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description
Review of the two-stream instability: beam and Ion instability
3rd Low Emittance Ring Workshop,
Oxford University, 8-10 July 2013
Lanfa Wang, SLAC
TWO-STREAM INSTABILITIES
Electron beam and ion-cloud
Positron/proton beam and electron cloud
(schematic)
Low Emittance'13 L. Wang 2
3Low Emittance'13 L. Wang
Contents
Reviews of ObservationsReviews of theories in linear regimeBeam ion instability in nonlinear regimeMitigationsSummary
I apologize for many works which couldn't be
mentioned here!
Reviews of Observations
5Low Emittance'13 L. Wang
Early Observation of vertical beam size blow-up in ELETTRA
ELETTRA
C. J. Bocchetta, et. al. 1153, EPAC94, 1994
Beam current effect(Beam energy 1.1 GeV)
Beam filling pattern effect
Before beam current threshold
After threshold
100%96%
75%
6Low Emittance'13 L. Wang
First Direct Observations--ALS, with Helium added, 1997(J. Byrd et al., PRL, 79 (1997), 79
ALS y~30m
a factor of 2–3 increase in the vertical beam size
Nominal0.25nTorr
He added
Vertical sideband Vertical emittance growth
Single bunch train with 26% gap, Nb=240, 240mA
7Low Emittance'13 L. Wang
Pohang Light Source (1998)
Single bunch train 250 bunches (46% gap), 180mA
No beam ion instability observed at normal condition (although a instability is expected).
Instability observed with injection of Helium Bunch size blowup of ~ 2y and the
oscillation amplitude of ~ 0.75 y. Suppression of the FBII was also
demonstrated in the presence of the multiple gases or an extra clearing gap in the bunch train.
0.4ntorr0.7mA
Ion pumps off0.64mA
0.2ntorr He0.61mA
3.34ntorr He0.52mA
3.34ntorr He0.6mA
3.34ntorr He0.6mA
J. Y. Huang, et al., Phys. Rev. Lett. 81, 4388 (1998)
Non-monotonic growth
head
tail
8Low Emittance'13 L. Wang
KEK ATF
Bunch 1
Bunch 5
Bunch 15
Bunch 3
Bunch 12
N. Terunuma1, et.al. EPAC08
9Low Emittance'13 L. Wang
SSRF with nominal vacuum 2010 (Bocheng Jiang, et. al. NIMA 614, 2010)
Single bunch train with bunch Number 450, 37.5% gap (0.54s)
Beam current: 200mA Vertical emiittance: 27.3pm Horizontal emittance 3.9nm
Question: Is it true emittance growth?
y=2.04
y=0.61
y=2.04
Vertical beam size measured from the interferometer
amplitude of bunch centroid from BPM
y=0.61
10Low Emittance'13 L. Wang
Observation in SPEAR3(L. Wang, et. al. MOPS090, IPAC11)
Beam spectrum, 200mA, single bunch train Vertical amplitude along the single bunch train
0
0.5
1
1.5
2
Skew Quadpoles on
0 5 10 15 20 25 300
0.5
1
1.5
Amp( m)
Skew Quadpoles off
f(MHz)
Coupling effect, Singe bunch train 192mA
0
5
10
15P=0.37nTorr
0
5
10P=0.86nTorr
0
5
10P=1.29nTorr
0 20 40 60 80 1000
5
10
Amp(m)
P=1.75nTorr
f(MHz)
=2.0 in all cases
05
1015
100200
300
0
5
10
15
a) Osc. Envelopes in Time Domain
Am
pli
tud
e ( m
)
010
0200
0
0.5
1
Time (ms)
b) Evolution of Modes
Mode No.
