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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
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E. Benedetto, NUFACT’09 Beam 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,...
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E. Benedetto, NUFACT’09 Beam 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
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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 (=0), no RF, ~400s, beam frozen longitudinally to preserve p/p
» 6 bunches, 120 ns total bunch length
– Compressor ring » rapid phase rotation in ~36s, strong RF, large slippage factor » ~2ns rms bunch length @ extraction to the Target
• Fast (<400s) 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
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E. Benedetto, NUFACT’09 Beam 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
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E. Benedetto, NUFACT’09 Beam 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
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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
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
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E. Benedetto, NUFACT’09 Beam 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
-110 8 -510 7 510 7 110 8
-110-16
110-16
210 -16
Re(Z)
m=0
m=1 m=2
bunch spectrum of mode m
• Simulations w. HEADTAIL confirm
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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
• 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
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E. Benedetto, NUFACT’09 Beam 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:• Rt = 1 M /m• QR = 1• fR ~ c/(2b) ~ 1GHz
z
<x Nz>
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E. Benedetto, NUFACT’09 Beam 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 → Qrms ~ 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, -6Q’x=0
Q’x=8, -8
Q’x=10, -10
~28s
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E. Benedetto, NUFACT’09 Beam stability in the SPL Proton Driver accumulator for a…
-4 -2 2 4
-1
-0.5
0.5
1
R
Rt
R
-Rt
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
I0 = e Nb/b
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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 M/m)
If Q’=0 →~28s / 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
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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
Qrms~0.006 (for x~10 mm)
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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 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
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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 kZl=8 k
Zl=6 k
Zl=5 kZl=4 kZl=3 k
• Zl < 4 k→Zl/n < 4 → OK! a few easily achieved
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E. Benedetto, NUFACT’09 Beam 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
Nb twice as much
it was =20
# turns: ~1.6 more
Parameters for the 3-bunches accumulator
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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: • 1M/m• Q=1• 1GHz
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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 k5 k
4 k3k
Zl=2 k
1 k
0.5 k
→ (Zl/n)MAX~ 3.2
OK!
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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 + error-bar (fR) (~few Ohm easily achieved in modern machines)
– transverse BB → OK! fast rising instability cured by Q (chromaticity (||~ 1.3) or octupoles)
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E. Benedetto, NUFACT’09 Beam stability in the SPL Proton Driver accumulator for a…
Conclusions (2/2)
– transverse BB • need Q ~ 0.02, → ok for tune footprint/ resonance
• assumed Rt=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
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Additional material
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E. Benedetto, NUFACT’09 Beam stability in the SPL Proton Driver accumulator for a…
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E. Benedetto, NUFACT’09 Beam stability in the SPL Proton Driver accumulator for a…
Trev~1 sPhase rotation:
36 turns
R.Garoby, NuFact’06
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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-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 (s) 12 16 0.6-16(?)
Total duration of the burst (s) 60 ~50 40-60
RMS bunch length (ns) ~2 2 1-3
Beam power on target (MW) 4 - -
M.Aiba, NuFact’07
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SPL beam
M.Aiba, poster NuFact’08
6- bunches 3- bunches
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M.Aiba, poster NuFact’08