Refined analysis of electron-cloud blow-up data at CesrTA using Coded Aperture and Pinhole X-ray Beam Size Monitor data J.W. Flanagan, KEK Ecloud :20-12:40

Introduction At CesrTA, we have been taking bunch-by-bunch beam size data to measure electron-cloud induced beam size blow-up. The onset of beam size growth is accompanied by a synchro- betatron sideband in the BPM pickup signal. – Similar to what was seen at KEKB LER, though with some differences. KEKB: sideband-betatron peak separation starts at 1 s, grows with increasing cloud density along train. Transverse feedback does not noticeably affect peak height. CesrTA: sideband-betatron peak separation starts at 1 s, and stays there along train. Transverse feedback has some effect on peak height. – Believed to be a signal of head-tail instability. Some questions possibly about the exact type of head-tail instability, and whether it is the same as at KEKB. Q: Can we see the beam shape distortion that should accompany head-tail motion?

Simulations of head-tail motion (at KEKB LER, using PEHTS) Betatron phase-subtracted bunch slice motions

Instrumentation Source bend (not shown) Detector box Screens, slits etc. for alignment Diamond window Optics box (CA, FZP, slit) D Line x-ray beam line CA mask (Applied Nanotools) 0.5  m Au mask 2.5  Si substrate

Coded Aperture Source SR wavefront amplitudes: Kirchhoff integral over mask (+ detector response)  Detected pattern: Measured slow-scan detector image (red) at CesrTA, used to validate simulation (blue) t(y m ) is complex transmission of mask element at y m. Sum intensities of each polarization and wavelength component. Sum weighted set of detector images from point sources. K.J. Kim, AIP Conf. Proc. 184 (1989). J.D. Jackson, “Classical Electrodynamics,” (Second Edition),John Wiley & Sons, New York (1975). Pinhole/slit Adjustable Hevimet Gap (horizontal slit, vertically-limiting) Adjusted to give smallest measured beam size at 2 Gev  45 um gap separation

Fitting Use template fitting – Generate template images over a range of sizes and positions (offsets) – Compare measured beam image with each template, pick the one with the lowest residuals. Beam profile models: – 1) Gaussian – 2) Cumulants: In addition to beam size, add parameters for skew and kurtosis by using Gram-Charlier A cumulant function: H3, H4 = Hermite polynomials Plot: – Normalized Skew: k3/(2!  ) – Normalized Kurtosis: k4/(4!  ) – 3) Asymmetric gaussian: Left and right sides of profile have sizes  L and  R Average  ave = (  L +  R )/2 Asymmetry  (  R +  L )/(2  ave ) Using  and  ave as defining parameters,   R = (1+  )  ave and  L = (1-  )  ave Note: In plots that follow, asymmetry is often denoted as “skew,” for ease of programming.

Fitting Models Cumulant functionAsymmetric Gaussian

Template images: Cumulant model  y = 20  m  y = 40  m  y = 80  m Coded Aperture Pinhole Slit Skew

Template images: Cumulant model  y = 20  m  y = 40  m  y = 80  m Coded Aperture Pinhole Slit Kurtosis

Template images: Asymmetric gaussian model  y = 20  m  y = 40  m  y = 80  m Coded Aperture Pinhole Slit “Skew” (Asymmetry)

Measuring “Head-Tail” distortion of the Sun During partial eclipseAfter eclipse (Shadow asymmetry noticed by my kid, )

Single-shot resolution estimation Want to know, what is chance that a beam of a certain size is misfit as one of a different size? Tend to be photon statistics limited. So: – Calculate simulated detector images for beams of different sizes – “Fit” images pairwise against each other: One image represents true beam size, one the measured beam size Calculate  2 / residuals differences between images: N = # pixels/channels n = # fit parameters (=1, normalization) S i = expected number of photons in channel i Weighting function for channel i: – Value of  2 / that corresponds to a confidence interval of 68% is chosen to represent the 1-s confidence interval

Size resolution for 75 um bunch currents Coded AperturePinhole/Slit

Asymmetric Gaussian Skew Resolutions 20 um80 um40 um Coded Aperture Pinhole Slit

Cumulant Function Skew Resolutions 20 um80 um40 um Coded Aperture Pinhole Slit

Cumulant Function Kurtosis Resolutions 20 um80 um40 um Coded Aperture Pinhole Slit

Choice of Model Asymmetric gaussian shows good discrimination across a range of beam sizes Cumulant function skew generally not as good as asymmetric gaussian, and kurtosis not very compelling either. –  Focus on Asymmetric Gaussian fits for now.

