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,...

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

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

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

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

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

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

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

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>

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

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

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

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)

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

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

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

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

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!

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)

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

Additional material

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

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

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