of the detector, allowing the measurement of some well know channeled beam and crystal characteristics. The crystal assisted collimation prototype is composed essentially by the crystal bending in the horizontal plane and the absorber (Fig. 1). The crystal acts as a primary collimator deflecting the particles of the halo toward the absorber $\\sim 6 5 \\mathrm { m }$ downstream the crystal area) which has the right phase advance to intercept them and represents the secondary target. The CpFM is placed downstream to the crystal $( \\sim 6 0 \\mathrm { m } )$ and intercepts and counts the particles before they are absorbed. More details about the UA9 setup and the procedures to test the crystal collimation system can be found in [3]. 5.1. Standard operation: angular scan The angular scan of the crystal is the UA9 standard procedure through which the channeling orientation of the crystal is identified and the experimental setup becomes operational. It consists in gradually varying the orientation of the crystal with respect to the beam axis, searching for the planar channeling and volume reflection3 regions [16], while the crystal transverse position is kept constant. When the optimal channeling orientation is reached, the number of inelastic interactions at the crystal is at minimum and the number of deflected particles is at its maximum. Consequently the loss rate measured by the BLMs close to the crystal should show a suppression while in the CpFM signal rate a maximum should appear.
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1
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Yes
| 0
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expert
|
How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
|
$$ \\theta _ { k } = \\frac { x _ { C p F M } - \\sqrt { \\frac { \\beta _ { C p F M } } { \\beta _ { c r y } } } x _ { c r y } c o s \\varDelta \\phi } { \\sqrt { \\beta _ { c r y } \\beta _ { C p F M } } s i n \\varDelta \\phi } $$ being $\\beta _ { C p F M }$ and $\\beta _ { c r y }$ the betatron function at the CpFM and at the crystal location respectively and $\\Delta \\phi$ the phase advance between the crystal and the CpFM. These values are tabulated for the SPS machine [1] $\\mathit { \\hat { \\beta } } _ { c r y } = 8 7 . 1 1 5 4 \\mathrm { m } , \\beta _ { C p F M } = 6 9 . 1 9 2 0 \\mathrm { m } , \\Delta \\phi / 2 \\pi = 0 . 2 3 2 4 4$ . More details about this mathematical procedure can be found in [13]. When $x _ { C p F M } = c$ , the equivalent kick $\\theta _ { k }$ corresponds to the bending angle of the crystal $\\theta _ { b e n d }$ . Using the value of $c$ as extrapolated by the fit (see Fig. 8(b)) it is now possible to determine $\\theta _ { b e n d }$ corresponding to the crystal used during the scan: $\\theta _ { b e n d } = ( 1 6 7 \\pm 6 ) \\mu \\mathrm { r a d }$ . Its bending angle was previously measured by means of interferometric technics (Veeco NT1100) and resulted to be 176 μrad. The ${ \\sim } 5 \\%$ discrepancy with respect to the CpFM indirect measurement of the bending angle could depend on the imprecise evaluation of the primary beam center during the CpFM alignment procedure, not accounted in the error.
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1
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Yes
| 0
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
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After the calibration, the detector was used to observe the particle population exiting $1 \\mathrm { m }$ long CFC (Carbon Fiber Composite) LHC-like collimator when Xenon ions are deflected onto it. The collimator is part of the UA9 crystal-assisted collimation setup. It is located downstream the crystals region and about $1 7 \\mathrm { m }$ upstream the CpFM. During the case study, the Xe ions were channeled and deflected onto the collimator. The CpFM were thus inserted to detect the channeled beam after the passage through the collimator. The measurement was repeated retracting the collimator. The results are shown in Fig. 11. The CpFM successfully discriminated the low-Z particle population (mostly $Z < 6 j$ ) resulting from the fragmentation of Xe ions inside the collimator from the Xe ions themselves. 7. Conclusion The CpFM detector has been developed in the frame of the UA9 experiment with the aim to monitor and characterize channeled hadron beams directly inside the beam pipe vacuum. It consists of fused silica fingers which intercept the particles deflected by the crystal and generate Cherenkov light. The CpFM is installed in the UA9 crystal collimation setup in the SPS tunnel since 2015. It has been successfully commissioned with different beam modes and with proton and ion beams and it is now fully integrated in the beam diagnostic of the experiment, providing the channeled beam flux measurement and being part of the angular alignment procedures of bent crystals. It is able to provide the channeled beam horizontal profile and the measurement of crystal-extracted flux with a relative resolution of about $1 \\%$ for 100 protons/bunch (CpFM 2.0). In order to improve the detector resolution for lower fluxes a new radiator geometry is under study.
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1
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Yes
| 0
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
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File Name:CpFM_paper.pdf Commissioning and operation of the Cherenkov detector for proton Flux Measurement of the UA9 experiment F.M. Addesa a,∗, D. Breton d, L. Burmistrov d, G. Cavoto a,b, V. Chaumat d, S. Dubos d, L. Esposito c, F. Galluccio e, M. Garattini c,g, F. Iacoangeli a, J. Maalmi d, D. Mirarchi c, S. Montesano c, A. Natochii $^ { \\mathrm { c , d , f } }$ , V. Puill d, R. Rossi c, W. Scandale c, A. Stocchi d a INFN - Istituto Nazionale di Fisica Nucleare - sezione di Roma, Piazzale A. Moro 2, Roma, Italy b Università degli Studi di Roma "La Sapienza" -Department of Physics, Piazzale A. Moro 2, Roma, Italy c CERN, European Organization for Nuclear Research, Geneva 23, CH 1211, Switzerland d LAL - Laboratoire de l’Accélérateur Linéaire - Université Paris-Sud 11, Centre Scientifique d’Orsay, B.P. 34, Orsay Cedex, F-91898, France e INFN Sezione di Napoli, Complesso Universitario di Monte Sant’Angelo, Via Cintia, 80126 Napoli, Italy f Taras Shevchenko National University of Kyiv (TSNUK), 60 Volodymyrska Street, City of Kyiv, 01033, Ukraine g Imperial College, London, United Kingdom A R T I C L E I N F O Keywords: Beam instrumentation (beam flux monitors,
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augmentation
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Yes
| 0
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expert
|
How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
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1. Introduction The primary goal of the UA9 experiment [1] is to demonstrate the feasibility of a crystal-based halo collimation as a promising and better alternative to the standard multi-stage collimation system for high-energy hadron machines. The main installation of the experiment is located in the Long Straight Section 5 (LSS5) of the CERN Super Proton Synchrotron (SPS) and consists of a crystal-assisted collimation prototype. It is made by preexisting optical elements of the SPS and new installations including three goniometers to operate different crystal types used as primary collimators, one dedicated movable absorber, several scrapers, detectors and beam loss monitors (BLMs) to study the interaction of the crystal with the beam halo [3]. A schematic of the layout of the experiment is shown in Fig. 1. The main process investigated is the so-called planar channeling: particles impinging on a crystal having a small angle (less than $\\theta _ { c }$ , called the critical angle for channeling) with respect to the lattice planes are forced by the atomic potential to move between the crystal planes. If the crystal is bent, the trapped particles follow the bending and are deflected correspondingly. When an optimized crystal intercepts the beam halo to act as collimator, about $8 0 \\%$ of the particles are channeled, coherently deflected and then dumped on the absorber (see Fig. 1), effectively reducing the beam losses in the sensitive areas of the accelerator [4–7].
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augmentation
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Yes
| 0
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expert
|
How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
In order to fully characterize this collimation system, it is essential to steadily monitor the flux of the halo particles deflected by the crystal towards the absorber. Typical crystal-extracted fluxes range from $1 0 ^ { 5 }$ up to $1 0 ^ { 7 }$ protons/s (i.e. from 1 up to 200 protons per SPS revolution) and about $1 0 ^ { 5 }$ ions/s (1–3 ions per SPS revolution). Such a low flux does not allow to use the standard SPS instrumentation, for example BCTs (Beam Current Transformer [8]) which are optimized for higher fluxes ${ \\mathrm { ( > ~ } } 1 0 ^ { 9 }$ protons/s). For this reason, the Cherenkov detector for proton Flux Measurement (CpFM) was designed and developed. 2. The Cherenkov detector for proton flux measurement The CpFM detector has been devised as an ultra-fast proton flux monitor. It has to provide measurements of the extracted beam directly inside the beam pipe vacuum, discriminating the signals coming from different proton bunches in case of multi-bunch beams, with a 25 ns bunch spacing. It is also able to stand and to detect very low ion fluxes (1–3 ions per turn). The sensitive part of the detector is located in the beam pipe vacuum in order to avoid the interaction of the protons with the vacuum–air interface, hence preserving the resolution on the flux measurement. All the design choices are explained in detail in [9].
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augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
The relative resolution on the flux measurement of the CpFM for 100 incoming electrons was assessed to be $1 5 \\%$ , corresponding to a 0.62 photoelectron (ph.e.) yield per single particle [9,11,12]. The CpFM is installed in the SPS tunnel since 2015. 2.1. Electronic readout and DAQ system The CpFM electronic readout is realized by the 8-channels USBWaveCatcher board [10,13]. This is a 12-bit $3 . 2 \\mathsf { G S } / \\mathsf { s }$ digitizer; 6 other frequencies down to $0 . 4 \\ : \\mathrm { G S } / s$ are also selectable via software. Each input channel is equipped with a hit rate monitor based on its own discriminator and on two counters giving the number of times the programmed discriminator threshold is crossed (also during the dead time period corresponding to the analog to digital conversion process) and the time elapsed with a 1 MHz clock. This allows to measure the hit rate. Each input channel is also equipped with a digital measurement block located in the front-end FPGA which permits extracting all the main features of the largest amplitude signal occurring in the acquisition window in real time (baseline, amplitude, charge, time of the edges with respect to the starting time of the acquisition).
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augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
3.2. PMT gain optimization While choosing the PMT gain for both proton and ion runs, the maximum expected flux has to be considered together with the photoelectron yield per charge and the WaveCatcher dynamic range. To determine the optimal gain is noticed that the saturation of the ADC occurs at $2 . 5 \\mathrm { V }$ . The typical proton beam setup during UA9 experiments is a single 2 ns long bunch of $1 . 1 5 \\times 1 0 ^ { 1 1 }$ protons stored in the machine at the energy of $2 7 0 \\mathrm { G e V }$ [14]. For this beam intensity, the beam flux deflected by the crystal toward the CpFM ranges from 1 up to $\\simeq 2 0 0$ protons per turn (every ${ \\sim } 2 3 ~ \\mu \\mathrm { s } .$ ), depending on the aperture of the crystal with respect to the beam center. In this case the optimal PMT gain is $5 \\times 1 0 ^ { 6 }$ corresponding to bias the PMT at $1 0 5 0 \\mathrm { V } .$ . When the PMT is operated at such a gain a $S _ { p h . e }$ corresponds to $\\mathord { \\sim } 1 5 \\mathrm { \\ m V }$ (Fig. 3); considering the calibration factor (0.62 photoelectron yield per charge, measured at BTF and H8 line) the average amplitude of the signal produced by 200 protons is much lower than the dynamic range of the digitizer, allowing furthermore a safety margin of about 70 protons per pulse.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
The typical ion beam setup during UA9 data taking consists in few bunches of $1 . 1 \\times 1 0 ^ { 8 }$ fully stripped Lead (Pb) or Xenon (Xe) ions [14]. As in the case of protons, the ion beam is in coasting mode at the energy of $2 7 0 { \\mathrm { ~ G e V } }$ per charge. With such a beam intensity the ions to be measured by the CpFM per bunch and per turn is very low, from 0 to 3 ions. Nevertheless, since the Cherenkov light produced by a charged particle is proportional to the square of the charge of the particle , few ions can be enough to saturate the dynamic range of the electronics. Therefore the PMT gain has to be 1 to 2 orders of magnitude smaller than the gain used for protons. The procedure followed for ions foresees to start with a bias voltage of $5 0 0 \\mathrm { V }$ , corresponding to a gain of $\\sim 2 . 5 \\times 1 0 ^ { 4 }$ . Then, depending on the expected flux, it can be increased in steps of $1 0 0 \\mathrm { V }$ up to a maximum value of $7 0 0 \\mathrm { V }$ . This bias corresponds to a gain of $\\sim 2 . 5 \\times 1 0 ^ { 5 }$ , at which a flux of more than 1 ion per turn results, according to the calibration factor, in the saturation of the electronics.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
3.3. WaveCatcher settings optimization In the following the optimal readout electronic settings are discussed with respect to the characteristics of the signal to be sampled. Sampling frequency and digitizer window length. Since the PMT reading out the CpFM signal is very fast (rise time $\\simeq 1 . 5 \\mathrm { n s } ^ { \\cdot }$ ), the highest sampling frequency, $3 . 2 \\ { \\mathrm { G S } } / { \\mathrm { s } }$ , represents the best choice because it allows for a better reconstruction of the signal shape. To use the $3 . 2 \\mathsf { G S } / \\mathsf { s }$ sampling frequency a fine synchronization of the CpFM signals and the UA9 trigger is needed, the digitizer being started by the latter. The choice of the sampling frequency and therefore of the window length, defined as 1024 sample points divided by the sample frequency, is also influenced by the setup of the beam. For example, with an ion beam in multi-bunch mode it could be useful to first study all the bunches and then choosing to sample and to reconstruct more precisely only one of them (see Fig. 4). In this case, first the $4 0 0 \\mathrm { M S } / s$ sampling mode has to be selected in order to have an overview of all the bunches. Using then the $3 . 2 \\mathsf { G S } / \\mathsf { s }$ mode and playing with the onboard trigger delay parameter, it is possible to center the window of the digitizer around the selected bunch. Moreover, having just one bunch in the digitizer window is essential to directly use the measurement block of the WaveCatcher. If more peaks are present in the same digitizer window, the measurement of the average parameters of the signal shape would be biased.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
$$ y = \\frac { A _ { P b } } { Z _ { P b } ^ { 2 } \\times S _ { p h . e } \\left( m V \\right) } $$ where the $S _ { p h . e } ( \\mathrm { m V } )$ depends on the PMT bias and it can be obtained fitting the amplitude distributions in Fig. 3 and rescaling it to the PMT gain used for ions $_ { \\scriptstyle 7 0 0 \\mathrm { ~ V ~ } }$ in this case). The left side of the equation is provided by a data acquisition with both the bars intercepting the channeled beam. In this way the amplitude distribution of the channeled ions is easily obtained. This strategy has been applied for the first time during the Pb ion run in November 2016, providing reliable calibration factors for the flux measurement for those runs. In Fig. 5 the amplitude distributions of the CpFM channels are shown (CpFM 1 red line, CpFM 2 blue line) where only a rough requirement on the amplitude $( > 6 ~ \\mathrm { m V } )$ to cut the electronic noise has been applied. In the CpFM 1 distribution a three peak structure is present corresponding to 1, 2 and, just hinted, 3 ions. In the CpFM 2 distribution only one peak appears together with the ADC saturation occurring at 1.25 V.2 This is explained by different calibration factors. Fitting with a Gaussian function the single-ion peak as shown in Fig. 6(a) for CpFM 1 and inverting the Eq. (1), the calibration factors for the CpFM channels are: $y _ { C p F M 1 } = 0 . 0 6 6 \\pm 0 . 0 0 1 ( p h . e / p )$ and $y _ { C p F M 2 } = 0 . 1 8 6 2 \\pm 0 . 0 0 0 4 ( p h . e / p )$ for the CpFM 1 and the CpFM 2 respectively. The CpFM 2, devoted to the background measurement, results about 3 times more efficient than the CpFM 1; both the efficiency values are also lower with respect to the one of the CpFM prototype tested at the BTF. This was due to a problem during the installation investigated and solved during the SPS winter shut-down of 2016 [15].
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augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
The efficiency (ùúñ) of this version of the detector is well described by an upper cumulative distribution function of a Binomial distribution $B ( k , n , p )$ , being $n$ the real number of incoming protons to be detected, $k$ the total number of photoelectrons produced by the $n$ protons and p the single proton efficiency of the CpFM: $$ \\epsilon = Q ( 1 , n , p ) = \\sum _ { t = 1 } ^ { n } B ( 1 , n , p ) $$ Using this model with $p = y _ { C p F M }$ , the expected number of photoelectrons $( k )$ produced per $n$ protons can be determined. By multiplying $k$ with the value in $\\mathrm { m V }$ of one ph.e (corresponding to the peak in Fig. 3 at $1 0 5 0 \\mathrm { ~ V } )$ and by comparing the result with the amplitude of the electronic noise $\\zeta < 6 \\mathrm { m V }$ at 1050 V) is therefore possible to assert that the CpFM is effective in discriminating the proton signal if $n > 6$ for the CpFM 1 and $n > 2$ for the CpFM 2.
