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)
Elias Métral, LIS meeting, 02/04/2007 2/29
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
Elias Métral, LIS meeting, 02/04/2007 3/29
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
Elias Métral, LIS meeting, 02/04/2007 4/29
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
Elias Métral, LIS meeting, 02/04/2007 5/29
Montague resonance (2/8) Montague resonance (2/8)
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
Elias Métral, LIS meeting, 02/04/2007 6/29
Montague resonance (3/8) Montague resonance (3/8)
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
Elias Métral, LIS meeting, 02/04/2007 7/29
Montague resonance (4/8) Montague resonance (4/8)
( )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
Elias Métral, LIS meeting, 02/04/2007 8/29
Montague resonance (5/8) Montague resonance (5/8)
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
Elias Métral, LIS meeting, 02/04/2007 9/29
Montague resonance (6/8) Montague resonance (6/8)
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
Elias Métral, LIS meeting, 02/04/2007 10/29
Montague resonance (7/8) Montague resonance (7/8)
BENCHMARKING OF SIMULATION CODES BASED ON THE MONTAGUE RESONANCE IN THE CERN PROTON SYNCHROTRON
(I. Hofmann et al. PAC2005)
Elias Métral, LIS meeting, 02/04/2007 11/29
Montague resonance (8/8) Montague resonance (8/8)
Elias Métral, LIS meeting, 02/04/2007 12/29
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
Elias Métral, LIS meeting, 02/04/2007 13/29
Space charge driven resonance phenomena (2/6)Space charge driven resonance phenomena (2/6)
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
Elias Métral, LIS meeting, 02/04/2007 14/29
Space charge driven resonance phenomena (3/6)Space charge driven resonance phenomena (3/6)
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
Elias Métral, LIS meeting, 02/04/2007 15/29
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
Space charge driven resonance phenomena (4/6)Space charge driven resonance phenomena (4/6)
Elias Métral, LIS meeting, 02/04/2007 16/29
Latest results presented by Giuliano&Ingo (HB2006, Japan)
Space charge driven resonance phenomena (5/6)Space charge driven resonance phenomena (5/6)
Elias Métral, LIS meeting, 02/04/2007 17/29
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
Elias Métral, LIS meeting, 02/04/2007 18/29
Transverse Landau damping with space charge (1/6)Transverse Landau damping with space charge (1/6)
Elias Métral, LIS meeting, 02/04/2007 19/29
Transverse Landau damping with space charge (2/6)Transverse Landau damping with space charge (2/6)
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
Elias Métral, LIS meeting, 02/04/2007 20/29
Transverse Landau damping with space charge (3/6)Transverse Landau damping with space charge (3/6)
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
Elias Métral, LIS meeting, 02/04/2007 21/29
Transverse Landau damping with space charge (4/6)Transverse Landau damping with space charge (4/6)
Elias Métral, LIS meeting, 02/04/2007 22/29
From HB2006
Transverse Landau damping with space charge (5/6)Transverse Landau damping with space charge (5/6)
Stable point with octupole alone but unstable when SC
added
Unstable point with octupole alone but stable
when SC added
Elias Métral, LIS meeting, 02/04/2007 23/29
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?
Transverse Landau damping with space charge (6/6)Transverse Landau damping with space charge (6/6)
Elias Métral, LIS meeting, 02/04/2007 24/29
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
Elias Métral, LIS meeting, 02/04/2007 25/29
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
Elias Métral, LIS meeting, 02/04/2007 26/29
DecoherenceDecoherence without and with space charge at PS injection (3/4)without and with space charge at PS injection (3/4)
Elias Métral, LIS meeting, 02/04/2007 27/29
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)
Elias Métral, LIS meeting, 02/04/2007 28/29
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
Elias Métral, LIS meeting, 02/04/2007 29/29
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
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