SPACE CHARGE EXPERIMENTS AND BENCHMARKING ...2007/04/02 · Elias Métral, LIS meeting, 02/04/2007 1/29 SPACE CHARGE EXPERIMENTS AND BENCHMARKING IN THE PS E. Métral Crossing the

Elias Métral, LIS meeting, 02/04/2007 1/29

SPACE CHARGE EXPERIMENTSAND BENCHMARKING IN THE PS

E.E. MMéétraltralCrossing the integer or half-integer resonanceMontague resonance

Static & DynamicBenchmarking of the simulation codes

Space charge driven resonance phenomenaTransverse Landau damping with space charge î Comparison theory and PATRIC simulationsDecoherence without and with space charge at PS injectionPossible experiments in the PSB-PS to benchmark the space charge codes?Appendix: Some space charge codes characteristics (Oxford03)


Crossing the integer or halfCrossing the integer or half--integer resonance (1/2)integer resonance (1/2)

5.9 6.1 6.2Qx

5.9

6.1

6.2

QyvQ

hQ

Case 3

11.6≈xQ

24.6≈yQ

-40 -20 20 40

200

400

600

800

[mm]

5.9 6.1 6.2Qx

5.9

6.1

6.2

Qy

Case 1

16.6≈xQ

24.6≈yQ

vQ

hQ

Horizontal bunch profile+ Gaussian fit

Regime of loss-free core-emittance blow-up

xQ

xQ

yQ

yQ

M. Giovannozzi et al., PAC2003


Crossing the integer or halfCrossing the integer or half--integer resonance (2/2)integer resonance (2/2)

MeasurementsMeasurements

ORBIT simulationsORBIT simulations

S. Cousineau et al., EPAC2004


Montague resonance (1/8) Montague resonance (1/8)

Montague showed in 1968 that the space-charge potential could excite a 4th order coupling resonance

î Beating in amplitude between x and y for the single-particle motion, resulting in an apparent increase in emittance in the plane of smaller emittance î Growth in few (~ 1-5) turns for synchrotron at the space-charge limit

Montague said that this effect should be taken into account in the choice of parameters for future high-intensity synchrotrons

Baconnier knew in 1987 that “The Montague stop band was certainly one of the most effective in losing particles at injection in the CERN PS”

022 =− yx QQ



ORBIT, static

STATIC CASE in 2002 (constant tunes from injection to the measurement point)

6.21=yQ

06.00, −=Δ xincQ

107.00, −=Δ yincQ

S. Cousineau et al., EPAC2004



STATIC CASE in 2003 (constant tunes from injection to the measurement point)

5

10

15

20

25

30

35

40

6.15 6.17 6.19 6.21 6.23 6.25

Horizontal tune

Emit_H (norm, 2 σ) [μm]Emit_V (norm, 2 σ) [μm]Emit_H from 3D simul.Emit_V from 3D simul.

Asymmetrical stop-band predicted

by simulations

Fully 3D PIC code IMPACT

6.21=yQ

E. Métral et al., HB2004, Bensheim

054.00, −=Δ xincQ 109.00, −=Δ yincQ



( )σε 2,normx( )σε 2,normy

DYNAMIC CASE in 2003 (the horizontal tune was changed linearly from 6.15 to 6.25 in 100 ms)

μs3.2=revT î ~ 44 000 turns

Mixing due to longitudinal motion



î The crossing speed has to be slow compared to the time scale during which the coupling occurs

î The crossing speed has to be fast compared to the synchrotron motion

I. Hofmann et al., EPAC04

Simulations of the DYNAMIC CASE



5

10

15

20

25

30

35

40

6.15 6.17 6.19 6.21 6.23 6.25

Horizontal tune

3D simulation results (IMPACT code from R.D. Ryne) for the PS in the case where the synchrotron period is much larger than the crossing time

6.21=yQ

Fit by formulae similar to the ones with linear coupling

( )σε 2,normx( )σε 2,normy

Simulations of the DYNAMIC CASE



BENCHMARKING OF SIMULATION CODES BASED ON THE MONTAGUE RESONANCE IN THE CERN PROTON SYNCHROTRON

(I. Hofmann et al. PAC2005)


Space charge driven resonance phenomena (1/6)Space charge driven resonance phenomena (1/6)

Mechanism anticipated by G. Franchetti & I. Hofmann, which involvesSpace charge tune spreadNonlinear (octupole) resonanceSynchrotron motion

Qx

Qy

hQ

vQ Regime where continuous loss occurs ⇒ Due to longitudinal motion

Qx

QyvQ

hQ

Regime of loss-free core-emittance blow-up

Particles diffuse into a halo

xQ xQ

yQyQ Regime of loss-free core-emittance blow-up

Regime where continuous loss occurs î Due to longitudinal motion

254 =xQ



A 20−=octI

xQ

6.265

6.25

G. Franchetti et al.,ICFA workshop, Bensheim,

Germany, October 2004

Loss dominated regime

Emittance growth dominated regime



180 ms

1200 ms

Undershoot due to the measurement

device

6.27=xQ

[ms] Time

[ ]1010×bNOctupole ON (40 A)

170 300 1200

50% of losses

Regime where continuous loss occurs î Due to longitudinal motion


By lowering the working point towards the resonance 4 Qx = 25, a gradual transition from a regime of loss-free core emittance blow-up to a regime dominated by continuous beam loss has been observed, as expected by Ingo&Giuliano

Emittance growth in good agreement with predictions

The observed maximum losses (~30%) are still larger than predicted (~8%) í At COULOMB05, Senigallia



Latest results presented by Giuliano&Ingo (HB2006, Japan)



