1. Overview of SuperB Diagnostics Alan Fisher SLAC National Accelerator Laboratory SuperB General Meeting Annecy 2010 March 16 to 19

2. Diagnostics for SuperB Monitors: Beam position Beam profiles Beam loss Tunes Total current Bunch current Luminosity Polarization (LER) Measure/tweak in collision: Coupling Chromaticity Phase advance Feedbacks: Orbit Luminosity Tune Transverse motion Longitudinal motion Too much for 25 minutes Some are in other talks. Others are similar to PEP-II. I will concentrate on a few difficult issues. 2010-03-17Fisher — SuperB Diagnostics2

3. BPM Button Issues Two existing button designs should work for SuperB: 7-mm redesigned PEP-II buttons 6-mm test buttons developed for SuperKEKB Detailed modeling needed to choose BPM thermal motion With  y ≈ 10 µm, what is the tolerance? Can we lock the buttons securely to the quadrupoles? To the floor? Measure button position? Relative to what? Distortion or roll of BPM chamber (coupling)? Buttons near the IP Crossing angle allows buttons closer to the IP than in PEP-II (72 cm) Buttons in cryostat of superconducting IP quads? Special design? 2010-03-17Fisher — SuperB Diagnostics3

4. BPM Processor Issues What are the specifications for the BPMs? Single bunch Do we need the turn-by-turn positions of single bunches in collision? At how many places in the ring? Can we excite a single bunch using the TFB to an amplitude large enough to sample nonlinearities? Like the light sources, use a fast global orbit feedback Rate? Typically1kHz for light sources Processor design and overall architecture Distributed processing with a layout that reflects the natural symmetries of the orbit response matrix 2010-03-17Fisher — SuperB Diagnostics4

5. Libera BPM Processors Commercial product from Instrumentation Technologies Integrates BPM processing with networking for fast orbit feedback Used by many light sources Share codes and architecture Specifications Turn by turn: 2 µm Orbit feedback data at 10 kHz: 0.25 µm ADC clock frequency near 117 MHz: Use 119 MHz = f RF /4 Front-end filter at 19 MHz Cannot see individual bunches turn by turn Bunch positions are smeared together over ~20 ns 2010-03-17Fisher — SuperB Diagnostics5

6. Luminosity Feedback PEP-II dithered LER position and angle against HER Initially dithered x, y, and y' sequentially, in steps Later simultaneously, with small sinusoidal drive at 3 frequencies Rate limited to 1 Hz by software magnet controls Often ran at 0.3 Hz to use smaller dithers Integrate luminosity feedback with orbit feedback Avoids having orbit feedback “fix” the luminosity dither Especially in x, which the BPMs will see 2010-03-17Fisher — SuperB Diagnostics6

7. Tune Monitor and Tune Feedback PEP-II used downconversion in a mixer, followed by: A spectrum analyzer A phase-locked loop, with single-frequency excitation and detection by a lock-in amplifier Both should be good for SuperB Direct Diode Detection (or “barbeque”, for Baseband Q), now used for LHC protons, is very sensitive Can measure the tune of a single bunch without driving the beam. Tune feedback Tune spectrum in collision is too wide for a single value Need a “pilot” (noncolliding) bunch Unstable when colliding tune is just above 0.5 Must shake the pilot to raise its tune above the half integer 2010-03-17Fisher — SuperB Diagnostics7

8. Synchrotron-Light Monitors Measuring with low vertical emittance Visible light: Direct image formation with visible Interferometer Null in vertical polarization X rays: Pinhole camera Zone plate And yesterday Pantaleo cut the emittance used here by a factor of 2 Typically size at arc QDs is then  y = 6 µm Locations identified with high and low dispersion for each ring I stayed away from the IP, to avoid coupling. A problem with the PEP-II LER SLM Today Pantaleo recommended a location 45 m from IP.  y is much higher, and the IP coupling is already corrected. Low x dispersion. But a second spot at high dispersion is still needed. 2010-03-17Fisher — SuperB Diagnostics8

9. Proposed SLM Locations IP RF LER Spin Rot LER Spin Rot HER arc LER arc HER arc LER arc C = 1258.3582 m Synchrotron Light Monitors: Low DispersionHigh Dispersion 562 m, 569 m508 m, 511 m e−e− e+e+ LER injection 475 m HER injection 713 m Synchrotron Light Monitors: (Pantaleo's proposal) -45 m, 45 m

