mr: space charge different particle distribution & working points
DESCRIPTION
MR: Space charge different particle distribution & working points. Alexander Molodozhentsev for MR-Group. June 21, 2006. Simulation approach…. Q x = 22.42 / Q y = 20.82 … for some reason (not clear yet). Number of macroparticles = 15 10 4. Transverse bin points = 128 128. - PowerPoint PPT PresentationTRANSCRIPT
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MR: Space chargedifferent particle distribution
& working points
Alexander Molodozhentsev
for MR-Group
June 21, 2006
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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
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What…
(1)
Initial (transverse) particle distribution to provide reasonable / practical Incoherent tune shift…
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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
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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
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Binomial - Parabolic
MJoho=2, RMS=100%/2(MJoho+1)
RMS = 54/6 = 9
xMAX = (6)1/2RMS
Initial transverse distributions (#2.3)
Footprint without walls
Qx0 = 22.42Qy0 = 20.82
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Initial transverse distributions (#3.3)
Binomial - Gaussian
MJoho=3, RMS=100%/2(MJoho+1)
RMS = 54/8 = 6.75
xMAX = (8)1/2RMS
Footprint without walls
Qx0 = 22.42Qy0 = 20.82
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X-Y plane: Initial particle distribution
MJoho=1 MJoho=2
MJoho=3
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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
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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
MJoho=2, RMS=100%/2(MJoho+1)
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
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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
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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
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What is going on here?
What is the source for the emittance growth?
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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
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“TAIL” particles
“testHerd” which feels “mainHerd”
What is going on here? What is the source for the emittance growth?
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
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What is going on here? What is the source for the emittance growth?
“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]
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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
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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
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TAIL
CORE
Resonance region forthe 54 mm.mrad particles
4Qx = 90
Structure resonance
What is going on here? What is the source for the emittance growth?
Wp3: Qx=22.42, Qy=20.82
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What is going on here? What is the source for the emittance growth?
“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
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What is going on here? What is the source for the emittance growth?
300 turnsX0 = 20, 22, 24, 26, 28 mmX0
/ = 0Y0 = 23, 25, 27, 29, 30 mmY0
/ = 0 Wp3: Qx=22.333, Qy=20.774
“testHerd” which feels “mainHerd”
Effect of Sextupole Field & SpaceCharge
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What is going on here? What is the source for the emittance growth?
“testHerd” which feels “mainHerd”
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 !!!
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What is going on here? What is the source for the emittance growth?
Wp3: Qx=22.333, Qy=20.774
600…1000 turnsX0 = 20, 22, 24, 26, 28 mmX0
/ = 0Y0 = 23, 25, 27, 29, 30 mmY0
/ = 0
“testHerd” which feels “mainHerd”
Effect of Sextupole Field & SpaceCharge
Initial conditions for the Test_Particle are NOT changed !!!
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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
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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