m
(courtesy Dmitry Teytelman)
Vacuum pressure effect (by turning off vacuum pump)
6 bunch train
11
Resistive wall Instability (RW) in SEPAR3
Low Emittance'13 L. Wang
12
2)sgn(1)(
03
0
Z
c
b
LZiZ
The resistive wall impedance
0 5 10 15 20 25 30 35 400
10
20
30
40
50
60
70
80
f (MHz)
amp
( m
)
y=2.0
0 20 40 60 80 100 1200
20
40
60
80
100
120
140
160
180
f (MHz)
amp
( m
)
y=-2.5
Six bunch train=0.9RW
Uniform filling=5.4RW only Ion effect is hard to see
Recent experiment in SPEAR3 shows an instability (resistive wall type) threshold with chromaticity about 0.9 with 4 and six bunch train, 500mA beam
Vertical low sideband: stronger vertical instability (1) uniform filling pattern (2) multiple bunch train filling with low chromaticity
(1) (2)
12Low Emittance'13 L. Wang
Summary of the Observations
(Vertical) Coupled bunch instability
(Vertical) Beam Emittance growth
The growth in amplitude and beam size is always small,
order of beam size
The growth in amplitude and beam size along the bunch is
not necessarily monotonic
Remain Questions:
Why the predicted instability is much faster? ( 1ms vs. 16ms in
PLS)
Can we explain the non-monotonic growth in the experiment?
(Note that Linear theory shows faster growth for the tail
bunches)
Reviews of theories in linear regime
14Low Emittance'13 L. Wang
-0.4 -0.2 0 0.2 0.40
0.2
0.4
0.6
0.8
1
X (mm)
BeamIon(Analytic)Ion (numerical)
beam size
x=0.1mm
y=0.004472mm
Ion distribution (steady status)
2
2
04
0000 42
1)(),()(
2
2
x
x
xx
xKedxxxxfx x
)8
log(2
1)(
2
24 2
2
x
x
x
xex xThe distribution at x0 is
[P.F. Tavares, CERN PS/92-55 (LP) (1992), also L. Wang, PRSTAB14, 084401 (2011) ]
The ion-cloud has sharp peak near center, non-Gaussian Ion dimension is smaller than the electron bunch and simply decided by the
electron bunch
1D theory
=0.577215
15Low Emittance'13 L. Wang
First prediction of Fast Ion Instability (FII),1995
Single bunch train Single gas species Linear space charge force Constant beam size
Good model for FODO lattice
Quasi-exponential growth
10 20 30 40 50 60 7010
-4
10-3
10-2
10-1
100
Turns(1/2)
Am
p (
)
T.O. Raubenheimer and F. Zimmermann, Phys. Rev. E52, No. 5, 5487 (1995).
2/12/32/3
2/12/12/1
33
41
A
SnNrcr
yxy
Bbyipe
c
cte /
e-bunch size
Bunch population N Bunch Spacing
Mass number
Bunch number
Ion density ')'( zkT
Pz ei
Linear regime
Nonlinear
Simulation
1sigma
16Low Emittance'13 L. Wang
FII with the variation of beam size (beam optics), 1996(Gennady Stupakov, KEK Proceedings 96-6)
2/1
,,, )(
2
xyyxb
peyxi kAS
rNc
0 20 40 60 80 100 12024
26
28
30
32
34
36
38
40
42
S (m)
f y (
MH
z)
Calculated oscillation frequency of CO+ along the SPEAR3 ring, 500mA
Exponential growth
rmsiixyy
iye
e
cr
/
1
)(3
1
Note that it doesn’t apply when i is close to zero (constant beam size);
Single bunch train Single gas species Linear space charge force Variation of the beam size (optics effect) good for weak instability and lattice with
large frequency spread
17Low Emittance'13 L. Wang
Wake field Model (Nonlinear space charge force), 2007- 2011
1. L. Wang, Y. Cai, and T. O. Raubenheimer, PAC20072. E. Kim and K. Ohmi, Japanese Journal of Applied Physics 48 (2009) 0865013. L. Wang, Y. Cai and T. O. Raubenheimer, H. Fukuma. PRSTAB 14, 084401, 2011
The nonlinear space charge force is included. The Q of the wake represents the nonlinearity of the E-force. Typically, it is below 10.
The wake has good linearity when the bunch offset is smaller than the beam size where the fastest instability occurs
0 10 20 30 40 50 60 70-8000
-6000
-4000
-2000
0
2000
4000
6000
8000
10000
Z (m)
Wy (
m-2)
Numerical MethodAnalytical Method
Comparison with analysis
)sin()(
1
3
4)( 2
c
se
csW iQc
s
xyye
iii
2/1
, )(3
4
2
yyx
peyi A
rcf
18Low Emittance'13 L. Wang
FII with nonlinear space charge force, 2009 (E. Kim and K. Ohmi, Japanese Journal of Applied Physics 48 (2009) 086501)
Single bunch train Single gas species Constant beam size (no beam optics) with nonlinear space charge force (Q in the wake field)
Note that the ion cloud is assumed to be the same dimension as the electron bunch in their study!
