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Accelerator Physics Topic VII Coupled Bunch Effects

Accelerator Physics Topic VII Coupled Bunch Effects. Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin-Madison. Coupled Bunch Instabilities. We have discussed instabilities internal to a single bunch of charged particles

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Accelerator Physics Topic VII Coupled Bunch Effects

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  1. Accelerator PhysicsTopic VIICoupled Bunch Effects Joseph Bisognano Engineering Physics & Synchrotron Radiation Center University of Wisconsin-Madison J. J. Bisognano

  2. Coupled Bunch Instabilities • We have discussed instabilities internal to a single bunch of charged particles • Typically in a storage ring or linear accelerator there are trains (finite or cw) of bunches separated by nanoseconds to maybe milliseconds • Say we have a resonant structure at 300 MHz, with an angular frequency of 2(300) 2 GHz • If it has a Q of 20,000 (typical of Cu), its fields ring for 20,000/2 GHz=10 microsecond; if the Q were 2 109 more typical of superconducting RF, the ringing would last a full second • So a sequence of bunches can talk to each other through resonant structures • Whereas low Q impedances have a large bandwidth and can “see” the peak current, these high Q structures have a narrow bandwith and only see the average current. • In other words, broadband impedances generate peak current limitations in accelerators, narrowband impedances generate average current limitations J. J. Bisognano

  3. Bunch Spectrum J. J. Bisognano

  4. Robinson Instability Following A. Hoffman, CERN77-13 J. J. Bisognano

  5. Robinson/cont. J. J. Bisognano

  6. Robinson/cont. R+ R- J. J. Bisognano

  7. Robinson/cont. J. J. Bisognano

  8. Robinson/cont. Damping or antidamping J. J. Bisognano

  9. Robinson Conclusions J. J. Bisognano

  10. Robinson Stability Condition Above transition Below transition - + - + 0 r r 0 J. J. Bisognano

  11. Coupled Bunch Instabilities phase definition change J. J. Bisognano

  12. Coupled Bunch/cont. J. J. Bisognano

  13. General Phase Relationship J. J. Bisognano

  14. Normal Modes N=4 J. J. Bisognano

  15. Spectrum/cont. 4 4 3 1 2 2 1 3 4 4 3 1 2 2 1 3 4 4 -4 -3 -2 -1 0 1 2 3 4 J. J. Bisognano

  16. Growth Rates J. J. Bisognano

  17. Fixes J. J. Bisognano

  18. Mode Coupling J. J. Bisognano

  19. Mode Coupling at SRC J. J. Bisognano

  20. Transverse Phenomena J. J. Bisognano

  21. Transverse Coupling J. J. Bisognano

  22. Deflecting Modes Particle on axis doesn’t see Ez , doesn’t deposit energy Particle off axis can excite mode through Ez But deflection is constant through derivative of Ez J. J. Bisognano

  23. Resonant Wakefield J. J. Bisognano

  24. Beam Breakup in Linear Accelerators • In a linac there the higher order cavity modes produce the same basic resonant self-interaction, both longitudinal and transverse • For relativistic linacs, the longitudinal motion is more “frozen” than in a storage ring, which has bending. So transverse effects are often the limiting factor in linacs • For transverse effects, the primary difference in the dynamics is number of times the same bunch sees a given cavity HOMs • Straight linac: once, amplification • Recirculated linac: several times, instability with finite threshold • Storage ring: infinite times, zero threshold unless some form of damping present • In linacs, these effects are call Beam Breakup J. J. Bisognano

  25. Regenerative Beam Breakup • Basic mechanism: a train of bunches excites a transverse deflecting mode of a single cavity • Feedback loop • Say, HOM has small excitation • Even a bunch perfectly aligned on axis will receive a transverse kick • If energy is low and structure long, a significant deflection will occur while the bunch is in the cavity • The offset bunch is now in a region of longitudinal electric field and can deposit energy into mode • Go to next bunch • We have a feedback loop that can go unstable unless the cavity losses (more with lower Q) exceed the gain of the loop • An honest instability J. J. Bisognano

  26. Regenerative Beam Breakup J. J. Bisognano

  27. Threshold Condition J. J. Bisognano

  28. Cumulative BBU Amplification 1 2 3 4 5 J. J. Bisognano

  29. Cumulative BBU/cont. • Cavity 1: Bunch will coherently excite cavity, later bunches will receive transverse kick • Cavity 2: Bunch will enter cavity 2 with an extra offset; cavity 2 experiences an enhanced excitation • Cavity N: DITTO • Overall, initial offset causes growing excitation of subsequent cavities which can increase offset downstream: Amplification • Since there is no closure of loop, there is no instability as such J. J. Bisognano

  30. Cumulative Beam Breakup • Typically bunching frequency and transverse HOM frequency are not harmonically related • So, there can be a large transient, but the equilibrium excitation can be rather small. For a pulsed linac, however, the transient can cause beam loss, limiting currents to ~100 mA • For CW operation with equally spaced bunches, the excitation settles down to a DC value that can be steered away J. J. Bisognano

  31. Multipass Beam Breakup • A “new” feature of SRF linacs is the possibility of recirculation, and even energy recovery • SRC allows CW operation and the beam can pass through the linac several times • The “cumulative” beam breakup amplifier now has its feedback loop closed and at high enough gain there can be instability • Limited the first generation of SRF linaces to 10 microamps average currents when HOM Q’s were in the 10,000,000 range • In some ways it’s a combination of cumulative and regenerative BBU J. J. Bisognano

  32. Multipass BBU Mechanism • Displaced bunch excites a HOM • Following bunches deflected • Recirculation optics transforms kick into a displacement • Displaced bunch further excites HOM in same cavity • Again threshold occurs when excitation rate exceeds damping rate J. J. Bisognano

  33. Beam Breakup Mechanism Initial noise excitation of cavity mode kicks particle bunch beam on pass n cavity On subsequent pass, bunch enters off axis and coherently excites cavity mode Beam on pass n+1 J. J. Bisognano

  34. CEBAF J. J. Bisognano

  35. Jlab FEL J. J. Bisognano

  36. Multipass BBU Theory J. J. Bisognano

  37. Multipass BBU Theory/cont. J. J. Bisognano

  38. Multipass BBU Theory/cont. J. J. Bisognano

  39. Multipass BBU Theory/cont. J. J. Bisognano

  40. Multipass BBU Theory/cont. J. J. Bisognano

  41. Multipass BBU Theory/cont. J. J. Bisognano

  42. Multipass BBU Theory/cont. J. J. Bisognano

  43. Multipass BBU Theory/cont. J. J. Bisognano

  44. Multipass BBU Theory/cont. J. J. Bisognano

  45. Simulation: transient and steady state below threshold (cumulative-like) J. J. Bisognano

  46. Simulation: instability J. J. Bisognano

  47. Longitudinal Multipass BBU Theory J. J. Bisognano

  48. Longitudinal Multipass BBU Theory J. J. Bisognano

  49. Longitudinal Multipass BBU Theory J. J. Bisognano

  50. Longitudinal Multipass BBU Theory J. J. Bisognano

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