1. Beam stability in the SPL - Proton Driver accumulator for a Neutrino Factory at CERN E.Benedetto (CERN) 21/7/09 NUFACT’09 Workshop, 20-25 July ‘09

2. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Beam stability in the SPL Proton Driver accumulator for a  -Factory at CERN Introduction & motivations Stability for the 6-bunches option –Simulations & analytical considerations Resistive-wall Broad-band impedance Electron cloud Longitudinal (BB-impedance) 3-bunches option –Preliminary considerations Conclusions Acknowledgements: M. Aiba, R. Garoby, M. Martini, E. Metral, G. Rumolo,...

3. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Separate accumulator & compressor rings: –to adapt the SPL time structure to the target Intro: CERN SPL-Proton Driver → M. Aiba, Feasibility Study of Accumulator and Compressor for the 6- bunches SPL-based Proton Driver, CERN-AB-2008-060 BI (& NuFact’07) 3/1-bunches scenario option → M.Aiba, CERN-AB-Note-2008-048 BI (& Poster @ NuFact’08) → R. Garoby, NuFact’06 6-bunches design meets the 3rd ISS requirements 4 MW proton beam @ 5 GeV, from HP-SPL

4. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Intro: CERN SPL-Proton Driver 6-bunches scenario (the CERN baseline) –Accumulator ring »Isochronous (  =0), no RF, ~400  s, beam frozen longitudinally to preserve  p/p »6 bunches, 120 ns total bunch length –Compressor ring »rapid phase rotation in ~36  s, strong RF, large slippage factor  »~2ns rms bunch length @ extraction to the Target Fast (  <400  s) instabilities may arise in accumulator No synchrotron motion to stabilize Collective effects studies aim at:  finding cures for instabilities  setting limits to the machine impedance

5. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… EM interactions of the beam with the environment → wake-fields(t) & impedances(  ) In the transverse plane: –Resistive wall (beam pipe finite resistivity) –Narrow-band resonators (RF cavities, cavity-like objects) –Broad-Band (BB) resonator (beam-pipe discontinuities) –Electron cloud In the longitudinal plane: –Narrow-band resonators (RF cavities,…) –BB resonator (kickers & other discontin) Mainly single-bunch (since neglecting narrow-band) Intro: Machine impedance PESSIMISTIC analysis: → assumed full intensity, while: → accumulation (400  s): intensity going from 0 →max

6. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Localized impedance source Intro: Machine impedance Analytical estimations & simulations HEADTAIL: macroparticles code → G.Rumolo, F.Zimmermann, CERN-SL-Note-2002-036-AP → D.Quatraro, G.Rumolo et al., Proceedings PAC’09 –Impedance localized @ few positions transfer matrix to the next one –Bunch sliced longitudinally –Each slice interacts w. impedance: leaves a wake-field behind gets a kick

7. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… 6-bunches Accumulator parameters Parameters designed to match: –SPL incoming beam –Compressor requirements for time-structure @ target Flat bunch with smooth edges → longitud SC Transverse emittance (not normalized) 3  mm mrad: → beam size @ target → space-charge → injection foil heating Bunch length 120ns & energy spread  5 MeV → structure @ target - → M. Aiba, CERN-AB-2008-060 BI

8. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Resistive wall transverse impedance In the “classical” regime: Complex modes frequency shift: Instability rise-time: Mode m=0 is unstable, but  = 8.2 ms >> 400  s Re(Z) m=0 m=1 m=2 bunch spectrum of mode m Simulations w. HEADTAIL confirm

9. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Electron cloud e- trapped in the bunch may contribute to instabilities e- released at the bunch tail (“trailing-edge” multipacting) can extract secondaries form the wall. Dependence on: –SEY → Surfaces coating/conditioning (studies @ CERN for LHC injectors upgrade) –Longitudinal bunch profile: →Truncated tails or flat is good! –gap between bunches, intensity, transverse shape, … e-cloud should not to be an issue “Long bunch” regime: many e- oscillations in a bunch

10. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Broad-band transverse impedance No synchrotron motion → cfr. Beam Break Up Can be cured by introducing some tune spread: –Chromaticity –Detuning w. amplitude (octupoles) BB parameters: R t = 1 M  /m Q R = 1 f R ~ c/(2  b) ~ 1GHz z

11. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Broad-band transverse impedance Cured by chromaticity Positive/negative values of Q’ are OK (  =0) Needed chromaticity |Q’| > 10 →  Q rms ~ 0.01 for (dp/p) rms ~10 -3 Horiz. Beam size vs. # turns, for different chromaticities  x (m) Q’ nat,x = - 8.4 Q’ x =6, -6 Q’ x =0 Q’ x =8, -8 Q’ x =10, -10  ~28  s

12. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… RR RtRt  R -R t BB analytical estimation  Q 1GHz >> 1/120ns Coasting beam formula w. peak values  *~  R the most critical one Im (Z) Re (Z) ~ 9  s Approx. stability criterion:  > 2 |U-jV| →  Q > ~0.025 I 0 = e N b /  b

13. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Broad-band transverse impedance Scan over impedance values (R s =1,2,3 M  /m) If Q’=0 →  ~28  s / Z [M  /m] Q’ th > 10 x Z [M  /m] Threshold proportional to Z Q’ th / Z [M  /m]  -1 [  s] / Z [M  /m] For a given Q’, risetime inversely prop. to Z Rs

14. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Broad-band transverse impedance Cured with octupoles (detuning w. amplitude) Beam size is growing, then saturation Q’’ xx ~1200 (-2000 if negative polarity) needed to cure instability  Q rms ~0.006 (for  x ~10 mm)

15. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Longitudinal BB impedance Isochronous ring –No RF cavities → negligible Narrow-band impedance –Beam frozen longitudinal BB impedance → microwave instability If only  0 (=0) taken into account: –The threshold is zero –Risetime is  Need to consider second order momentum compaction = 0.117 (for Q’ nat ) =0.0365 =0

16. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Longitudinal BB impedance Scan over BB shunt impedance (Q R =1, f R =1 GHz) Zl=10 k  Zl=8 k  Zl=6 k  Zl=5 k  Zl=4 k  Zl=3 k  Z l < 4 k  →  Z l /n < 4  → OK! a few  easily achieved

17. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… 3-bunches option same bunch length, dp/p similar emittance, Q, Q’ nat Circumference ~ 1.7 x smaller N b twice as much it was  =20 # turns: ~1.6 more Parameters for the 3-bunches accumulator

18. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… 3 bunches option: Transverse BB Natural chromaticity can cure transverse BB BB resonator: 1M  /m Q=1 1GHz

19. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… 3-bunches: Longitudinal BB Scan over BB shunt impedance (Q R =1, f R =1 GHz) 6 k  5 k  4 k  3k  Zl=2 k  1 k  0.5 k  → (Zl/n) MAX ~ 3.2  OK!

20. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Conclusions (1/2) Stability in the P-Driver accumulator → isochronous ring The 6-bunch option is under control Space Charge → OK! it guided in definition of emittance & bunch length/shape in the design Machine impedance: –narrow-band component → negligible (no RF-cavities) –resistive wall → not an issue (long risetime) –longitudinal BB → Z l /n < 4  + error-bar (f R ) (~few Ohm easily achieved in modern machines) –transverse BB → OK! fast rising instability cured by  Q (chromaticity (|  |~ 1.3) or octupoles)

21. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… Conclusions (2/2) –transverse BB need  Q ~ 0.02, → ok for tune footprint/ resonance assumed R t =1M  /m → Scaling laws with higher value of BB impedance –e-cloud → not an issue (flat & long bunch → no multipacting) 3-bunches option as well seems feasible

22. Additional material

23. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a…

24. E. Benedetto, NUFACT’09Beam stability in the SPL Proton Driver accumulator for a… T rev ~1  s Phase rotation: 36 turns R.Garoby, NuFact’06

25. Introduction: SPL-based proton driver (1) SPL=Superconducting Proton Linac SPL-based proton driver for neutrino factory –Design parameters has been determined to meet the summary of the 3rd ISS SPL-based3rd ISS (by R. Palmer) Parameter Basic valueRange Beam energy (GeV)5105-15 Burst repetition rate (Hz)50 (?) Number of bunches per burst641-6(?) Bunch spacing (  s) 1216 0.6-16(?) Total duration of the burst (  s) 60~5040-60 RMS bunch length (ns)~221-3 Beam power on target (MW)4- - M.Aiba, NuFact’07

26. SPL beam M.Aiba, poster NuFact’08 6- bunches3- bunches

27. M.Aiba, poster NuFact’08