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
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
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
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
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
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
“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
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]
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
What is going on here? What is the source for the emittance growth?
Wp3: Qx=22.42, Qy=20.82
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
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
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 !!!
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 !!!
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