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augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
In Fig. 7 the angular scan of the UA9 crystal-1 during a proton run is shown. It is displayed both by the BLMs and the CpFM (CpFM position is such that both the bars intercept the whole channeled beam when the crystal is in the optimal channeling position). The first and the last angular regions (angle $< - 2 7 0 0$ μrad and angle $> - 2 4 0 0 ~ \\mathrm { \\mu r a d } )$ correspond to the amorphous orientation. As expected, here the loss rate registered by the BLMs is maximum while the CpFM signal rate is minimum. After the first amorphous region, the channeling peak appears (around angle of $- 2 6 2 0 \\ \\mu \\mathrm { r a d } )$ as a maximum in the CpFM rate and as minimum in the BLMs rate. Just after, only in the BLMs signal, the volume reflection area is clearly visible. In this angular region the particles experience a deflection to the opposite side with respect to the planar channeling deflection. For this reason volume reflection is not detectable by the CpFM except as a slight reduction in the background counts. Although the BLMs rate profile is an effective instrument for the estimation of the best channeling orientation, it is based on beam losses and is generally less sensitive than the CpFM rate profile which on the contrary measures directly the presence of channeled protons.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
Using the value above and the value of the $\\sigma$ of the channeled beam obtained by the fit shown in Fig. 8(b), it is also possible to extrapolate the angular spread of the particles exiting the crystal. It can be derived subtracting the equivalent kick for $x _ { C p F M } = { \\bf c } \\pm \\sigma$ from $\\theta _ { b e n d }$ , corresponding to the equivalent kick calculated in the center $c$ of the channeled beam: $$ \\theta _ { s p r e a d } = [ \\theta _ { k } ] _ { c \\pm \\sigma } \\mp \\theta _ { b e n d } $$ applying the Eq. (5) to the fit results in Fig. 8(b), the angular spread has been evaluated to be: $\\theta _ { s p r e a d } = ( 1 2 . 8 \\pm 1 . 3 ) \\mu \\mathrm { r a d }$ . The angular spread at the exit of the crystal is directly connected to the critical angle value which defines the angular acceptance of the channeled particles at the entrance of the crystal. Therefore the angular spread should be comparable with respect to the critical angle. From theory [16], for $2 7 0 { \\mathrm { G e V } }$ protons in Si $\\theta _ { c }$ is $1 2 . 2 \\mu \\mathrm { r a d }$ .5 It can be then asserted that the angular spread derived by the fit results and the critical angle computed from the theory are well comparable.
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augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
Finally, particular attention has to be paid to the shape of the distributions in Fig. 9(b). They are not Gaussian. For such a high fluxes, this cannot depend on the detector resolution, at least for the CpFM 2 channel which has the better efficiency. This can be demonstrated deriving the CpFM 2 resolution for an incident and constant flux of 180 protons per turn, as measured by the BCTDC. From the single ion distributions in Fig. 6(a), the resolution with respect to a single incident lead ion can be computed. The CpFM 2 resolution for 180 protons is easily derived scaling the ion resolution by the factor $\\sqrt { ( 6 7 2 4 / 1 8 0 ) }$ . It corresponds to $9 \\%$ . Thus, if the number of protons extracted by the crystal was constant and equal to 180 (distributed according a Gaussian distribution centered in 180), the CpFM 2 signal would be characterized by a narrower peak having 15 protons $\\sigma$ . The beam extracted by the crystal is therefore not constant on the time scale probed by the CpFM. There are several possible reasons for this: the diffusion dynamics of the halo beam, goniometer instabilities or orbit instabilities. The CpFM detector offers an interesting chance to address this issue at the μs scale but the current data acquisition electronics of the detector represent a limit. The CpFM detector is indeed able to accept only 1/1000 SPS trigger, since the data acquisition electronics are not fast enough $( < 1 \\mathrm { k H z } )$ . Faster electronics, matching the revolution frequency of the machine, could strengthen the detector capability in studying the impact of the listed factors on the crystal halo extraction.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
|
The WaveCatcher is triggered by the UA9 trigger (common to all the other UA9 instrumentation). This trigger signal is the SPS revolution signal $( 4 3 \\\\mathrm { k H z } )$ down-scaled by a factor of 1000 and synchronized with the passage of a filled bucket in LSS5. The acquisition rate corresponds to the trigger frequency $( 4 3 ~ \\\\mathrm { H z } )$ . Three signals are acquired: two CpFM channels and the UA9 trigger itself. The board is equipped with a USB 2.0 interface for the data transfer. The off-line analysis used to characterized the CpFM signal and to perform the event identification [13] is mainly based on the output of the measurement blocks. 3. Procedures preliminary to data taking: readout settings optimization Prior to every UA9 data taking a standard procedure is followed to prepare the detector for operation. It consists of checking the PMT gain stability and optimizing the gain of the PMTs and the settings of the WaveCatcher with respect to the characteristics of the beam to be measured. 3.1. PMT gain stability check The reliability of flux measurements depends on the stability of the calibration factor for which in turn the stability of the PMT performance is fundamental. For this reason, before every UA9 data taking, the stability of the PMT gain is checked through a simple procedure. It consists in a high-statistic ( $\\\\mathrm { 1 0 ^ { 5 } }$ trigger events) data acquisition of the CpFM signals when the detector is located at the parking position ${ \\\\mathrm { . 1 0 ~ c m } }$ from the beam pipe center) and the beam in the SPS is already in coasting mode.1 In this way, the amplitude distribution of the detector signals corresponds to the amplitude distribution of the background (Fig. 3), the latter being mostly composed by single photoelectron $( S _ { p h . e } )$ events plus a long tail due to particles showering by interacting with the aperture restrictions of the machine. If the PMTs are not affected by any gain variation, for example by radiation damage, the $S _ { p h . e }$ position in the amplitude distribution is unchanged.
|
augmentation
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Yes
| 0
|
expert
|
How does the detector provide for the horizontal beam profile?
|
It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
|
Reasoning
|
CpFM_paper.pdf
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Hit rate monitor threshold. The hit rate monitor cannot be used to count the channeled particles because, if the beam is well bunched, they are deflected at the same time (or more precisely within the 2 ns of the bunch), producing a single signal shape proportional to their number. Nevertheless, the hit rate monitor can be effectively used to quickly find the channeling orientation of the crystal or to align the CpFM with respect to the beam. In this case the CpFM has to detect only changes in the counts rate. The absolute value of the rate is not important and thus the threshold of the hit rate monitor can be kept just over the electronic noise, corresponding to the pedestal of the amplitude distribution of the background shown in Fig. 3. 4. An in-situ calibration strategy with ion beams The SPS ion runs at the end of each year offer a possibility to calibrate in situ the detector. In fact in this case, the ph.e. yield per ion allows an excellent discrimination of the signal coming from 1, 2 or more ions. The Cherenkov light produced by a single ion of charge $Z$ is $Z ^ { 2 }$ times the light produced by a single proton. For example, as the charge of a completely stripped Lead (Pb) ion is 82, the light produced by a single ion is equal to 6724 times the light produced by a proton. During SPS ion runs for the UA9 experiment, each $\\\\mathrm { \\\\sf P b }$ ion charge is accelerated to $2 7 0 { \\\\mathrm { ~ G e V } }$ , exactly as in UA9 proton beam runs. Identifying the amplitude signal corresponding to a single ion $( A _ { P b } )$ , the photoelectron yield per proton $( y )$ can be obtained as:
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augmentation
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Yes
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
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5.2.2. Crystal bending angle and angular spread of the channeled beam at the crystal position The results of the fits performed on the integrated beam profiles in Fig. 8(b) provide two additional functionality tests of the detector allowing to derive channeled beam and crystal characteristics already well known. In particular the center $( c )$ of the channeled beam can be used to determine the value of the bending angle $\\\\theta _ { b e n d }$ of the crystal. This represents a non perturbative method to measure in-situ the crystal bending angle, alternative to the linear scan of the LHC-type collimator used in the past [17]. The CpFM, unlike the collimator $\\\\mathrm { ~ \\\\ i m }$ of carbon fiber composite), is indeed almost transparent to the channeled protons which produce Cherenkov light losing a negligible amount of their energy. $\\\\theta _ { b e n d }$ is derived calculating the equivalent crystal kick $\\\\theta _ { k }$ at the CpFM position along the ring. The latter corresponds to the angular kick that a particle should receive by the crystal to be horizontally displaced by $\\\\mathbf { x }$ with respect to the beam core at the CpFM position. It is derived applying the general transfer matrix to the phase-space coordinates of the particle at the crystal position $( x _ { 0 } , x _ { 0 } ^ { \\\\prime } ) _ { c r y }$ to get the new coordinate at the CpFM position $( x , x ^ { \\\\prime } ) _ { C p F M }$ :
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augmentation
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Yes
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expert
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How does the detector provide for the horizontal beam profile?
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It provides the integrated beam profile in the horizontal plane which can be fitted by an erf function to get the standard deviation
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Reasoning
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CpFM_paper.pdf
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6. CpFM 2.0: in-situ calibration with Xenon ions and first case study During the winter shut-down of 2016, the layout of the CpFM detector was modified. In order to improve the detector efficiency, the fiber bundles were removed being indeed responsible for a reduction factor of 10 in the light yield per proton. They were initially foreseen to enhance the radiation hardness of the photo-detection chain and to make the detector concept eventually applicable also in the Large Hadron Collider (LHC). Only one PMT was directly coupled to the viewport and in such a way that the transversal cross section of both bars is covered. Moreover CpFM 1 and CpFM 2 bars were inverted, the latter being better polished and thus more efficient. In December 2017, the second version of the CpFM detector was calibrated with a 270 GeV/charge Xenon (Xe, $Z ~ = ~ 5 4 )$ ion beam using the same procedure described in Section 4. In Fig. 10 the signal amplitude distribution focused on the Xenon ion events is shown. It is referred to a data taking performed during a crystal angular scan when only the inner bar intercepted the channeled beam. Beside the main peak due to Xe ions, two other structures appear. They are associated with fragments of charge $Z = 5 3$ and $Z = 5 2$ respectively, produced when the crystal is not in the optimal channeling orientation. Using the results of the fit, the new calibration factor is derived: $y _ { C p F M } =$ $2 . 1 \\\\pm 0 . 2 ( p h . e / p )$ . As expected it results improved by a factor of 10 with respect to the old version of the detector.
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augmentation
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Yes
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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This fast shutter has two modes. One is the ‘‘NORMAL’ mode, where the shutter opening time is determined by the input transistor-transistor logic (TTL) pulse width fed into the shutter controller. Another is the ‘‘HIGH’’ mode, where the shutter opening time is fixed to $0 . 3 ~ \\mathrm { m s }$ and synchronized with the input TTL trigger timing. These modes are changed by a shutter controller. A beam-injection timing signal is divided and provided into the CCD trigger signal (‘‘ch1’’ in Fig. 6) and the shutter trigger (‘‘ch2’’ in Fig. 6) via a function synthesizer. The timing of the fast mechanical shutter is synchronized with the beam-injection timing of the damping ring. The shutter opening time is controlled by changing the trigger pulse width set by the function synthesizer. Both the trigger timing and the timing delay between the fast shutter and $\\mathbf { \\boldsymbol { x } }$ -ray CCD signal are also independently changed and set by this function synthesizer. On the other hand, the previous shutter trigger timing was adjusted to only the CCD internal trigger timing and controlled by the CCD controller via a PC. 2. Performance Prior to installation of the fast mechanical shutter, the performance of this shutter was measured on a test bench. The setup of the test bench is shown in Fig. 7. The shutter opening time was controlled by a TTL pulse produced by a pulse generator through the power supply and controller. Only when the shutter was open, the continuous-wave laser light through the shutter was detected by a Si p-i-n photodiode. The fast mechanical shutter opening time was estimated by measuring the width of the signal of the photodiode via an oscilloscope. Figure 8 shows the measured shutter opening time in the NORMAL mode as a function of the input TTL pulse width. The measurement was performed with $1 \\ \\mathrm { H z }$ repetition. The opening time is given by the full-width half maximum of the measured pulse width detected by $\\mathrm { S i } p$ -i-n photodiode. The measured shutter opening time follows the input TTL pulse width down to $1 \\mathrm { m s }$ , but it is saturated at less than 1 ms TTL pulse width. We then found that the minimum shutter opening time of this new shutter was 1 ms in the NORMAL mode. We also measured the shutter opening time in the HIGH mode, and the $0 . 3 ~ \\mathrm { m s }$ shutter opening time was obtained. These values are consistent with the catalogue values of the minimum shutter opening time in both the NORMAL and HIGH modes. The NORMAL mode was mainly used in beam-profile measurement, unless otherwise noted. We note that this shutter performance was kept stable for at least one day in this test bench.
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1
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Yes
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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Beam emittance in the ATF damping ring is dominated by the intrabeam scattering effect [2]. In a high current of the single-bunch mode, the emittance increases as the beam current become high, and the coupling ratio decreases. In order to estimate the coupling ratio of the ATF damping ring and validate these measured beam sizes, we compared the measured beam sizes with calculation obtained by using the optics data of the ATF damping ring in Table IV and the computer program SAD [21] including the intrabeam scattering effect [22,23]. Figure 16 shows comparisons of the measured beam size (boxes) and the calculation (lines) on $2 0 0 5 / 4 / 8$ . Figure 17 also shows the data of the measured data (boxes and circles) and calculation (lines) on $2 0 0 5 / 6 / 1$ . The horizontal axes show the beam current of the damping ring in the single-bunch mode, and the vertical axes are the measured and calculated beam sizes. These two measurements agree well with the calculation when it is assumed that the coupling ratio is $( 0 . 5 \\pm 0 . 1 ) \\%$ and are almost consistent with the other measurement by the laser wire monitor in the ATF damping ring, described in Ref. [2]. In order to confirm the assumption of coupling ratio, the energy spread was also measured. Figure 18 shows the measured energy spread at the extraction line on $2 0 0 5 / 4 / 8$ . The errors of the measured momentum spread at higher beam current are mainly caused by the measurement error of the dispersion function at the screen monitor. On the other hand, the errors of the momentum spread at lower beam current are mainly caused by the statistical error because of the poor signal of the screen monitor. As shown in Fig. 18, the measured energy spread at the extraction line on $2 0 0 5 / 4 / 8$ also agrees well with a calculation under the assumption of a $( 0 . 5 \\pm 0 . 1 ) \\%$ coupling ratio.
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Yes
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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$$ where the $\\lambda$ is the wavelength of a photon and $f$ is the focal length for the wavelength. The spatial resolution $\\delta$ which is the transverse size of a point-source image for the 1st-order diffraction on the focal plane, is determined by $$ \\delta = 1 . 2 2 \\Delta r _ { N } , $$ where $\\Delta r _ { N }$ is the width of the outermost zone and the suffix $N$ means the total number of zones. If $N \\gg 1$ , it can be expressed as $$ \\Delta r _ { N } = f \\lambda / 2 r _ { N } = \\frac { 1 } { 2 } \\sqrt { \\frac { \\lambda f } { N } } . $$ The spatial resolution $\\delta$ of FZP corresponds to the distance between the center and the first-zero position of the Airy diffraction pattern. When we apply a Gaussian distribution with the standard deviation $\\sigma$ to its Airy diffraction pattern, the spatial resolution $\\delta$ almost equals the $3 \\sigma$ distance $( \\delta \\simeq 3 \\sigma )$ . C. Expected spatial resolution of the FZP monitor In order to measure a small beam profile, the spatial resolution of the FZP monitor must be smaller than the beam size. The total spatial resolution of the FZP monitor is determined by three mechanisms. One is the diffraction limit of $\\mathbf { \\boldsymbol { x } }$ -ray SR light. Another is the Airy diffraction pattern of FZP, as described in Eqs. (2) and (3). The other is the pixel-size of the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera, itself. We summarize the spatial resolution determined by each parameter in Table I.
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4
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Yes
| 1
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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This $1 0 0 \\mathrm { H z }$ oscillation was also found from data taken on 2 other different days with almost the same amplitudes and phases. In order to eliminate the $1 0 0 ~ \\mathrm { H z }$ oscillation from the measurement, we fixed the shutter opening time to 1 ms and adjusted the shutter trigger timing to an optimum phase condition of the $1 0 0 ~ \\mathrm { H z }$ oscillation in all of the beam-profile measurements. We note that we did not use the HIGH mode with a $0 . 3 ~ \\mathrm { m s }$ shutter opening time from the view point of increasing the signal-to-noise ratio. Furthermore, whenever we measured the beam profiles by the FZP monitor, we superposed ten beam profiles on the xray CCD in order to increase the signal-to-noise ratio more. In order to survey the source of $1 0 0 ~ \\mathrm { H z }$ oscillation, we checked all of the components of the FZP monitor: two FZPs, the Si crystal monochromator, and the $\\mathbf { X }$ -ray CCD. First, mechanical vibrations of the two FZPs, including their folders, were measured at frequencies below $1 2 0 \\mathrm { H z }$ with a compact seismometer (VSE-15D Tokyo Sokushin Co.). Figure 14 shows the measurement results of vertical vibrations of the two FZP folders. The cumulative displacement at each frequency is defined by a square root of the displacement power spectrum integrated from the frequency up to $1 2 0 ~ \\mathrm { H z }$ . We found a $5 \\ \\mathrm { n m }$ rms displacement of the CZP and $4 \\mathrm { n m }$ rms displacement of the MZP at $1 0 0 ~ \\mathrm { H z }$ frequency, as shown in Fig. 14. The scaled displacements at the source point due to the CZP and MZP displacements of $\\Delta y$ , are expressed as $( 1 + 1 / M _ { \\mathrm { C Z P } } ) \\Delta y$ and $( 1 / M _ { \\mathrm { C Z P } } ) \\Delta y$ , respectively. In our case $ { M _ { \\mathrm { C Z P } } } = 1 / 1 0$ and $M _ { \\mathrm { { M Z P } } } = 2 0 0 )$ ), they are $1 1 \\Delta y$ and $1 0 \\Delta y$ . Assuming the observed vibrations, 55 and $4 0 \\ \\mathrm { n m }$ beam oscillations are expected by the CZP and the MZP, respectively. These values are too small to explain the $1 0 0 \\mathrm { H z }$ beam oscillation with the vertical amplitude, $A _ { b }$ , of $7 . 8 4 \\pm 0 . 4 5 \\mu \\mathrm { m }$ , as shown in Fig. 13. Therefore, the vibrations of the FZPs are not the reason for the $1 0 0 ~ \\mathrm { H z }$ oscillation of the beam center. Second, we doubted that the Si crystal monochromator might vibrate at $1 0 0 \\mathrm { H z }$ through its power supply of the motor and goniometer. For a confirmation, we remeasured the shutter opening time dependence when the power supply of the stepping motor and goniometer attached with Si monochromator were turned off. Figure 15 shows the shutter opening time dependence of the vertical beam sizes. The solid boxes (open circles) show the data when the power supply was turned off (on). We found a vertical beam-size enhancement by increasing the shutter opening time on both cases, as shown in Fig. 12. No clear difference between both conditions was observed. Finally, we measured the x-ray SR illuminated image of the CZP on the xray CCD camera, as shown in the right picture of Fig. 5 by changing the trigger timing of the $\\mathbf { X }$ -ray CCD camera. If the beam image oscillation is due to any vibration of the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera, itself, we will also see a similar oscillation of the image of CZP because it does not follow the beam motion without focusing. We found no image oscillation of more than 1 pixel of the x-ray CCD camera horizontally and vertically, in spite of changing the trigger timing every 1 ms from 0 to $2 0 ~ \\mathrm { { m s } }$ with a $1 ~ \\mathrm { m s }$ shutter opening time.
