MR: Space charge different particle distribution & working points

MR: Space chargedifferent particle distribution

& working points

Alexander Molodozhentsev

for MR-Group

June 21, 2006

Simulation approach…

Qx = 22.42 / Qy = 20.82 … for some reason (not clear yet)

Number of macroparticles = 15104

Transverse bin points = 128128

Longitudinal bin points = 128

Number of kicks per element = 2

Space Charge - ONRF - ON

Chromatic Sextupoles - ON

CPU_time/turn ~ 130 secSingle processor

Initial:Binomial Transverse distributionUniform Longitudinal distribution

What…

(1)

Initial (transverse) particle distribution to provide reasonable / practical Incoherent tune shift…

Estimation of Incoherent tune shift

Bf Nppbunch W F G( ) rpNppbunch F G

2 W( )2 W( )

3 W( ) Bf

Form_Factor=1(NO chamber) or 2 (image coefficients)Distribution_Factor=1(Uniform)_1.56…2(Gaussian)… as a function of Bunching_Factor

0

0.5

Bf Nppbunch 3000 2 1.56( )

Bf Nppbunch 3000 1 1( )

Bf Nppbunch 3000 1 1.56( )

Bf Nppbunch 3000 1 2( )

0.60.15 Bf0.1 0.2 0.3 0.4 0.5

0.4

0.3

0.2

0.1

0Incoherent Tune Shift

Form-factorDistribution-factor

Bf ~ 0.33

Bunching-factor

Beam from RCS:QINC ~ -0.15

Uniform

MJoho=1, RMS=100%/2(MJoho+1)

RMS = 54/4 = 13.5

xMAX = (4)1/2RMS

Initial transverse distributions (#1.3)

Footprint without walls

Qx0 = 22.42Qy0 = 20.82

Binomial - Parabolic


RMS = 54/6 = 9

xMAX = (6)1/2RMS



Qx0 = 22.42Qy0 = 20.82


Binomial - Gaussian


RMS = 54/8 = 6.75

xMAX = (8)1/2RMS


Qx0 = 22.42Qy0 = 20.82

X-Y plane: Initial particle distribution

MJoho=1 MJoho=2

MJoho=3

RMS and 99% emittance

0 50 100 150 200 250 300 350 400 450 500 550 600 6509.000

9.005

9.010

9.015

9.020

9.025

9.030

mJoho=2

H_RMS V_RMS

RM

S_E

mitt

ance

Number of Turns

0 50 100 150 200 250 300 350 400 450 500 550 600 650

48.8

49.0

49.2

49.4

49.6

49.8

50.0

mJoho=2Number of Turns

H_99% V_99%

99%

_Em

ittan

ce

Binomial - Parabolic MJoho=2, RMS=100%/2(MJoho+1)

RMS = 54/6 = 9

xMAX = (6)1/2RMS

Qx0 = 22.42Qy0 = 20.82

600 turns

RMS emittance variation during 10 turns

0 2 4 6 8 109.0000

9.0025

9.0050

9.0075

9.0100

9.0125

9.0150

9.0175

9.0200

H_RMS V_RMS

RM

S_E

mitt

ance

Number of Turns


RMS = 54/6 = 9

xMAX = (6)1/2RMS

RMS,X = 9.0023

RMS,Y = 9.0017

Initial RMS-Emittance

Binomial - Parabolic

Qx0 = 22.42Qy0 = 20.82

99% emittance: Gaussian & Parabolic

0 200 400 600 800 100042

43

44

45

46

47

48

49

50

99%

Em

ittan

ce H-mJoho3 V-mJoho3 H-mJoho2 V-mJoho2

Number of Turns

Qx = 22.42 / Qy = 20.82

Emittance variation

0 100 200 300 400 500 600 700 800 900 1000 11009.000

9.005

9.010

9.015

9.020

9.025

9.030

9.035

9.040

mJoho=2

H_RMS V_RMS

RM

S_

Em

ittan

ce

Number of Turns

0 100 200 300 400 500 600 700 800 900 1000 1100

48.8

49.0

49.2

49.4

49.6

49.8

50.0

50.2

50.4

mJoho=2Number of Turns

H_RMS V_RMS

99

%_

Em

itta

nce

Qx = 22.42 / Qy = 20.82

TD: Binomial - Parabolic

1000 turns

What is going on here?