When Q=0, got similar solution as Tor and Frank, When Q is finite and short distance (time)?, the exponential growth rate
per revolution of the tail bunch with the train length
cte /
19Low Emittance'13 L. Wang
How can we get good model to compare with the experiments?
A realistic model should include the following in one analysis:
1. The nonlinear space charge force
2. The real beam optics (variation of the beam size)
3. The realistic vacuum (multiple gas species, variation along
the ring, important to compare with observations)
4. The chromaticity
5. …
Note All these factors provide damping to the beam ion
instability.
20Low Emittance'13 L. Wang
An accurate model with nonlinear space charge, realistic beam optics and multiple gas species vacuum, 2012, 2013
1. SLAC-PUB-15353: L. Wang, J. Safranek, T. O. Raubenheimer, M.Pivi, 20122. SLAC-PUB-15638, L. Wang, J. Safranek, Y. Cai, J. Corbett, B. Hettel, T. O. Raubenheimer, J.
Schmerge and J. Sebek, 2013, submitted to PRSTAB
The total wake function of ions along the whole ring
CicQ
zs
xyye
iyiring ds
c
zse
sss
s
c
szW
i
0
2
)(, )
)(sin(
))()()((
1)()(
3
4)( 0
0 50 100 150 200 250 300 350
0
2
4
6
8
10
12
14
f (MHz)
Z (
M
/m)
H2
CH4
H2O
COCO
2
all
(b)
Impedance of ion cloud in ILC DR with KCS configuration. The total pressure is 0.5nTorr. The partial pressure is 48%, 5%, 16%,14% and 17% for H2, CH4, H2O, CO and CO2 gas, respectively.
Impedance directly relate to beam optics and vacuum, and growth rate
21
Compassion with simulation and experiment
Low Emittance'13 L. Wang
py
ee pMZT
cMrNi ))((
2 020
When the beam is evenly filled along the ring, the exponential growth rate
2402602803003203403600
50
100
150
200
250
300
350
400
Mode Number
Gro
wth
rate
(1/s
ec)
H2
CH4
H2O
COCO
2
Total growth rate
0 5 10 1510
-4
10-3
10-2
10-1
100
101
Time (ms)
Am
p ( m
)
(a)
analysis
Simulation
The fast growth time is 2.72 ms and 3.18 ms from analysis and simulation.
Experimentally, the growth time is close to, but slightly shorter than radiation the damping time of 5.0 ms
SPEAR3, Six bunch train, 500mA. P=0.37nTorr
SLAC-PUB-15638, 2013
22Low Emittance'13 L. Wang
0 50 100 150 200 250 300 350
0
2
4
6
8
10
12
14
f (MHz)
Z (
M
/m)
H2
CH4
H2O
COCO
2
all
(b)
Summary of Damping factors
Damping mechanism Nonlinear space charge force Beam optics Multiple gas species
Linear force only
Q~
Non-Linear space charge force
Q~10
With realistic Optics
Q~4 (SPEAR3) ~2 (ILC DR)
Ion induced impedance in ILC Damping ring
Sharp spectrum broadbroader
Multiple gas species
Much broader
opticsring QQQ
111
0
opticsQ
Beam ion instability in nonlinear regime
24Low Emittance'13 L. Wang
Instability at nonlinear regime
Theory (S. A. Heifets, SLAC Report No. SLAC-PUB-7411, 1997)
A linear Growth at saturation (Y>beam size)
Tr is the revolution period
0 500 1000 1500 2000 2500 300010
-6
10-5
10-4
10-3
10-2
10-1
100
101
Turns
Am
p (
)
Simulation Experiment
The amplitude of beam ion instability saturates at order of beam sigma although the instability can be very fast in the linear regime.
Slow growth with amplitude beating which can be well explained!
