beam stability in the spl - proton driver accumulator for a neutrino factory at cern e.benedetto...

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

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,...


• 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


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


• 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


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


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


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


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


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>



• 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


-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



• 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



• 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)


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


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


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


3 bunches option: Transverse BB

• Natural chromaticity can cure transverse BB

BB resonator: • 1M/m• Q=1• 1GHz


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!


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)


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

Additional material


Trev~1 sPhase rotation:

36 turns

R.Garoby, NuFact’06

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

SPL beam

M.Aiba, poster NuFact’08

6- bunches 3- bunches

M.Aiba, poster NuFact’08

beam stability in the spl - proton driver accumulator for a neutrino factory at cern e.benedetto...

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