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Beam stability in the SPL - Proton Driver accumulator for a Neutrino Factory at CERN

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. Beam stability in the SPL Proton Driver accumulator for a n -Factory at CERN. Introduction & motivations

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Beam stability in the SPL - Proton Driver accumulator for a Neutrino Factory at CERN

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  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. Beam stability in the SPL Proton Driver accumulator for a n -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,... Beam stability in the SPL Proton Driver accumulator for a…

  3. Intro: CERN SPL-Proton Driver • Separate accumulator & compressor rings: • to adapt the SPL time structure to the target • 4 MW proton beam @ 5 GeV, from HP-SPL → R. Garoby, NuFact’06 • 6-bunches design meets the 3rd ISS requirements → 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) Beam stability in the SPL Proton Driver accumulator for a…

  4. Intro: CERN SPL-Proton Driver • 6-bunches scenario (the CERN baseline) • Accumulator ring • Isochronous (h=0), no RF, ~400ms, beam frozen longitudinally to preserve Dp/p • 6 bunches, 120 ns total bunch length • Compressor ring • rapid phase rotation in ~36ms, strong RF, large slippage factor h • ~2ns rms bunch length @ extraction to the Target • Fast (t<400ms) 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 Beam stability in the SPL Proton Driver accumulator for a…

  5. Intro: Machine impedance • EM interactions of the beam with the environment → wake-fields(t) & impedances(w) • 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) • PESSIMISTIC analysis: • → assumed full intensity,while: • → accumulation (400 ms): intensity going from 0 →max Beam stability in the SPL Proton Driver accumulator for a…

  6. Localized impedance source Intro: Machine impedance • Analytical estimations & simulations • HEADTAIL:macroparticles code • 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 → G.Rumolo, F.Zimmermann, CERN-SL-Note-2002-036-AP → D.Quatraro, G.Rumolo et al.,Proceedings PAC’09 Beam stability in the SPL Proton Driver accumulator for a…

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

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

  9. Electron cloud • e- trapped in the bunch may contribute to instabilities • “Long bunch” regime: many e- oscillations in a bunch • 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 orflat is good! • gap between bunches, intensity, transverse shape, … e-cloud should not to be an issue Beam stability in the SPL Proton Driver accumulator for a…

  10. 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: • Rt = 1 MW /m • QR = 1 • fR ~ c/(2pb) ~ 1GHz <x Nz> z Beam stability in the SPL Proton Driver accumulator for a…

  11. t~28ms Broad-band transverse impedance • Cured by chromaticity Horiz. Beam size vs. # turns, for different chromaticities Q’x=6, -6 Q’x=0 Q’x=8, -8 sx (m) Q’x=10, -10 Q’nat,x= - 8.4 • Positive/negative values of Q’ are OK (h=0) • Needed chromaticity |Q’| > 10 → DQrms ~ 0.01 for (dp/p)rms~10-3 Beam stability in the SPL Proton Driver accumulator for a…

  12. Rt -wR wR -Rt BB analytical estimation DQ • Coasting beam formula w. peak values Re (Z) Im (Z) w*~ wR the most critical one I0 = e Nb/tb 1GHz >> 1/120ns ~ 9 ms • Approx. stability criterion: Dw > 2 |U-jV| → DQ > ~0.025 Beam stability in the SPL Proton Driver accumulator for a…

  13. If Q’=0 → t~28ms / Z [MW/m] Q’th > 10 x Z [MW/m] Broad-band transverse impedance • Scan over impedance values (Rs=1,2,3 MW/m) Rs • Threshold proportional to Z t-1[ms] / Z [MW/m] • For a given Q’, risetime inversely prop. to Z Q’th / Z [MW/m] Beam stability in the SPL Proton Driver accumulator for a…

  14. 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 DQrms~0.006 (for sx~10 mm) Beam stability in the SPL Proton Driver accumulator for a…

  15. Longitudinal BB impedance • Isochronous ring • No RF cavities → negligible Narrow-band impedance • Beam frozen longitudinal • BB impedance → microwave instability • If only h0 (=0) taken into account: • The threshold is zero • Risetime is • Need to consider second order momentum compaction = 0.117 (for Q’nat) =0 =0.0365 Beam stability in the SPL Proton Driver accumulator for a…

  16. Longitudinal BB impedance • Scan over BB shunt impedance (QR=1, fR=1 GHz) Zl=10 kW Zl=8 kW Zl=6 kW Zl=5 kW Zl=4 kW Zl=3 kW • Zl < 4 kW → Zl/n < 4 W → OK! a few W easily achieved Beam stability in the SPL Proton Driver accumulator for a…

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

  18. 3 bunches option: Transverse BB • Natural chromaticity can cure transverse BB • BB resonator: • 1MW/m • Q=1 • 1GHz Beam stability in the SPL Proton Driver accumulator for a…

  19. 3-bunches: Longitudinal BB • Scan over BB shunt impedance (QR=1, fR=1 GHz) 6 kW 5 kW 4 kW 3kW → (Zl/n)MAX~ 3.2 W Zl=2 kW OK! 1 kW 0.5 kW Beam stability in the SPL Proton Driver accumulator for a…

  20. 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→ Zl/n < 4 W + error-bar (fR) (~few Ohm easily achieved in modern machines) • transverse BB→ OK! fast rising instability cured by DQ (chromaticity (|x|~ 1.3) or octupoles) Beam stability in the SPL Proton Driver accumulator for a…

  21. Conclusions (2/2) • transverse BB • need DQ ~ 0.02, → ok for tune footprint/ resonance • assumed Rt=1MW/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 Beam stability in the SPL Proton Driver accumulator for a…

  22. Additional material

  23. Beam stability in the SPL Proton Driver accumulator for a…

  24. R.Garoby, NuFact’06 Trev~1 ms Phase rotation: 36 turns Beam stability in the SPL Proton Driver accumulator for a…

  25. Introduction:SPL-based proton driver (1) M.Aiba, NuFact’07 • SPL=Superconducting Proton Linac • SPL-based proton driver for neutrino factory • Design parameters has been determined to meet the summary of the 3rd ISS

  26. SPL beam M.Aiba, poster NuFact’08 6- bunches 3- bunches

  27. M.Aiba, poster NuFact’08

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