Emittance Dilution In Electron/Positron Damping Ringsdlr/talks/CesrTAEmittanceDilution.pdf ·...

Emittance Dilution In Electron/Positron Damping Rings

David Rubin (for Jeremy Perrin, Mike Ehrlichman, Sumner Hearth, Stephen Poprocki, Jim Crittenden, and Suntao Wang)

•  CESR Test Accelerator •  Single Particle Emittance •  Current dependent effects

–  Intra-beam scattering – Emittance growth from transverse wakefields – Electron cloud induced emittance growth

•  Summary/Conclusions

Outline

January 4, 2016 University of Chicago 2

CESR Test Accelerator R&D

3

768 m circumference Energy reach: 1.8 GeV < E < 6 GeV

Cornell Electron/Positron Storage Ring (CESR)

CESR operates at 5.3 GeV for CHESS (Cornell High Energy Synchrotron Source) Horizontal emittance εx ~ 100 nm

2.1 GeV as CesrTA (CESR Test Accelerator) Horizontal emittance εx ~ 2.5 nm

January 4, 2016 University of Chicago

Storage Ring - CESR


Manipulate/control beams ~ 300 magnets

•  Dipoles - Steer •  Quadrupoles - Focus •  Sextupoles -Compensate energy

spread •  Skew quadrupoles - Compensate

coupling •  Wigglers - Vary radiation damping •  Pulsed magnets – drive oscillations

4 SRF Accelerating cavities – focusing and vary bunch length Monitor beams

•  100 Beam position montors •  X-ray and visible synchrotron light

beam size monitors •  Tune tracker •  Current monitors •  Bunch length measurement •  Spectral measurement

Monitor beam environment •  Retarding field analyzers,

shielded pickups, resonant microwave detection > electron cloud

•  Residual gas analyzers •  Pressure gauges •  Thermometry

Control System

Modeling codes •  Lattice design and correction •  Orbit,coupling,beta – closed bumps •  Tracking simulations

Laboratory


CESR, reconfigured as CesrTA is a laboratory for investigating the physics of low emittance charged particle beams

•  Intra-beam scattering •  Fast ion effect •  Single particle emittance •  Emittance tuning •  Wakefields and impedances •  Particle beam optics •  Electron cloud growth and mitigation •  Electron cloud beam dynamics

Emittance εx ~ σxσx’ (product of size and divergence) Two broad categories of effects contribute to emittance of a stored electron (or positron beam) •  Single particle effects – volume of a single particle in phase

space on multiple turns •  Collective effects – that depend on the number and density of

particles in a bunch.

Emittance

January 4, 2016 6

σx σx'

University of Chicago

LOW EMITTANCE

D. RUBIN

1. Introduction

(1) Much of our research is focused on the production and physics of ultra-low emit-tance particle beams.

(2) Emittance refers the the phase space volume of the particles

� =q

hx2ihpx

2i+ hxpx

i2

(3) Emittance corresponds to the temperature of the beam.(4) Typically an electron bunch emitted from a photocathode has a relatively low

emittance(5) And on circulation in a storage ring the beam heats up as it comes into equilibrium

with its environment, which is defined by the magnetic lattice.(6) The storage ring guide field can be arranged to minimize that equilibrium emit-

tance.

2. CESR

(1) In CESR we have exploited superconducting damping wigglers to reduce horizontalemittance from a high at 2GeV of 130 nm-rad when colliding beams for D-mesonproduction to 2.5 nm-rad for investigations of the electron cloud in CesrTA.

(2) The vertical emittance is dominated by misalignments and field errors.(3) We have learned to identify and correct those errors to reduce vertical emittance

to as few as 5 pm-rad, which is about a factor of 20 greater than the theoreticalminimum.

(4) At higher energy, which is more interesting for the hard xrays that can be produced,and also for the study of electron cloud and other collective e�ects, the dampingwigglers are less e�ective and the CESR ring layout limits minimum emittance to> 40nm-rad at 5GeV

3. Goal

(1) Lower emittance - test our understanding of the limits imposed by the guide field.Provide an ideal laboratory for the pursuit of ever colder beams, and the investi-gation of their properties. Also, an intense source of hard xrays.