Space charge driven resonance phenomena (6/6)Space charge driven resonance phenomena (6/6)Beam losses on the PS injection Beam losses on the PS injection

flatflat--bottom (2006)bottom (2006) ⇒⇒ SSpace charge pace charge driven resonance trapping phenomenadriven resonance trapping phenomena

0 500 1000 1500 20000

50

100

150

200

@nsD

@kturns D

800 900 1000 1100 1200@msD

25

50

75

100

125

150

@E10D LHC

50000 100000 150000 200000@turns D

140

160

180

@nsD LHC

Courtesy S. Hancock


Transverse Landau damping with space charge (1/6)Transverse Landau damping with space charge (1/6)



SpaceSpace--charge forcecharge force

-2 0 2

x ê s

-20

2y ê s

-1

-0.5

0

0.5

1

Fx μ2 e0 s g2ÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅÅ

e2 n0

-

02



64.3086 64.3088 64.309 64.3092 64.3094 64.3096 64.3098

59.3186

59.3188

59.319

59.3192

59.3194

59.3196

59.319864.3086 64.3088 64.309 64.3092 64.3094 64.3096 64.3098

59.3186

59.3188

59.319

59.3192

59.3194

59.3196

59.3198

xQ

yQ

xQ

yQ

xQ

yQ

2D tune footprint2D tune footprint 3D tune footprint3D tune footprint

This case has been studied analytically

Low-intensity working point

Large-(synchrotron)

amplitudeparticles

Case of the LHC at injectionCase of the LHC at injection


From HB2006


Stable point with octupole alone but unstable when SC

added

Unstable point with octupole alone but stable

when SC added


Interesting new PATRIC simulations by V. Kornilov et al. seem now in good agreement with Mohl&Schonauer1974 theory (which we extendedwith FR) ⇒ End (at least qualitatively) of a long-standing problem…

What is in addition in the extended theory and not (yet) in the previous simulations

2-dimensional betatron tune spread ⇒ In the absence of space charge the stability diagrams from Berg&Ruggiero are recovered

2 stability diagrams in the presence of both space charge and octupoles: same or opposite sign of the detuning with amplitude

Stability diagrams plotted in the complex tune diagram (instead of the LNS coefficients U and V) ⇒ Much more convenient in practice

Future (collaboration) work: Make the PATRIC (and HEADTAIL) simulations for the PS, LHC… at injection?



DecoherenceDecoherence without and with space charge at PS injection (1/4)without and with space charge at PS injection (1/4)

MD 29/10/2003 1.4 GeV Flat

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

-0.001 0 0.001 0.002 0.003 0.004

time [s] Start = C320 = Kick time

Del

ta h

[25m

m/V

]

TFB OFFTFB ON

2 ms

Measurements from F. Blas with a nominal LHC bunchMeasurements from F. Blas with a nominal LHC bunch


DecoherenceDecoherence without and with space charge at PS injection (2/4)without and with space charge at PS injection (2/4)HEADTAIL simulations from E. HEADTAIL simulations from E. BenedettoBenedetto (PHD thesis)(PHD thesis)

[turns] Time

[m]motion centroidBunch

20 40 60 80 100

-0.01

-0.005

0

0.005

0.01

0.015

[turns] Time

[m] emittance rmsBunch

20 40 60 80 100

1μ 10-62μ 10-63μ 10-64μ 10-65μ 10-66μ 10-67μ 10-6

Comparison between HEADTAIL and theory

(with chromaticity only), RLC meeting 18-02-05


DecoherenceDecoherence without and with space charge at PS injection (3/4)without and with space charge at PS injection (3/4)


DecoherenceDecoherence without and with space charge at PS injection (4/4)without and with space charge at PS injection (4/4)Note:Note: HEADTAIL simulations from G. HEADTAIL simulations from G. RumoloRumolo + F. Zimmermann in SPS+ F. Zimmermann in SPS

(Practical User Guide for HEADTAIL, 2002)(Practical User Guide for HEADTAIL, 2002)


Possible experiments in the PSBPossible experiments in the PSB--PS to benchmark the SC codes? (1/2) PS to benchmark the SC codes? (1/2)

Study the emittance sharing/exchange mechanism with unsplitand split (by 1 integer) transverse tunes in the PSB

The Montague resonance works only near Qx = Qy

Emittance transfer with linear coupling works near Qx = Qy + any integer

We could measure for the first time (to my knowledge) in the same machine with unsplit and split tunes to disentangle the space charge effect from the linear coupling effect

Another proposition from A. Franchi (PHD thesis): Suppress the space charge driven emittance exchange using “normal quadrupoles to detune the machine and make the beam cross the resonance with an effective speed such to prevent any exchange and mismatch” î To be tested


Possible experiments in the PSBPossible experiments in the PSB--PS to benchmark the SC codes? (2/2) PS to benchmark the SC codes? (2/2)

Study the PS low energy resistive-wall instability (large incoherent space charge tune spread of ~ 0.3) î We started this already with Benoit et al.

Effect of external nonlinearities (both signs of the detuning coefficients) + space charge on Landau damping mechanism and decoherence î Coherent tune inside or outside the incoherent tune spread to be studied

Use the flat bunches (a la Christian) to reduce the SC tune spread at PS injection, to move the working point and perhaps reduce the losses on the long injection flat bottom î (Rapidly) tested in the past and not conclusive at that time… But we should perhaps try it again

î Giuliano could make the corresponding simulations to see if and how flat bunches can help

Documents

SPACE CHARGE EXPERIMENTS AND BENCHMARKING ...2007/04/02 · Elias Métral, LIS meeting, 02/04/2007 1/29 SPACE CHARGE EXPERIMENTS AND BENCHMARKING IN THE PS E. Métral Crossing the