review of the two-stream instability: beam and ion instability

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


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%


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


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


KEK ATF

Bunch 1

Bunch 5

Bunch 15

Bunch 3

Bunch 12

N. Terunuma1, et.al. EPAC08


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


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)


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


-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


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


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


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


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 /


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.


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


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


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


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)

http://iopscience.iop.org/1748-0221/


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)


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)


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!


0 50 100 150 2000

0.2

0.4

0.6

0.8

1

f (MHz)

Z (

M

/m)


2002503003500

100

200

300

400

500

600

700

800

Mode No.

Go

wth

rate

(1/s

ec)


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)


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)


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)


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)


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


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!


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.


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


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


Contents

Characteristics of CSR Spectra Long CSR wakeTowards full 3D modelCancellation of emittance growth due to CSRSummary


Spectra at NSLS-VUV Ring

G. L. Carr, S. L. Kramer, N. Jisrawi, L. Mihaly, and D. Talbayev, PAC’01, p377


Comparison with simulation(D. Zhou, IPAC12 talk, MOOBB03)


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).


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


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


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


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


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

http://dictionary.reference.com/browse/self-consistent




Example of fields


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.


Snap shot of CSR field at a particular s


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) .........


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


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


Cancellation of emittance growth by CSR in LCLSII


Emittance growth, HXR, 250pC

There is a large horizontal emittance growth at BC2 and HBENDTwo phase shifter is checked independently

AB


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)


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


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


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

review of the two-stream instability: beam and ion instability

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