10. Beam Sizes at High and Low Dispersion 2010-03-17Fisher — SuperB Diagnostics10

11. 2010-03-17Fisher — SuperB Diagnostics11 Opening Angle of the Radiation At critical wavelength c, the RMS angular width  ≈ 0.6/  1/  is also the typical angular width over the full spectrum. But for visible light ( >> c ),  ~ (  ) 1/3, where  is the bending radius, and is nearly independent of . (unpolarized) For = 400 nm: HER has  = 80 m and  = 1.23 mrad LER has  = 27 m and  = 1.77 mrad

12. Imaging with Visible Light: Diffraction A Gaussian source (TEM 00 mode) has the slowest angular spread for a RMS waist size  r. The relationship is: If we model our light as a Gaussian at = 400 nm: HER has  = 1.23 mrad, and so  r = 26 µm LER has  = 1.77 mrad, and so  r = 18 µm Diffraction blurs the vertical resolution, even before considering the actual synchrotron-emission pattern or diffraction in the optics. 2010-03-1712Fisher — SuperB Diagnostics

13. Imaging with Visible Light: Depth of Field A SuperB beam has a small emittance, but the light does not. The ellipse of synchrotron light in vertical phase space has: A very narrow y spread, since the beam is thin (~10 µm) A very wide y' spread, since the RMS emission angle is large (>1 mrad) And this ellipse rotates with motion along the orbit. How the optical system images a ray depends only on its yy coordinates as it crosses the nominal source plane. The optics can’t tell where on the orbit a ray originated. 2010-03-17Fisher — SuperB Diagnostics13

14. Vertical Phase Space of the Light 2010-03-17Fisher — SuperB Diagnostics14 y' [mrad] y [µm] 1σ ellipses of light emitted at: −5 cm 0 cm +5 cm from nominal source point Phase space of 400-nm light in HER Low-dispersion source point Rays that hit edge of a 40-mm- high mirror, 7 m from source 1σ ellipse of positrons at the source point Projection of ellipses onto y >>  y. Do optics accept these rays? Look at the horizontal plane.

15. 2010-03-17Fisher — SuperB Diagnostics15 Horizontal Phase Space of the Light Consider the orbit both in the xz plane and in xx phase space Which rays, at which angles, are reflected by M1?

16. 2010-03-17Fisher — SuperB Diagnostics16 Plotting Horizontal Phase Space A point on the orbit near the xz origin is given by: For a point on the orbit, the angle x to the z axis is equal to . The rays striking the +x and −x ends of M1 are given by: We plot these curves in phase space, along with the beam’s 1-sigma phase- space ellipse at three points along its orbit.

17. Horizontal Phase Space: HER 2010-03-17Fisher — SuperB Diagnostics17 x' [mrad] x [µm] 1σ ellipses of light emitted at: −5 cm 0 cm +5 cm from nominal source point Phase space of 400-nm light in HER Low-dispersion source point Edge of 500-mm-long mirror, at 50 mrad to grazing, 7 m from source Slit at one focal length from first focusing optic: determines the acceptance of the optics. Beam orbit in dipole Optics accept rays from  5 cm. Projections onto x,y >>  x,y

18. Visible Light: Two-Slit Interferometer Monochromatic point source at Y on the (X,Y) plane Two slits are on the (u,v) plane Find intensity at a point y on the image plane (x,y) using a Fraunhofer diffraction integral over the slit plane Next use a wider source, and then add a range of wavelengths 2010-03-17Fisher — SuperB Diagnostics18

19. Calculated Fringe Patterns 2010-03-17Fisher — SuperB Diagnostics19 y [mm on camera] PEP-II HER interferometer with 0.5-mm slits placed 5 mm apart Fringe contrast decreases with beam size Point source at 450 nm 450-nm, 200-µm-RMS Gaussian sourceGaussian filter at 450 nm, 30 nm FWHM, and 200-µm Gaussian source

20. 2010-03-17Fisher — SuperB Diagnostics20 PEP-II Interferometers

21. Can This Work for SuperB? To distinguish beam sizes from 5 to 20 µm: 10-nm-FWHM filter centered at 400 nm 10 m from source to slits Slit width = 1.2 mm Wide slit separation = 30 mm Fringe visibility, at right, is defined as: 2010-03-17Fisher — SuperB Diagnostics21 y [mm] Intensity Visibility  y [µm] —  y =0 µm —  y =10 µm —  y =20 µm

22. Visible Light: Null in Vertical Polarization Angular emission pattern of vertically polarized emission Two lobes, above and below the horizontal plane, with opposite polarization (due to symmetry) Perfect cancellation at the image of a point source Some light above and below (diffraction) But for a nonzero beam size: Sources at different heights have their nulls at different heights Contrast is reduced as size increases Developed by Andersson and Chubar at MAX-Lab in Sweden Demonstrated resolution of 1 µm at the Swiss Light Source, where it has measured  y = 2.8 pm Repeat Bartolini’s slide from December’s SuperB meeting 2010-03-17Fisher — SuperB Diagnostics22