Mitigations
26Low Emittance'13 L. Wang
Mitigations
Mitigations Better Vacuum: heavy ions are more important, large cross section, more stable. Beam filling pattern (almost free):
1. long bunch train gap (most existing light source use it);
2. multiple bunch train with short gap (very effective for low emittance, high beam current
machine, future ultra low emittance machine );
3. longer bunch spacing (work in some case, such as APS, high bunch charge with longer
bunch pacing) Chromaticity Clearing electrode (not recommended)
Suitable for small ring only due to impedance contribution
(a)Eva S. Bozoki and Henry Halama, NIMA A307 (1991) 156-166)
(b) M. Zobov, Journal of Instrumentation 2, P08002 (2007)
Beam Shaking (not recommended): E. Bozoki and D. Sagan, Nucl. Instrum. Meth. A340, 259(1994)
Feedback
Natural Damping mechanism Nonlinear space charge force; Beam optics; Multiple gas species ; Frequency spread along the bunch trains(weak)
27Low Emittance'13 L. Wang
Filling pattern effect: Observation in SPEAR3(L. Wang, et. al. MOPS090, IPAC11)
Now SPEAR3 using 4-6 bunch train and a slightly larger chromaticity to completely suppress the instability!!
Beam filling pattern effect, 500mA, vertical chromaticity 2 SPEAR3 beam filling pattern
1
2
3
4
One Bunch Train
1
2
3
4
Four Bunch Train
0 10 20 30 40 50 60
1
2
3
4
Amp( m)
Six Bunch Train
f(MHz)
28Low Emittance'13 L. Wang
0 50 100 150 2000
0.2
0.4
0.6
0.8
1
f (MHz)
Z (
M
/m)
One bunch trainTwo bunch trainFour bunch trainSix bunch train
2002503003500
100
200
300
400
500
600
700
800
Mode No.
Go
wth
rate
(1/s
ec)
One bunch trainTwo bunch trainFour bunch trainSix bunch train
Multiple bunch train effect in SPEAR3: Theory and SimulationSimulation and analyses can predict the multiple bunch train effect! Both agree well with the observation (SLAC-PUB-15638)
Simulation, single bunch train
Radiation damping
0 5 10 15 2010
-3
10-2
10-1
100
101
102
Time (ms)
Y (
m)
one bunch-train, =0.38mstwo bunch-trains, =0.93msfour bunch-trains,=1.60mssix bunch-trains, =1.62ms
H2
CO2CO
H2O
CO2H2O
H2 is very weak
Simulation
Analysis, 0.37ntorr
Instability driven by H2 is damped by radiation damping in most case!
29Low Emittance'13 L. Wang
0 50 100 150 2000
0.2
0.4
0.6
0.8
1
f (MHz)
Z (
M
/m)
One bunch trainTwo bunch trainFour bunch trainSix bunch train
2002503003500
100
200
300
400
500
600
700
800
Mode No.
Go
wth
rate
(1/s
ec)
One bunch trainTwo bunch trainFour bunch trainSix bunch train
Multiple bunch train effect in SPEAR3: Theory and SimulationSimulation and analyses can predict the multiple bunch train effect! Both agree well with the observation (SLAC-PUB-15638)
Simulation, single bunch train
Radiation damping
0 5 10 15 2010
-3
10-2
10-1
100
101
102
Time (ms)
Y (
m)
one bunch-train, =0.38mstwo bunch-trains, =0.93msfour bunch-trains,=1.60mssix bunch-trains, =1.62ms
H2
CO2CO
H2O
CO2H2O
H2 is very weak
Simulation
Analysis, 0.37ntorr
Instability driven by H2 is damped by radiation damping in most case!
1
2
3
4
One Bunch Train
1
2
3
4
Four Bunch Train
0 10 20 30 40 50 60
1
2
3
4
Amp( m)
Six Bunch Train
f(MHz)
30Low Emittance'13 L. Wang
Chromaticity effect in SPEAR3: experiment and analysis
123
y=2.0,=10hrs
123
y=3.1,=8.8hrs
123
y=4.2,=8.1hrs
123
y=5.1,=7.0hrs
123
y=6.2,=6.0hrs
0 10 20 30 40 50 600123
Amp( m)
f(MHz)
y=7.0,=4.7hrs
single bunch train, 500mA
2002503003500
100
200
300
400
500
600
700
800
Mode No.