(2) Lower emittance requires stronger focusing and closely spaced quadrupoles.1

Single Particle Emittance Outline


In the rest frame of a bunch - •  Kinetic energy of the particles corresponds to a temperature,

and we can assign an equivalent temperature to motion in each of x,y and z

•  Hot bunches are injected into a damping ring, and cold bunches extracted

•  i.e. - ILC damping ring reduces emittance of positron bunch by 6 orders of magnitude at a repetition rate of 5 Hz

Damping Ring


h~pi = 0

Phase space coordinates are mapped through a single turn

Closed Orbit


0

BB@

x

p

x

y

p

y

1

CCA

start

Full Turn(!)

0

BB@

x

p

x

y

p

y

1

CCA

end

For particles with coordinates on the closed orbit 0

BB@

x

p

x

y

p

y

1

CCA

start

=

0

BB@

x

p

x

y

p

y

1

CCA

end

Closed orbit


closed orbit

Simple closed orbit in uniform vertical B-field

If the initial coordinates are displaced from the closed orbit the trajectory will oscillate about it.

x(s) = a

p�(s) cos(�(s)� �0) �(s = C) = 2⇡Q

The area in phase space mapped out in subsequent turns is the single particle emittance

Closed Orbit


IP_L0

ElectronTransfer

PositronTransfer

ElectronsPositronsXray SourceFeedback KickerSeparator

Two beam operation for CHESS Electrostatic separators differentially kick electrons and positrons generating distinct closed orbits

The closed orbit is generally not a simple circle

The closed orbit depends on the energy Dispersion


On energy closed orbit

High energy closed orbit

~⌘ =d~x

d�

Dispersion

Dispersion


0

20

40

60

0 100 200 300 400 500 600 700s[m]

0

20

40

60

β y[m]

β x[m]

0

100

200

300

η[cm

] L0 L1 L3 L5 L0

3840511-441

Dispersion in CesrTA optics

The form of the dispersion is determined by the bending field and the quadrupole focusing

⌘(s)

In the absence of any disturbance, a particle on the closed orbit will remain there and the single particle emittance is zero. Electrons emit photons due to synchrotron radiation with some probability distribution depending on energy and local B-field. Photons are emitted very nearly tangent to particle trajectory To first order, only the energy of the electron is changed. The electron is abruptly displaced from the appropriate closed orbit by The electron begins to oscillate about its new closed orbit

Radiation excitation


~p� ⇡ ~pe

�~x =�E

E

~⌘

CESR parameters 5.3 GeV Beam energy ~ 800 photons are emitted/electron/turn corresponding to ~1 MeV Energy is restored by RF cavities

Radiation damping


pz = pz + qhVzi

��

pz✓

✓0 = ✓(1� �pzpz

)

✓0

Equilibrium


The radiation damping time corresponds to the number of turns to radiate all of the energy – CESR at 5.3 GeV => 5300 turns (~15 ms) Equilibrium of radiation excitation due to photon emission and radiation damping which depends on the average energy loss per turn => emittance Equilibrium horizontal emittance depends on •  Beam energy (number and energy of radiated photons ~ ) •  Dispersion function •  Energy loss/turn

�2

CesrTA Low Emittance Optics

17

0

20

40

60

0 100 200 300 400 500 600 700s[m]

0

20

40

60

β y[m]

β x[m]

0

100

200

300

η[cm

] L0 L1 L3 L5 L0

3840511-441

CesrTA – 2.1 GeV Superconducting wigglers in zero dispersion straight increase radiation damping (X10) without adding to radiation excitation εx ~ 2.5 nm


Iron poles with superconducting coils

7.6cm

20cm

7cm thick “yoke plate” flux return and support.

