Details of space charge calculations for J-PARC rings.

38
Details of space charge calculation s for J-PARC rings

Transcript of Details of space charge calculations for J-PARC rings.

Page 1: Details of space charge calculations for J-PARC rings.

Details of space charge calculations for J-PARC rings

Page 2: Details of space charge calculations for J-PARC rings.

J-PARC accelerator complex

– Phase 1 + Phase 2 = 1,890 Oku Yen (= $1.89 billions if $1 = 100 Yen).

– Phase 1 = 1,527 Oku Yen (= $1.5 billions) for 7 years.– JAERI: 860 Oku Yen (56%), KEK: 667 Oku Yen (44%).

JAERI Portion

KEK Portion

Page 3: Details of space charge calculations for J-PARC rings.

Repetition of 3GeV Synchrotron

• injection    500μs• injection turns   ~350• particles per pulse   8.3e13

• acceleration    20 ms

• extraction     <1μs

injection

extraction

acceleration

Page 4: Details of space charge calculations for J-PARC rings.

Repetition of 50 GeV Synchrotron

• injection    0.17s• particles per pulse    3.3e14

• acceleration     1.96 s

• extraction (slow)   0.7sinjection

extraction

acceleration

Page 5: Details of space charge calculations for J-PARC rings.

Two approaches

• A whole cycle of 3 GeV synchrotron takes 20 ms.– Full simulation with self-consistent model is possible.– Tracking parameters (# of macro particles, grid size, etc)

have to be optimized.

• Only injection period of 50 GeV synchrotron takes 0.6 s (or a bit less).– Not realistic to make self-consistent simulation.– Frozen space charge model might be justified because of well defi

ned particle distribution.

Page 6: Details of space charge calculations for J-PARC rings.

Examples of full tracking for 3GeV Syn.

Different colors shows results of differentnumber of macro particles.

Things are included.• Injection painting• Multipole errors• Misalignment• Acceleration• Aperture of all elements• Image in a circular pipe

3 months (100,000)

5 weeks (50,000)

2 weeks (20,000)

Results within 3 months (1,000,000~200,000)

Things are not included.• Scattering at foil.• RF jitter• Impedance

Page 7: Details of space charge calculations for J-PARC rings.

Other tracking parameters

Number of azimuthal mode

Number of z grids

Max. mode= 4, 8, 16

z grids= 10, 20, 30, 40, 50

Page 8: Details of space charge calculations for J-PARC rings.

Detailed study results

• Correlated and anti-correlated painting• COD and beam loss

– Coupled with strong chromaticity correction sextupole, COD introduces nonlinearity of all harmonics.

• Beam intensity dependence

Page 9: Details of space charge calculations for J-PARC rings.

Correlated and anti-correlated painting

There is particle loss even during injection period.

correlatedanti-correlated

0.5 s for injection

Page 10: Details of space charge calculations for J-PARC rings.

Phase space density right after injection and at 3 ms later

horizontal vertical

at 0.5 ms

at 3 msat 3 ms

at 0.5 ms

correlatedanti-correlated

Page 11: Details of space charge calculations for J-PARC rings.

COD and beam loss

rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm

Coupled with strong chromaticity correction sextupole, COD introduces nonlinearity of all harmonics.

Page 12: Details of space charge calculations for J-PARC rings.

Phase space density for different COD

• No difference in core density.• Tails are developed with COD.

rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm

rms COD 0 mm 0.2 mm 0.5 mm 1.0 mm

Hor. Ver.

Page 13: Details of space charge calculations for J-PARC rings.

Beam intensity dependence

30mA

20mA

cf. 30mA is design value which deliver 0.6 MW beam from RCS with tune spread of ~0,25.

Page 14: Details of space charge calculations for J-PARC rings.

Intensity dependence

• Core density is reduce with 30 mA. (lower order resonance is involved?)• Tails are also developed.

20mA30mA

20mA30mA

Page 15: Details of space charge calculations for J-PARC rings.

Summary of self-consistent simulation

• A whole cycle of 3 GeV Syn can be simulated even though it takes a few months.

• Horizontal and vertical coupling is the source which makes anti-correlated painting worse.

• Increase of particle loss due to larger COD is attributed to tail development. Higher order effects are involved.

• Intensity limitation may be explained with lower order resonance. That is a regime where coherence picture is applicable.

Page 16: Details of space charge calculations for J-PARC rings.