Go
wth
rat
e (1
/sec
)
chromaticity=0chromaticity=2chromaticity=4chromaticity=6chromaticity=8
p
ceff zeZZ222 /)()( /0
The effective impedance of a bunched beam is given by
Analysis
(L. Want, et. al. SLAC-PUB-15638)
31Low Emittance'13 L. Wang
Bunch-by-bunch Feedback
(A. W. Chao and G. V. Stupakov, KEK Proceedings 97-17, 110 (1997))
Noise in the feedback:Noise in the pickup or amplifier may be transferred to the kicker, which then induces some jitter on the beam. The net result of the feedback is that the beam will reach certain rms oscillation amplitude which is determined by the feedback damping and noise
010
2030
100200
300
0
10
20
30
Am
pli
tud
e (
m)
0
20
0
200
0
2
4
6
Time (ms)
b) Evolution of Modes
Mode No.
m
(a)
0
20100
200300
0
10
20
30
Time (ms)
a) Osc. Envelopes in Time Domain
Bunch No.
m
010
2030
0100
200300
0
2
4
6
Time (ms)
b) Evolution of Modes
Mode No.
Am
pli
tud
e (
m)
(b)
The feedback is initially turned off and turned on around 20ms. Close to uniform filling, total beam current of 448mA
(courtesy Dmitry Teytelman)Test in SPEAR3
32Low Emittance'13 L. Wang
Summary and discussion (1/2)
Many observations included normal machine condition
The instability can be well explained using Impedance
model, which includes nonlinear space charge, realistic
beam optics, multiple gas species vacuum and chromaticity;
There are reasonable good agreements in SPEAR3: growth
rate, filling pattern effect, beam spectrum (frequency), etc.
The beam ion instability is broad band due to the beam
optics and multiple gas species in the vacuum. It is
essential to includes both of them in analysis and simulation
(Most of ) the experiment results are in saturation regime:
small amplitude in the order of beam size and non-monotonic
growth along the bunch train!
33Low Emittance'13 L. Wang
Summary and discussion (2/2)
Some issues need to be addressed
There is a difficulty to separate the coupled instability and
emittance growth in the experiment if average method is
used.
The initial experiment shows feedback works to suppress
the instability amplitude to sub-sigma, However, more
studies are required to look at the noise level.
While the coupled instability is well studied, the emittance
growth is not studied much, which is a concern for
Ultimate Storage Ring, such as PEPX.
34Low Emittance'13 L. Wang
Acknowledgements
thanks to Y. Cai, A. Chao, J. Corbett, H. Fukuma, K.
Ohmi, M. Takao , T. Raubenheimer, J. Safranek, J.
Sebek, Ryutaro Nagaoka, Dmitry Teytelman, SSRL
operators
Thanks Riccardo, Susanna and Yannis
Beam ion instability in Ultra Small emittance Ring--- A special case
36Low Emittance'13 L. Wang
Beam Ion Instability in the Ultimate Storage Ring--PEPX
The growth time is order of 1ms! Theory doesn't work in this case
x=1.34ms
y=1.89msx=3.35ms
No hori instability USR
FEL
Y. Cai, et. al.,Synchrotron Radiation News, Vol.26,37, 2013
Multiple bunch train filling: 10 bunch train200mA Vacuum: total pressure 0.4nTorr, H2(20%),CH4(20%),H2O(20%),CO(20%),CO2(20%)
CSR Spectra & cancellation of emittance growth
3rd Low Emittance Ring Workshop,
Oxford University, 8-10 July 2013
Lanfa Wang, SLAC
38Low Emittance'13 L. Wang
Contents
Characteristics of CSR Spectra Long CSR wakeTowards full 3D modelCancellation of emittance growth due to CSRSummary
39Low Emittance'13 L. Wang
Spectra at NSLS-VUV Ring
G. L. Carr, S. L. Kramer, N. Jisrawi, L. Mihaly, and D. Talbayev, PAC’01, p377
40Low Emittance'13 L. Wang
Comparison with simulation(D. Zhou, IPAC12 talk, MOOBB03)