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2
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Yes
| 0
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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The beam-profile monitor with x-ray imaging optics will allow precise and direct beam imaging in a nondestructive manner because the effect of the diffraction limit can be neglected by using x-ray SR. Some beam-profile monitors based on the x-ray imaging optics were performed by using FZP and a refractive $\\mathbf { \\boldsymbol { x } }$ -ray lens [11,12]. However, they used a knife-edge scanning technique to measure the beam profile because the beam image was reduced by using only one FZP or a single refractive $\\mathbf { \\boldsymbol { x } }$ -ray lens. Therefore, it took a long time to measure a beam profile. In order to overcome this defect, we proposed a real-time beam-profile monitor based on magnified $\\mathbf { \\boldsymbol { x } }$ -ray imaging optics using ‘‘two’’ FZPs (hereafter called as ‘‘FZP monitor’’) [13]. We originally developed the FZP monitor in the ATF damping ring to measure a small beam profile. For this purpose, the spatial resolution of this monitor was designed to be less than $1 \\ \\mu \\mathrm { m }$ . With this FZP monitor, we succeeded to obtain a clear electron-beam image enlarged by 20 times with two FZPs on an x-ray CCD, and measuring an extremely small electron-beam size of less than $1 0 \\ \\mu \\mathrm { { m } }$ [14]. Recently, a beam-profile monitor using a single FZP and an $\\mathbf { X }$ -ray zooming tube has been developed at the SPring-8 storage ring [15]. In this monitor, the magnified beam image was also obtained by using an $\\mathbf { X }$ -ray zooming tube, where x rays were converted to photoelectrons before magnification. It has a small spatial resolution of $4 \\mu \\mathrm m$ . With this monitor at the SPring-8 storage ring, $\\mathbf { X }$ -ray images of the electron beam were clearly obtained, and the vertical beam size with $1 4 \\ \\mu \\mathrm { m }$ in root mean square (rms) was successfully measured with a 1 ms time duration.
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4
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Yes
| 1
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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Table: Caption: TABLE I. Expected spatial resolution of each parameter and the total expected spatial resolution. Body: <html><body><table><tr><td>Parameters</td><td>Definition</td><td>Resolution (1σ)[μm]</td></tr><tr><td>Diffraction limit (λ= 0.383 nm)</td><td>λ/4TTOSR</td><td>0.24</td></tr><tr><td>Airy pattern of CZP (△rn = 116 nm)</td><td>0czp/MczP</td><td>0.55</td></tr><tr><td>Airy pattern of MZP (△rn = 128 nm)</td><td>OMZP/M</td><td>0.002</td></tr><tr><td>CCD(1 pixel= 24 μm × 24 μm）</td><td>σcCD/M</td><td>0.35</td></tr><tr><td>Total</td><td></td><td>0.7</td></tr></table></body></html> Table: Caption: TABLE II. Specifications of the two FZPs. Body: <html><body><table><tr><td>Fresnel zone plate</td><td>CZP</td><td>MZP</td></tr><tr><td>Total number of zone</td><td>6444</td><td>146</td></tr><tr><td>Radius</td><td>1.5 mm</td><td>37.3 μm</td></tr><tr><td>Outermost zone width △rn</td><td>116 nm</td><td>128 nm</td></tr><tr><td>Focallength at 3.24 keV</td><td>0.91 m</td><td>24.9 mm</td></tr><tr><td>Magnification</td><td>Mczp = 1/10</td><td>MmZp = 200</td></tr></table></body></html> Table: Caption: TABLE III. Specifications of the x-ray CCD camera. Body: <html><body><table><tr><td colspan="2">X-ray CCD camera</td></tr><tr><td>Type</td><td>Direct incident type</td></tr><tr><td>CCD</td><td>Back-thinned illuminated type</td></tr><tr><td>Data transfer</td><td>Full-frame transfer type</td></tr><tr><td>Quantum efficiency at 3.24 keV</td><td>>90%</td></tr><tr><td>Pixel size</td><td>24 μm X 24 μm</td></tr><tr><td>Number of pixels</td><td>512 × 512</td></tr></table></body></html> III. IMPROVEMENTS ON THE EXPERIMENTAL SETUP In this section, we present the setup of FZP monitor while concentrating on the improvements of the present setup compared to the former setup referred to as ‘‘old setup’’ in the following. A. Experimental layout Figure 2 shows the setup of the FZP monitor. SR light is extracted at the bending magnet (BM1R.27) just before the south straight section in the $1 . 2 8 \\mathrm { G e V }$ ATF damping ring, where the horizontal beam size is expected to be about $5 0 \\ \\mu \\mathrm { m }$ and the vertical beam size is expected to be less than $1 0 \\ \\mu \\mathrm { m }$ . This system consists of a Si crystal monochromator, two FZPs (CZP and MZP), and an $\\mathbf { X }$ -ray CCD camera. The specifications of the two FZPs are summarized in Table II. A beryllium window with $5 0 \\ \\mu \\mathrm { m }$ thickness is installed to isolate the relatively low vacuum of the monitor beam line from that of the ATF damping ring. $3 . 2 4 \\mathrm { k e V }$ x-ray SR light is selected by the Si(220) crystal monochromator with a Bragg angle, $\\theta _ { B }$ , of $8 6 . 3 5 ^ { \\circ }$ . The CZP and MZP are mounted on folders set on movable stages in order to align these two optical components precisely across the beam direction. Furthermore, the MZP folder can move in the longitudinal direction of the beam line to search the focal point of the MZP. The monochromatized $\\mathbf { \\boldsymbol { x } }$ -ray SR is precisely focused on the xray CCD camera by adjusting the positions of the two FZP (CZP and MZP) folders. The magnifications of the FZPs, $M _ { \\mathrm { C Z P } }$ , and $M _ { \\mathrm { M Z P } }$ , are $1 / 1 0$ and 200, respectively. Therefore, an image of the electron beam at the bending magnet is magnified with a factor of 20 on the $\\mathbf { X }$ -ray CCD camera. The specifications of the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera (C4880-21, HAMAMATSU) are summarized in Table III. The data taking timing of the $\\mathbf { X }$ -ray CCD camera is synchronized with the beam-injection timing in order to detect a beam image during the beam operation, in which the electron beam stayed within only $5 0 0 ~ \\mathrm { { m s } }$ associated with $1 . 5 6 \\ \\mathrm { H z }$ repetition of a beam injection in the ATF damping ring. A mechanical shutter is installed in front of the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera to avoid irradiating x-ray SR on the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera during data transfer. The minimum shutter opening time of this shutter is $2 0 \\mathrm { m s }$ . A new fast mechanical shutter is set between the CZP and the MZP to improve the time resolution of the FZP monitor. A detailed description of the performance is given in Sec. III D.
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5
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Yes
| 1
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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File Name:Sakai_2007.pdf Improvement of Fresnel zone plate beam-profile monitor and application to ultralow emittance beam profile measurements Hiroshi Sakai,\\* Masami Fujisawa, Kensuke Iida,† Isao Ito, Hirofumi Kudo, Norio Nakamura, Kenji Shinoe, and Takeo Tanaka Synchrotron Radiation Laboratory, Institute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan Hitoshi Hayano, Masao Kuriki, and Toshiya Muto‡ High Energy Accelerator Research Organization (KEK), Ibaraki 305-0801, Japan (Received 26 September 2006; published 30 April 2007) We describe the improvements of a Fresnel zone plate (FZP) beam-profile monitor, which is being developed at the KEK-ATF damping ring to measure ultralow emittance electron-beam profiles. This monitor, which is designed to have a submicrometer spatial resolution, is based on x-ray imaging optics composed of two FZPs. Various improvements were performed to the old setup. First, a new crystal monochromator was introduced to suppress the beam image drift. Second, the two FZP folders were improved in order to realize a precise beam-based alignment during x-ray imaging. Third, a fast mechanical shutter was installed to achieve a shorter time resolution, and an $\\mathbf { X }$ -ray mask system was also installed to obstruct direct synchrotron radiation through the FZPs. These improvements could make beam-profile measurements more precise and reliable. The beam profiles with less than $5 0 \\ \\mu \\mathrm { m }$ horizontal beam size and less than $6 \\mu \\mathrm { m }$ vertical beam size could be measured within a 1 ms time duration. Furthermore, measurements of the damping time and the coupling dependence of the ATF damping ring were successfully carried out with this upgraded FZP monitor.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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D. Coupling dependence of the measured beam profiles The coupling dependences were measured by changing the currents of the skew-quadrupole coils wound on two kinds of sextupole magnets. Figure 20 shows the typical beam profiles when a skew correction was carefully carried out [Fig. 20(a)] and all of the skew-quadrupole coils were turned off on purpose [Fig. 20(b)]. As shown in Fig. 20, we found that the vertical beam size increased and the measured beam profile was tilted when a skew correction was not applied. In order to measure the coupling dependence precisely, we measured the two sets of beam profiles at the same beam current when a skew correction was applied (hereafter called ‘‘skew on’’ condition), and the skewquadrupole coils were turned off (called ‘‘skew off’’ condition). Figure 21 shows all of the results of the two conditions of skew on and skew off. As shown in Fig. 21, the vertical beam sizes increased for all of the stored currents under the skew off condition compared with those under the skew on condition, while the horizontal one decreased. In order to estimate the coupling ratio, we also plot the calculation data including intrabeam scattering effect in Figs. 21(a) and 21(b). The data set of the skew on (skew off) condition agree with the calculation assuming the $0 . 5 \\%$ $( 3 . 0 \\% )$ coupling ratio. The absolute values of the measured tilt angles of the skew off condition are $( 6 \\pm$ 2) degrees, which is much larger than that of skew on condition of $( 0 . 7 \\pm 0 . 3 ) \\$ degrees.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
|
One of our interests is to confirm the generation of the low-emittance beam, especially vertical emittance in the damping ring. The measured vertical beam size $( \\sigma _ { y } )$ and the vertical emittance $( \\varepsilon _ { y } )$ are related by $$ \\beta _ { y } \\varepsilon _ { y } = ( \\sigma _ { y } ) ^ { 2 } - \\biggl ( \\eta _ { y } \\frac { \\sigma _ { p } } { p } \\biggr ) ^ { 2 } , $$ where $\\beta _ { y }$ and $\\eta _ { y }$ are, respectively, the ring’s $\\beta$ function and the dispersion function in the $y$ direction at the source point, and $\\sigma _ { p } / p$ is the momentum spread. We note that, from Table IV, the term $\\eta _ { \\mathrm { y } } ( \\sigma _ { p } / p )$ contributes less than $1 \\ \\mu \\mathrm { m }$ , and that it can be neglected compared with the measured beam sizes $( \\sigma _ { y } )$ of about $6 \\mu \\mathrm m$ , as shown in Table V. Finally, we used Eq. (4) in order to evaluate $\\varepsilon _ { y }$ ; the results are listed in the 6th column of Table V. From these results, when low-emittance tuning was carefully done, the measured vertical emittance was found to be about 11 pm rad for above $3 \\mathrm { m A }$ in the single-bunch mode.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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DOI: 10.1103/PhysRevSTAB.10.042801 PACS numbers: 07.85.Qe, 07.85.Tt, 41.75.Ht, 41.85.Ew I. INTRODUCTION A. Introduction to the FZP monitor The production of low-emittance beams is one of the key techniques for electron accelerators and synchrotron light sources. For example, a third-generation synchrotron light source and future synchrotron light sources, like an energy recovery linac (ERL), require an unnormalized emittance of a few nm rad or less (hereafter we redefine the word of ‘‘emittance’’ as ‘‘unnormalized emittance’’). In highenergy physics, the linear collider also requires such ultralow emittance beams to realize the necessary luminosity. The Accelerator Test Facility (ATF) was built at High Energy Accelerator Research Organization (KEK) in order to develop the key techniques of ultralow emittance beam generation and manipulation. The ATF consists of a $1 . 2 8 \\ \\mathrm { G e V }$ S-band electron linac, a damping ring, and an extraction line [1]. A low-emittance beam is generated in the ATF damping ring, where the horizontal emittance at a zero current is $1 . 1 \\times 1 0 ^ { - 9 }$ m rad. The target value of the vertical emittance at a zero current is $1 . 1 \\times 1 0 ^ { - 1 1 }$ m rad, which has been generated by applying precise vertical dispersion corrections and betatron-coupling corrections [2]. The typical beam sizes are less than $5 0 \\ \\mu \\mathrm { m }$ horizontally and less than $1 0 \\ \\mu \\mathrm { m }$ vertically. Such small beam sizes cannot be measured by the typically used visible-light imaging optics for synchrotron radiation (SR) because of the large diffraction limit of visible light. Beam-profile monitoring with good spatial resolution is crucially important to confirm whether the required extremely small emittance beam is stably generated and manipulated. Therefore, there are some special monitors set and developed in the ATF: tungsten and carbon wire scanners in the extraction line, a double-slit SR interferometer, a laser wire monitor, and a Fresnel zone plate monitor.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
|
By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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IV. MEASUREMENT OF THE ULTRALOW EMITTANCE BEAM IN THE ATF DAMPING RING A. Beam tuning and condition We obtained a data set of the beam profile mainly for three days with various damping-ring conditions after improving the FZP monitor. In all cases the ATF ring was operated at $1 . 2 8 \\mathrm { G e V }$ in single-bunch mode. Typical stored beam current in the ATF damping ring is above $3 . 5 ~ \\mathrm { m A }$ , which corresponds to $1 . 0 \\times 1 0 ^ { \\hat { 1 0 } }$ electrons per bunch, during beam-profile measurements. Before the measurement, the electron beam in the ATF damping ring was tuned as follows. First, the closed-orbit distortion and verticalmomentum dispersion were reduced as much as possible. Second, the coupling between the horizontal and vertical betatron oscillations was minimized by optimizing two sets of skew magnets wound around two series of sextupole magnets, respectively. This process, called ‘‘skew correction,’’ is a key to production of a low-emittance beam [19]. In 2005, a study of the effect by damping wigglers set on the two straight sections in the ATF damping ring was started [20]. We also studied the effect of the damping wigglers on the damping time by using the improved FZP monitor. The measurement dates and beam conditions are listed below.
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augmentation
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Yes
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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B. Si monochromator The Si crystal monochromator can be rotated horizontally by using a goniometer and vertically by using a stepping motor, which is attached to the support of a Si crystal in a vacuum. With the old monochromator, the vertical position of the beam image on the CCD camera had largely drifted because the support of the Si crystal was deformed by heat from the stepping motor. In order to avoid any drift, a new Si crystal monochromator was produced. Figure 3 shows a picture of the new monochromator. In the new monochromator, a stepping motor was thermally isolated from the Si crystal by ceramic insulators and thermally stabilized by copper lines connected with a water-cooled copper plate. Figure 4 shows measurements of the beam centroid by the old and new monochromator, respectively. After this improvement, the drift was drastically reduced by a factor of about 100 and stabilized within a few $\\mu \\mathrm { m }$ for a long time, as shown in Fig. 4. C. Fresnel zone plate The new FZP folders were designed and fabricated so that the FZPs could be controlled and removed from the optical path in the vacuum if necessary. The removed FZPs are protected from the air pressure during any leaks in maintenance and repair of the monitor beam line, or the installation of new beam line components. The FZPs have never been damaged by air pressure during vacuum work since the new FZP folders were installed. Furthermore, the new folders allowed us to establish a more precise beambased alignment scheme by using only the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera. A precise alignment of the FZP monitor component is crucial to avoid degradation of the spatial resolution due to aberration. The alignment procedure was greatly improved with respect to the old setup: first the center position of the $\\mathbf { \\boldsymbol { x } }$ -ray beam reflected by the Si crystal (corresponding to the position of the optical axis) is measured with the x-ray CCD without FZP imaging. After that, the CZP is inserted to the optical path and the CZP position is adjusted to the optical axis. After inserting the CZP on the optical path, a clear image of the CZP can be detected by illumination of the raw $\\mathbf { X }$ -ray SR light, and hence the center position of the CZP can be obtained. Figure 5 shows an image of a raw $\\mathbf { X }$ -ray SR detected by the x-ray CCD and an image of the CZP on the $\\mathbf { X }$ -ray CCD after inserting the CZP. The MZP position is also adjusted in the same manner. The minimum alignment error can be one pixel of the CCD $( 2 4 \\ \\mu \\mathrm { m } )$ for the CZP and $1 / 2 0 0$ (the reciprocal of the MZP magnification $M _ { \\mathrm { M Z P , } }$ ) of one pixel for the MZP. The FZP tilt angle to the optical path is decided mainly by the machining accuracy and estimated to be less than $0 . 5 ^ { \\circ }$ . We note that the effect of these aberrations of the FZP monitor is calculated by not only ray-tracing analysis, but also the wave optics [17,18].