130cm

Vertical emittance

January 4, 2016 18

y


In the horizontal plane, dispersion cannot be avoided. The particles have to go around in a circle. But not so the vertical. •  In a planar ring with magnets perfectly aligned, there are no vertical dipole kicks •  The vertical component of the closed orbit is independent of energy. •  Radiation of straight ahead photons contributes nothing to the emittance. •  Single particle vertical emittance is typically dominated by misalignments

Photon emission is not precisely straight ahead The small but nonzero transverse momentum of the photon recoils off of the particle. The theoretical minimum vertical emittance, the quantum limit, obtains when the vertical dispersion vanishes. In a couple of storage rings (considerably smaller than CESR), vertical emittance approaching the quantum limit has been achieved. In CesrTA, εy ~ 10 – 15 pm (< 1% εx) The quantum limited vertical emittance < 0.1 pm

Quantum Limit

January 4, 2016 19

θ~1/γ


Intra-beam scattering (Mike Ehrlichman)

Current Dependent Effects


y x transfer horizontal

momentum into vertical

Intra-beam scattering can

x

z

px px

py

py

pz pz

px

px

Horizontal into longitudinal

Exchange z momenta

pz

Beam moving in z direction

z

IBS - 2.1 GeV

January 4, 2016 University of Chicago 21 21

Zero Current High Current

(data)

Run ID εy0 (pm)

εx0 (nm)

εx (7.5 1010 part)

(nm)

Low εy0 9.6 – 13.9 3.6 7.25

Med εy0 54.2 – 63.8 3.6 6.55

High εy0 163.6 – 179.9 3.5 5.18

Bands come from systematic uncertainty in measurement of zero-current vertical beam size

2.3 GeV Results (V15)


Input Parameters Result at high

current

Run ID εy0 (pm)

εx0 (nm)

εx (7.5 1010) (nm)

Low εy0 4.9 – 8.1 5.7 10.4

High εy0 52.3 – 61.8 5.7 7.62

Intra-Beam Scattering


•  The direct transfer of momentum from horizontal to vertical by IBS is small •  Dominant contribution to IBS emittance growth is due to exchange of longitudinal

momentum coupled with dispersion •  IBS effects are most evident in the horizontal dimension •  And small in the vertical since •  The amount of the blow-up can be controlled by varying the vertical emittance,

and thus the particle density.

⌘v ⌧ ⌘h

-4-2 0 2 4

0 100 200 300 400 500 600 700Verti

cal d

ispe

rsio

n[cm

]

s[m]

ηy

-2

-1

0

1

2

0 100 200 300 400 500 600 700

Cou

plin

g [%

] C12

3840511-450

Closed vertical dispersion/coupling bump through wigglers generate vertical emittance without introducing global coupling

Wakefield induced emittance growth


11

240

260

280

300

320

340

0 2 4 6 8 10 12 14

Hor

izon

tal B

eam

Siz

e (µ

m)

(N/bunch)×1010

a)

Model (with tail-cut)Model (without tail-cut)

Data

46

47

48

49

50

51

0 2 4 6 8 10 12 14

Ver

tical

Bea

m S

ize

(µm

)

(N/bunch)×1010

b)

Model (with tail-cut)Data

10.2 10.4 10.6 10.8

11 11.2 11.4 11.6 11.8

12 12.2 12.4

0 2 4 6 8 10 12 14

Bun

ch L

engt

h (m

m)

(N/bunch)×1010

c)


FIG. 11. (a) Horizontal, (b) vertical, and (c) longitudinalbeam size versus current for e+ bunch with increased zerocurrent vertical emittance.