What is the source for the emittance growth?

What is going on here? What is the source for the emittance growth?

“testHerd” which feels “mainHerd”

300 turnsX0 = 5, 10, 15, 20, 25 mmX0

/ = Y0 = Y0/ = 0

NO Coupling.

Wp3: Qx=22.42, Qy=20.82

“TAIL” particles



300 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0 Coupling…Sources: CCSX & SpCh

Wp3: Qx=22.42, Qy=20.82


“testHerd” which does NOT feel “mainHerd”

300 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0

Effect of Chromatic Sextupole Field…

Wp3: Qx=22.42, Qy=20.82

Coupling…Sources: CCSX !!!

[4,0]

Beam survival: scanning of QX: 22.20…22.50

0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.550.4

0.6

0.8

1.0

1.2

1.4

1.6

BEAM

SCRAPER

2x-2

z=3

2x-z

=24

2x=

45

PLUS:Sextupole-TILT (sigma=5e-4)PLUS: Q-strength-ERROR (sigma=5e-4)FF+CC+MER[3+5&6]

QV=20.78

Be

am

su

rviv

al

Horizontal fractional tune

ATAC’2 meeting, March 7, 2003

COSY Infinity

Betatron tune-shift budget

Incoherent

space-charge

tune shiftNppp =3.3 1014

Linear amplitude dependent tune-shift at 2 full=54mmmra

d

Chromatic tune shift after the linear correction p/p=0.01

Horizontal - 0.16 + 2.2 10-2 + 1.2 10-2

Vertical - 0.16 + 2.0 10-2

+ 1.7 10-3

ATAC’2 meeting, March 7, 2003

TAIL

CORE

Resonance region forthe 54 mm.mrad particles

4Qx = 90

Structure resonance


Wp3: Qx=22.42, Qy=20.82


“testHerd” which does NOT feel “mainHerd”

Effect of Chromatic Sextupole Field…

Wp3: Qx=22.333, Qy=20.774

300 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0


300 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0 Wp3: Qx=22.333, Qy=20.774


Effect of Sextupole Field & SpaceCharge




Wp3: Qx=22.333, Qy=20.774

300…600 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0

Initial conditions for the Test_Particle are NOT changed !!!


Wp3: Qx=22.333, Qy=20.774

600…1000 turnsX0 = 20, 22, 24, 26, 28 mmX0

/ = 0Y0 = 23, 25, 27, 29, 30 mmY0

/ = 0



Initial conditions for the Test_Particle are NOT changed !!!

RMS_emittance behavior

0 200 400 600 800 10009.00

9.01

9.02

9.03

9.04

9.05 H_RMS_w2 V_RMS_w2 H_RMS_w3 V_RMS_w3

RM

S e

mitt

ance

Number of Turns

w2: Qx = 22.333 Qy = 20.774

w3: Qx = 22.42 Qy = 20.82

0 200 400 600 800 10009.00

9.01

9.02

9.03

9.04

9.05

H_RMS V_RMS

RM

S e

mitt

ance

Number of Turns

99% emittance behavior

0 200 400 600 800 1000

48.6

48.8

49.0

49.2

49.4

49.6

49.8

50.0

50.2

50.4

H V

Qx=22.333

Qy=20.774

99%

em

ittan

ce

Number of turns0 200 400 600 800 1000

48.6

48.8

49.0

49.2

49.4

49.6

49.8

50.0

50.2

50.4 wp2_H wp2_V wp3_H wp3_V

99%

Em

ittan

ce

Number of Turns

w2: Qx = 22.333 Qy = 20.774

w3: Qx = 22.42 Qy = 20.82

MR: Space charge different particle distribution & working points

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