“Standard Conditions” 0.75 mA/bunch, 14 ns spacing,  y = ~1.9 Note: “Big D” Optics => beta function enlarged at x-ray source point to increase minimum beam size (So can use pinhole slit in addition to coded aperture) Gaussian FitAsymmetric Gaussian FitCumulant Function Fit Coded Aperture Pinhole Slit

“Standard Conditions” Focus on one case: Asymmetric Gaussian Skew/Asymmetry Apply some cuts to the underlying data Beam positionResiduals Coded Aperture Pinhole Slit

“Standard Conditions” With cuts applied: Beam SizeSkew Coded Aperture Pinhole Slit

“Standard Conditions” Spread of Skew (RMS) Beam SizeSpread of Skew (RMS) Coded Aperture Pinhole Slit Bunch 2 Bunch 10

Beam-size blow-up for some other conditions Lower Chrom. (~1.5)Higher Chrom. (~2.2) Coded Aperture Pinhole Slit 12 ns Spacing High chrom. (~1.3)

RMS skew for some other conditions Lower Chrom. (~1.5) 12 ns Spacing High chrom. (~1.3) Higher Chrom. (~2.2) Coded Aperture Pinhole Slit

“Standard Conditions” Position Spectrum Coded AperturePinhole/Slit

“Standard Conditions” Size Spectrum Coded AperturePinhole/Slit

“Standard Conditions” Skew Spectrum Coded AperturePinhole/Slit

Bursting behavior Seen at KEKB LER Can we find it at CesrTA? – If so, would we might expect to see greatest skew spread near threshold

“Standard Conditions” Trend plots Bunch 2Bunch 10 Beam Size Beam Position Coded Aperture (Pinhole data look similar)

Trend Plots for Standard Conditions (Pinhole) Bunch 15Bunch 25Bunch 20 Size Position

How about under some other conditions? Trend plots for Lower chromaticity (~1.5) (Coded Aperture) Bunch 15Bunch 20 Beam Size Beam Position

Low-Chromaticity case (Coded Aperture) PositionSize Skew Size line at + s sideband around bunch 20? SizeRMS Skew

12-ns spacing, Low Chrom. (~ 0.5) (Pinhole) Bunch 20 Beam Size Beam Position

Dipole bursts Where we can see bursting, beam size changes are small. Bursting seems to accompany blown-up bunches – For these bunches, the skew and skew RMS tend to be very small – These are also the bunches for which we can measure the skew best… – Unless, perhaps, it is smaller than the scanning step size, and we are thereby missing it. Homework to try before proceedings deadline

Cumulant Function Model revisited: Spread of Cumulant Fcn Kurtosis (RMS) (Pinhole) Beam SizeSpread of Kurtosis (RMS) Standard Conditions 12 ns High Chrom. (~1.3)

Cumulant Function Model revisited: Spread of Cumulant Fcn Kurtosis (RMS) (Pinhole) Beam SizeKurtosis Standard Conditions 12 ns High Chrom. (~1.3)

Summary Attempts to measure non-Gaussian distributions have been started, to bunch profile distortions due to head-tail instability. No clear sign of such distortion has been seen yet in either CA or Pinhole data taken at CesrTA. – Do get some peaks near blow-up threshold, BUT – Peaks in RMS skew (and RMS kurtosis) do not necessarily coincide with sideband locations, for the most part, though a couple of possibly- interesting isolated cases exist. If real bunch-shape distortion is being observed, it should be possible to identify a spectral line with it (at least before it smears). But, if Head-tail motion is occurring, it should in principle be possible to observe bunch shape distortions. Goal from here: Refine analysis further to either conclusively identify such bunch-shape distortions, or else be able to rule them out above some meaningful limit, to help clarify blow-up mechanism.