VI. DISCUSSION

A. Data

IBS effects are most evident in the horizontal dimen-sion, where large horizontal dispersion leads to signifi-cant blow-up. In comparison, IBS is not a strong effectin the vertical. This is because the vertical dispersionis so small. The direct transfer of momentum from thehorizontal to the vertical by IBS is small at high energy.The amount of the blow-up can be controlled by vary-

240

260

280

300

320

340

360

380

400

0 2 4 6 8 10 12 14

Hor

izon

tal B

eam

Siz

e (µ

m)

(N/bunch)×1010

a)

Model (with tail-cut)Model (without tail-cut)

Data

26

28

30

32

34

36

38

0 2 4 6 8 10 12 14

Ver

tical

Bea

m S

ize

(µm

)

(N/bunch)×1010

b)


10.2 10.4 10.6 10.8

11 11.2 11.4 11.6 11.8

12 12.2 12.4

0 2 4 6 8 10 12 14

Bun

ch L

engt

h (m

m)

(N/bunch)×1010

c)


FIG. 12. (a) Horizontal, (b) vertical, and (c) longitudinalbeam size versus current for e− bunch in conditions tuned forminimum vertical emittance.

ing the vertical emittance, and thus the particle density.The simulations show bunch lengthening due to IBS, butwe are unable to distinguish IBS lengthening from po-tential well distortion in our measurements.

An interesting anomaly we have encountered is the be-havior of the vertical beam size at high currents. Theeffect is seen in Figs. 9b and 12b above 8 × 1010 parti-cles/bunch. We observe that vertical beam size plottedversus current increases with positive curvature. Muchmore severe cases of this blow-up have been observedduring the machine studies. We find that adjusting be-

Puzzle •  Abrupt change in slope of vertical beam vs current at ~6 X1010 particles •  Observed to depend on synchrotron tune and vertical betatron tune •  The phenomenon is not intra-beam scattering (positive curvature) •  Observed with both electron and positron beams

Transverse Wakefields (Jeremy Perrin, Stephen Poprocki)



•  Two particles, drive (a) and witness (b), travel through some vacuum chamber geometry.

•  Wake is time-integrated force on witness particle •  Longitudinal and transverse components •  Depends on , the delay of the witness relative to the drive •  Depends on transverse displacement of drive and witness

particle

Wake Formalism

26 January 4, 2016 University of Chicago

⌧

Wake Formalism

27

Vertical Monopole Wake

Vertical Dipole and Quadrupole Wakes (Cause tune shifts, etc.)

Transverse monopole wakes only occur in the absence of top-down symmetry


Expand vertical wake about the transverse coordinates

Wakefields

Or if the beam is displaced in a symmetric structure

Motivation: Asymmetric Vacuum Chamber Measurements

28

Bottom scraper Both scrapers Scrapers out


Asymmetric Wake

Scrapers can be inserted to within 3.5 mm of chamber axis With both scrapers inserted we observe current dependent tune shift, but no blow up. A single scraper causes significant increase in vertical beam size

December 2014

Recent Measurements (April

2015)


Off Center beam

Measure current dependence of vertical size as a function of displacement in a narrow gap (undulator) chamber (4.5 mm aperture) Displacement generates an effective monopole wake

Resonance fy – nfs =0 fs= 22.65 kHz

April 2015

Plan A •  Compute single particle wake (already difficult) •  Track a distribution of macro-particles •  Each particle generates a wake that kicks all of the

trailing macro-particles Statistical noise dominates effect we are looking for unless the number of macro-particles is impractically large


Simulation of Wakefield Effect

Plan B Note that transverse monopole wakes depend only on longitudinal structure of bunch, but do not influence longitudinal structure of bunch. Therefore, the longitudinal dependence of the wake kick will not vary turn-to-turn. •  Represent the wake as a single element that applies vertical kick

with longitudinal (temporal) dependence



Narrow gap chamber wake

W yba(0, 0, ⌧)

0

BBBBBB@

x

p

x

y

p

y

z

�

1

CCCCCCA



Simulations failed to reproduce the observed emittance growth

The wake couples longitudinal motion to vertical Perhaps the effect of the wake is to tilt the beam about a horizontal axis increasing the effective (observed) vertical size

32

Scraper Wake Element


Consider the scraper wake Compute the wake due to the asymmetric scraper

Collimator

Vertical Scraper:

