1. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 1 Harmonic Cavities:the Pros & Cons Jörn Jacob

2. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 2 Content Main motivation for harmonic cavities:  Touschek Harmonic cavities on existing light sources / achievements, problems –NC passive cavities –NC active cavities Projects for SC harmonic cavities Harmonic cavities for the ESRF ? Pros & Cons Conclusions

3. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 3 Motivation for harmonic cavities Optimized brilliance for 3 rd generation sources: => lower  Touschek Low energy machines: => lower  Touschek RF or dynamic acceptance: => limits  Touschek Bunch lengthening: => increases  Touschek Penalizes few bunch operation Exponential increase of  Touschek with if  x very small: future sources?

4. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 4 Harmonic Cavities for bunch lengthening Cavity at f harm =n f RF (often n=3) Passive / active Normal/Super-conducting (NC/SC) Maximum bunchlength for: V harm = V opt  harm =  opt

5. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 5 V harm /V opt = 0 ss U 0 /e (ESRF parameters)  Lo = 4.8 mm Synchrotron frequency distribution (f s0 = 2 kHz)

6. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 6 V harm /V opt = 0.25 ss U 0 /e

7. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 7 V harm /V opt = 0.5 ss U 0 /e

8. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 8 V harm /V opt = 0.6 ss U 0 /e

9. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 9 V harm /V opt = 0.7 ss U 0 /e

10. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 10 V harm /V opt = 0.8 ss U 0 /e

11. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 11 V harm /V opt = 0.9 ss U 0 /e

12. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 12 V harm /V opt = 1 ss U 0 /e [A. Hofmann & S. Myers]

13. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 13 ss U 0 /e V harm /V opt = 1.05 Over stretching => formation of two bunches

14. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 14 maximum typically

15. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 15 NC passive harmonic cavities The beam drives V harm => multibunch operation (I beam > I minimum ) => V harm controlled by Cavity tuning (typ.: f harm  n f RF + f 0 /3) =>  harm =  opt only possible at one current [Å. Andersson, M. Georgsson et al.] MAX II: E max = 1.5 GeV, I beam = 250 mA ->100 … 70 mA f RF = 500 MHz 4 copper pillbox HC’s, f harm = 3 f RF, 2 tuners Achievements:   Life doubled (I x  Life : 3 Ah  5…6 Ah)  Landau damping of multibunch instabilities (not fully stable):  Energy spread: 0.7 x 10 -3 for I beam = 0 4…5 x 10 -3 at nominal Ibeam for V harm = 0 1.1 x 10 -3 with Landau damping

16. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 16 NC passive harmonic cavities (continued) ALS: E max = 1.9 GeV, I beam = 400 mA  200 mA, LFB & TFB 5 Cu reentrant HC’s, f harm = 3 f RF / 2 tuners, HOM absorber Achievements:  in experiment:  Life increase by factor 2.5 (  Life : 4 h  10 h)  Length : 55  120 ps, f s : 11.5  5 kHz  LFB f s filter (now 4 kHz) limits  Length-max  in operation: 50% increase in  Life  6 h (2 cavities tuned in)  no energy spread => detuning of HC-HOM (TM011 at ALS) Problems:  Users require 20 % gap in filling  transient beam loading  strong beam and Voltage  modulation  less average bunch lengthening  TFB: heterodyne  homodyne receiver: solved the problem  LFB:  s modulation  factor 6 at 3 GHz detection frequency  feedback saturates if |  s | >15° [J. Byrd et al.] f RF = 500 MHz

17. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 17 NC passive harmonic cavities (continued) BESSY II: E max = 1.9 GeV, I beam = 220 mA, LFB & TFB 4 Cu Pillbox HC’s, f harm = 3 f RF / 2 tuners Achievements (still in commissioning):   Life : 3.2 h  5.2 h at 200 mA   Length : increase by factor 2.5 to 3 [W. Anders et al.] 122 mA, LFB on, V harm = 0 200 mA, LFB off, V harm = 140 kV Streak Camera: same time scale, V acc = 1 MV f RF = 500 MHz

18. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 18 NC passive harmonic cavities (continued) BESSY II:  TFB: operational  LFB: not yet compatible (filter bandwidth)  Phase transients with gap: max 50   HOM problems still present: [W. Anders et al.] 200 mA, V harm = 140 kV 200 ns Coupled bunch mode with some bunch shape oscillation 10 ms 200 mA, V harm = 140 kV Relaxation effect, Period = 6 ms

19. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 19 NC active harmonic cavities NSLS VUV: E = 0.8 GeV  Operation alternatively in bunch lengthening or shortening mode  Powered cavities allow operation near V opt,  opt for any I beam  No Beam power [S. L. Kramer, N. Towne et al.] f RF = 52.9 MHz, f harm = 4 f RF ACTIVE PASSIVE 52 MHz alone Data from 1994 Latest Figures: ModeI beam  Length  Life HC detuned700 mA0.9 ns2.5 h lengthened700 mA1.7 …2 ns4 h (unstable above 700 mA  nominal 1 A) shortened600 mA0.48 ns2 h (constant length)

20. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 20 NC active harmonic cavities (continued) NSLS VUV / Slow tuning, amplitude and phase feedback Principle using a Complex Phasor Modulator:  Voltage error signal  real part a r regulated to “zero” by tuning =>  harm = -90  ( and not  opt  -93  )  In lengthening, phase error signal from beam PU  imaginary part a i (at  harm   opt, due to flat RF potential  GAIN  beam /  Vcav  -4.5)  In shortening, phase error signal from cavity  imaginary part a i  System can be switched to standard tuning for passive operation  Stable operation in shortening mode difficult (high beam loading)  constant bunch length, but limited to 600 mA [S. L. Kramer, N. Towne et al.] a r + j a i amplified and fed to the cavity

21. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 21 NC active harmonic cavities (continued) NSLS VUV / Observed related instabilities:  Lengthening mode: Landau Damping of coupled bunch instabilities  Injection: partially stretched mode => needs LFB  Occurrence of non-rigid bunch instabilities in particular if over-stretched:  chaotic appearance of broad, strong sidebands  beam lost if high I beam  For nearly optimum lengthening: peak beam response at 1.1 f s0 to 1.4 f s0  insensitive to Ibeam, Cavity tuning  sensitive to V harm [S. L. Kramer, N. Towne et al.]

22. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 22 7 / 9 bunches filled, I beam = 1000 mA Leading bunch Last bunch time 10 ns0 NC active harmonic cavities (continued) NSLS VUV: Stretched bunch shapes = f(small variations of RF potential) [N. Towne] 3 Reasons:  Shape very sensitive to  harm near V opt,  opt  Gap in filling against ion trapping:  Phase transients  Gap in filling:  additional revolution harmonics  excite HOMs  different potential distortion for different bunches

23. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 23 NC active harmonic cavities (continued) Super ACO: E = 0.8 GeV Bunch shortening for FEL operation and time resolved experiments  Shortening by a factor up to 3.5 achieved (f s : 14  40 kHz) New types of instabilities observed:  Vertical single bunch instability at 10 mA/bunch: no sensitivity to z,  z, V harm  Vertical TMCI starting at 30 mA, m=0 and -1 modes merging at 40 mA: cured by high  z : +2.5  4  Interference between 2 longitudinal single bunch oscillations – Low frequency sawtooth oscillations (< 300 Hz), at any current – High frequency oscillations at mainly f s and 2 f s, only between 2 and 8 mA/bunch Bunch lengthening mode:  Landau damping of LCBI  expected Robinson II instability ? [G. Flynn et al.] f RF = 100 MHz, f harm = 5 f RF [M.P. Level, M. Georgsson, et al.]

24. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 24 SC passive cavities Elettra, SLS,... collaboration project with CEA-Saclay  HOM free harmonic cavities = scaling of 352.2 MHz SOLEIL cavities (pair of cavities within a single cryostat)  Tuning angle   90  => P beam  0, and as for NSLS:  harm  90   Simple amplitude control by frequency tuning such as:  Expected Bunch lengthening by a factor 4 (V harm < V opt )  Passive operation down to very low currents,  However, possible Robinson instability on m f s for low  f harm at low I beam  Phase transients also expected with SC cavities SRRC: abandon NC harmonic cavities  required space, HOMs,…  Feasibility study for SC harmonic cavities [K.T. Hsu ] (2 GeV) (2.4 GeV) f RF = 500 MHz, f harm = 1500 MHz V harm  I beam (R/Q) f harm /  f harm [P. Marchand, M. Svandrlik, A. Mosnier et al.]  [J. Byrd ]

25. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 25 Harmonic Cavity for the ESRF ? Operation modes: Multibunch at 200 mA,  v = 0.4 to 0.5  Life = 60... 70 h => NO 16 bunch at 90 mA (5.5 mA/b):  v = 0.6  Life = 12 h => yes Single bunch at 15 mA:  v = 0.9  Life = 4 h => yes Optimistic assumption Lengthening factor 6: f RF = 352.2 MHz, Example: f harm = 3 f RF Reason for an HC ? Longer bunches lower  more gain in  Life than from  Length

26. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 26 Harmonic Cavity for the ESRF ? (continued) Tracking simulations  unchanged energy spread with HC /  -wave instability More sensitive to HOM driven Longitudinal Coupled Bunch Instabilities:  Increasing harmonic voltage Synchrotron frequency density n = 3 n = 7 n = 11 n = 19 V harm /V opt LCBI threshold with a harmonic cavity I th /I th0

27. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 27 Harmonic cavities: Pros & cons Points of debate for the subsequent working group discussions Longer bunches:  Length Less spectral width of beam signals Effects in bunch lengthening: RF slope  zero: Phase sensitivity  Especially low energy machines or high I/bunch: gain in Lifetime + Consequences: Pros / Cons  Probing less of the BBR:  Less prone to transverse single bunch head tail instability ?  Less HOM losses:  Reduced heating in few bunch operation + +  Gap induced Phase transients NC & SC (increased by HOMs)  Reduced gain in Lifetime  TFB must be adapted  LFB saturation - o -

28. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 28 Harmonic cavities: Pros & cons, (continued) RF slope  zero: Smaller f s Distorted RF potential: Spread of f s Difficult to control V opt,  opt  limited bunch lengthening  Over-stretching  non rigid bunch instability (NSLS) - -  LCBI: lower thresholds -  Single bunch fast head tail (TMCI) : lower threshold ? [S.Myers, Y.C. Chin, CERN] -  More sensitivity to low frequency noise / power supplies -  Landau damping for: LCBI, TMCI ?, transverse instabilities with m  0 ? + More impedance (BBR, HOM)  Bad for all kind of instabilities- Effects in bunch lengthening:Consequences:Pro / Con  Robinson stability to be checkedo

29. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 29 Harmonic cavities: Pros & cons, (continued) Resistive wall instability:  Smaller spectral width  less chromaticity needed to shift the modes or  Less overlap with BBR  less damping ? Operation in bunch shortening:  NSLS: current limited by slow RF feedback stability  Super ACO: new types of instabilities  deserve further investigations  No experience from low emittance machines + -

30. Beam Instability Workshop, ESRF, 13th - 15th March 2000J. Jacob / 30 Conclusion NC passive harmonic cavities:  sufficient voltage for low or medium energy machines /multibunch operation  tuning not easy to handle for simultaneous Voltage and HOM control  operate mostly below V opt  Gain in Lifetime by typically a factor 2 to 2.5 => good for these machines ! NC active harmonic cavities:  allow operation at low current (e.g. single bunch operation)  operation in bunch shortening demonstrated SC HOM free harmonic cavities:  only way for high energy machines, where interest is mainly for high I/bunch  no major problems with HC HOMs, Robinson, …  tuning should be easier  still needs R&D to check performance, reliability and operational costs Transient beam loading and Beam instability issues with Harmonic cavities:  good candidates for extensive discussions in this workshop