41Low Emittance'13 L. Wang
The VUV spectrum also is explained by the theory
Robert Warnock and John Bergstrom, PAC11, WEP119
Toroidal Vacuum Chamber
R. L.Warnock and P. Morton, SLAC-PUB-4562; Part. Accel. 25, 113 (1990).
42Low Emittance'13 L. Wang
Another explanation of the resonance
D. Zhou, et al., Jpn. J. Appl. Phys. 51 (2012) 016401.
L=0.5m L=2mp.l. L=8m
Outer wall reflection causes the modulation The spike in impedance induces long wake tail
xbA
B
s=AC+CB-arc(AB)C
43Low Emittance'13 L. Wang
CSR Spectrum from CLS
The spectrum is repeatableNote that the frequencies of the peaks is more important than the amplitude
Robert Warnock and John Bergstrom, PAC11, WEP119
44Low Emittance'13 L. Wang
CSR spectrum at CLS
0 2 4 6 8 10 12-1.5
-1
-0.5
0
0.5
1
1.5
2x 10
5
1/ (1/cm)
Z (
)
RealImaginary
0 2 4 6 8 10 12
2
4
6
8
10
12
14
16
x 104
1/ (1/cm)
Z (
)
Torus Model, only magnets With straight section, realistic layout but a constant cross section
measurement
Indeed, the spikes in CLS can’t be explained by a single magnet mode, and even the torus model (long magnet);
Besides the geometry of the cross section of the beam pipe; The realistic layout of the ring, including straight section, is crucial.
“Long Range” (~meter) CSR Wake
46Low Emittance'13 L. Wang
Wake filed measured by EO detector and Interbunch communication at ANKA
N. Hiller, et. al. IPAC13, MOPME014
The “long range” wake cause multiple bunch effect Multiple bunch effect observed:
ANKA & CLS: Increasing the charge in preceding bunch enhances theradiation. Strong evidence of interbunch cooperation! Vitali Judin, Lowemittance’11 Robert Warnock,5th Microwave instability workshop, 2013
47Low Emittance'13 L. Wang
Long range Wake in Super-KEKB DR
0 1 2 3-4
-2
0
2
4
6x 10
4
f (THz)
Z (
)
RealImaginarybunch spectrum,
z=0.05mm
L. Wang, H. Ikeda, K. Oide K. Ohmi and D. Zhou, IPAC13, TUPME017
0 50 100 150 200 250 300
-1500
-1000
-500
0
500
1000
1500
S (mm)
W||(V
/pC
)
CSR wakebunch shapeGeometric wake
The spikes in the impedance (interference) causes “long range” wake
D. Zhou, et al., Jpn. J. Appl. Phys. 51 (2012) 016401.
Single bend; 1/32 of the ring6/32 of the ring; 16/32 of the ring;
CSR impedance with realistic geometry
Similar as the geometry impedance, the CSR impedance depends on the geometry of the whole beam pipe.
Low Emittance'13 L. Wang 49
New CSR code with arbitrary cross section of the pipe
00
22 ~
22
ne
ski
R
xk
E
br
R
xk
ski
R
xk
EE
222 2~
22
br EEE
Initial field at the beginning of the bend magnet
0)0(~2 srE
After the bend magnet
0~
22
r
ski E
00
2 1 bE
Required for Self-consistentcomputation
Agoh, Yokoya, PRSTAB 054403,2004G. Stupakov, PRSTAB 104401, 2009K. Oide, PAC09D. Zhou, JJAP (2012) 016401.
),( yx
222yx
50Low Emittance'13 L. Wang
Example of fields
51Low Emittance'13 L. Wang
Compassion with CSRZ
0 2 4 6 8 10-50
0
50
100
150
200
250
300
350
400
k (1/mm)
Z (
)
Real, ZhouImaginary,ZhouReal, WangImaginary,Wang
Longitudinal CSR impedance of a bend magnet with bending radius 1 meter and rectangular cross-section of beam chamber(60mm width and 20mm height).
CSRZ: D. Zhou, et al., Jpn. J. Appl. Phys. 51 (2012) 016401.
