Transcript スライド タイトルなし - Synchrotron SOLEIL

Comparison between Simulation
and Experiment on Injection
Beam Loss and Other Beam
Behaviours in the SPring-8
Storage Ring
Presented by Hitoshi TANAKA,
Contributors: Jun SCHIMIZU,
Kouichi SOUTOME, Masaru TAKAO
JASRI/SPring-8
1
Contents
1. Motivation
2. Simulation Model
3. Comparison between Simulation
and Experiments
4. Summary
5. Tentative FMA Results
2
1. Motivation
•In ideal top-up operation, reduction of injection
beam loss and suppression of stored beam
oscillation by frequent beam injections are
critically important.
•Aiming at understanding of mechanism of
injection beam loss and its suppression, a
precise simulation model has been developed.
Key: Precise simulation of particle motion
with a large amplitude (x=~10mm)
3
2. Simulation Model
2.1. Hamiltonian
H = p -h 
o
r(s )
{( 1 + 
( x(s) •ex, y(s)•ey )
r0(s )
s
ey
es
ex
Refs.
}
- e A x )2 - ( py - e A y )2
P0
P0
- e As ,
P0
(1)
p
where (x, px  px ),
0
py
(y,py  p ) ,
0
p-p
E-E
(s -v 0t, p p v 0 ), = p 0 ,
0 0
0
y
x
h1+
+
.
x (s) y (s)
)2 - ( px
1/2
[1] D.P. Barber, G. Ripken, F. Schmidt; DESY 87-036
[2] G. Ripken; DESY 87-036
4
2.2. Components and their Simplectic
Integration
(a) Bending Magnet
Equation (1) is integrated without expanding
the square root part.
Analytical solutions derived by E. Forest
are used for “rectangular” and “sector”
magnet integration.
Ref. [3] E. Forest, M.F. Reusch, D.L. Bruhwiler, A. Amiry;
Particle Accel.45(1994)65.
5
2.2. Component Model and Simplectic
Integration (2)
(b) Quadrupole and Sextupole Magnets
In this case, Eq. (1) has a separating form
of A(p) +V(x).
4th order explicit integration method is
adopted. Sextupoles are treated as thick
elements.
Refs.
[4] E. Forest and R.D. Ruth; Pysica D 43 (1990)105.
[5] H. Yoshida; Celestial Mechanics and Dynamical
Astronomy 56 (1993) 27.
6
2.2. Component Model and Simplectic
Integration (3)
(c) Other Magnets (except for IDs)
All other magnetic components are treated
as thin kicks.
Multi-pole up to 20 poles available.
(d) RF Cavities
(Ref. [1])
Cavities are treated as thin elements.
e A = -L  e  V(s) cos( 2k   +  ) + G 2k   sin , (2)
p0 s 2k p0
L
L
G =1 without Radiation, G=0 with radiation.
7
2.2. Component Model and Simplectic
Integration (4)
Ref. [6] M. Sands; Report SLAC-121
(e) Radiation Effects (1970).
Normalized photon energy spectrum +
random number ranging from 0 to 1
Radiation from BMs, QMs, SMs and IDs
are considered.
(f) Fringe Fields
Lowest order effect is only considered for
BMs, QMs and SMs. 1 2
(Ref. [3])
BM fringe -> H = Kx
 y  px
2
1 . (3)
,
K
=
x

(1+)2 - px2 - py2
8
2.3. Magnetic Errors
(a) Normal and Skew Quadrupole Errors
[7]
236 Q-error kicks and 132 SQ-error kicks
are considered. These strengths are
estimated by fitting measured beam
response with 4x4 formalism.
(b) Multipole errors
Systematic errors lower than 20 poles are
considered. 10pole for BM and 12pole for
QM.
Ref. [7] J. Safranek; NIMA 388 (1997)27.
9
2.4. ID Model
0-1
e Ax =
cos (kx x)cosh ( ky y)sin (kz  z)
p0
kz
-1 ky
-0 
sinh (kx x)sin ( ky y)sin (kz  z+)
kz  kx
e A =  -1 kx sin (kx x)sinh ( ky y)sin (kz  z)
0
p0 y
kz  ky
-
0-1
kz
(4)
cosh (kx x)cosh ( ky y)sin (kz  z+)
For ID integration, the square root of Eq.(1) is
expanded and the lowest order parts are only
integrated by means of a generating function.