Example of beam loss during injection with frozen space charge model

Model assumes• Particle distribution is Gaussian.• Emittance is constant.• dp/p is finite and there are synchrotron oscillations.• Transverse space charge force depends on longitudinal position.

Page 17: Details of space charge calculations for J-PARC rings.

Tracking model

• “Frozen model” of space charge is adopted.– Space charge potential is fixed throughout a tracking.– No self-consistency.– No coherent oscillations.– Gaussian charge distribution in 3D is assumed.

• Lattice nonlinearities and misalignment errors are included.• Aperture of magnets and collimator are included so that we can

estimate beam loss.• Macro particles (1,000) of 3D Gaussian distribution with 2 sigma

cut are tracked for 0.12s (original design value for accumulation) or more.

Page 18: Details of space charge calculations for J-PARC rings.

Some numbers

• Emittance(2sigma) 54 pi mm-mrad (36pi, 45pi, 64pi)

• Acceptance at collimator 71 pi mm-mrad for H and V• Acceptance at magnets > 81 pi mm-mrad• Circulating current 10 A (3.3E14 ppp)• Incoherent tune shift -0.16• Bare tune (22.42, 20.80)

Page 19: Details of space charge calculations for J-PARC rings.

COD

• Chromaticity sextupoles coupled

with COD introduce beta modulation

and higher harmonics of nonlinearity.

• Survival at 0.12s after injection.

• COD shows a rms value.

Maximum is about 3 times.

• Collimator aperture is adjusted

taking a local COD into account.

• We expect COD(rms) is less than

0.5mm after correction.

• The loss is not linear as COD.

sur

viva

l at 0

.12s

(%)

80

85

90

9

5

10

0

0 0.5 1.0 1.5 2.0 COD (rms) (mm)

Page 20: Details of space charge calculations for J-PARC rings.

Different lattices

• Although rms COD is almost same,

different lattices (seeds) give

different results.• Previous example is the worst

case among three.

sur

viva

l (%

)96

97

9

8

99

10

0

0 0.05 0.1 time (s)

Page 21: Details of space charge calculations for J-PARC rings.

Beam current

• The pattern of COD is the

same for both. Magnitude is

different.

• The design current is 10A.

Blue: COD=0.5mm

Red: COD=1.0mm

sur

viva

l at 0

.12s

(%)

80

85

90

9

5

10

0

0 5.0 10 15 beam current (A)

Page 22: Details of space charge calculations for J-PARC rings.

Initial emittance

• Acceptance at collimator is fixed at

71 pi mm-mrad.

• Space charge force is fixed according

to the initial emittance.

• We expect 54 pi mm-mrad emittance

shaped at the 3-50BT collimator.

• Collimator acceptance should be

optimized to have the maximum

survival.

sur

viva

l at 0

.12s

(%)

80

85

90

9

5

10

0

30 40 50 60 70 80 initial emittance (pi mm-mrad)

Page 23: Details of space charge calculations for J-PARC rings.

Location of loss

COD Magnet acceptance

Collimator acceptance

Initial emittance

Loss at collimator

Loss at magnet

Total number

0mm > 81 pi

mm-mrad

71 pi

mm-mrad

54 pi

mm-mrad

3 (100%) 0 (0%) 3/1000

0.2 > 81 pi 71 pi 54 pi 4 (100%) 0 (0%) 4/1000

0.5 > 81 pi 71 pi 54 pi 11 (92%) 1 (0%) 12/1000

1 > 81 pi 71 pi 36 pi 33 (97%) 1 (3%) 34/1000

1 > 81 pi 71 pi 45 pi 33 (92%) 3 (8%) 36/1000

1 > 81 pi 71 pi 54 pi 21 (88%) 3 (12%) 24/1000

1 > 81 pi 71 pi 64 pi 59 (88%) 8 (12%) 67/1000

Page 24: Details of space charge calculations for J-PARC rings.

Beam loss at collimator (h=18)total 0.72 MW

COD 0 mm 0.2 mm 0.5 mm

Loss 670 W 800 W 1370W

COD (rms) = Red: 0mm Yellow: 0.2mm Green: 0.5mm

1000

980

960

940

920

900

survival

0.60.50.40.30.20.10.0

time [s]

All the particles hit collimator first.

Page 25: Details of space charge calculations for J-PARC rings.

Beam loss at collimator (h=18)total 0.58 MW

COD 0 mm 0.2 mm 0.5 mm

Loss 350 W N/A 690 W

COD (rms) = Red: 0mm Yellow: 0.2mm Green: 0.5mm

1000

980

960

940

920

900

survival

0.60.50.40.30.20.10.0

time [s]

All the particles hit collimator first.