52Low Emittance'13 L. Wang
Snap shot of CSR field at a particular s
53Low Emittance'13 L. Wang
Snap shot of CSR field at a particular s
54Low Emittance'13 L. Wang
Snap shot of CSR field at a particular s
55Low Emittance'13 L. Wang
Snap shot of CSR field at a particular s
56Low Emittance'13 L. Wang
Towards 3D– ultimate goal
The CSR impedance with exact the 3D geometry of the beam pipe is crucial to accurately compare the measurement, also important for microwave instability simulation
To do 3D calculation around the whole ring will be challenge.
Cancellation of the transverse emittance growth due to CSR
D. Douglas, Thomas Jefferson National Accelerator Facility Report No. JLAB-TN-98-012, 1998. (theory)
Rui Li and ya. S. Derbenev, JLAB-TN-02-054 (theory) S. Di Mitri, M. Cornacchia and S. Spampinati, PRL 109,
244801 (2013). (experiment) .........
58Low Emittance'13 L. Wang
Emittance Growth due to CSR
Coherent Synchrotron Radiation (CSR) emission in dispersive systems induces the transverse emittance growth
Emittance growth due to Collective effects
o Space charge (SC) forces;o Geometric longitudinal and transverse wake field in the accelerating structureso Coherent Synchrotron Radiation (CSR) emission in dispersive systems
Here we focus on the CSR effect
Coupling of longitudinal CSR kicker to transverse oscillation
exx ex ' A perfect cancellation of the CSR requires the symmetry of the optics
and a appropriate phase advance, (2n+1) (assumes that the CSR energy kicker is the same)
A smaller betatron function at BC’s is desired to reduce the CSR effect
59Low Emittance'13 L. Wang
Projected emittance Cancellation: Measurement: S. Di Mitri, M. Cornacchia and S. Spampinati, PRL 109, 244801 (2013).
Simplify by assuming x= between consecutive dipoles Dispersion asymmetry
( nea1= near3= - near5=- near7)(’1=-’3= -’5=+ ’7)
1= -3= 5=- 7;
exx
ex ' =(2n+1)
Two identical csr kickerThe slice emittance doesn’t change Head
>0
<0
60Low Emittance'13 L. Wang
Cancellation of emittance growth by CSR in LCLSII
61Low Emittance'13 L. Wang
Emittance growth, HXR, 250pC
There is a large horizontal emittance growth at BC2 and HBENDTwo phase shifter is checked independently
AB
62Low Emittance'13 L. Wang
Emittance canceallation, HXR, 250pC
0 50 100 150 200 250 300 3501
2
3
4
Phase (degree)
x (m
)
0 50 100 150 200 250 300 3500.6
0.7
0.8
0.9
y (m
)
Horizontal emittanceVertical emittance
0 50 100 150 200 250 300 3500
2
4
6
Phase (degree)
x (
m)
0 50 100 150 200 250 300 3500.6
0.7
0.8
0.9
y (
m)
Horizontal emittanceVertical emittance
A B
There is a maximum horizontal emittance of 3.4 µm and a minimum one of 1.09 m at 167.5o.
A
B: the 2nd phase before DL2 is not necessary for current design (already close to optimal)
63Low Emittance'13 L. Wang
Optimal emittance, 250pC HXR
0 500 1000 1500 2000 2500 30000
0.5
1
1.5
2
2.5x 10
-6
S (m)
(
m)
x, nominal
y,nominal
x, optimal
y,optimal HBEND
BC2 DL2
Example with one phase shifter A
64Low Emittance'13 L. Wang
Summary
The CSR spectrum can be explained by the csr
impedance with detail and accurate geometry of the
whole ring, including the straight section. The long range
wake is due to the resonances; A full 3D is desired,
especially for the port of field output
The cancellation of emittance growth due to csr in the
real machine is attractive and feasible
65Low Emittance'13 L. Wang
Acknowledgements
Thanks D. Zhou for providing his results
Thanks K. Oide K. Ohmi, Y. Sun, Yunhai Cai, Robert
Warnock, Hitoshi Fukuma, Kaoru Yokoya, Tomonori Agoh,
Mitsuo Kikuchi, Jack Bergstrom, T. O. Raubenheimer, Y.
Sun
Thanks Riccardo, Susanna and Yannis