Refs.
[8] K. Halbach; NIM 187(1981)109.
[9] E. Forest and K. Ohmi; KEK Report 92-14 (1992).
10
3. Comparison between
Simulation and Experiments
3.1. Amplitude Dependent Tune Shift
Set 1: chromaticity = (+7, +6)
0.5
0.3
0.2
Horizontal
0.1
0
0.4
Vertical
Tune (Fractional P art)
Tune (Fractional Part)
0.4
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
- [mrad] at Bump2
Vertical
0.3
0.2
Horizontal
0.1
0
0
Set 3: chromaticity = (+0.13, +0.13)
0.5
0
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
- [mrad] at Bump2
11
Amplitude [mm]
Amplitude [mm]
Amplitude [mm]
3.2. Smear of Coherent Oscillation
6
4
2
0
-2
-4
-6
-8
6
4
2
0
-2
-4
-6
-8
6
4
2
0
-2
-4
-6
-8
Experiment
SET-2
Hori.
Vert.
-300urad; 0.23mA/bunch
Simulation
SET-2
Refs. [10] K. Ohmi
et.al.; PRE 59
(1999)1167.
[11] J. Schimizu
et.al.; Proc. of
EPAC02 (2002)
p.1287.
Hori.
Vert.
-300urad; 0.23mA/bunch
SET-2
0
Simulation w/o Wake Field
200
400
600
Turn Number
Hori.
Vert.
-300urad
800
1000
12
3.3. Nonlinear Momentum Compaction
Alpha=+0.02627
0.04
Alpha=-0.02638
0
UVSOR 750MeV SR
UVSOR 750MeV SR
0.035
-0.01
0.03
-0.02
Alpha
Alpha
0.025
0.02
0.015
0.01
0.005
0
-0.0004
Ref.
Exp. (SF=0)
Exp. (SF=43.0)
Calc. (SF=0)
Calc. (SF=43.0)
Exp. (SF=25.8)
Exp. (SF=60.2)
Calc. (SF=25.8)
Calc. (SF=60.2)
-0.0002
0
f/f
0.0002
-0.03
-0.04
-0.05
-0.06
-0.07
0
0.0004 -0.0006 -0.0004 -0.0002
f/f
Exp. (SF=0)
Calc. (SF=0)
Exp. (SF=17.2)
Calc. (SF=17.2)
Exp. (SF=34.4)
Calc. (SF=34.4)
0.0002 0.0004
[12] H. Tanaka et.al.; NIMA 431(1999)396.
13
3.4. Nonlinear Dispersion
Ref. [12]
h()=h1 + h2 + h32 + h43 + h54 ….
150
20
measurement
calculation
measurement
calculation
100
10
h3 [m]
h2 [m]
50
0
0
-50
-10
-100
-150
-20
0
100
200
300
Path Length [m]
400
500
0
100
200
300
Path Length [m]
400
500
400
500
5 10 5
60000
measurement
calculation
40000
M easurement
Calculation
h5 [m]
h4 [m]
20000
0
0
-20000
-40000
-60000
0
100
200
300
Path Length [m]
400
500
-5 105
0
100
200
300
Path Length [m]
14
3.5. 3D Closed Orbit
Orbit Difference between
RF-A OFF and RF-A ON
0.1
RF-A
RF-B
Calculated Beam Energy along the Ring
8003
RF-D
Horizontal
x [mm]
0.05
RF-C
RF-D
0
-0.05
Beam Energy [MeV]
8002
359
718
1077
Path Length [m]
RF-A
RF-B
8001
8000
7999
7998
Calculation
Measurement
-0.1
0
RF-C
1436
7997
0
RF-A OFF (A: 0M V, Total: 12M V)
RF-A ON (A: 4M V, Total: 16MV)
359
718
1077
Path Length [m]
1436
15
3.6. Injection Beam Loss
3.6.1. Parameters of Injection Beam and
Injection scheme
•Ring Parameters
ex=2.8~6.6 nmrad, Coupling(ey/ex)=0.002
=0.0011, t=13 psec
nx=40.15, ny=18.35
Optical Functions at IP
bx=~23m, ax= -0.2
by=~7.5m, ay=-0.45
40
1.5
32
bx
b and b [m]
x
y
24
16
8
•Aperture Limit
0
Septum Inner wall: -19.5mm
-8
Chamber Aperture 70(H) / 40(V) mm -16
In-vacuum ID Vert. Lim.: min.7mm -24
hx
by
1
0.5
0
I.P.