17 / 27

CUBIT: cubit.sandia.gov T3P: confluence.slac.stanford.edu/display/AdvComp

Wake Induced Crabbing


✓tilt ⇠ ✓0 sin(�v(s)� �z(s))

z

y

Tilt depends on the observation point

Measurement of Tilt


scraper

positrons Vary vertical phase advance from source of tilt (scraper) to beam size monitor to determine if observed increase is due to a tilt or emittance growth

Create multiple lattice configurations


Each of 12 lattices has same global tune but with varying vertical phase from scraper to beam size monitor

These are the 5 that we tested

Change in crabbing phase (degrees)

60 40 20 0

pm

40 20 0

pm

Change in crabbing phase (degrees)

Projected vertical emittance Projected vertical emittance

Bunch tilt Bunch tilt

4 0 -4

mra

d 4

0

-4

mra

d

Baseline Lattice

37

25

30

35

40

45

1 1.5 2 2.5 3 3.5 4

V si

ze [µ

m]

Current [mA]

Phase +0 latticeScrapers

Out-OutIn-In

In-Out

200

220

240

260

280

300

1 1.5 2 2.5 3 3.5 4

H si

ze [µ

m]

Current [mA]


Out-OutIn-In

In-Out

6

8

10

12

14

16

18

20

1 1.5 2 2.5 3 3.5 4

Bunc

h Le

ngth

[mm

]

Current [mA]

Scrapers out outScrapers

Out-OutIn-In

In-Out


December 2015

Bunch height, width and length vs current •  Scrapers inserted symmetrically •  Scrapers withdrawn symetrically •  One in and one out

Tilt vs Crabbing Phase – 0& 36 deg

38

25

30

35

40

45

1 1.5 2 2.5 3 3.5 4

V si

ze [µ

m]

Current [mA]

Phase -36 latticeScrapers

Out-OutIn-In

In-Out

200

220

240

260

280

300

1 1.5 2 2.5 3 3.5 4

H si

ze [µ

m]

Current [mA]


Out-OutIn-In

In-Out


25

30

35

40

45

1 1.5 2 2.5 3 3.5 4

V si

ze [µ

m]

Current [mA]


Out-OutIn-In

In-Out

200

220

240

260

280

300

1 1.5 2 2.5 3 3.5 4

H si

ze [µ

m]

Current [mA]


Out-OutIn-In

In-Out

Bunch height vs current Bunch width vs current

Tilt vs Crabbing Phase, 54&72 deg

39

25

30

35

40

45

1 1.5 2 2.5 3 3.5 4

V si

ze [µ

m]

Current [mA]


Out-OutIn-In

200

220

240

260

280

300

1 1.5 2 2.5 3 3.5 4

H si

ze [µ

m]

Current [mA]


Out-OutIn-Out

25

30

35

40

45

1 1.5 2 2.5 3 3.5 4

V si

ze [µ

m]

Current [mA]


Out-OutIn-Out

200

220

240

260

280

300

1 1.5 2 2.5 3 3.5 4

H si

ze [µ

m]

Current [mA]


Out-OutIn-Out


Bunch height vs current Bunch width vs current

Wake Induced Growth


Monopole wake due to asymmetric structure tilts bunch in y-z plane Effect of wake on true emittance is small •  Current dependent increase in vertical size is almost entirely compensated by

adjusting the crabbing phase •  The current dependent growth in horizontal size is indifferent •  However – the coupling of transverse kick and longitudinal phase space

coordinates effectively generates vertical dispersion, same as a vertical bend Simulations are underway to determine if our model includes the relevant physics and to make more quantitative comparison of theory and measurements Implications ? •  Vacuum chamber design must preserve top down symmetry •  Misalignment of the beam in small aperture chambers can generate significant

growth in vertical beam size Especially in ultra-low emittance rings with high bunch charge What about the anomalous emittance growth observed in the IBS measurements?

Electron Cloud (Stephen Poprocki, Sumner Hearth, Jim Crittenden)



January 4, 2016 42

Electron cloud


Electron Cloud Focusing

January 4, 2016 43

What is the effect of the cloud on the beam ?