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augmentation
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Yes
| 0
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Expert
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How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
|
As the shutter opening time becomes shortened, the background component becomes larger than the peak signal of the obtained beam image. In order to measure the beam profiles precisely and analyze them in detail, we carefully subtracted this background component from the data of $\\mathbf { X }$ -ray CCD, as follows. The transverse position of the beam image is much more sensitive, by a factor of 200 of the magnification of MZP, than a transverse change of the MZP. Thanks to the newly installed x-ray pinhole mask, the area of the transmitted x ray, which is one of the background, is drastically reduced. Therefore, by changing the transverse position of the MZP by only a few microns vertically, the beam image does not overlap the transmitted x ray. The alignment error of this position change of the MZP is too small to deform the obtained beam image on the x-ray CCD by the effect of aberrations. After changing the position of the MZP, the background of $\\mathbf { X }$ -ray CCD is subtracted. These procedures for background subtraction allow us to measure the beam profiles easily and precisely. Figure 10 shows a measured beam image after background subtraction. The shutter opening time was fixed with $1 ~ \\mathrm { m s }$ . A clear beam image was observed on the $\\mathbf { \\boldsymbol { x } }$ -ray CCD camera. This beam image, as shown in Fig. 10, was obtained by superposing 10 different beam images with the same current and same trigger timing from beam injection after background subtraction in order to gain the signal-tonoise ratio. The horizontal and vertical beam profiles were obtained by projecting the beam image to each direction. In
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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B. Motivation for the improvements There are several motivations for the improvements. First of all, to obtain long-term position stability of the beam image on an $\\mathbf { X }$ -ray CCD, a new Si monochromator was installed to suppress the beam image drift. Second, the effect of aberrations due to a misalignment of the $\\mathbf { \\boldsymbol { x } }$ -ray imaging optics was not estimated and compensated in the FZP monitor because the center of $\\mathbf { X }$ -ray SR could not be detected with the x-ray CCD camera by intercepting the FZPs with fixed folders. The measured beam profile with the FZP monitor was sometimes deviated from a Gaussian distribution. However, we could not conclude whether the observed non-Gaussian character was caused by instrumental aberration or was a real feature of the beam itself. To eliminate the aberrations of the $\\mathbf { \\boldsymbol { x } }$ -ray imaging optics due to misalignment, two FZP folders were newly installed. Third, penetrated $\\mathbf { \\boldsymbol { x } }$ rays through two FZPs, which appeared on the $\\mathbf { X }$ -ray CCD as a square of $3 \\ \\mathrm { m m } \\times 3 \\ \\mathrm { m m }$ reflecting the FZP structure, is one of the background components of the FZP monitor and affect the beam-profile measurement. In order to reduce this background, an $\\mathbf { \\boldsymbol { x } }$ -ray mask system has been installed. Finally, we improved the time resolution for reducing any short-term movements of the monitor and/or beam oscillation. Especially the AC line noise might affect the beam oscillation. In the original setup of the FZP monitor, the minimum exposure time was $2 0 ~ \\mathrm { m s }$ ; therefore, the obtained beam images with different centers might be superposed by the AC line noise effect on the x-ray CCD. In order to remove the effect of short-term movement, like AC line noise and perform precise beam-profile measurements, a new fast mechanical shutter with a shorter exposure time was installed.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
|
V. CONCLUSION In this paper, we have presented an improvement of the FZP monitor and measurement results of the ultralow emittance beam in the ATF damping ring under various conditions. First, by thermally disconnecting the Si crystal from the stepping motor, the position drift of the obtained image was drastically reduced by a factor of 100, and fully stabilized within a few $\\mu \\mathrm { m }$ for one day. Second, we modified the FZP folder for a more precise beam-based alignment using $\\mathbf { \\boldsymbol { x } }$ -ray SR. This avoids the effects of aberrations due to any misalignments of the FZPs. Third, the newly installed fast mechanical shutter allowed us to measure a beam image within $1 \\mathrm { m s }$ . In addition, the $\\mathbf { \\boldsymbol { x } }$ -ray CCD was synchronized with the beam-injection timing. We could measure the beam profile under the fully damped condition in the normal operation mode. At last, installation of the $\\mathbf { \\boldsymbol { x } }$ -ray pinhole mask system greatly reduced the background of x rays passing through the MZP. With the improved system, beam-profile measurements were performed on three days. By using a fast mechanical shutter, we could remove the effect of an unknown $1 0 0 \\mathrm { H z }$ oscillation, which enlarged the measured vertical beam size, for the beam-profile measurement. We therefore could perform precise beam-profile measurements with a 1 ms shutter opening time. After carefully applying the skew correction, the measured horizontal beam sizes were about $5 0 \\ \\mu \\mathrm { m }$ , and the vertical beam sizes were about 6 $\\mu \\mathrm { m }$ at above $3 \\ \\mathrm { m A }$ stored current in the single-bunch mode, which corresponded to about $1 1 \\ \\mathrm { p m }$ rad of the vertical emittance. The measured beam sizes were in a good agreement with a calculation assuming coupling ratios of $( 0 . 5 \\pm$ $0 . 1 ) \\%$ . In addition, the measured energy spread also agreed well with the calculation. Thanks to the improved x-ray CCD and shorter time resolution of the newly installed fast mechanical shutter, we could also precisely measure the damping time of the ATF damping ring when the damping wigglers were turned on and off. The measurement results of the vertical damping ring agreed well with the design values. Furthermore, the coupling dependence of the beam profiles was obtained. Not only the horizontal and vertical beam sizes, but also the beam tilt angles, were measured precisely under the two coupling conditions. From these measurements, good performance of the improved monitor was confirmed.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
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By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
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Sakai_2007.pdf
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C. Measurement of the damping time By changing the trigger timing of the $\\mathbf { X }$ -ray CCD camera from the beam-injection timing, a beam-profile measurement during radiation damping could be carried out. Furthermore, the improved time resolution by the newly installed fast mechanical shutter allowed us to measure the damping time. We then precisely measured the damping time with/without damping wigglers by using FZP monitor for the study of the damping wigglers. Figure 19 shows the measurements of the damping time with/without the damping wigglers. Damping phenomena were clearly observed in the vertical direction. In order to evaluate the vertical damping time, we use the following function [24], described as $$ \\sigma _ { y } = \\sqrt { \\sigma _ { \\mathrm { i n j } } ^ { 2 } e ^ { - 2 t / \\tau _ { y } } + \\sigma _ { \\mathrm { r i n g } } ^ { 2 } ( 1 - e ^ { - 2 t / \\tau _ { y } } ) } , $$ where $t$ is the elapsed time from injection timing. The injection beam size $( \\sigma _ { \\mathrm { i n j } } )$ , the beam size after complete damping $( \\sigma _ { \\mathrm { r i n g } } )$ , and vertical damping time $( \\tau _ { y } )$ are used as free parameters for fitting. By fitting this function to the vertical beam-size measurement in Fig. 19, we obtained that the vertical damping time $( \\tau _ { y } )$ without damping wigglers was $( 3 0 . 9 \\pm 0 . 6 ) \\$ ms and with damping wigglers $( 2 0 . 7 \\pm 0 . 8 )$ ms. A clear difference in the measured damping time between with and without damping wigglers was observed. The design values of the damping time with/ without damping wigglers are 21.1 and $2 8 . 5 ~ \\mathrm { m s }$ , respectively. These values agree well with the damping-time measurements.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
|
By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
|
Reasoning
|
Sakai_2007.pdf
|
From these measurements, we conclude that the beamsize enhancement, especially vertically, is caused by the $1 0 0 ~ \\mathrm { H z }$ oscillation; the FZP monitor, itself, is working well, and electron beam might be oscillated with $1 0 0 ~ \\mathrm { H z }$ frequency. 3. Data analysis and results For data analysis, fitting with a two-dimensional Gauss function was applied to the beam images. We set 7 free parameters with horizontal and vertical centers, horizontal and vertical widths, peak height, the tilt angle, and the offset. The positive direction of tilt angle was counterclockwise to the electron-beam motion. The fitting results of the horizontal beam size $\\sigma _ { x }$ , vertical beam size $\\sigma _ { y }$ , and tilt angle $\\theta _ { b }$ are summarized in Table V for three different days after the skew correction. The two sets of data (named as ‘‘1st’’ and ‘‘2nd’’) were taken on $2 0 0 5 / 6 / 1$ . The 1st data were taken after first making a skew correction. To confirm the reproducibility, skew magnets were turned off once, and turned on again; 2nd data on $2 0 0 5 / 6 / 1$ were taken under this condition. The shutter opening time was fixed at
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
|
By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
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Reasoning
|
Sakai_2007.pdf
|
We briefly summarize the history of measurements of emittance in the ATF damping ring. First, the horizontal emittance was successfully measured by the tungsten and/ or carbon wire scanner set on the extraction line [3], and was also measured by a double-slit SR interferometer. However, the vertical emittance was not clearly measured with these monitors. In the case of the wire scanner, the spurious dispersion and coupling from the large horizontal emittance could be easily mixed with the vertical direction [4]. On the other hand, a vertical beam-size measurement by a double-slit SR interferometer, which used the spatial pattern of the interference of the visible SR passed through a double slit with an fixed interval [5], had an uncertainty because the measured vertical beam size in the ATF damping ring was almost at its resolution limit [6]. To avoid these uncertainties, a laser wire monitor was developed to measure directly the vertical beam size in the ATF damping ring [7]. This monitor is based on the Compton scattering of electrons with a thin laser light target, called a laser wire. By scanning the laser wire instead of the solid tungsten and carbon wire, quasinondestructive measurements can be performed in the ATF damping ring, and the vertical emittance was successfully measured [8–10]. Unfortunately, we could measure the beam size only in one direction. Therefore, we did not know the $x$ -y coupling of the transverse beam profile. When there is a $x { - } y$ coupling in the transverse beam motion, the measured vertical beam size is contaminated by the horizontal one and the beam profile will become tilted by rotating toward the original two transverse directions perpendicular to the electron-beam motion. The vertical beam size cannot be measured precisely as long as the tilt of the beam profile caused by the $x \\cdot$ -y coupling is unknown. Furthermore, it takes several minutes to finish the measurement of the one directional beam size by the laser wire monitor. Thus, the effects of the beam drift and/or the mechanical vibration, which excites the beam motion of the same order as vertical beam size, cannot be removed off during the vertical beam-size measurement by the laser wire monitor. For precise beam-profile monitoring, it is necessary to know the beam image, which has much information about not only the horizontal and vertical beam sizes, but also the beam positions, beam current, tilt of the beam profile caused by the $x { - } y$ coupling, and its distribution, by direct monitoring of the beam image in a short time. This situation led us to develop a new beam-profile monitor based on $\\mathbf { \\boldsymbol { x } }$ -ray imaging optics by using Fresnel zone plates (FZPs).
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
|
By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
|
Reasoning
|
Sakai_2007.pdf
|
(i) A skew correction was carefully carried out to make the vertical emittance as small as possible. The damping wigglers were turned off. We examined the basic performance of the upgraded FZP monitor and measured the beam profile. The damping time was also measured $( 2 0 0 5 / 4 / 8 )$ . (ii) The damping wigglers were turned on. A skew correction was also carefully carried out. The damping time was measured with the damping wigglers $( 2 0 0 5 / 4 / 1 3 )$ . (iii) The damping wigglers were turned off. The skew magnets were toggled to measure the beam profiles on the different coupling conditions after a skew correction was carefully carried out $( 2 0 0 5 / 6 / 1 )$ . In order to show the beam conditions for these three days in detail, we summarize the parameters of the ATF damping ring for three days in Table IV. The measurements of only the relevant parameters will be briefly given. The $\\beta$ function at source point of the FZP monitor, where $\\mathbf { \\boldsymbol { x } }$ -ray SR was emitted, was measured as follows. By changing the strength of a quadrupole near the source point, we measured any change of the betatron tune with beam position monitors (BPMs). This tune variation is related to the $\\beta$ function at the quadrupole magnet. We measured the $\\beta$ functions at three quadrupole magnets and these $\\beta$ functions were used to evaluate the $\\beta$ function at the source point with the help of a ring’s lattice model. Dispersions $\\eta _ { x }$ and $\\eta _ { y }$ were measured directly by monitoring the change of the beam image center related to the change of the rf frequency. The measured vertical dispersions were less than $\\pm 1 . 3 ~ \\mathrm { m m }$ . The momentum spread $\\sigma _ { p } / p$ was measured by observing the electron-beam size with a screen monitor at the extraction line, where the dispersion was very large [3]. Because of the worse beam tuning and condition at the extraction line, we could not measure the momentum spread, except on $2 0 0 5 / 4 / 8$ . The measured momentum spread on $2 0 0 5 / 4 / 8$ was $8 . 5 \\times 1 0 ^ { - 4 }$ at the beam current of $3 . 5 \\ \\mathrm { m A }$ . The current dependence of the measured momentum spread will be shown later.
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augmentation
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Yes
| 0
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Expert
|
How does the dual-FZP setup achieve beam magnification in the KEK-ATF monitor?
|
By combining two zone plates with different focal lengths, producing a 20√ó magnified X-ray image.
|
Reasoning
|
Sakai_2007.pdf
|
Finally, we note that the improved FZP monitor is now routinely used and helps to produce and manipulate the ultralow emittance beam of the ATF damping ring during beam operation. ACKNOWLEDGMENTS First of all, we would like to express our gratitude to all members of the KEK-ATF group for their helpful support. We would like to thank Professor K. Ueda and Professor A. Kakizaki for their support and encouragement. We are also grateful to Professors Y. Totsuka, Y. Kamiya, S. Iwata, and A. Enomoto for their continuous support of this work. This research was partially supported by Grant-in-Aid Scientific Research (16540234) from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and Joint Development Research at KEK. [1] F. Hinode, S. Kawabata, H. Matsumoto, K. Oide, K. Takata, S. Takeda, and J. Urakawa, KEK Internal Report No. 95-4, 1995. [2] Y. Honda et al., Phys. Rev. Lett. 92, 054802 (2004). [3] T. Okugi, T. Hirose, H. Hayano, S. Kamada, K. Kubo, T. Naito, K. Oide, K. Takata, S. Takeda, N. Terunuma, N. Toge, J. Urakawa, S. Kashiwagi, M. Takano, D. McCormick, M. Minty, M. Ross, M. Woodley, F. Zimmermann, and J. Corlett, Phys. Rev. ST Accel. Beams 2, 022801 (1999).
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augmentation
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Yes
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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Collimators One pair of horizontal and vertical collimators is installed at each of the two long straights of SLS 2.0, where the quadrupole triplets are located: after the ${ 5 0 0 } \\mathrm { M H z }$ RF cavities in straight 5, and after the Super-3HC in straight 9. At these locations, the horizontal and vertical beta functions can reach very large values [1]. Figure 4 shows the schematic volume used for the impedance calculations. The goal of the two movable tungsten jaws seen in Fig. 4 consists in capturing the halo-particles, localizing the losses and preventing the radiation damages to critical devices, such as the cooled in-vacuum undulators. The minimum aperture the collimator chamber can achieve is 7.2 mm, while $8 \\mathrm { m m }$ will be more often used during beam operations. The jaw taper angle measures $1 6 . 5 ^ { \\circ }$ . Trapped HOMs are here efficiently avoided by copper beryllium (CuBe) RF fingers – ten at the entrance and ten at the exit of the collimator - which guarantee the electrical contacts between the internal tapered chamber and the external volume. Also, the beam pipe transition to the collimator was carefully designed to minimize the overall impedance.
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
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DESIGN PROCESS Based on the magnetic field from the bending magnets, SYNRAD [3] and SPECTRA [4] simulations of the ring lattice were perform do define the heat load distribution. Maximal power was found to be at the level of $3 . 7 \\mathrm { k W }$ and $7 . 1 ~ \\mathrm { k W }$ for the normal and super bend magnets, respectively. Example of the results are shown in Fig. 3. The following design criteria were applied in the process:  Maximum $1 0 \\mathrm { \\ W / m m } ^ { 2 }$ power density on the watercooled walls of the vacuum chambers  Maximum $5 0 \\mathrm { W / m m } ^ { 2 }$ and $4 0 0 ^ { \\circ } \\mathrm { C }$ on the absorber body if made out of glidcop $2 5 0 ^ { \\circ } \\mathrm { C }$ in case of $\\mathrm { C u C r Z r } )$ .  No Power dissipated in the gaskets and on flanges  Maximum cooling water temperature lower than cooling water boiling point The existing SLS1 absorber design was considered but this geometry was not meeting the abovementioned criteria. Main optimizations included adding a second toothed jaw with a smaller opening angle. Additionally, it was decided to add a second absorber a few meters downstream which can be transversally moved for fine adjustment of pointing direction if needed.
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
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MECHANICAL MODEL mance was estimated via SYNRAD. The simulation predicts that only $2 . 5 \\%$ of the photons hitting the absorber are reflected back into the electron channel, mainly due to the grazing incidence on the vertical half tooth face. All other photons are successfully trapped. To simulate the interface between the absorber bulk and the reflection shield, a thermal conductance of $1 \\times 1 0 ^ { - 3 } \\mathrm { W } \\mathrm { m m } ^ { - 2 } \\mathrm { K } ^ { - 1 }$ was chosen [9]. The results show that the reflection shield reaches the maximum temperature of $1 4 1 ^ { \\circ } \\mathrm { C }$ while absorbing $5 6 \\mathrm { W }$ . CONCLUSIONS The proposed absorber is capable of handling with a compact design the high spatial power densities that are induced by the short dipole-absorber distances. The results are within the chosen validation criteria both stress and temperature wise, also taking into account loose positional and angular tolerances $( \\pm 2 \\mathrm { m m } , \\pm 1 ^ { \\circ } )$ . The design can successfully be inserted from the inner side of the storage ring, allowing for better sighting of the alignment surveys. The Monte-Carlo, ray-traced simulation shows that the lightweight reflection shield proposed is effective at capturing the reflected photons, protecting the vacuum chamber walls without overheating.