Dispersion Function hx [m]
•Injection Beam Parameters
ex=220 nmrad, (ey/ex)=0.002
=0.0013, t=63 psec
Optical Functions at IP
bx=~13.5m, ax=-0.11
by=~13.7m, ay=-0.20
•Injection Bump System
Injection Point: x=-24.5mm
Bump height=~14.5mm
Bump Pulse Width=~8usec
(Revolution=~4.7usec)
-0.5
-1
16
3.6.2. ID Parameters(1)
#
19
20
9
10
11
12
13
16
22
24
29
35
37
39
40
41
44
45
46
47
Min.Gap
[mm]
12
7
9.6
9.6
9.6
9.6
9.6
12.9
9.98
9.6
8.8
9
8
8.6
8.3
9.6
9
8
8
9.6
Kx
1.3
1.1
Ky
1.8
2.1
2.1
2.2
2.2
2.2
2.2
2.4
2.9
1.4
2.4
2.3
2.6
2.3
1.0
2.0
2.3
1.7
1.5
2.1
Power Type
[kW]
35
14
8.8
9.6
9.9
9.6
9.8
7.4
12.3
4
11.2
10.8
13.3
10.9
3.5
8.1
10.9
1.4
8.1
9.1
In-Vacuum Long
In-Vacuum Hybrid
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum
In-Vacuum
In-Vacuum Figure-8
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Helical
In-Vacuum Standard
In-Vacuum Standard
In-Vacuum Vertical tandem
In-Vacuum Hybrid
In-Vacuum Standard
17
3.6.2. ID Parameters(2)
#
8
15
25
27
23
17*
Min.Gap
[mm]
25.5
20.0
20.0
30.0
37.0
36.0
36.0
36.0
20.0
Kx
1.1
3.4
4.8
3.9
3.4
4.2
Ky
11.2
2.2
3.4
4.6
5.4
3.4
5.8
Power Type
[kW]
18.04
5.4
5.6
2
6.6
Out-Vacuum Elliptical Wiggler
Out-Vacuum Revolver (Linear)
Out-Vacuum Revolver (Helical)
Out-Vacuum Helical tandem
Out-Vacuum Figure-8
Out-Vacuum APPLE-II (Circular)
Out-Vacuum APPLE-II (Linear)
Out-Vacuum APPLE-II (Vertical)
Installed but under commissioning
* ID 17 was recently installed in the ring. Gap of ID 17 is usually closed.
The phase is shifted so that the magnetic field is cancelled out at the
center. The field is no zero and nonlinear at the off-center.
18
3.6.3. Behaviour of Injection Beam (1-Calc)
7
Entrance of ID19
15
Beam Size (1 ) [mm]
Transverse Envelope of
Tracking Particles
20
10
5
0
-5
-10
-15
-20
0
200
400 600 800
Turn Number
4
3
2
1
0
200
400 600 800
Turn Number
1000
3
HHLV+4LLS s
50
by
2.5
Normal CG Cel ls
40
Mat ching Sect ion
30
bx
Normal CG Cel ls
2
1.5
20
1
hx
10
LSS
0
0
50
hx [m]
b x , b y [m]
5
0
1000
60
-10
Entrance of ID19
Hori.
Vert.
6
0.5
0
100
P ath Lengt h s [m]
-0.5
150
In simulation, particles
are mainly lost :
Septum wall (Hori.)
LSS beta-peak (Vert.)
IDs (Vert.)
19
3.6.3. Behaviour of Injection Beam (2-Calc)
Horizontal Phase Space
1
301
501
0.4
0.4
0.2
0.2
0
-0.2
Vertical Phase Space
1
301
501
0
-0.2
-0.4
-0.4
-0.6
-20-15-10 -5 0 5 10 15 20
x [mm]
-0.6
-8 -6 -4 -2 0 2 4 6 8
y [mm]
8100
Longitudinal Phase Space
1
301
-50
0
50
ds [mm]
501
8050
E [MeV]
0.6
y' [mrad]
x' [mrad]
0.6
Observation Point:
Entrance of ID19
8000
7950
7900
-100
100
20
3.6.4. Beam Loss v.s. Gap of ID47(1)
Measured Gap Dependence@High 
100
(x =7.2, y =4.0)
Measured Gap Dependence@Low 
100
(x =1.3, y =0.9)
ID47
ID47
95
90
gap=50mm
gap=15mm
gap=13mm
gap=12mm
gap=11mm
gap=10mm
gap=9mm
gap=8mm
85
80
gap=50mm
gap=20mm
gap=15mm
90
-2 10-5
Decay Constant [a.u.]