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

W',!%)OP(!%)$%*$/,()$5*!$&4*$/,5E(7/!(*8"(5%+"()%*%(58/0,($,(C$2-(I-(A/($+1!/3"(*8"(7$*E(,"0(!"7"!",6"(18/*/"#"6*!/,(1%!%+"*"!5( 9<4%,*4+("77$6$",6'(/7( N-INT( 7/!( )$1/#"5( %,)(N-NZ[( 7/!( )!$7*5;E( %,)( %( ?/!",*V$%,( 18/*/"#"6*!/,( ","!2'(51"6*!4+E(0$*8(1%!%+"*"!5(5$+$#%!(*/(*8/5"(!"1/!*")($,(Q\R;(8%3"( &"",( 45")-( F/*"( *8"( $+1!/3")( %2!""+",*( 7/!( *8"(!%*8"!(5+%##(8/!$V/,*%#(*4,"(58$7*5E(6/+1%!")(*/(C$2-(I-(

(C$24!"( OM( @/+1%!$5/,( &"*0"",( *8"( 5%+"( )%*%( %5( C$2-( I(%,)( %( ,"0( 5$+4#%*$/,( 0$*8( !%)$%*$/,( )$5*!$&4*$/,5( 7!/+(W',!%)OPE(%,)(,"0(!"7"!",6"(18/*/"#"6*!/,(1%!%+"*"!5(%5()"56!$&")( $,( *8"( *":*-( ( B#%6H( 1/$,*5( %!"( )%*%E( !")( %!"(5$+4#%*$/,-(A8"(*/*%#(5"6/,)%!'('$"#)(0%5(L-N-(

WEP108 Proceedings of 2011 Particle Accelerator Conference, New York, NY, USA

2 Beam Dynamics and EM Fields

Electron cloud tune shift

Cloud density increases along a train of bunches The cloud electrons focus the traversing positron bunch, shifting the tune

The differential focusing (tune shift) is our measure of the increasing cloud density along the train of bunches

January 4, 2016 44 University of Chicago

Train witness

January 4, 2016 45

Electron cloud emitance growth


20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

Bunc

h si

ze [µ

m]

Bunch Number

Total Current [mA]21.56 mA21.31 mA19.23 mA10.93 mA

Threshold for emittance growth at bunch 13.

Model for emittance growth


Physics models for electron cloud growth and beam dynamics •  Codes like ECLOUD (Rumolo and Zimmermann) and POSINST (Furman)

with SYNRAD3D (Sagan) predict cloud distribution in reasonable agreement with direct measurements (RFA, resonant microwave, shielded pickups) and tune shifts

•  Quantitative estimates of emittance growth are more elusive -  CMAD (Pivi) and PHETS (Ohmi) are strong-strong simulations -  Both electron cloud and positron bunch are represented as distributions

of macro-particles that interact with each other -  Limited to tracking through hundreds of turns -  But damping times are 20,000 turns in CesrTA it is impractical to track

long enough to equilibrate

Weak Strong Model


The electron cloud is the strong beam Compute the cloud distribution using cloud growth codes (i.e. ECLOUD)

Job 41306: Beampipe-averaged Cloud Density (1012 m-3)

Time (ns)

Elec

tron

Den

sity

(1012

m-3

)

0.02

0.03

0.04

0.050.060.070.080.09

0.1

0.2

0.3

0.4

0.50.6

-100 0 100 200 300 400 500 600

30 bunch train, 14ns spacing

The cloud is pinched by the passing bunch, the density increasing from head to tail

Electron cloud pinch

48

Job 41306: Cloud charge snapshots (units are cm)