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augmentation
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NO
| 0
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IPAC
|
How does the horizontal “finger” absorber protect the first mirror at SLS?
|
It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
|
BEAM SCREEN DESIGN Silver fingers serve as a conductive path for the image current of the beam, which shields the ferrite yoke from the electromagnetic (EM) wakefields of the beam, and therefore reduces the heat dissipation in the ferrite yoke [8]. The fingers cannot be the full length of the aperture of a module, as they would conduct current during the magnetic field rise and fall times, greatly increasing the overall field rise and fall times. Similarly, the cells of the MKP-L module are too short to apply the fingers directly to the ferrite yoke [3, 8]. Hence, a carrier is required to mechanically support the fingers in the aperture: alumina is used for this purpose. Alumina Carrier The alumina will reduce the aperture available to the beam in the MKP-L modules. Hence, a detailed model of the injection region was constructed and subsequent aperture studies carried out [9]. These studies defined both the required beam aperture and good field regions at the entrance and exit of the MKP-L modules [9], and hence defined the maximum allowable thickness of the alumina. In the initial design of the low-impedance MKP-L the carrier for the silver fingers was envisaged to be two flat plates, one at each of the top and bottom of the aperture. However, a pressure rise, due to electron cloud in the aperture of this low-impedance MKP-L, could result in an HV electrical breakdown between the silver fingers and the module busbars. Hence, to prevent this, the alumina chamber is closed on its sides (Fig. 3): to be able to apply the silver fingers to the chamber, it is constructed from two U-chambers. The MKP-L modules installed in the SPS prior to the Year End technical Stop (YETS) 2022-23 exhibited high pressure rise, with circulating beam, due to electron-cloud (Fig. 1). Measurements of the secondary electron yield (SEY) of the ferrite typically used at CERN for kicker magnets gave a maximum value of ${ \\sim } 2 . 1$ [10]. However, alumina has a significantly higher SEY $( \\sim 9 )$ [11]. To mitigate electron-cloud in the low-impedance MKP-L, each set of U-chambers was coated on their ends with amorphous Carbon [12], at CERN, and on their interior surface with $\\mathrm { C r } _ { 2 } \\mathrm { O } _ { 3 }$ , by Polyteknik [13]. To verify the SEY of the $\\mathrm { C r } _ { 2 } \\mathrm { O } _ { 3 }$ , two witness samples were coated together with each chamber. The SEY of each witness sample was measured: the maximum values were in the range 1.5 to 2.0 [14]. Even with the $\\mathrm { C r } _ { 2 } \\mathrm { O } _ { 3 }$ coating electron cloud will occur until the $\\mathrm { C r } _ { 2 } \\mathrm { O } _ { 3 }$ is conditioned with beam [15] and the coatings maximum SEY is reduced to ${ \\sim } 1 . 4$ or less.
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
|
SLS 2.0 VACUUM CONCEPT The SLS 2.0 storage ring [1] is based on a seven bend achromat design which combines longitudinal gradient bends with reverse bends. Permanent magnets are used to achieve this high magnet density per unit cell with the consequence that magnet aperture minimum must be 22 mm to get enough field strength. The nominal inner cross section of the SLS2.0 arc vacuum chamber is $1 8 ~ \\mathrm { m m }$ , which means poor pumping conductance and high photon flux impinging on the inner chamber surfaces. These surfaces are coated with Non-Evaporable-Getter (NEG) to limit photon stimulated desorption (PSD) [2-4]. Storage Ring Layout and Simulations The storage ring consists of twelve identical arcs, each approximately $1 8 \\mathrm { ~ m ~ }$ in length (Fig. 1). Due to the high packing of magnets, no bellows can be installed, thus preventing any bake-out and NEG activation after installation in the tunnel. The arc includes seven bending magnet vacuum chambers each ending with a stainless steel cube with a $5 5 \\mathrm { l / s }$ ion pump (#Vaclon Plus 55), a getter pump (#CapaciTorr Z400) and a Glidcop crotch absorber [5]. The arc design of Fig.1 was simulated in MOLFLOW [6] to predict the pressure profile along the beam orbit (Fig. 2). The outgassing rate of the inner surfaces was preliminary simulated with the code SYNRAD[6], taking into account the magnetic field maps, the presence or not of NEG, and the different cumulated photon dose illumination, which is proportional to the beam dose in A.h. NEG coating of the inner surface helps speed up the vacuum conditioning time allowing the required pressure for nominal beam lifetime of $1 . 0 \\mathrm { x } 1 0 ^ { - 9 }$ mbar equivalent CO to be reached after $1 0 0 \\mathrm { A . h }$ of beam time. Without NEG coating at least an order of magnitude more conditioning time (1000 A.h) would be required.
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augmentation
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NO
| 0
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IPAC
|
How does the horizontal “finger” absorber protect the first mirror at SLS?
|
It blocks most power while minimally affecting the useful spectral flux.
|
Reasoning
|
Andersson_2008.pdf
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Short crystal strips can be cut with respect to specific Miller indices and are mechanically bent to impart an anticlastic curvature [3]. Such crystals can deflect charged particles by tens or hundreds of microradians [4, 5]. Anticlastic crystals are used in several applications at CERN. For example, to improve the collimation efficiency and reduce power load on sensitive equipment in the LHC, crystal-assisted halo collimation [1, 2] has been implemented as a baseline for the $^ { 2 0 8 } \\mathrm { { P b } ^ { 8 2 + } }$ beam operation of the HL-LHC upgrade. The system relies on primary beam halo cleaning using bent crystal as primary collimators (TCPCs). The channeled halo particles are absorbed by a secondary collimator and the cleaning efficiency of the collimation system benefits from a reduction of inelastic interactions within the crystal, thus limiting nuclear fragmentation and decreasing collimation losses or activation of sensitive equipment. Table: Caption: Table 1: Main Crystal Target Parameters for LHC and SPS Applications Body: <html><body><table><tr><td>Ring</td><td>Usage</td><td>Lemmh,</td><td>ange, dirad]</td><td>Target C</td></tr><tr><td>LHC</td><td>Collim.</td><td>4</td><td>50.0 ± 2.5</td><td>>65%</td></tr><tr><td>SPS</td><td>Extract.</td><td>1</td><td>175 ± 75</td><td>>55%</td></tr></table></body></html> Using a similar device in the CERN Super Proton Synchrotron (SPS), the beam losses on a wire-based anode of the electrostatic septum (ZS) are reduced during the resonant slow extraction of $4 0 0 \\mathrm { G e V / c }$ protons to the North Area. Such scheme is referred to as the “shadowing”, since the crystal deflects the protons of the extracted separatrix that would otherwise impinge on the anode wires [5]. At present, about $1 0 ^ { 1 9 } / \\mathrm { y r }$ protons are extracted from SPS toward the existing North Area experimental facility. This mitigation will be even more necessary in view of the future flux demand of $4 1 0 ^ { 1 9 }$ protons on target (POT) per year by the SHiP experiment [6].
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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Figure 4 shows the carbon wire temperature increase during an acceleration cycle in the SPS with 4 injections from the PS (intensity steps) for a tank without mitigation in green (2023) and with ferrites and coupler in purple (2024). It is observable that the maximum temperature is notably lower when mitigation techniques are used, even under the most severe beam conditions (higher beam intensity). BREAKAGE SCENARIO SIMULATIONS The wire heating measurements suggested that the failures occurred with a high intensity beam during a long flattop, used for scrubbing (electron cloud reduction [7]) of SPS components. Simulations were performed of the instrument and tank assembly [8] which revealed a coupling between the beam spectrum and an impedance peak coming from the geometry of the instrument in the tank at close to ${ 8 0 0 } \\mathrm { M H z }$ . This was confirmed by RF measurements using a spare instrument and tank [9]. Beam-induced heating simulations were made for this coupled mode which predicted an average power dissipation in the wire of $2 0 \\mathrm { W }$ (with a range from $1 9 3 \\mathrm { W }$ to 7 W), which would be sufficient to heat the wire to sublimation temperature for less optimistic assumptions.
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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ION AND LASER BEAMS OVERLAP Because the SIS100 is a large accelerator, which is completely filled with components, is was challenging to find a good place for the laser cooling facility. For laser cooling it is crucial to have the best possible overlap between the ion beam and the laser beams. Therefore, a straight section of the SIS100 lattice is the best choice. In sector 3, several cavities will not be installed directly (MSV 0-3), which leaves space for the components required for laser cooling. However, to get laser beams in and out of the vacuum of the accelerator, a straight section is not so easy as a curved section. In a straight section, the light must enter and exit perpendicularly to the beampipe. Ergo, one mirror couples the laser light into the vacuum, then the laser light travels against the ion beam direction (i.e. anti-collinearly), and a second mirror couples the laser light out of the vacuum. The mirrors must be UHV compatible, i.e. they must be bakeable up to $\\mathord { \\sim } 1 5 0$ degrees Celcius. Since they will only be used for laser cooling, they should be fully retractable and thus move towards (‘in’) and away from (‘out’) the ion beam repeatedly, for which they must be robust. Because they should reflect high power (several Watts) laser light in the UV and visible range, the best material choice is highlypolished solid aluminium. The mirrors must also be large enough (2-inch diameter), else the laser beams will either not be fully reflected or cannot be moved over the mirror surface in order to optimize their position. Due to their size, the mirrors can only come fairly close to the ion beam and the laser beams must thus make an angle with respect to an ion beam ‘on axis’. This would considerably reduce the e"ectiv overlap between ion and laser beams. Therefore, the idea came up to slightly tilt the ion beam locally, and thus increase the overlap range again. The tilt (1-2 mrad) will be made by a horizontal closed-orbit distortion. Fig. 3 shows a simulation of the orbit of a stored ion beam in the SIS100 in sector 3, which is where the laser cooling area is. The ion beam (as seen from above) is injected from the left, the laser beams enter from the top right. Please note the di"erent scale of the two axes (mm and m). The total length the laser light travels inside the accelerator vacuum is about $4 5 \\mathrm { ~ m ~ }$ the e"ective overlap of ion and laser beams is about $2 2 \\mathrm { m }$
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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The beam halo collimation system is installed in section PF (see Fig. 1), and has been studied with particle tracking using the Xtrack-BDSIM coupling simulation framework [11]. Good protection has been demonstrated for halo beam losses assuming a beam lifetime of $5 \\mathrm { m i n }$ at the most critical Z mode [11]. SR collimators have been implemented in the IR region to intercept synchrotron radiation upstream of the IR. Their positions are shown in Fig. 3 in which the blue and red filled curves highlight the aperture corresponding to the primary and secondary beam halo collimators for the Z and tt¯ energies respectively. There are six SR collimators, four horizontal and two vertical, and two masks. While SR collimators and beam halo collimators have minimal interference, tracking simulations of beam halo losses were performed including the SR collimators, with the results presented in Ref. [12]. SIMULATION RESULTS The main sources of synchrotron radiation background in the IR come from the last dipole magnets before the IP, the solenoid fringe field, and the final focus quadrupoles. Simulations have shown that the synchrotron radiation power deposition increases near the IP and beyond as the transverse beam tails widen. The transverse beam tails are difficult to predict and depend on the stored beam conditions. Therefore several beam lifetimes have been considered and this paper focuses on the least optimistic lifetime of $5 \\mathrm { m i n }$ .
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augmentation
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NO
| 0
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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1)Closed Absorber that dissipates all the Synchrotron Radiation (SR) power generated by bending magnets where no light extraction is foreseen 2)First Crotch Absorber located near the bending magnets. It has a large window opening to pass maximal possible beam size while protecting downstream chamber. It dissipates most of the power. 3)Second Crotch Absorber located at the Front Ends entrance of the beamlines. They function is to precisely match the beam requirements of the beamlines, protect the optics components downstream and to dissipate the residual heat from the first absorber. The undulator light goes through the windows of both absorber and is cut in special absorbers located in the front end. The goal for the vacuum system of SLS 2.0 Storage Ring is to reach an average pressure of $1 . 0 \\mathrm { x } 1 0 ^ { - 9 }$ mbar (CO equivalent) with $1 0 0 \\ \\mathrm { m A . h }$ of integrated beam current [2]. Seven discrete pumping units (with an Ion Getter and a NEG Pump) will be located along each of the twelve vacuum arc sectors. They will help to maintain the low pressure after the NEG coating inside the vacuum chambers is saturated. The Absorbers will be located inside those assemblies to minimize the effect of the high outgassing rates coming from their bodies, especially during the conditioning. Example of a crotch absorber integrated inside a pumping block is shown in Fig. 2.
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4
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NO
| 1
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IPAC
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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BROADBAND IMPEDANCE BUDGET The resistive wall represents a major contribution to the broadband impedance budget which is used for the determination of the single bunch instability thresholds of SLS 2.0. The cross section of the arc vacuum chamber has an octagonal shape, with $1 8 ~ \\mathrm { m m }$ distance between opposite faces and a $3 \\mathrm { m m }$ opening slit between the electron channel and the antechamber. In the straight sections, where RF cavities and undulators are installed, the cross section of the vacuum chamber is round, with diameters suitable for the different components located there. Compared to the current design of the SLS ring, mainly in stainless steel and aluminium and with a $3 2 ~ \\mathrm { m m }$ vertical gap, the $1 8 ~ \\mathrm { m m }$ aperture of SLS 2.0 causes higher resistive wake-field effects, partially compensated by copper material. The Non Evaporable Getter (NEG) coating, applied for better vacuum pumping and desorption, has a nominal thickness of $5 0 0 \\mathrm { n m }$ in order to avoid a major increase of the resistive wall impedance. The injection straight design is characterized by metallised ceramic, stainless steel and copper chambers, with a wide variation in the vertical beam aperture, from a minimum of $1 1 ~ \\mathrm { m m }$ (thin septum) to $4 0 ~ \\mathrm { m m }$ maximum (injection kickers). Finally, the cross sections of the Insertion Devices (IDs) include round, elliptical and rectangular shapes, with vertical gaps varying from 3.5 to $9 \\mathrm { m m }$ according to the beamlines.
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1
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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A one-dimensional profile of the intensity distribution through the two maxima, $I ( x _ { \\mathrm { m a x } } , y )$ , gives a distribution of the vertically polarized focused light that displays a dual peak separated by a zero minimum at the centre, $I ( x _ { \\mathrm { m a x } } , 0 ) = 0$ . A vertical beam size may be determined even for the smallest of finite vertical beam sizes where the minimum of the acquired image significantly remains nonzero. While results presented in Section 4 demonstrate support for the Chubar model, it is worth noting that, with the present set-up at SLS, results to an accuracy of within $10 \\%$ may already be achieved through use of the approximate model [36], which uses the square of Eq. (1) as the FBSF. For high current measurements a vertically thin ‘‘finger’’ absorber is inserted to block the intense mid-part of SR. It is incorporated into the model in Section 4. The vertical acceptance angle of 9.0 mrad, being slightly smaller than the total SR opening angles at the observed wavelengths, is also included in the model. However, these modifications only marginally affect the FBSF.
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1
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
|
The branch used for the $\\pi$ -polarization method has a maximum clearance of $7 \\mathrm { { m r a d } _ { H } \\times 9 \\mathrm { { m r a d } _ { V } } }$ . The vis–UV light is twice directed through $9 0 ^ { \\circ }$ angles due to space constraints. This arrangement is also of benefit for optical reasons as a partial polarization of the light is obtained from the substantial attenuation of the (horizontal) $\\sigma$ -polarization component. The first mirror is made of SiC, a material, which has an advantageous ratio of thermal conductivity to expansion (a factor 6 better than $\\mathrm { { C u ) } }$ . This allows for low current measurements $\\mathrm { \\Gamma } ( < 1 0 \\mathrm { m A } )$ , when the vertical gradient of the surface power density on the mirror is still moderate. At higher currents, however, the mirror must be protected from an excessive heat load that would otherwise result in its deformation. To achieve this, a horizontal ‘‘finger’’ absorber, of $4 \\mathrm { m m }$ height, has been inserted immediately before the mirror, while obstructing only the mid $\\pm 0 . 4 5$ mradV of the SR. This prevents $98 \\%$ of the $2 3 0 \\mathrm { W }$ power, at $4 0 0 \\mathrm { m A }$ current, reaching the mirror, while blocking only $1 \\%$ of the $\\pi$ -polarized spectral flux in the vis–UV range used for measurements. Cooling of the SiC mirror was not a viable option since mirror deformation would inevitably result from the large vertical temperature gradient. The second mirror is an angular movable aluminized fused silica (FS) mirror. Both mirrors have a surface flatness better than $3 0 \\mathrm { n m }$ peak to valley. A FS symmetric spherical lens is positioned $5 . 0 7 8 \\mathrm { m }$ from the source point, between the two mirrors. It has a surface accuracy of $4 0 \\mathrm { n m }$ peak to valley. The vis–UV light is guided out from within the vacuum region through a FS window at the end of the beamline, approx. $9 \\mathrm { m }$ from the source point. This serves to minimize the light footprint on the vacuum window, which, in the absence of optical window specifications, was deemed necessary in order to minimize the risk of wavefront distortions. Blades that determine the acceptance angle of the light are positioned in the locality of the lens. External to the vacuum, grey filters, narrow bandpass (BP) filters and a Glan–Taylor polarizer are all placed on remotely controlled rotational movers. These, together with a neighbouring Pointgrey FleaTM [34] CCD camera (pixel size $4 . 6 5 \\mu \\mathrm { m }$ ), can also be remotely moved longitudinally in order to adjust for a new image plane when different BP filters are used. The camera roll error is less than 10 mrad. Since the filters and polarizer are situated close to the image plane, the specifications for their surface accuracies need not be the most stringent, and can duly be purchased from off-the-shelf optical component vendors. The magnifications in the vis–UV branch for the chosen wavelengths are $0 . 8 5 4 / 0 . 8 4 1 / 0 . 8 2 0$ at $\\lambda = 4 0 3 / 3 6 4 / 3 2 5 \\mathrm { n m }$ , respectively.
