Landau cavity parameters to damp coupledbunch instabilities H

Landau cavity parameters to damp coupled-bunch instabilities H. Damerau, A. Lasheen, E. Shaposhnikova LIU-PS Beam Dynamics Working Group 09/11/2017

Introduction and motivation • Longitudinal dipole coupled-bunch instabilities ® Damped by dedicated feedback up to at least 2 · 1011 ppb ® Insufficient damping at higher intensity • Quadrupole coupled-bunch instabilities ® No effect of feedback ® Other stabilization techniques? ® Landau RF system • Existing 40 MHz RF system can be used at flat-top ® Similar longitudinal conditions than in SPS ® Proof-of-principle MD in 11/2016 Damped dipole oscillations ® Studies in 2017 Damped quadrupole oscillations • What is required for damping during acceleration? 2

Existing feedback for quadrupole damping? ® BUT: phase advance wrong (set for dipole oscillation damping) Nb = 4 · 2. 0 · 1011 ppb Quadrupole mode spectrum Feedback off Feedback on ® No damping from dipole coupledbunch feedback ICFA mini-workshop, Benevento, 09/2017 • Side-bands at ± 2 f. S also pass the filters of the coupled-bunch feedback 3

Dephasing test with coupled-bunch feedback ® Scanned phase of signal processing channels trying to act on quadrupole modes of specific mode number Quadrupole oscillations at flat-top Quadrupole mode spectrum (Nb = 4 · 1. 8 · 1011 ppb) 4. 7 n =4… 5 5. 8 n =5… 6 3 · 7/6 = 3. 5 n =3… 4 Beyond dipole phase margin ® No beneficial effect on quadrupole oscillations of feedback in range of ~135° ® Drives dipole instability beyond 4

® Nb = 4 · 2 · 1011 ppb together with dipole coupled-bunch feedback ® Bunch shortening (BS, in-phase) and lengthening (BL, counter-phase) ® Reduce higher harmonic voltage down to ratio V 40 MHz/V 10 MHz = 0. 1 Quadrupole mode spectrum Bunch lengthening (BL) No effect 20 k. V (h = 21) + 2 k. V (h = 84) Stable Bunch shortening (BS) ® Encouraging results with combination 10 MHz/40 MHz ICFA mini-workshop, Benevento, 09/2017 Landau cavity against quadrupole instability 5

Landau cavity studies during acceleration? • Existing 40 MHz cavities optimized for maximum RF voltage (~300 k. V) at fixed frequency • Measurements to explore frequency range at low RF voltage 40 MHz frequency during cycle Measured frequency range of C 40 -78 at 20 k. V Usable frequency range: VRF C 40 -77 C 40 -78 10 k. V 110 k. Hz 170 k. Hz 20 k. V 50 k. Hz 90 k. Hz (preliminary, no beam) 84 frev (protons) from transition to flat-top ® Range of existing cavities most likely too small for beam tests 6

Acceleration of LHC multi-bunch beams • Longitudinal parameters of the present acceleration cycle Single-harmonic bucket area Total energy Synchronization Transition Total RF voltage, all harmonics h = 7/9 Triple splitting h = 21 Central synchrotron frequency Synchronization 7

Possible harmonic number ratio • 1 st order calculation: fs distribution during acceleration 8

Possible harmonic number ratio • Synchrotron frequency spread versus emittance Transition Arrival at flat-top ® 3 rd harmonic not very efficient, 5 th harmonic too high for 1. 4 e. Vs ® 4 th harmonic (h = 84) seems interesting compromise 9

Possible Landau RF system parameters • Frequency ranges and preliminary RF voltages Df/f [%] h 2/h 1 = 3, h = 63 h 2/h 1 = 4, h = 84 h 2/h 1 = 5, h = 105 2 Ge. V to 26 Ge. V 5. 3 28. 49… 30. 04 MHz 37. 98… 40. 05 MHz 47. 48… 50. 07 MHz Transition to 26 Ge. V 1. 3 29. 65… 30. 04 MHz 39. 53… 40. 05 MHz 49. 42… 50. 07 MHz RF voltage ~60… 80 k. V ~40… 50 k. V < 40 k. V (V 2/V 1 = 0. 3… 0. 4) (V 2/V 1 = 0. 2… 0. 25) (V 2/V 1 < 0. 2) • Vaccum cavity similar to 40 MHz with ferrite tuner(s)? ® Moderate voltage, but relatively large tuning range ® Long pulse operation (~ 1 s every 3. 6), large duty cycle • Similar RF systems, e. g. : ® FNAL Main Injector: ® FNAL Booster: ® CERN study: 240 k. V, 52. 8… 53. 1 MHz (Df/f ~ 1%) 55 k. V, 37. 8… 52. 8 MHz (Df/f ~ 30%) up to 60 k. V, 18… 40 MHz (Df/f ~ 70%) 10

Summary and open questions • Beam tests with 40 MHz higher-harmonic at flat-top ® Demonstrated dipole and quadrupole coupled-bunch oscillation damping ® Damping only in bunch-shortening mode (as in SPS) • Synchrotron frequency distributions for parameter choice ® Higher harmonic cavity at 3 rd or 4 th harmonic of h = 21 also interesting during acceleration ® RF system technically feasible ® Damping of dipole, quadrupole and higher order modes • Degradation (distribution, etc. ) due to Landau RF system? ® Cycle using 40 MHz at flat-top in combination with manipulations ongoing • Confidence in parameter choice? Impedance model • Tuning range to cover complete cycle from 2 Ge. V? 11

12 12 THANK YOU FOR YOUR ATTENTION! H. Damerau, S. Hancock, CERN/GSI Meeting on RF Manipulations and LLRF in Hadron Synchrotrons