00.0050.010.0150.020.0250.030.035

15/12/13 11.24

15222 macroparticles, 27356802 e- at T=406.561 ns

00.00250.0050.00750.010.01250.0150.01750.020.0225


00.00250.0050.00750.010.01250.0150.01750.02


00.00250.0050.00750.010.01250.0150.01750.020.0225


00.0050.010.0150.020.025


00.0050.010.0150.020.0250.030.0350.04


00.010.020.030.040.05


00.010.020.030.040.050.060.07


00.0050.010.0150.020.0250.030.0350.040.045


00.0050.010.0150.020.0250.030.0350.04


00.0050.010.0150.020.0250.03


-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

-0.2

0

0.2

-0.2 -0.1 0 0.1 0.2

Job 41306: Fits to cloud charge Y distribution 132.7 / 57

P1 0.1275P2 -0.1477E-02P3 0.7977E-01P4 0.3810

15/12/13 11.24

406.561 ns 91.42 / 57

P1 0.1995E-01P2 0.1239E-02P3 0.1000E+00P4 0.2393

434.046 ns

86.83 / 57P1 0.1942E-01P2 -0.3222E-02P3 0.1000E+00P4 0.2409

434.097 ns 97.69 / 57

P1 0.2270E-01P2 -0.1255E-01P3 0.6123E-01P4 0.2465

434.149 ns

106.8 / 57P1 0.2178P2 0.3630E-04P3 0.9616E-02P4 0.2500

434.2 ns 135.6 / 57

P1 0.5041P2 0.5515E-03P3 0.1169E-01P4 0.2424

434.252 ns

136.1 / 57P1 0.6414P2 -0.4990E-03P3 0.1940E-01P4 0.2313

434.304 ns 213.7 / 57

P1 0.6392P2 -0.5563E-04P3 0.3111E-01P4 0.2197

434.355 ns

263.9 / 57P1 0.5665P2 0.5373E-03P3 0.4892E-01P4 0.2069

434.407 ns 218.7 / 57

P1 0.5111P2 -0.1083E-02P3 0.8467E-01P4 0.1412

434.458 ns

Y(mm) 190.3 / 57P1 0.3249P2 -0.1214E-02P3 0.1000P4 0.2282

434.51 ns

Y(mm)

0

0.25

0.5

-0.2 -0.1 0 0.1 0.20

0.2

-0.2 -0.1 0 0.1 0.2

0

0.2

-0.2 -0.1 0 0.1 0.20

0.2

-0.2 -0.1 0 0.1 0.2

0

0.2

0.4

-0.2 -0.1 0 0.1 0.20

0.5

-0.2 -0.1 0 0.1 0.2

0

0.5

1

-0.2 -0.1 0 0.1 0.20

0.5

1

-0.2 -0.1 0 0.1 0.2

0

0.5

-0.2 -0.1 0 0.1 0.20

0.5

-0.2 -0.1 0 0.1 0.2

0

0.25

0.5

-0.2 -0.1 0 0.1 0.2


With ECLOUD we compute electron distribution in 11 time slices that extend the length of the bunch

The distribution is ~ Gaussian with varying width and amplitude

Strong Beam – The Cloud


Model the cloud as strong beam with Gaussian charge distribution The parameters of the Gaussian depend on the longitudinal coordinate Compute with ECLOUD Particles at the head of the positron bunch experience a relatively weak kick Particles near the tail get a much stronger kick Does this representation of the positron bunch / electron cloud interaction predict emittance growth?

⇢(x, y, t) = A

x

(t)Ay

(t)e� x

2

�

x

(t)2� y

2

�

y

(t)2

Ax

(ti

), Ay

(ti

),�x

(ti

),�y

(ti

)

Simulation


CesrTA Collaboration Meeting, Dec. 1, 2015

• Note that cloud charge increases as bunch passes through (left) - Was treated as constant in simple model

• Very preliminary results with ECLOUD data driven model show qualitatively similar behavior (right)

Preliminary results

6

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420.1 420.20

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616.1 616.20

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616.1 616.2

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Bgxy

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420.1 420.20

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616.1 616.2

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Bgxy

0

2

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420.1 420.20

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Char

ge[1

06e−

]

Time [ns]

Bunch 31, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Bgxy

0

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420.1 420.20

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Char

ge[1

06e−

]

Time [ns]

Bunch 31, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 31, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 33, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 37, Bgxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Totalxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Cloudxy

Char

ge[1

06e−

]

Time [ns]