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5
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NO
| 1
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
|
Andersson_2008.pdf
|
The horizontal acceptance angle of the X-ray branch is 0.8 mrad. The water cooled pinhole array, fabricated from a $1 5 0 \\mu \\mathrm { m }$ thick tungsten sheet interspersed with $1 5 \\mu \\mathrm { m }$ diameter holes, is located $4 . 0 2 0 \\mathrm { m }$ from the source point. The light escaping these holes carries low power and can be released through a $2 5 0 \\mu \\mathrm { m }$ thick non-cooled aluminium window. Monochromating molybdenum filters and phosphor $( 6 \\mu \\mathrm { m }$ thick P43) are placed on a common optical table at the end of the beamline. The same type of camera as in the vis–UV branch is used to observe the phosphor via a zoom and focus adjustable lens system [35]. The magnification in the $\\mathrm { \\Delta X }$ -ray branch, to the phosphor screen, is 1.276. 3. SR imaging model The ideal goal would be to capture an exact image of the electron distribution in the transverse plane. However, certain features inherent to SR, such as a narrow vertical opening angle and radiation generation along the longitudinal electron trajectory, make this impossible. A more realistic scenario would be to form an image, which although affected by the afore-mentioned SR features, is nevertheless free from optical component aberrations. The transverse electron distribution could then be derived from a model that describes the image of a single electron, or ‘‘filament’’ beam. The acquired image is, to a good approximation, given by the convolution of the single electron image and the transverse electron distribution. Conversely, the transverse electron distribution is a deconvolution of the acquired image with the ‘‘filament’’ beam image. For stable beam conditions, the transverse electron distribution can be assumed to be a twodimensional Gaussian of unknown widths, which simplifies the de-convolution.
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augmentation
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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5. Emittance determination The stability of the SLS as given by the vertical beam size is illustrated in Fig. 10, which shows archived data over a period of 4.5 days dedicated to user operation and for which changes to the ID parameters by experimenters are the norm. However, the beam had been deliberately tuned (last tuning at (a)) towards a small vertical beam size, and minimal beam rotation $\\phantom { + } < 1 5 \\mathrm { m r a d } )$ , using eight skew quadrupoles, all with integrated field strengths below $\\bar { 0 . 0 0 6 } \\mathrm { { m } } ^ { - 1 }$ . This still gave an acceptable lifetime of approx. $5 \\mathrm { h }$ . The circulating current was $4 0 0 . 7 { \\pm } 0 . 7 \\mathrm { m A }$ over the whole period. The upper data (right scale) shows the central rms vertical beam size. An average central rms vertical beam size of $\\sigma _ { \\mathrm { e y 0 } } = 6 . 8 \\mu \\mathrm { m }$ was sustained over a period of more than 3 days, with the exception of a few hours (b), due to one undulator gap change. The horizontal beam size (lower data line, left scale) varies slightly more. During a nine-hour period (c), a wiggler gap was opened. All other stepwise variations of $\\sigma _ { \\mathrm { e x } }$ are due to undulator gap changes. For emittance and emittance ratio determinations we will use the average value $\\sigma _ { \\mathrm { e x } } = 5 7 . 3 \\mu \\mathrm { m }$ measured over the whole time period.
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augmentation
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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The FWHM value is used for converting to $\\sigma _ { \\mathrm { e x } }$ . During measurements small beam ellipse rotations, originating either from betatron coupling or from a local vertical dispersion, are sometimes present. In this case, the vertically measured quantity is sey0 such that sey0osey, since only the vertical size of the central beam region is observed. This quantity will be termed the central rms vertical beam size. Horizontally the result is unaffected by a beam rotation, since the full image is used to obtain $\\sigma _ { \\mathrm { e x } }$ . 4.1. Horizontal measurements While it is more challenging to determine the beam size in the vertical plane, it is also of interest to verify that the model predictions agree with measurements in the horizontal plane, where the beam size is typically much larger. Fig. 5 shows a profile of the horizontal image in its entirety. The lines are profile predictions calculated from the SRW model by convoluting the FBSF of the vertically polarized light with a Gaussian electron beam and then integrating over the entire image, as is done with the on-line monitor. In this particular example $\\sigma _ { \\mathrm { e x } } = ( 5 7 . 0 \\pm 1 . 5 ) \\mu \\mathrm { m }$ is measured at the monitor. The error margins represent the maximum systematic errors. The statistical rms error is considerably smaller, $0 . 3 \\mu \\mathrm { m }$ for a single sample. Of particular note is the good agreement in the tails, which deviate from a Gaussian shape (dashed line). This is as anticipated since the predicted profile is a convolution of a Gaussian and a function of approximate form $\\operatorname { s i n c } ^ { 2 } ( x )$ .
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augmentation
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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Table: Caption: Table 1 Nominal (no IDs) and measured parameter values at the observation point, together with derived emittances and emittance ratio Maximum error margins are linearly added when deducing the maximum emittance and emittance ratio errors. Body: <html><body><table><tr><td>Parameter</td><td>Nominal value</td><td>Measured value</td><td>Max.error margin</td></tr><tr><td>σs (%)</td><td>0.086</td><td>1</td><td>+0.009/-0.000</td></tr><tr><td>βx (m)</td><td>0.452</td><td>0.431</td><td>±0.009</td></tr><tr><td>nx (mm)</td><td>29</td><td>27.3</td><td>±1.0</td></tr><tr><td>σex (μm)</td><td>56</td><td>57.3</td><td>±1.5</td></tr><tr><td>εx (nmrad)</td><td>5.6</td><td>6.3</td><td>+0.7/-0.9</td></tr><tr><td>βy (m)</td><td>14.3</td><td>13.55</td><td>±0.14</td></tr><tr><td>ny (mm)</td><td>0</td><td>2.3</td><td>±0.55</td></tr><tr><td>δeyo (μm)</td><td>1</td><td>6.8</td><td>±0.5</td></tr><tr><td>εy (pmrad)</td><td>1</td><td>3.2</td><td>±0.7</td></tr><tr><td>g (%)</td><td>1</td><td>0.05</td><td>±0.02</td></tr></table></body></html> The diagnostic beamline comprising the two optics schemes is described in Section 2. The pinhole camera scheme is still under development. Preliminary results have been presented elsewhere [4]. Here we place emphasis on the $\\pi$ –polarization method. The model for the SR emission and focusing is described in Section 3. In Section 4 we present measured data at SLS and compare it to the SRW predictions of a finite emittance beam. In Section 5 we perform the emittance determinations while estimating different error contributions. Finally in Section 6, we discuss whether the vertical emittance minimization is of local or global nature. 2. The diagnostic beamline The source point of the beamline is the centre of the middle-bending magnet in the SLS triple bend achromat lattice (see Table 1 for machine parameters). Fig. 1 shows a schematic top view of the beamline. The angular separation of the vis–UV branch and the $\\mathrm { \\Delta X }$ -ray branch is 5 mrad, corresponding to an arc length of $3 0 \\mathrm { m m }$ .
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augmentation
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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$$ where $\\gamma = E / m _ { \\mathrm { e } } c ^ { 2 }$ , $E$ is the electron energy, $\\lambda$ is the observed radiation wavelength, $\\lambda _ { \\mathrm { c } } = 4 \\pi R / 3 \\gamma ^ { 3 }$ is the critical wavelength, $R$ is the radius of the electron trajectory, $p$ and $p ^ { \\prime }$ are the distances from the source point to the lens and from the lens to the image plane, respectively, and $E _ { \\pi 0 }$ is a constant. Squaring Eq. (1) gives an intensity distribution in the image plane as shown in Fig. 2, where we have used numbers resembling our actual imaging scheme at SLS. This two-dimensional distribution function is of the form $f ( x ) g ( y )$ , where $f ( x ) = \\mathrm { s i n c } ^ { 2 } ( x )$ and $g ( y )$ is given by the square of the integral expression in Eq. (1). The model used to describe our $\\pi$ -polarization scheme was outlined by Chubar [37,38]. It is based on a near-field SR calculation at the first optical element, using the Fourier transform of the retarded scalar- and vector potentials [21], preserving all phase information as the electron moves along its trajectory. The integral theorem of Helmholtz and Kirchoff [23] is now applied to this Fourier transform (rather than the more usual spherical wave) at different apertures in the beamline. One benefit of this approach is that the model now includes, in a natural way, the so-called depth-of-field effect appearing in the image plane. Using Fourier optical methods, the SRW code, based on the described model, calculates the intensity distribution, $I ( x , y )$ , in the image plane. This distribution, resulting from a single relativistic electron, is termed the ‘‘filament-beam-spread function’’ (FBSF). It is equivalent to point-spread functions for optical systems in the case of virtual point sources. The intensity distribution is shown in Fig. 3, for the same SLS case as above, and is seen to no longer maintain the simple $f ( x ) g ( y )$ form. This is a consequence of the fact that the wavefront produced by the relativistic electron is more complicated than that of a point source [39].
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augmentation
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NO
| 0
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expert
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How does the horizontal “finger” absorber protect the first mirror at SLS?
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It blocks most power while minimally affecting the useful spectral flux.
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Reasoning
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Andersson_2008.pdf
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We now address the question as to whether the small vertical emittance achieved when performing the skew quadruple betatron coupling correction, is of a global or local nature. One could argue that the minimization of the vertical beam size at one observation point in the ring does not necessarily constitute evidence for a minimal vertical emittance throughout the entire ring. Indeed, the inverse effect could also be true. In Ref. [30] an imperfect SLS machine was modelled by the 6D code TRACY [43], and betatron coupling correction was simulated by using six skew quadrupoles in nondipersive regions, for 200 distorted machine lattices (seeds). The minimisation was performed on $\\varepsilon _ { \\mathrm { I I } }$ , since this is the relevant quantity — though not easily measured — to evaluate the success of the correction. A minimization of $\\varepsilon _ { \\mathrm { I I } }$ assures, for this skew quadrupole scheme, a minimization of the average vertical emittance around the ring, $\\langle \\varepsilon _ { y } ( \\mathsf { s } ) \\rangle _ { \\mathsf { s } }$ , as well. We repeated the same procedure for 100 seeds with the only exception that the minimization was now performed on the vertical beam size at the position of our monitor. As can be seen from Fig. 11a, $\\varepsilon _ { \\mathrm { I I } }$ , can also be minimized in this way. The quantity, $\\sigma _ { \\mathrm { e y } } ^ { 2 } / \\beta _ { y }$ , in Fig. 11a is not the local vertical emittance, since $\\sigma _ { \\mathrm { e y } }$ includes the local spurious vertical dispersion. This explains the lower than unity slope $( a = 0 . 7 6 )$ ) of the correlation of $\\varepsilon _ { \\mathrm { I I } }$ vs. $\\sigma _ { \\mathrm { e y } } ^ { 2 } / \\beta _ { y }$ . In fact, when minimizing on the beam size at the monitor we get on average for the 100 seeds, $\\langle \\varepsilon _ { y } ( \\mathrm { s } _ { \\mathrm { m o n } } ) \\rangle = 1 . 0 2 \\langle \\varepsilon _ { \\mathrm { I I } } \\rangle$ . Furthermore, Fig. 11b shows that essentially the same $\\varepsilon _ { \\mathrm { I I } }$ is reached for the two minimization processes, since all corrected seeds are clustered along the diagonal $( a = 1 )$ ) line. In conclusion, all three quantities $\\varepsilon _ { \\mathrm { I I } }$ , $\\varepsilon _ { \\mathrm { y } } ( \\mathrm { s } _ { \\mathrm { m o n } } )$ and $\\langle \\varepsilon _ { y } ( \\mathsf { s } ) \\rangle _ { \\mathsf { s } }$ are minimized by minimizing the vertical beam size at the monitor.
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augmentation
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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Beam Size For this study a precise and reliable measurement of the beam size is critical. The beam images are recorded on luminescent screens with digital cameras. Different methods to compute the $1 \\sigma$ beam sizes from the beam profiles were investigated (Fig. 4). RMS beam sizes with $5 \\%$ amplitude or $5 \\%$ area cut-off [4] depend on the image section, which is used for the analysis and wrong results are produced, if the beam spot is cut on one side. Fitting a Gaussian or uniform distribution to the profiles does not well represent the data and depend on the image section. Skew Gaussian and Super Gaussian distributions proposed in [5] yield a better result, but are also not optimal. The best agreement with the data and the least sensitive to the choice of the image section is a combination of these two fit functions, a Skew Super Gaussian distribution $$ I = \\frac { I _ { 0 } } { \\sqrt { 2 \\pi } \\sigma _ { 0 } } \\exp \\left( \\frac { - \\mathrm { a b s } ( x - x _ { 0 } ) ^ { n } } { 2 \\big ( \\sigma _ { 0 } ( 1 + \\mathrm { s i g n } ( x - x _ { 0 } ) E ) \\big ) ^ { n } } \\right) + I _ { b g }
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augmentation
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NO
| 0
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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BEAM SIZE CALCULATION The measurement for the remaining term in the beam size calculation (Eq. (5)) is shown in Fig. 8. The value for the horizontal orbit kick slope of $- 4 . 7 8 1 \\pm 0 . 0 9 2 \\mu \\mathrm { r a d } / \\mathrm { m } ^ { - 2 }$ results in a calculated value for the horizontal beam size of $\\sigma _ { x } = 1 . 9 5 5 \\pm 0 . 0 4 8 \\mathrm { { m m } }$ when neglecting the vertical beam size, which is a factor of 5 smaller according to the optics functions. We obtain at present typical beam size calculations which are significant overestimates when compared to the values expected from the emittance and Twiss functions, which give $\\sigma _ { x } = 1 . 0 9 \\ : \\mathrm { m m }$ for the example at hand. DISCUSSION An improvement over the analysis presented in Ref. [2] achieved during the past year is our ability to perform a complete analysis of all our data sets in a few hours, thus showing results for all sextupoles, such as in Fig. 7. Our calculations of beam size generally give beam size values greater than those expected from the optics, i.e. our measured values of $\\Delta p _ { \\mathrm { X } } / \\Delta K _ { 2 } L$ appear to have contributions other than those we have considered here. The prime suspects are nonlinear effects stemming from beam movement in the sextupoles around the ring when the strength of the sextupole under study changes. We are now mounting a modeling campaign to understand these effects.
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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$$ where $r _ { I I }$ and $r _ { I 2 }$ are elements of the transport matrix from the quadrupole to the screen. Usually, dispersion is neglected and using thin lens approximation the above equation becomes a parabola with the variable $K$ [6]. A parabola fit then yields $\\varepsilon , \\beta _ { \\mathcal { Q } }$ and $\\alpha _ { \\mathcal { Q } }$ . For the measurement described in this paper, however, the thin lens approximation criterion $( K L ) ^ { - 1 } \\gg L$ is not valid over a large range of $K L$ values and the dispersion is non-zero. Therefore, the dispersion contribution has to be subtracted from the measured beam size, yielding the following system of equations: $$ \\binom { \\sigma _ { S , 1 } ^ { 2 } - \\bigcup _ { S , 1 } ^ { 2 } \\delta p ^ { 2 } } { \\vdots } = \\left( \\begin{array} { c c c } { { r _ { 1 1 , 1 } ^ { 2 } } } & { { 2 r _ { 1 1 , 1 } r _ { 1 2 , 1 } } } & { { r _ { 1 2 , 1 } ^ { 2 } } } \\\\ { { \\vdots } } & { { \\vdots } } & { { \\vdots } } \\\\ { { r _ { 1 1 , N } ^ { 2 } } } & { { 2 r _ { 1 1 , N } r _ { 1 2 , N } } } & { { r _ { 1 2 , N } ^ { 2 } } } \\end{array} \\right) \\cdot \\left( \\begin{array} { c } { { \\varepsilon \\beta _ { Q } } } \\\\ { { - \\varepsilon \\alpha _ { Q } } } \\\\ { { \\varepsilon \\gamma _ { Q } } } \\end{array} \\right)
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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QUADRUPOLE SCAN METHOD The transverse (horizontal) emittance for a well centered and aligned beam $\\mathbf { \\bar { x } } , \\mathbf { x ^ { \\prime } } = 0 \\mathbf { \\bar { \\Psi } } .$ ) can be determined as: $$ \\varepsilon _ { x } = \\sqrt { d e t \\sigma } = \\sqrt { \\left( \\sigma _ { 1 1 } \\sigma _ { 2 2 } \\right) - \\sigma _ { 1 2 } ^ { 2 } } , $$ where $$ \\sigma = \\left[ { \\begin{array} { c c } { \\sigma _ { 1 1 } } & { \\sigma _ { 1 2 } } \\\\ { \\sigma _ { 2 1 } } & { \\sigma _ { 2 2 } } \\end{array} } \\right] $$ $$ \\sigma _ { 1 1 } = \\langle x ^ { 2 } \\rangle , \\sigma _ { 1 2 } = \\langle x x ^ { \\prime } \\rangle , \\sigma _ { 2 2 } = \\langle x ^ { \\prime 2 } \\rangle $$ The Fig. 2 shows the beam ellipse and the physical interpretation of its physical components. In the Fig. $2 \\mathrm { ~ \\bf ~ x ~ }$ and $\\mathbf { x } ^ { \\prime }$ are the position and angle of the particles, respectively.