23. SLS experience with low V emittance SLS has reported a vertical emittance of 2.8 pm (±0.4 pm) The coupling correction procedure is similar to the one used at Diamond. But less skew quadrupoles and separated dispersion free regions High precision emittance measurement with the “emittance monitor” Resolution of 1 um Courtesy SLS 2010-03-1723Fisher — SuperB Diagnostics

24. Can This Work for SuperB? Comparison with a complete model of the emission geometry, including diffraction and depth of field, gives the beam size. Model uses the code SRW (Synchrotron Radiation Workshop). At SLS, the limit of the technique appears to be around 5 µm. The code must be run with a realistic SuperB beam-size monitor to see if it can work. Measures only the vertical size 2010-03-17Fisher — SuperB Diagnostics24

25. 2010-03-17Fisher — SuperB Diagnostics25 X Rays: Pinhole Camera Resolution  on image plane with a pinhole of radius r: Neglects other effects: scintillator, camera pixels Distance a from source to pinhole, b from pinhole to image Geometric optics: Pinhole should be << beam size But diffraction blurs image if the pinhole is too small: Pinhole size for best resolution: Geometric mean of and a or b Optimum resolution on the source plane: Want small, small a, and large magnification b/a

26. Resolution with a Pinhole If = 0.1 nm (12.4 keV) and a = b/2 = 7 m: r opt = 13 µm and  opt = 16 µm: a bit larger than  y Better resolution requires even shorter and a. Shorter a is hard, since room is needed to: Extract the light from the beamline Filter unwanted power outside the hole’s radius and at longer wavelengths, to avoid deformation and damage Critical energy is 8.3 keV (HER) and 6.0 keV (LER) Spectrum has flux up to ~10 E c At best a factor of 2 to 3 available Makes signal weaker (less flux and a smaller pinhole) Pinhole camera always throws away most of the light Pinhole plate must be thick enough to stop x rays at 10E c 2010-03-17Fisher — SuperB Diagnostics26

27. 2010-03-17Fisher — SuperB Diagnostics27 Pinhole Camera at ESRF Their 10-μm pinhole gives a resolution of 13 μm.

28. 2010-03-17Fisher — SuperB Diagnostics28 X Rays: Zone Plate A diffractive lens, made by microlithography Rings of a high-Z metal (gold) deposited on a thin low-Z membrane (SiN) Ring widths as narrow as 50 nm are possible

29. 2010-03-17Fisher — SuperB Diagnostics29 Imaging with a Fresnel Zone Plate A zone plate is designed to focus at a single wavelength. Bandwidth must be  1% Power must be kept low to avoid damage. First foil filters remove ≈50% of the synchrotron power Pair of monochromator crystals or multilayer x-ray mirrors reflect a narrow band while absorbing the remaining out-of-band power. Two reflection keep the entering and exiting rays parallel. Source Double-crystal monochromator Zone plate Screen

30. 2010-03-17Fisher — SuperB Diagnostics30 Multilayer X-Ray Mirrors Multilayer mirror designed for a narrow passband at 8 keV Unpolarized light incident at 1.51 degrees 200 periods with alternating layers of low- and high-Z materials: B 4 C and Mo 3-nm spacing: 2.1 nm of B 4 C and 0.9 nm of Mo, with an interdiffusion thickness of 0.5 nm

31. 2010-03-17Fisher — SuperB Diagnostics31 Zone Plate at SPring-8 Monochromator transmits 8.2-keV photons ( = 0.151 nm) Total magnification = 13.7 (0.2737 by FZP, 50 by XZT) 4-μm resolution with the help of the x-ray zooming tube Observed a transient in the beam size during top-off operation

32. 2010-03-17Fisher — SuperB Diagnostics32 SPring-8 Diagnostic Beamline

33. 2010-03-17Fisher — SuperB Diagnostics33 Zone-Plate Imaging at the ATF at KEK < 1ms exposure time Injection transient

34. 2010-03-17Fisher — SuperB Diagnostics34 Specifications of the ATF Zone Plates Total magnification = 20 Detecting 3.24-keV photons ( = 0.383 nm) Ideal Airy resolution is given by thickness  r N of outer ring: r A = 1.22  r N