Bunch 45, Bgxy

Electron cloud is represented in the tracking code as a time dependent “beam-beam” kick •  11 time slices •  Each slice the kick from a Gaussian

charge distribution •  Charge distribution is computed by

ECLOUD for a witness bunch in slot 31 An electron cloud “element” is place in each dipole in the CesrTA lattice Positron bunch represented as a distribution of macro-particles Tracking simulation includes all magnets in the storage ring lattice, (dipoles, quad, sextupoles, wigglers) and radiation excitation and damping Track positrons for several damping times

We find •  Significant emittance growth at

nominal ecloud charge density •  Cloud density threshold for

emittance growth ~ half nominal •  No growth at 10% nominal density

30 Bunch train

51

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30

Bunc

h si

ze [µ

m]

Bunch Number

Total Current [mA]21.56 mA21.31 mA19.23 mA10.93 mA

0.594

0.596

0.598

0.6

0.602

0.604

0 5 10 15 20 25 30

201512170.7mA/bunchve

rtic

al tu

ne

bunch

14W15W16W17W18W

Vertical emittance increases with cloud density – with threshold at bunch 13

Tuneshift increases ~ linearly with cloud density


Witness bunch measuements


Generate a cloud with a long train •  Explore dependence on cloud density by varying delay of

witness with respect to train •  Measure dependence on bunch charge for fixed density by

varying charge in witness bunch

Witness Bunch Measurements

53

0.588

0.59

0.592

0.594

0.596

0.598

0.6

30 35 40 45 50 55 60

vert

ical

tune

bunch

1 mA0.75 mA

0.5 mA0.25 mA

20

40

60

80

100

120

140

160

30 32 34 36 38 40 42

Bunc

h Si

ze [µ

m]

Bunch Number

Witness Bunch Current [mA]1.0

0.750.5

0.25

Witness bunches trailing a 30 bunch train (0.7mA/bunch)

(1mA = 1.6 X 1010 positrons)

Vertical emittance growth increases with: •  Density of the cloud (bunch number) •  Witness bunch charge (pinch effect)

Vertical tune shift •  increases with cloud density •  ~ Decreases with pinch


Horizontal emittance growth

54

0 10 20 30 40 50 60280

300

320

340

360

380

400

420

Bunch number

Sigm

a x (um

)

train0.25mA0.5mA0.75mA1.0mA

0.565

0.57

0.575

0.58

0.585

0.59

30 35 40 45 50 55 60

horiz

onta

l tun

e

bunch

1 mA0.75 mA

0.5 mA0.25 mAHorizontal emittance increases with

Cloud density (proximity to train) Tune shift increases with cloud, Decreases with pinch


Electron Cloud Summary


Goal: Model that quantitatively predicts vertical and horizontal emittance growth and tune shifts due to the cloud We measure All three quantities depend on •  average cloud density, which we control via the train length,

bunch current and delay of the witness with respect to the train •  pinch, independently controlled via the witness bunch current

�Qx

,�Qy

, ✏x

, ✏y

The weak-strong model has promise. We plan to further develop the model and compare predictions with measurements

Sources of Emittance Growth Summary


Single particle emittance (well understood) •  Correct or compensate sources of vertical dispersion Intra-beam scattering (theory and measurements in good agreement) •  Minimize dispersion

Wakefields (developing the fixed wakefield model) •  Symmetrize vacuum chambers •  Minimize transverse impedance of chambers •  Center beam

Electron cloud(developing “weak-strong” model) •  Mitigate cloud growth •  Explore bunch spacing

Speculation


Can we learn to exploit collective effects ? •  Shape the vacuum chamber better focus or stabilize the beam? •  Taylor the electron cloud to compensate intra-beam scattering? Depends on developing predictive models

Emittance Dilution In Electron/Positron Damping Ringsdlr/talks/CesrTAEmittanceDilution.pdf ·...

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Transcript of Emittance Dilution In Electron/Positron Damping Ringsdlr/talks/CesrTAEmittanceDilution.pdf ·...