I/IINJ [%]
I/IINJ [%]
95
85
gap=12mm
gap=10mm
gap=8mm
De cay C on stan t v.s. ID Gap
-4 10-5
-6 10-5
-8 10-5
-0.0001
HC
LC
-0.00012
-0.00014
0
10
20 30 40 50
ID Gap [m m]
60
80
0
200
400
600
Turn Number
800
1000
0
200
400
600
Turn Number
800
1000
21
3.6.4. Beam Loss v.s. Gap of ID47(2)
ID Gap Dependence@Low 
ID Gap Dependence@High 
100
100
HC
95
95
HCm2
85
I/I40 [%]
I/I40 [%]
90
80
75
90
(x =7.2, y =4.0)
85
HCm2: Hamonic sextupole S1
+1.55%
(x =1.3, y =0.9)
70
gap.8mm
gap=6.4mm (10mm+1.8mmBUMP)
gap=5.6mm (9.2mm+1.8mmBUMP)
gap=4.8mm (8.4mm +1.8mmBUMP)
65
60
0
200
400
600
Turn Number
800
1000
80
gap=8mm
gap=7.4mm (11mm+1.8mmBump)
gap=6.9mm (10.5mm+1.8mmBump)
75
0
200
400
600
Turn Number
800
1000
22
Gap Dependence of Loss Rate @ID20
with Symmetry Restoration
1
0.95
0.9
0.85
0.8
G12_Exp
G12_SIM
G10_Exp
G10_Sim
G9_Exp
0.75
0.7
0
200
400
G09_Sim
G8_Exp
G8_Sim
G7_Exp
G7_Sim
600
Turn Number
800
1000
Beam Loss Rate Normalized by Rate at GFO [-]
Beam Loss Rate Normalized by Rate at GFO [-]
3.6.5. Beam Loss v.s. Symmetry
restoration of Optics
Gap Dependence of Loss Rate @ID20
without Symmetry Restoration
1
0.95
0.9
0.85
0.8
G12_Exp
G12_Sim
G10_Exp
G10_Sim
0.75
0.7
0
200
G9_Exp
G9_Sim
G8_Exp
G8_Sim
400
600
G7_Exp
G7_Sim
800
1000
Turn Number
23
3.6.6. Beam Loss v.s.Initial Condition (Calc)
0.5
Horizontal Phase Space
Vertical Phase Space
Lost
y' [mrad]
x' [mrad]
Survived
0.02
0
0.01
0
-0.01
-0.02
-0.5
-16 -14 -12 -10
x [mm]
0.006
0.004
-8
-6
Longitudinal Phase Space
Survived
Lost
0.002
[-]
Survived
Lost
-0.03
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
y [mm]
0
Lost particles have clear
correlation with
horizontal emittance .
-0.002
-0.004
-0.006
-60 -40 -20 0 20 40 60
ds [mm]
24
3.6.7. Beam Loss v.s. Beam Collimation (1)
1.0
Injection Efficiency
Chromaticity (+8, +8) 0.8
0.8
0.7
0.7
SSBT
0.6
0.5
0
1
simulation (2,2)
simulation (2,2)
w/o ID radiation
simulation (8,8)
simulation (8,8)
w/o ID radiation
2
3
4
5
Slit Width Normalized
by 1-Sigma of Beam Size
0.6
0.5
6
0.4
SSBT Transmission Rate
Chromaticity (+2, +2) 0.9
0.9
1.0
0.9
Injection Efficiency
1.0
0.8
0.7
Normal Optics
Chromaticity (+2, +2)
0.6
0.5
GFC+ID17 close
simulation
simulation w/o ID radiation
0
1
2
3
4
Slit Width Normalized
by 1-Sigma of Beam Size
Planner type IDs are only considered in the simulation.