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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$$ where $N$ is the number of particles, $e$ is the charge of each particle, $s - u t = : z$ is the longitudinal position relative to a reference particle with the trajectory $u t$ . Here, without writing out explicitly, the horizontal and vertical beam sizes $\\sigma _ { x }$ and $\\sigma _ { y }$ vary with $s$ $$ \\sigma _ { i } ( s ) = \\sqrt { \\epsilon _ { i } \\beta _ { i } ^ { * } } \\cdot \\left( 1 + \\frac { s ^ { 2 } } { \\beta _ { i } ^ { * } } \\right) ^ { 1 / 2 } \\quad i \\in \\{ x , y \\} $$ with $\\epsilon _ { i }$ the beam emittance and $\\beta _ { i } ^ { * }$ the beta function at $s = 0$ . We will follow this convention throughout this article. With Eq. (1), the corresponding electric field in each direction can be calculated by $$ E _ { x } = - \\frac { \\partial \\phi } { \\partial x } , E _ { y } = - \\frac { \\partial \\phi } { \\partial y } , \\mathrm { ~ a n d ~ } E _ { s } = - \\frac { \\partial \\phi } { \\partial s } - \\frac { 1 } { \\gamma ^ { 2 } } \\frac { \\partial \\phi } { \\partial z } ,
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augmentation
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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$$ using emittance $\\varepsilon$ and twis parameters $\\alpha , \\beta , \\gamma$ . Since $\\beta \\varepsilon$ is equal to the square of the beam width, Eq. (1) can be used to derive the relation as follows. $$ \\begin{array} { r l } & { \\sigma _ { \\mathrm { f i n a l } , y 1 1 } = \\sigma _ { \\mathrm { i n i t i a l } , y 1 1 } R _ { 3 3 } ^ { 2 } } \\\\ & { ~ + ~ 2 R _ { 3 3 } R _ { 3 4 } \\sigma _ { \\mathrm { i n i t i a l } , y 1 2 } + \\sigma _ { \\mathrm { i n i t i a l } , y 2 2 } R _ { 3 4 } ^ { 2 } } \\\\ & { \\sigma _ { \\mathrm { f i n a l } , x 1 1 } = \\sigma _ { \\mathrm { i n i t i a l } , x 1 1 } R _ { 1 1 } ^ { 2 } + 2 R _ { 1 1 } R _ { 1 2 } \\sigma _ { \\mathrm { i n i t i a l } , x 1 2 } } \\\\ & { ~ + ~ \\sigma _ { \\mathrm { i n i t i a l } , x 2 2 } R _ { 1 2 } ^ { 2 } + \\sigma _ { \\mathrm { i n i t i a l } , z 2 2 } R _ { 1 6 } ^ { 2 } } \\end{array}
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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THEORY Equation (1) shows the geometric luminosity $\\mathcal { L }$ from a head-on collision of two Gaussian beams. The transverse sizes $( \\sigma _ { x } , \\sigma _ { y } )$ should be minimized to maximize luminosity. $$ \\mathcal { L } = \\frac { N _ { 1 } N _ { 2 } f N _ { b } } { 4 \\pi \\sigma _ { x } \\sigma _ { y } } $$ where $N _ { 1 , 2 }$ is the number of particles contained by each beam, $f$ is the revolution frequency [2]. However, small transverse beam sizes lead to an intense electromagnetic (EM) field [4], which deflects the charged particles and causes them to emit radiation (Fig. 1). The intensity of these interactions is characterized by the beamstrahlung parameter $\\Upsilon$ in Eq. (2). For Gaussian beams, the average and maximum $\\Upsilon$ are estimated with Eq. (3). $$ \\Upsilon = \\frac { 2 } { 3 } \\frac { \\hbar \\omega _ { c } } { E _ { 0 } } $$ $$ \\langle \\Upsilon \\rangle \\sim \\frac { 5 } { 6 } \\frac { N r _ { e } ^ { 2 } \\gamma } { \\alpha \\sigma _ { z } ( \\sigma _ { x } + \\sigma _ { y } ) } \\sim \\frac { 5 } { 1 2 } \\Upsilon _ { \\mathrm { m a x } }
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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THEORY In order to comprehend the concept of the beam profile reconstruction using the spectral resolved set-up, it is required to briefly review the theory of the interferometric beam size monitor utilizing synchrotron radiation, which was first proposed by T. Mitsuhashi [4]. The interference pattern for Young’s double-slit interferometer with a finite source size can be described as: $$ I ( x ) = ( I _ { 1 } + I _ { 2 } ) \\mathrm { s i n c } ^ { 2 } \\left( \\frac { a } { \\lambda f } x \\right) \\left[ 1 + V \\mathrm { c o s } \\left( \\frac { 2 \\pi d } { \\lambda f } x + \\psi \\right) \\right] , $$ where $x$ is the position on the detector, $a$ is the full width of a single slit, $d$ is the distance between slits, $f$ is the distance between the focusing lens and the detector screen, $\\lambda$ is the wavelength, $I _ { 1 }$ and $I _ { 2 }$ are intensities of the light at both slits, respectively, $\\psi$ is the phase, and $V$ is the absolute amplitude of coherency which is called as visibility. The visibility of the interferogram depends not only on the spatial coherency between photons from two slits but also on the intensity imbalance ratio. It can be roughly represented by the ratio of the di!erence and sum between the maximum intensity value $I _ { m a x }$ and intensity in the first local minima $I _ { m i n }$ as
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augmentation
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
$$ or more conveniently written as: $$ \\frac { \\Delta x _ { s } } { \\sqrt { \\epsilon _ { G } \\beta _ { s } } } \\leq \\left| \\sum _ { i } \\theta _ { s _ { i } } A _ { i } \\exp ( j 2 \\pi \\phi _ { s _ { i } } ) \\right| , $$ where $A _ { i }$ is a function that can be computed for a given optics, and the geometric emittance normalisation $1 / { \\sqrt { \\epsilon _ { G } } }$ is used to conveniently express the displacements in terms of the local beam size, which can be a metric for comparing di!erent optics or machines, even if this does not take into account the available or required aperture (which is not considered here). The phase advance $\\phi _ { s _ { i } }$ in Eq. (3) is defined with respect to an arbitrary location. σy/ max(Tm) 102 6 101 10 ujujjiujuuuu 24mod(2⇡φsi, 2⇡) 0 AAHN 2 101 102 1 V 1 0 600 400 200 0 200 400 600 s [m] σy/0.1 max(Tm) 102 6
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augmentation
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
METHODS Here we focus on two methods for measuring emittance, solenoid scans and 4D phase space scans. Emittance was measured for each laser spot size using both methods. The photocathode used for all measurements shown here was K-Sb grown on niobium at room temperature, with typical beam currents ranging within $0 . 5 \\mathrm { ~ - ~ } 1 \\mathrm { { n A } }$ . Solenoid Scan The beam is imaged at the detector while the solenoid current is varied such that the beam size crosses the waist. At each solenoid current, a background image is taken with the beam steered offscreen and the rms beam size in both transverse directions is calculated from a supergaussian fit of the beam image with the background subtracted. An example of a full set of solenoid scans is shown in Fig. 3, where effects of the quadrupole field correction can also be seen in the close agreement between the $\\mathbf { \\ ' } _ { x } \\mathbf { \\ ' }$ and ${ \\bf \\ ' } _ { y } ,$ beam sizes. From known electromagnetic fieldmaps of the beamline elements, we calculate 2D linear transfer matrices $\\mathbf { R } _ { i }$ for all solenoid currents using the methods described in Ref. [5]. The beam sizes vs solenoid current data is fitted to $\\mathbf { R } _ { 1 1 , i } ^ { 2 } \\sigma _ { x } ^ { 2 } +$ $\\mathbf { R } _ { 1 2 , i } ^ { 2 } \\sigma _ { p x } ^ { 2 } \\ : = \\ : \\sigma _ { x , i } ^ { 2 }$ , where $\\sigma _ { x }$ and $\\sigma _ { p x }$ are the initial beam sizes in position and momentum and $\\sigma _ { x , i }$ is the beam size measured for the ùëñth data point. Assuming zero correlation between the position and momentum at the surface of the photocathode, as well as no coupling between the transverse directions, the covariance matrix in Eq. 2 is purely diagonal and the 4D emittance is simply $\\epsilon _ { n } = \\sqrt { \\sigma _ { x } \\sigma _ { p x } \\sigma _ { y } \\sigma _ { p y } } / ( m _ { e } c )$ The error of the emittance is propagated from the beam size uncertainty using a Monte Carlo method.
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augmentation
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NO
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
MEASUREMENT ERRORS The accuracy of beam size measurements is a!ected by various factors, such as CCD noise, beam jitter, and beamline vibrations. The resulting errors, denoted by $\\Delta \\sigma$ , are related to the errors in visibility measurements, $\\Delta \\lvert \\gamma \\rvert$ , by the formula $$ \\Delta \\sigma = - \\frac { 1 } { \\sqrt { 8 } } \\frac { \\lambda L } { \\pi D } \\frac { 1 } { | \\gamma | \\sqrt { \\ln \\frac { 1 } { | \\gamma | } } } \\Delta | \\gamma | . $$ Assuming a visibility measurement error of 0.01, Fig. 2 shows the beam size measurement error as a function of beam size for di!erent acceptance angles of two slits. Achieving an accuracy of $0 . 2 \\mu \\mathrm { m }$ for a beam size of around $1 0 \\mu \\mathrm { m }$ requires an acceptance angle of approximately 6 mrad. Ideally, two diagnostic beamlines at di!erent source points are needed to measure both beam emittance and energy spread independently. These two source points should have di!erent dominant beam size contributions from either Betatron oscillation or dispersion functions. Due to cost and space constraints, a single diagnostic beamline will be built based on dipole 7, sharing the similar front-end vacuum system design as the IR user beamline. The energy spread will be measured independently with a extracted beam at the Storagre-Ring-to-Accumulator (STA) transferline with less than $5 \\%$ resolution.
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augmentation
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NO
| 0
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expert
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
|
Andersson_2008.pdf
|
The FWHM value is used for converting to $\\sigma _ { \\mathrm { e x } }$ . During measurements small beam ellipse rotations, originating either from betatron coupling or from a local vertical dispersion, are sometimes present. In this case, the vertically measured quantity is sey0 such that sey0osey, since only the vertical size of the central beam region is observed. This quantity will be termed the central rms vertical beam size. Horizontally the result is unaffected by a beam rotation, since the full image is used to obtain $\\sigma _ { \\mathrm { e x } }$ . 4.1. Horizontal measurements While it is more challenging to determine the beam size in the vertical plane, it is also of interest to verify that the model predictions agree with measurements in the horizontal plane, where the beam size is typically much larger. Fig. 5 shows a profile of the horizontal image in its entirety. The lines are profile predictions calculated from the SRW model by convoluting the FBSF of the vertically polarized light with a Gaussian electron beam and then integrating over the entire image, as is done with the on-line monitor. In this particular example $\\sigma _ { \\mathrm { e x } } = ( 5 7 . 0 \\pm 1 . 5 ) \\mu \\mathrm { m }$ is measured at the monitor. The error margins represent the maximum systematic errors. The statistical rms error is considerably smaller, $0 . 3 \\mu \\mathrm { m }$ for a single sample. Of particular note is the good agreement in the tails, which deviate from a Gaussian shape (dashed line). This is as anticipated since the predicted profile is a convolution of a Gaussian and a function of approximate form $\\operatorname { s i n c } ^ { 2 } ( x )$ .
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4
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NO
| 1
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
$$ where $\\gamma$ denotes the Lorentz factor, $I _ { t o t }$ the total beam current, $\\xi _ { y }$ the beam-beam parameter, $R _ { G }$ the hour-glass effect, $e$ the electron charge, $r _ { e }$ the classical electron radius, and $\\beta _ { y } ^ { * }$ the vertical $\\beta$ -function at the interaction point (IP). Any alignment error or source of coupling can lead to spurious vertical dispersion or transverse coupling, as well as a change of $\\beta$ -function at the IP, which in turn affects the vertical beam size as shown in Eq. (2), $$ \\begin{array} { r c l } { { \\sigma _ { y } ^ { * } } } & { { \\approx } } & { { \\sqrt { \\varepsilon _ { y } \\beta _ { y } ^ { * } + D _ { y } ^ { 2 * } \\delta _ { p } ^ { 2 } + \\beta _ { y } ^ { * } \\varepsilon _ { x } | \\hat { F } _ { x y } ^ { * } | ^ { 2 } } \\ , } } \\\\ { { \\hat { F } _ { x y } } } & { { = } } & { { \\displaystyle \\frac { \\sinh \\sqrt { | 2 f _ { 1 0 1 0 } | ^ { 2 } - | 2 f _ { 1 0 0 1 } | ^ { 2 } } } { \\sqrt { | f _ { 1 0 1 0 } | ^ { 2 } - | f _ { 1 0 0 1 } | ^ { 2 } } } ( f _ { 1 0 0 1 } - f _ { 0 1 0 1 } ) \\ , } } \\end{array}
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2
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NO
| 0
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IPAC
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
Over the past few years, we have focused on testing two beam size measurement setups, both based on x-ray diffraction optics. The first one is based on using Fresnel zone plates (FZP) and the second is based on diffraction using multiple crystals. FZPs allow imaging the beam in 2D, providing size and tilt information simultaneously. The first possibility of using a single zone plate to image the source in the dipole was explored and reported in [3, 4]. However, with a very small vertical beam size at the focus $( \\sim 2 - 3 ~ \\mu \\mathrm { m } )$ , it was not possible to measure correctly with a $5 \\mu \\mathrm { m }$ thick scintillator. Since there is a trade-off between scintillator thickness and yield, we focused on testing a transmission $\\mathbf { x }$ -ray microscope (TXM) using two FZPs. The magnified image allows relaxing the resolution requirements on the detector. Here, we report on the recently set up TXM for measuring the beam height at the SLS. Another technique that was explored was the multi-crystal diffraction-based $\\mathbf { \\boldsymbol { x } }$ -ray beam property analyser (XBPA). The XBPA uses a double crystal monochromator (DCM) along with a Laue crystal in dispersive geometry, to preserve the energy-angle relationship [5]. The Laue crystal is set to diffract near the centre angle of the DCM diffracted beam. Due to the dispersive geometry, the profile of the transmission beam contains a sharp valley. Its width is proportional to the beam size in a single dimension (the diffraction plane). The valley is a convolution of the valley profile of a point source and the projected spatial profile of the source on the detector, which gives a broadened valley width. The source profile can thus be obtained by deconvolution of the projected spatial profile from the measured profile. This has been meticulously reported in Ref. [5], where the vertical beam size was measured at the SLS from a bending magnet source. To measure the horizontal beam size, a horizontally deflecting DCM and Laue crystal setup is required.
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NO
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expert
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
Hofmann and Me´ ot [36] describe diffraction effects from the SR spectral-angular distribution on the beam profile image formation in different cases of radiation by relativistic electrons. For the bending magnet SR case, a simple point source is assumed to emit an $E$ -field amplitude distribution over a vertical angle identical to the one given by Jackson [22], including the $\\pi$ phase shift between upper and lower lobes of the vertically polarized light. Horizontally, the $E$ -field amplitude distribution is assumed to be uniform, extending to a width defined by an aperture of $\\pm x _ { \\mathrm { c } }$ at the location of an ideal focusing lens. The full vertical SR distribution is accepted by the lens. In the case of small observation angles Hofmann and M ´eot arrive at the following $E _ { \\pi }$ -field (vertical $E$ -vector component) distribution in the image plane: $$ \\begin{array} { r } { E _ { \\pi } ( x , y ) = E _ { \\pi 0 } \\mathrm { s i n c } \\displaystyle \\left( \\frac { 2 \\pi x _ { \\mathrm { c } } } { \\lambda p ^ { \\prime } } x \\right) } \\\\ { \\times \\displaystyle \\int _ { 0 } ^ { + \\infty } ( 1 + \\xi ^ { 2 } ) ^ { 1 / 2 } \\xi K _ { 1 / 3 } \\left( \\frac { 1 } { 2 } \\frac { \\lambda _ { \\mathrm { c } } } { \\lambda } ( 1 + \\xi ^ { 2 } ) ^ { 3 / 2 } \\right) \\mathrm { s i n } \\left( \\frac { 2 \\pi p } { \\lambda \\gamma p ^ { \\prime } } y \\xi \\right) \\mathrm { d } \\xi } \\end{array}
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5
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NO
| 1
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expert
|
How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
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The branch used for the $\\pi$ -polarization method has a maximum clearance of $7 \\mathrm { { m r a d } _ { H } \\times 9 \\mathrm { { m r a d } _ { V } } }$ . The vis–UV light is twice directed through $9 0 ^ { \\circ }$ angles due to space constraints. This arrangement is also of benefit for optical reasons as a partial polarization of the light is obtained from the substantial attenuation of the (horizontal) $\\sigma$ -polarization component. The first mirror is made of SiC, a material, which has an advantageous ratio of thermal conductivity to expansion (a factor 6 better than $\\mathrm { { C u ) } }$ . This allows for low current measurements $\\mathrm { \\Gamma } ( < 1 0 \\mathrm { m A } )$ , when the vertical gradient of the surface power density on the mirror is still moderate. At higher currents, however, the mirror must be protected from an excessive heat load that would otherwise result in its deformation. To achieve this, a horizontal ‘‘finger’’ absorber, of $4 \\mathrm { m m }$ height, has been inserted immediately before the mirror, while obstructing only the mid $\\pm 0 . 4 5$ mradV of the SR. This prevents $98 \\%$ of the $2 3 0 \\mathrm { W }$ power, at $4 0 0 \\mathrm { m A }$ current, reaching the mirror, while blocking only $1 \\%$ of the $\\pi$ -polarized spectral flux in the vis–UV range used for measurements. Cooling of the SiC mirror was not a viable option since mirror deformation would inevitably result from the large vertical temperature gradient. The second mirror is an angular movable aluminized fused silica (FS) mirror. Both mirrors have a surface flatness better than $3 0 \\mathrm { n m }$ peak to valley. A FS symmetric spherical lens is positioned $5 . 0 7 8 \\mathrm { m }$ from the source point, between the two mirrors. It has a surface accuracy of $4 0 \\mathrm { n m }$ peak to valley. The vis–UV light is guided out from within the vacuum region through a FS window at the end of the beamline, approx. $9 \\mathrm { m }$ from the source point. This serves to minimize the light footprint on the vacuum window, which, in the absence of optical window specifications, was deemed necessary in order to minimize the risk of wavefront distortions. Blades that determine the acceptance angle of the light are positioned in the locality of the lens. External to the vacuum, grey filters, narrow bandpass (BP) filters and a Glan–Taylor polarizer are all placed on remotely controlled rotational movers. These, together with a neighbouring Pointgrey FleaTM [34] CCD camera (pixel size $4 . 6 5 \\mu \\mathrm { m }$ ), can also be remotely moved longitudinally in order to adjust for a new image plane when different BP filters are used. The camera roll error is less than 10 mrad. Since the filters and polarizer are situated close to the image plane, the specifications for their surface accuracies need not be the most stringent, and can duly be purchased from off-the-shelf optical component vendors. The magnifications in the vis–UV branch for the chosen wavelengths are $0 . 8 5 4 / 0 . 8 4 1 / 0 . 8 2 0$ at $\\lambda = 4 0 3 / 3 6 4 / 3 2 5 \\mathrm { n m }$ , respectively.