Page 26: Details of space charge calculations for J-PARC rings.

Frozen model with acceleration

phis

bunch length dp/p

Page 27: Details of space charge calculations for J-PARC rings.

300

280

260

240

220

200

2.52.01.51.00.50.0-0.5

horizontal vertical

300

280

260

240

220

200

2.52.01.51.00.50.0-0.5

horizontal vertical

1000

990

980

970

960

950

940

1.51.00.50.0-0.5

1000

990

980

970

960

950

940

1.51.00.50.0-0.5

99% emittance and beam loss

Acceleration starts right after injection.

Acceleration starts at 0.16 s after injection.

Page 28: Details of space charge calculations for J-PARC rings.

300

280

260

240

220

200

2.52.01.51.00.50.0-0.5

horizontal vertical

1000

990

980

970

960

950

940

1.51.00.50.0-0.5

Acceleration starts at 0.6 s after injection and h=18.

Page 29: Details of space charge calculations for J-PARC rings.

Single particle behavior

• Tracking without aperture limit

to see single particle behavior.

• Slow growth of amplitude.• Not obvious correlation with

synchrotron oscillations. Trapping?

Timing ofhitting collimator

0 0.01 0.02 0.03 0.04 0.05 time (s)

hori

zont

al p

osit

ion

(m)

-0.1

-0.0

5

0

0.5

0

0

.1

Page 30: Details of space charge calculations for J-PARC rings.

Single particle behavior

• Track a single particle which is lost in 0.6 s.• Look at betatron oscillation amplitude and transverse tune as a f

unction of turn until a particle is lost.

• For example, there are– 38 lost particles (out of 1000) when rms COD is 0mm.– 40 lost particles (out of 1000) when rms COD is 0.2 mm.– 52 lost particles (out of 1000) when rms COD is 0.5 mm.

Page 31: Details of space charge calculations for J-PARC rings.

#1 #2 #3

#5 #6#4

H

V

H

V

turn number (~ 10,000 turns)

ampl

itud

e

rms COD is 0.5 mm

Page 32: Details of space charge calculations for J-PARC rings.

H

V

H

V

#7 #8 #9

#11 #12#10

turn number (~ 10,000 turns)

ampl

itud

e

rms COD is 0.5 mm

Page 33: Details of space charge calculations for J-PARC rings.

H

V

• Horizontal amplitude always increases and gets to the aperture limit.• Vertical amplitude always decreases. Coupling between H and V is manifest.

#16

#15#14#13

H

V

turn number (~ 10,000 turns)

ampl

itud

e

rms COD is 0.5 mm

Page 34: Details of space charge calculations for J-PARC rings.

In tune space

Blue points are intermediatetune of lost particles.Red points are tune just beforeparticles are lost.

Tune before particle loss aresame with and without COD.

2x-y=24

x-2y=-19

bare tune

x-22 x-22

y-2

0

y-2

0

Page 35: Details of space charge calculations for J-PARC rings.

Coupling between H and V is manifest, but

• Tune space plot does not show resonance driving term.– 2x-y=24 is skew and cannot be excited even with finite dp/

p and dispersion in a lattice.• If there is any way to reduce a driving term.

– Since the source is not identified, it is difficult.

Page 36: Details of space charge calculations for J-PARC rings.

Summary of frozen space charge simulation

• Particle loss occurs because horizontal amplitude increases and hits the collimator aperture. The source of the increase is a coupling between H and V.

• With finite COD, particle loss occurs with less turns. However, transverse tune when a particle loss occurs does not depend on COD magnitude.

• Loss is very slow process: the order of 104 turns. Time scale of horizontal and vertical coupling is also same order.

Page 37: Details of space charge calculations for J-PARC rings.

Basic loop of calculation

Advance particle coordinatesdo ip=1,np (200,000)

Calculate space chargepotential based onparticle positions.

do imode=1,nmode (16)

Apply space charge kicksto all particles

do ip=1,np (200,000)

Simpsons uses Fourierexpansion in azimuthaldirection.

Make parallel processingof Fourier modes.

Page 38: Details of space charge calculations for J-PARC rings.

Distribution of workload (4 CPUs) with MPI

imode=3,4,5,6

imode=0,1,2

imode=7~11

imode=12~16

Add up all E-fields4 CPU worksin the same way