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Beam stability in the SPL Proton Driver accumulator for a Neutrino by gegeshandong

VIEWS: 3 PAGES: 27

									      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
                 Acknowledgements: M. Aiba, R. Garoby,
                 M. Martini, E. Metral, G. Rumolo,...

   • 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
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
             Intro: CERN SPL-Proton Driver
                                                      • 4 MW proton beam @
                                                        5 GeV, from HP-SPL
                                                      • Separate accumulator
                                                        & compressor rings:
                                                                  – to adapt the SPL time
                                                                    structure to the target

                                              → 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)
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
             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
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                   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) PESSIMISTIC analysis:
                                                 → assumed full intensity,
 • Mainly single-bunch                         while:
                                                 → accumulation (400 ms):
      (since neglecting narrow-band)
                                               intensity going from 0 →max
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                   Intro: Machine impedance
 • Analytical estimations & simulations
 • HEADTAIL: macroparticles code
      – Impedance localized @ few positions                               Localized
                                                                          impedance
           • transfer matrix to the next one                              source

      – 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

E. Benedetto, NUFACT’09   Beam 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
 → 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

E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
       Resistive wall transverse impedance
 • In the “classical” regime:

                                                                 bunch spectrum of mode m

 • Complex modes frequency shift:
                                                                                         Re(Z)



                                                                              m=0
                                                                                       m=1   m=2
 • Instability rise-time:




 • Mode m=0 is unstable, but t = 8.2 ms >> 400 ms
 • Simulations w. HEADTAIL confirm
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                               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 or flat is good!
        – gap between bunches, intensity, transverse shape, …
                                             e-cloud should not to be an issue
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
         Broad-band transverse impedance
                                                                BB parameters:
                                                                • Rt = 1 MW /m
                                                                • QR = 1
                                                                • fR ~ c/(2pb) ~ 1GHz

 • No synchrotron motion
           → cfr. Beam Break Up                       <x Nz>

 • Can be cured by introducing
   some tune spread:
      – Chromaticity
      – Detuning w. amplitude
        (octupoles)
                                                                                       z
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
         Broad-band transverse impedance
 • Cured by chromaticity
      t~28ms                                                     Horiz. Beam size vs. #
                                                 Q’x=6, -6
                             Q’x=0                               turns, for different
                                                                 chromaticities
          sx (m)




                                                    Q’x=8, -8


                                                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

E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                 BB analytical estimation DQ

 • Coasting beam formula w. peak values
                                                                                Re (Z)
                                                                      Rt    1




                                                                                        Im (Z)
                                                                         0.5




       I0 = e Nb/tb       w*~ wR
                          the most               -4          -2

                                                                   wR             wR
                                                                                         2       4




                          critical one                                  -0.5




                           ~ 9 ms                                     -Rt  -1
                                                                                  1GHz >> 1/120ns



  • Approx. stability criterion:
                               Dw > 2 |U-jV| → DQ > ~0.025
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                        Broad-band transverse impedance
 • Scan over impedance values (Rs=1,2,3 MW/m)
                          Rs                                       If Q’=0 → t~28ms / Z [MW/m]
   t-1[ms] / Z [MW/m]




                                                                  • Threshold proportional
                                                                    to Z
                                                                  • For a given Q’,
                                                                    risetime inversely
                                                                    prop. to Z
                                   Q’th / Z [MW/m]

                               Q’th > 10 x Z [MW/m]

E. Benedetto, NUFACT’09          Beam 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


                                                             DQrms~0.006 (for sx~10 mm)

E. Benedetto, NUFACT’09   Beam 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 h0 (=0) taken into account:
      – The threshold is zero
      – Risetime is 
 • Need to consider second order momentum compaction




                                    = 0.117                             =0
                                    (for Q’nat)        =0.0365

E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                 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
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                            3-bunches option
 Parameters for the 3-bunches accumulator
                                                                               Nb twice as much


                                                                                Circumference
                                                                                ~ 1.7 x smaller

                                                                                       # turns:
                                                                                       ~1.6 more


                                                                                  it was b=20




                                                      • same bunch length, dp/p
                                                      • similar emittance, Q, Q’nat
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
          3 bunches option: Transverse BB
 • Natural chromaticity can cure transverse BB

                                                                           BB resonator:
                                                                             • 1MW/m
                                                                             • Q=1
                                                                             • 1GHz




E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                 3-bunches: Longitudinal BB
 • Scan over BB shunt impedance (QR=1, fR=1 GHz)

                                  6 kW
                                     5 kW
                                            4 kW
                                                     3kW
                                                           Zl=2 kW →     (Zl/n)MAX~ 3.2 W


                                                               1 kW                    OK!
                                                              0.5 kW




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




E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
Additional material
E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
                                                                         R.Garoby, NuFact’06


                                                                            Trev~1 ms
                                                                            Phase rotation:
                                                                                   36 turns




E. Benedetto, NUFACT’09   Beam stability in the SPL Proton Driver accumulator for a…
  Introduction: SPL-based proton driver (1)
 SPL=Superconducting Proton Linac M.Aiba, NuFact’07
 SPL-based proton driver for neutrino factory
  – Design parameters has been determined to meet the
    summary of the 3rd ISS
                                   SPL-based   3rd ISS (by R. Palmer)
Parameter                                        Basic value        Range
Beam energy (GeV)                      5             10                 5-15
Burst repetition rate (Hz)             50            50                  (?)
Number of bunches per burst            6              4             1-6(?)
Bunch spacing (ms)                     12            16            0.6-16(?)
Total duration of the burst (ms)       60            ~50                40-60
RMS bunch length (ns)                  ~2             2                  1-3
Beam power on target (MW)              4              -                   -
             SPL beam
                         M.Aiba, poster NuFact’08




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

								
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