5
25
3.6.7. Beam Loss v.s. Beam Collimation (2)
GFO+ID17open
GFC+ID17open
GFC+ID17close
Injection orbit is shifted
to septum wall by 2mm
GFO+ID17close
GFO_simulation
GFC_simulation
1
1
Normal Optics
Chromaticity (+8, +8)
0.9
Injection Efficiency
Injection Efficiency
0.9
0.8
0.7
0.8
ID40
0.6
0.5
0.5
1
2
3
4
Slit Width Normalized
by 1-Sigma of Beam Size
5
ID19 ( 25 m Long Undulator)
Gap=12mm
0.7
0.6
0
Normal Optics Slit Width = 1 
Chromaticity (+8, +8)
0
5
10
15
Number of ID
Planner type IDs are only considered in the simulation.
ID47
20
25
26
4. Summary(1)
•Developed simulator well describes nonlinear
particle motion in a storage ring. However, the
simulator can not explain injection beam loss
quantitatively.
•Possible causes are:
•Ambiguity in injection beam distribution
•Incorrect ID Modeling at especially large amplitude
•Nonlinearity not included in the model
•Some mistake in calculation, etc
27
4. Summary(2)
•Frequency Map Analysis (FMA) could be a
powerful tool to investigate mechanism of
injection beam loss.
•To use FMA effectively, we need “ a precise
ring model”.
28
5. Tentative FMA Results
Tune modulation in damping of
injection beam
0.4
0.4
ny
0.35
0.35
Normal Optics (+2, +2)
0.3
Normal Optics (+8, +8)
0.3
0.25
0.2
nx
0.15
Tune
0.25
Tune
ny
0.2
nx
0.15
0.1
0.1
ns
0.05
0
0
5000
1 104
Turn Number
ns
0.05
1.5 104
0
0
5000
1 104
Turn Number
1.5 104
29
FMA of Normal Optics w/o Errors
Chromaticity (+8, +8)
0.5
tune
1st
2nd
3rd
4th
5th
0.4
ny
0.3
0.2
0.4
3.000
2.375
1.750
1.125
0.5000
-0.1250
-0.7500
-1.375
-2.000
-2.625
-3.250
-3.875
-4.500
-5.125
-5.750
-6.375
-7.000
-7.625
-8.250
-8.875
-9.500
0.3
0.1
0.0
0.0
tune
1st
2nd
3rd
4th
5th
0.1
0.2
nx
0.3
0.4
0.5
0.2
0.3
3.000
2.375
1.750
1.125
0.500
-0.12
-0.75
-1.37
-2.00
-2.62
-3.25
-3.87
-4.50
-5.12
-5.75
-6.37
-7.00
-7.62
-8.25
-8.87
-9.50
30
Stability Map of Normal Optics w/o Errors
Chromaticity (+8, +8)
5
0
-0.4500
-0.9000
-1.350
-1.800
-2.250
-2.700
-3.150
-3.600
-4.050
-4.500
-4.950
-5.400
-5.850
-6.300
-6.750
-7.200
-7.650
-8.100
-8.550
-9.000
y[mm]
4
3
2
1
0
0
2
4
6
x[mm]
8
10
31
FMA of Normal Optics with Errors
Chromaticity (+8, +8)
0.5
tune
1st
2nd
3rd
4th
5th
0.4
ny
0.3
0.2
0.1
0.0
0.0
0.1
0.2
nx
0.3
0.4
0.5
tune
1st
2nd
3rd
4th
5th
0.4
1.000
0.4500
-0.1000
-0.6500
-1.200
-1.750
-2.300 0.3
-2.850
-3.400
-3.950
-4.500
-5.050
-5.600
-6.150
-6.700
-7.250
0.1
-7.800
-8.350
-8.900
-9.450
-10.00
0.2
1.000
0.4500
-0.1000
-0.6500
-1.200
-1.750
-2.300
-2.850
-3.400
-3.950
-4.500
-5.050
-5.600
-6.150
-6.700
-7.250
-7.800
-8.350
-8.900
-9.450
-10.00
32
Stability Map of Normal Optics with Errors
Chromaticity (+8, +8)
5
0
-0.5000
-1.000
-1.500
-2.000
-2.500
-3.000
-3.500
-4.000
-4.500
-5.000
-5.500
-6.000
-6.500
-7.000
-7.500
-8.000
-8.500
-9.000
-9.500
-10.00
4
y[mm]
3
2
1
0
0
1
2
3
4 5
x[mm]
6
7
8
33