35. X Rays: Depth of Field, Horizontal 2010-03-17Fisher — SuperB Diagnostics35 x' [mrad] x [µm] Pinhole with optimum radius or Zone plate with radius of 1 mm, Each 10 m from source Phase space in HER at the low-dispersion source point, for 0.1-nm x rays 1σ ellipses of x rays emitted at: −5 cm 0 cm +5 cm from nominal source point

36. X Rays: Depth of Field, Vertical 2010-03-17Fisher — SuperB Diagnostics36 y' [mrad] y [µm] Pinhole with optimum radius or Zone plate with radius of 1 mm, Each 10 m from source Phase space in HER at the low-dispersion source point, for 0.1-nm x rays 1σ ellipses of x rays emitted at: −5 cm 0 cm +5 cm from nominal source point No depth-of-field blurring in either plane

37. 2010-01-18Fisher — Imaging with Synchrotron Light37 Laser Measurements: Laser Wire Laser crosses electrons at a waist smaller than the e-beam. e  beam is scanned across the fixed laser focus, over many measurements. Like a wire scanner, scattered radiation gives a profile. Submicron resolution possible: Ultraviolet wavelength: 250 nm Focus with a small F-number But what resolution is possible for SuperB?

38. Resolution of a Laser Wire for SuperB In one Rayleigh length z R on either side of the focus, a Gaussian laser beam diverges by  2 : z R = 4   2 / This divergence should be slow compared to  x : To get a true projection To be insensitive to x position of particles relative to laser waist z R > 2  x ≈ 140 µm Then the RMS radius  0 at the focus, for = 250 nm, is: 2010-03-17Fisher — SuperB Diagnostics38

39. 2010-01-18Fisher — Imaging with Synchrotron Light39 Laser Measurements: Interferometer Split a laser beam. Intersect both parts at an angle as they cross the electron beam. Interference fringes with maxima and minima across the electrons. Move the beam relative to the fringe pattern. When the beam is small compared to the fringe spacing, the scatter is heavily modulated by the shift in the fringes. Can measure down to tens of nm

40. Conclusions: Beam Profiles Visible light Beams are too small for forming a direct image Null in the vertical polarization looks promising But this only gives the vertical size Horizontal size can be measured with an interferometer Both give size, but not profile A visible beamline remains helpful for longitudinal profiling with a streak camera X rays X-ray zone plates may be best for sizes and profiles But thermal distortion of the x-ray mirror must be controlled Lasers Expensive but offering good resolution Measurements require multiple shots to scan beam across laser 2010-03-17Fisher — SuperB Diagnostics40

41. BPM Buttons: Upgraded PEP-II Design 7 mm diameter Button and center conductor made of single Mo piece Insulated by borosilicate glass and boron nitride Made by Kaman 2010-03-17Fisher — SuperB Diagnostics41

42. BPM Buttons: SuperKEKB Design 6 mm diameter Glass insulator for a lower dielectric constant Fewer high-frequency resonances Several test versions made in collaboration with Kyocera 2010-03-17Fisher — SuperB Diagnostics42

43. 2010-03-17Fisher — SuperB Diagnostics43 How Does a Zone Plate Work? Consider a transmissive diffraction grating. Parallel opaque lines on a clear plate, with period a Parallel rays of wavelength passing through adjacent lines and exiting at an angle  have a difference in optical path of a sin . They are in phase if this difference is n, giving the n th -order diffraction maximum: sin  n = n /a Now wrap these grating lines into a circle. 1 st order bends toward center: focusing −1 st order bends away from center: defocusing 0 th order continues straight ahead Make central circle opaque to block 0 th -order light around the focus (a “central stop”). But the 1 st -order rays are parallel and so don’t focus Vary the zone spacing as a function of ring radius r so that all the exiting rays meet at a focal point a distance f from the zone plate. 1 st order 0 th order −1 st order 11 a 1 st order 0 th order −1 st order 0 th order 1 st order

44. 2010-03-17Fisher — SuperB Diagnostics44 How the Zone Widths Vary To focus at f, the ray at radius r n must exit at an angle  n with: r n = f tan  n First-order diffraction gives = a n sin  n The grating period a now varies too: a n = r n+1 – r n –1 There are many, closely spaced zones, and so we treat n as a continuous variable: a(n) =  n dr(n)/dn = 2dr(n)/dn We use the expression for tan  (n) to substitute for sin  (n):

45. 2010-03-17Fisher — SuperB Diagnostics45 Zone-Plate Formulas = wavelength (monochromatic light)  = bandwidth f = focal length of lens at N = number of zones Counting both clear and opaque zones r n = radius of n th zone boundary  r = r N – r N−1 = thickness of outer zone D = 2r N = outer diameter F = F-number r A = (Airy) resolution