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NO
| 1
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expert
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How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
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Andersson_2008.pdf
|
4.2. Vertical measurements As an example of the vertical beam size measurement performed with vertically polarized light we present a profile (Fig. 8) obtained at $4 0 0 \\mathrm { m A }$ circulating current. This mode, using eight slightly tuned skew quadrupoles, all with integrated field strengths below $0 . 0 0 6 \\mathrm { { \\bar { m } } ^ { - 1 } }$ , gave a vertical rms beam size of $\\sigma _ { \\mathrm { e y } } = ( 6 . 4 \\pm 0 . 5 ) \\mu \\mathrm { m }$ at the monitor $( \\sigma _ { \\mathrm { e y } } = \\sigma _ { \\mathrm { e y 0 } }$ since no beam rotation could be detected). The error margins represent maximum systematic errors. The statistical rms error is considerably smaller, $0 . 0 8 \\mu \\mathrm { m }$ for a single sample. Again, the SRW model gives a good prediction of the profile. However, the example also shows that we may be reaching the resolution limit of the method. The slightly raised intensity levels in the tails most probably originate from one or several non-ideal optics elements. Such a contribution in the intensity valley can therefore not be excluded. However, the SRW code has an option to include phase and/or amplitude errors of different elements. After including systematic phase errors of the lens, originating from its grinding (data provided by the vendor), the behaviour in the tails can also be understood. The primary (Seidel) aberrations of the lens are smaller by an order of magnitude. In case of this systematic grinding phase error, the zero minimum in the FBSF is still preserved, and valley-to-peak ratios for finite beam sizes remain essentially unaltered.
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augmentation
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NO
| 0
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expert
|
How does the π-polarization method measure vertical beam size?
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By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
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Reasoning
|
Andersson_2008.pdf
|
Table 1 summarizes the emittance determinations. Measured values for the machine functions and for the rms beam sizes are presented. From the estimated maximum error in the measurement we give maximum error margins for the different quantities. The beam relative energy spread, $\\sigma _ { \\delta }$ , is the only quantity not to be measured. However, an energy spread deviation from the natural one can be probed, and most likely excluded, since while modulating the RF levels in the Higher Harmonic Cavities [40], no effect was seen on the horizontal beam size. Still, we estimate a maximum value of $10 \\%$ increase due to possible RF noise. The dispersion values can be measured, assuming a known momentum compaction, by the camera with a $0 . 2 5 \\mathrm { m m }$ precision error. We use the $2 \\sigma$ values as an estimate of the maximum deviations. The influence on the dispersion of the momentum compaction uncertainty (maximum $2 \\%$ ) is $0 . 5 \\mathrm { m m }$ horizontally and $0 . 0 5 \\mathrm { m m }$ vertically. In comparison to the measured $\\eta _ { y } = 2 . 3 \\ : \\mathrm { m m }$ , spurious vertical dispersion is also measured at all BPMs, resulting in an rms value of $3 . 0 \\mathrm { m m }$ . The beta function values cannot be measured at the source point but only in the adjacent quadrupoles. We perform an entire measurement of the (average) beta functions in all 177 quadrupoles and use this to fit the model beta functions. From this we get the values at the observation point. The precision of the horizontal and vertical beta function value measurements are $1 \\%$ and $0 . 5 \\%$ , respectively. The $2 \\sigma$ values are used as an estimate of the maximum model deviation from the actual value at the observation point. The maximum deviations in the beam size values are estimated from systematic profile fitting errors and errors due to possible optics wavefront distortions.
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augmentation
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NO
| 0
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expert
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How does the π-polarization method measure vertical beam size?
|
By analizing the peak-to-valley ratio in vertically polarized synchrotron light.
|
Reasoning
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Andersson_2008.pdf
|
$$ since the dispersive contributions to the particle distribution are of course correlated horizontally and vertically. Since the vertical beam size, $\\sigma _ { \\mathrm { e y 0 } }$ , is obtained from integration over a narrow corridor (width $\\leqslant \\sigma _ { \\mathrm { e x } }$ , see Fig. 4) the correction factor in Eq. (3) has to be applied to correctly de-convolute the dispersive contribution from the emittance contribution. In our case, however, the dispersive contribution is rather small, resulting in a rotation angle of only $\\vartheta = 1 4$ mrad of the beam ellipse, which is barely detectable with our experimental set-up (the corresponding vertical rms beam size is $\\sigma _ { \\mathrm { e y } } = 6 . 8 5 \\mu \\mathrm { m } \\approx \\sigma _ { \\mathrm { e y 0 } } )$ . In the horizontal, the full image is used to obtain $\\sigma _ { \\mathrm { e x } }$ and the simple de-convolution of Eq. (2) can be applied. In conclusion, we state that the vertical rms emittance at the observation point is $\\varepsilon _ { y } = ( 3 . 2 \\pm 0 . 7 )$ pmrad, where the error margins represent linearly added maximum systematic errors of measured quantities. Correspondingly, the emittance ratio, $g$ , is determined to be $g = ( 0 . 0 5 { \\pm } 0 . 0 2 ) \\%$ . With no skew quadrupoles excited, the vertical rms emittance is larger by a factor of 2.
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augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
Fascinatingly, advanced concepts employing DLA, in particular when integrating the accelerating structure with the laser oscillator, could achieve many orders of magnitude higher rates of single high-energy electrons entering into an NA64/LDMX-type detector [19–21]. Indirect DM searches call, e.g., for a beam with an energy of $1 0 { - } 2 0 \\mathrm { G e V }$ , and single electrons with a repetition rate of $1 0 0 \\mathrm { G H z }$ , as could be provided by advanced lasers [22] and DLA systems [19–21]. DLA BASED DM SEARCHES DLA relies on a structure with submicron features driven by an incoming electromagnetic laser wave. See Fig. 2. Similar to a conventional microwave linac, the laser wave drives the DLA structure in resonance with the motion of the electrons, thereby accelerating the latter. The DLA ingredients are: $( 1 ) \\mathtt { e } ^ { - }$ sources that provide subnanometer emittances; (2) structures to accelerate, focus and deflect the beam, as well as structures for instrumentation and control; (3) the scalability of the concept, requiring staging of multiple structures, their synchronization, and laser power delivery. The DLA structures have evolved from bonded silica gratings (2013) over silicon pillar structures (2015) to arrive at vertically pumped systems (2021) [23].
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
DLS currently uses a BPM-to-quad BBA method based on the standard functions in Matlab Middlelayer [2], which SYNCHRONOUS DETECTOR METHOD From Excitation to Line Fit The selected corrector magnet is driven with fixed number of cycles of a sine wave of the selected frequency $\\omega _ { 0 }$ and data $x _ { i } ( t )$ is captured for each corrector $i$ during this excitation. The response of each corrector can be modelled as a sine wave with the same phase and frequency, which we can write as $\\Re ( \\alpha _ { i } e ^ { i \\omega _ { 0 } t } )$ ; the component $\\alpha _ { i }$ is computed by taking the sum over the excitation interval of the product of the data and the excitation: $$ \\alpha _ { i } \\approx \\frac { 2 } { T } \\int _ { 0 } ^ { T } x _ { i } ( t ) e ^ { - i \\omega _ { 0 } t } d t . $$ To reduce noise on this result the cycle count $\\omega _ { 0 } T / 2 \\pi$ should be a whole number and reasonably large. The data in the calculation above can optionally be scaled by a window function, for example $1 - \\cos ( 2 \\pi t / T )$ , to further reduce the impact of noise out of band. It is also numerically wise to subtract the mean $\\overline { { x _ { i } } }$ from $x _ { i }$ before computing $\\alpha _ { i }$ .
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
$$ and itself transforms as: $$ \\frac { d \\mathbf { M } } { d s } = \\mathbf { F } ( s ) \\mathbf { M } . $$ TRANSOPTR uses an initial distribution $\\sigma _ { 0 }$ , and an $\\mathbf { F } ( s )$ matrix for each element, to solve for the $\\sigma$ and $\\mathbf { M } ( s )$ at each point by numerically solving the envelope equation. The standard $\\mathbf { F }$ -matrix for the IH-DTL is the axially symmetric linac matrix derived in [5], where here the on axis field, $\\mathcal { E } ( s )$ , was generated using Opera2D [6, 7]. Using this model, the DTL longitudinal tune can be solved with 8 optimizations ( $5 \\mathrm { I H }$ tanks and 3 bunchers) of $( \\phi , V )$ pair, followed by the 4 triplets for the transverse tune, using the TRANSOPTR function linac . This diminishes algorithm performance through solving for the longitudinal tune, slowing down tuning time for energy changes [8]. This laborious method is not necessary if we instead only focus on the transverse dynamics. Configuring the rf phase parameter such that $M _ { 6 5 } + M _ { 4 3 } + M _ { 2 1 } \\approx 0$ , [9]the cavity can be essentially treated as a drift. This ignores the longitudinal dynamics, and models the cavity as a step function increase in energy with the TRANSOPTR function rfgap. The $\\mathbf { F }$ -matrix for the autofocus method is simplified to:
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
From the fast beam-based alignment (FBBA) process detailed by ALBA [1], we have successfully implemented our own version alongside some new measurement and analysis methods. Like ALBA, our version takes advantage of using AC excitations alongside using the fast acquisition archiver system (FAA) [5] to enable orbit measurements at $1 0 \\mathrm { k H z }$ . ALBA presents the difference between the standard deviation of their BBA and FBBA methods as $\\pm 1 5 \\mu \\mathrm { m }$ at $7 \\mathrm { H z }$ and $\\pm 1 6 \\mu \\mathrm { m }$ at $6 \\mathrm { H z }$ in the horizontal and vertical axes respectively. This considers measurements at all BPMs whereas at DLS, only one BPM was tested, with the difference between BBA and FBBA systems being $0 . 5 2 \\mu \\mathrm { m }$ and $7 . 4 9 \\mu \\mathrm { m }$ in each axis. The experiments for FBBA consisted of checking the speed of focusing and stability of the process. This involved applying a constant $1 0 0 \\mu \\mathrm { m }$ offset before all experiments begin, indicated as run number 0 in the following figures, then repeating and applying measurements 16 times to see how many measurements are needed to find the correct offset. After this, the spread of FBBA results around that value is measured. This system was repeated across a range of frequencies and acquisition times. The range of frequencies was determined by Fig. 2, a discrete Fourier transform of the storage ring BPM orbit over 30 s and selecting sections on the figure that had low beam noise. Due to a drop off in CM response at higher frequencies, the upper frequency limit was set to $2 0 0 \\mathrm { H z }$ . To ensure stability throughout the experiment, the fast orbit and tune feedbacks were run for $3 \\mathrm { s }$ between measurements. After this, the beam was left for an additional $3 \\mathrm { s }$ to allow it to resettle at a stable orbit. The experiments shown were carried out at $1 0 \\mathrm { m A }$ .
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
DBA LATTICE Linear Optics The designed MLS II lattice consists of 6 identical DBA cells with $8 6 . 4 \\mathrm { ~ m ~ }$ circumference. Each cell contains two homogeneous dipole magnets with a bending radius of 2.27 m according to the critical photon energy of $5 0 0 ~ \\mathrm { e V } .$ . In accordance with the design strategy of MLS [3, 4], a single octupole has been positioned at the center of the DBA cell to adjust the third-order momentum compaction factor $\\scriptstyle a _ { 2 }$ , in addition to the sextupole families that are used to control the second-order term $\\scriptstyle { a _ { 1 } }$ . The linear optics of the DBA cell for the standard mode are shown in Fig. 1. Table: Caption: Table 1: Parameters of DBA Lattice for Standard User Mode Body: <html><body><table><tr><td>Parameter</td><td>Value</td></tr><tr><td>Energy</td><td>800MeV</td></tr><tr><td>Circumference</td><td>86.4 m</td></tr><tr><td>Working point (H/V)</td><td>5.261/4.354</td></tr><tr><td>Natural chromaticities (H/V)</td><td>-7.14/-11.75</td></tr><tr><td>Radiation loss per turn</td><td>15.9 keV</td></tr><tr><td>Damping partition (H/V/L)</td><td>1.023 /1.0 /1.976</td></tr><tr><td>Damping time (H/V/L)</td><td>28.244/28.908/ 14.626 ms</td></tr><tr><td>Natural emittance</td><td>38 nmrad</td></tr><tr><td>Natural energy spread</td><td>4.57 × 10-4</td></tr><tr><td>Momentum compaction</td><td>7.44 × 10-3</td></tr><tr><td>βh,β,@ straight section center</td><td>6.9 /1.4 m</td></tr></table></body></html> Nonlinear Dynamics One DBA cell contains two families of chromatic sextupoles. The momentum acceptance is maximized by adjusting the strength and positions of the two chromatic sextupoles, with the constraint that the linear chromaticities are corrected to $+ 1 . 0$ in both planes. However, it should be noted that the positions of the focusing chromatic sextupoles are located at the center of the DBA cell with large dispersion, while the defocusing chromatic sextupole’s position can be adjusted. The two families of harmonic sextupoles in the straight section are optimized to enlarge the dynamic aperture. The nonlinear dynamics optimization was carried out by using Elegant [5].
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
Applying adiabatic matching in FFA $@$ CEBAF presents a challenge due to the tunnel space constraints and the fact that it is not possible to keep the betatron phase advance per cell constant during match. Thus, we explore a two-step matching strategy. The different-energy orbits and dispersions are suppressed in the first step with their associated constraints thus eliminated in the second step when only Twiss $\\beta$ and $\\alpha$ must be matched. It has been suggested [8, 9] to realize the first step nonadiabatically using a two-dipole dogleg structure because it generates a pattern of different-energy orbits and dispersions resembling that of an FFA FODO cell. In fact, one subtlety in this picture is that the dispersion energy ordering is reversed in the two cases, i.e., contrary to a dogleg, the dispersion magnitude in an FFA cell becomes higher at higher energies. Nevertheless, with additional optical knobs involved, this approach works as illustrated in Fig. 6. The remaining second step involving match of Twiss $\\beta$ and $\\alpha$ is still challenging due to the necessity to control the optics of 6 beams simultaneously using common magnets. It is desirable to develop orthogonal knobs for independent control of the individual energies. We take advantage of the fact that different energies have different betatron phase advances in a periodic FFA cell [10]. Applying periodic quadrupole kicks over several cells at twice the rate of the betatron oscillations at a certain energy selectively excites a parametric resonance in Twiss $\\beta$ of that particular energy.
|
augmentation
|
NO
| 0
|
IPAC
|
How is alternating phase focusing applied to DLAs?
|
drift sections between grating cells lead to jumps in the synchronous phase, which can be designed to provide net focusing.
|
definition
|
Beam_dynamics_analysis_of_dielectric_laser_acceleration.pdf
|
The defocusing field remains quadrupole-like with changing beam size (Fig. 4). The vertical field appears approximately sextupole-like. In the horizontal axis $( x = 0 )$ ), a proportional relationship between focusing strength and $y$ is seen, however away from the axis a non-linear relationship is seen. Sextupole-like fields would lead to slice emittance growth in that transverse axis. Whilst slice emittance would be preserved in the direction of quadrupole-like fields (larger transverse size), given that all transverse wakefields are longitudinally varying, projected emittance would not be preserved in either axis. Defocusing in the direction of larger beam size suggests that beam astigmatism would grow as the beam propagates through a DWA stage. The strength of the defocusing grows exponentially with beam astigmatism (Fig. 5), leading to an extra source of instability in circular DWAs. The strength of these fields are significant, the average quadrupole-like field (b) Average vertical focusing fielσdxstrσeyngth, orthogonal to the direction of the axis of greatest beam width. for $\\sigma _ { x } / \\sigma _ { y } \\approx 1 . 8$ is the equivalent to a defocusing quadrupole with a $1 \\mathrm { T / m }$ quadrupole strength, or $k = 1 . 2 \\mathrm { m } ^ { - 2 }$ . Transverse field strength is a function of beam size in each axis. The black points in Fig. 5 demonstrates that a larger overall beam size, with the same aspect ratio, will excite stronger fields than a smaller total transverse beam size. This relationship leads to non-trivial beam dynamics, with the field strength a function of $\\sigma _ { x } , \\sigma _ { y }$ , and the combination of the two.
|
augmentation
|
NO
| 0
|
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