1. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 1 Damping an e-p Instability at the LANL Proton Storage Ring Rod McCrady R. J. Macek, T. J. Zaugg, LANL S. Assadi, C. E. Deibele, S. D. Henderson, M. A. Plum, ORNL (SNS) J. M. Byrd, LBNL S. Y. Lee, S. B. Walbridge, Indiana University M. F. T. Pivi, SLAC Journal of Applied Physics 102, 124904 (2007)

2. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 2 Outline Intro to the PSR and the e-p instability Overview of the damping sytem and its performance Details of the components Possible factors limiting performance More details Comb filter Bandwidth A noise source Summary

3. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 3 The LANL Proton Storage Ring LINAC macropulses: ~625µs @ 20Hz to PSR H+H+ HH 800 MeV LINAC 1L Target PSR Beams to other areas Accumulate ~1800 300ns-long minipulses Accumulated protons H  beam from linac PSR Deliver 5µC 300ns-long pulse to target @20Hz PSR

4. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 4 PSR Operating Parameters Beam kinetic energyT798 MeV Betatron tunes H, V 3.19, 2.19 Incoherent tune shifts @ 5  C  H,  V -0.22, -0.18 (calculated) Chromaticities  H,  V  -1.0 Transition gamma TT 3.1 Buncher harmonich1 Buncher frequencyf2.795 MHz Max. RF voltageV rf 18 kV Synchrotron tune @ 10kV 0 0.00042 CircumferenceC90.26 m

5. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 5 Electron Cloud and the e-p Instability Beam potential traps electrons Sources of electrons Scraping of beam on beampipe Stripper foil Residual gas ionization (small) Beam & electrons oscillate (vertically) Growth by secondary emission & trailing edge multipactor Loss of stored charge

6. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 6 Characteristics of the e-p Instability Growth time  50  s 25 to 250 MHz These data courtesy of Bob Macek Typical growth times  25  s to 100  s Broad band Rapid growthLarge pulse-to-pulse variations

7. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 7 Damping System Characteristics, etc. Requirements Fast response (short delay) Rapid damping (high power) Broad band (25 – 250MHz) Constant delay vs. frequency (“flat phase response”) Unique Long pulse Optimized for varying conditions Other methods to control instability increase beam spill Test bed for higher-power machines Spallation Neutron Source (SNS) at Oak Ridge Inexpensive prototype Used some existing parts (BPM, kicker) SNS supplied new equipment, e.g. amplifiers, LLRF components Vertical plane only

8. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 8 Damping System – Functional Overview Motion of a longitudinal slice of beam: (Betatron oscillation, f=6.1 MHz) 4 turns Kicker Pickup RF amp Signal Processing Beam Path of a proton around the ring

9. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 9 Expected Performance Damping rate: Beam orbit frequency  1 i.e. System gain Power to kicker Kicker shunt impedance (“effectiveness”) For P sat =100W at  y sat =0.5mm :  sat  30/ms = 1 / 33  s Deflection per unit beam offset Beam parameters

10. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 10 Damping System Overview     Variable Attenuator Input Level Control Monitor Gain Control Sensor  600 ns Pre Amp Fine Tuning Power Amps Beam Kicker Comb Filter  Variable Attenuator Variable Delay RF Switch Fiber Optic Delay Sensor and kicker are in the beam tunnel Everything else is “upstairs” about 100 away

11. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 11 Demonstration of Performance of the Damping System Unstable oscillations “decohere” (Landau damping) Quantitative measure of performance: Buncher voltage at threshold of instability is reduced by 30% with the damper on Maintains beam bunch Increases energy spread

12. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 12 System Performance System provides 30% improvement Why isn’t performance better? Power? Bandwidth? Signal fidelity? Horizontal instability? Beam dynamics / nature of the instability? Other?

13. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 13 Damp-Grow-Damp Experiments – Exploring System Performance Allow instability to grow, then turn damper back on Instability is damped … then it returns! Why? No evidence of horizontal instability:

14. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 14 Damp-Grow-Damp Experiments – Exploring System Performance Bandwidth probably isn’t the problem: Beam in the gap exacerbates electron cloud build-up Reduction of buncher voltage may not be the best measure of performance There seems to be more power available:

15. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 15 Damping System Details – Beam Position Sensor sin  t cos  t Signal at upstream end: Signal minus time-delayed copy  90  phase shift This looks like differentiation: (in the band of interest)

16. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 16 Damping System Details – Vertical Difference Signal Beam position:and Signal out: Top minus Bottom Rapid processing (  1 ns) so  Longitudinal “noise” in the feedback signal Broad-band (1 – 500 MHz)

17. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 17 System Details – Fiber Optic Delay Long delay needed  700ns in addition to what is intrinsic to the system Severe dispersion and attenuation in that much copper cable Fiber optic link used instead “Switchboard” reconfigurable

18. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 18 Damping System Details – Power Amplifiers Two of these (1 for each kicker electrode) Phase flatness is poor for f < 20MHz Gain is lower than expected

19. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 19 Damping System Details – Beam Kicker Kick power flows upstream Originally a stripline BPM Length = 37cm Effective shunt impedance: (for parallel-plate geometry) Shorter kicker  higher frequencies

20. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 20 Factors Possibly Limiting Performance of the System Beam in the gap Horizontal instability Power Amplifiers >1 kickers Coherent tune shift 10 to 15 % effect  v signal 90  shift  i(t) Bandwidth Amplifiers Kicker Phase shifts 10  here and there can add up Cables, amplifiers, delay box

21. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 21 Beam in the Gap A clean gap to allow extraction kickers to turn on Also allows electron cloud to dissipate as the gap passes by Not-so-clean gap Holds on to electron cloud Exacerbates instability (We’ve done experiments on this)

22. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 22 Horizontal Instability We damped the vertical oscillations only Because the instability is seen there Horizontal instability is expected But threshold intensity for vertical instability is lower than for horizontal Threshold intensity  tune Q H > Q v (3.2 vs. 2.2) We see signs of this when the vertical instability is damped Vertical damping enabled, Buncher set at threshold Horizontal instability Electron Cloud Vertical instability Maybe: Neuffer et al, “Observations of a fast transverse instability in the PSR” NIM A321 (1992) 1-12

23. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 23 More Kick Power Using More Kickers 2  amplifier power   2  damping rate 2  # kickers  2  damping rate This is on our wish list …

24. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 24 Phase Errors SNS is developing a digital LLRF system FIR filters can correct these problems Cables from amplifiers to kicker

25. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 25 The 90  Phase Shift in the Vertical Difference Signal V in V out C R  v signal  derivative of beam position  Use an integrator 1/   90  well above f 3dB For phase flatness, want a low f 3dB … but 1/  removes signal ! Other ideas: Differentiator (   90  ) We haven’t tried this (yet) Cable 90  long Works for narrow band Comb filter Gives 90  shift More on this later…

26. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 26 Signals from the Position Sensor - Sidebands Path of one proton around the ring Position signal: Pulses at 2.8 MHz (=f R ) Amplitude: Modulated at q  f R Betatron sidebands at (n  q)  f R Q = k + q = 2 + 0.19 # oscillations per revolution A deflecting field at a betatron sideband frequency can resonantly drive the beam …and the beam can drive such a deflecting field  Instability

27. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 27 Signals from the Position Sensor - Sidebands  v signals Relatively low frequenciesHigher frequencies Long beam bunch (  80% of  R ) Orbital harmonics seen at low frequencies Upper- and lower-sidebands ( q  0.2 )

28. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 28 Waves on the beam Snapshot of the beam with m=10 wave present Each proton oscillates at betatron frequency Amplitude of betatron oscillation = wave amplitude Betatron oscillations cause the wave pattern to rotate Wave moves around ring, but not at proton revolution frequency At a fixed location, one sees an oscillation frequency of m  m Betatron sideband frequencies m > 0 : fast waves upper sidebands m < 0 : slow waves lower sidebands

29. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 29 Instability and Lower Sidebands Model: Beam wave drives a deflecting field in a cavity Wave (drive) leads deflecting field (response) by 90  at resonance Proton phase relative to deflecting field changes turn-to-turn Deflecting field leads proton motion by 90   Unstable Deflecting field lags proton motion by 90   Stable

30. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 30 Comb Filters - Motivation Beam current: pulses at orbital frequency (f R ) If closed orbit is not centered at the BPM, position signal pulses at f R These are not associated with the instability. Lots of damper power can be wasted on harmonics of f R … in the time domain: remove what doesn’t change turn-to-turn

31. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 31 Comb Filter - Overview  coax  Optic fiber FO rcver INOUT FO xmitter Signal splitterSubtract signals (180  hybrid) “Long leg” 1 or 2 turns long (360ns or 720ns) Attenuator matches signal strengths This subtracts this turn’s signal from the previous turn’s signal Copper cable: Dispersion and attenuation in the long leg  Use a fiber optic link Subtract a signal from a time-delayed copy of itself  90  phase shift This could correct the phase shift from the BPM Developed by Craig Deibele, SNS (ORNL)

32. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 32 Comb Filter – Some Details 90  phase shift: Signal minus time-delayed copy Amplitude sin  cos (90  shift) delay Amplitude factor changes sign across a notch Damping at one LSB means Driving at the next LSB

33. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 33 Optimum Comb Filter Configuration 2-turn delay in the long leg Time-domain picture: 2 kicks Of opposite polarity 2-turn delay 2  180  shift between LSBs (from the amplitude factor) 90  overall shift is maintained 90  overall shift is not maintained in this configuration

34. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 34 Comb Filter – Some Details Amplitudes in the two legs determine notch depth As built:

35. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 35 Comb Filter - Results No improvement in system performance Closed orbit offset at the pickup had little effect on the system  Wasting power on revolution harmonics is not a major problem

36. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 36 Instability Bandwidth – Mechanisms for Growth These data courtesy of Bob Macek Oscillations begin in narrow band …then the band grows Why? Can we just damp the initial oscillation? (Would allow a narrow-band system) We’ve investigated two mechanisms for this growth: 1. Synchrotron motion 2. Coherent tune shift

37. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 37 Growth of Bandwidth – Synchrotron Motion Mechanism Rotation in longitudinal phase space changes the projection of the beam onto the phase axis  Changes frequency content

38. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 38 Growth of Bandwidth – Experiments with Synchrotron Motion These data are from experiments by McCrady, Rybarcyk, Kolski

39. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 39 Growth of Bandwidth - Non-uniform Coherent Tune Shift Coherent tune shift depends on charge density  changes along the beam bunch Tune (Q) is different here than it is here …due to image current Constant tune:Current-dependent tune: “Bob Macek’s mechanism”

40. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 40 Growth of Bandwidth – Single-Turn Kick Experiment These data courtesy of Bob Macek Tune variation can be measured:Growth of frequencies is observed:

41. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 41 Longitudinal Noise and PSR Orbital Frequency When PSR orbital frequency = Linac RF frequency  integer This was the case till recently High-frequency longitudinal structure is induced Linac micropulses are “stacked”

42. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 42 Longitudinal Noise and PSR Orbital Frequency  v  z  iLongitudinal structure shows up in  v signal Potential source of “noise” Longitudinal structure is reduced  v signal is less noisy … but damping system performance did not improve

43. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 43 Noise-Driven Beam Also: Does noise damp as well as the  v signal? Maybe head of proton beam stores phase information Try to destroy it with noise How does e-cloud remember phase turn-to-turn?

44. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 44 Further Work / Wish List Feedback in both planes More kickers …with higher frequency capability Better beam from the linac Constant energy Coasting beam studies Simpler system Example: Drive beam at one frequency, then damp

45. Operated by Los Alamos National Security, LLC for NNSA U N C L A S S I F I E D Slide 45 Summary The damping system to control vertical oscillations associated with the e-p instability provides 30% improvement Improvements to the system have not enhanced performance This work has motivated further understanding of the instability Work continues…