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TRANSCRIPT
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
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Storage Ring - CESR
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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
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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
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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
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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
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h~pi = 0
Phase space coordinates are mapped through a single turn
Closed Orbit
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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
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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
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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
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On energy closed orbit
High energy closed orbit
~⌘ =d~x
d�
Dispersion
Dispersion
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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
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~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
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pz = pz + qhVzi
������
pz✓
✓0 = ✓(1� �pzpz
)
✓0
Equilibrium
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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
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Iron poles with superconducting coils
7.6cm
20cm
7cm thick “yoke plate” flux return and support.
130cm
Vertical emittance
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y
University of Chicago
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
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θ~1/γ
University of Chicago
Intra-beam scattering (Mike Ehrlichman)
Current Dependent Effects
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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
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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)
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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
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• 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
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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)
Model (with tail-cut)Data
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)
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)
Model (with tail-cut)Data
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)
Current Dependent Effects
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• 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
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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
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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)
29 January 4, 2016 University of Chicago
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
30 January 4, 2016 University of Chicago
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
31 January 4, 2016 University of Chicago
Simulation of Wakefield Effect
Narrow gap chamber wake
W yba(0, 0, ⌧)
0
BBBBBB@
x
p
x
y
p
y
z
�
1
CCCCCCA
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Simulation of Wakefield Effect
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
33 January 4, 2016 University of Chicago
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
34 January 4, 2016 University of Chicago
✓tilt ⇠ ✓0 sin(�v(s)� �z(s))
z
y
Tilt depends on the observation point
Measurement of Tilt
35 January 4, 2016 University of Chicago
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
36 January 4, 2016 University of Chicago
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]
Phase +0 latticeScrapers
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
January 4, 2016 University of Chicago
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]
Phase -36 latticeScrapers
Out-OutIn-In
In-Out
January 4, 2016 University of Chicago
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]
Phase +0 latticeScrapers
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]
Phase -72 latticeScrapers
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]
Phase -72 latticeScrapers
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]
Phase -54 latticeScrapers
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]
Phase -54 latticeScrapers
Out-OutIn-Out
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Bunch height vs current Bunch width vs current
Wake Induced Growth
January 4, 2016 University of Chicago 40
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)
Current Dependent Effects
January 4, 2016 University of Chicago 41
January 4, 2016 42
Electron cloud
University of Chicago
Electron Cloud Focusing
January 4, 2016 43
What is the effect of the cloud on the beam ?
University of Chicago
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18/*/"#"6*!/,5(7!/+(*8/5"(/7(5"6/,)%!$"5E($*($5(3"!'(45"74#(*/( 5*4)'( %( 3%!$"*'( /7( &4,68( 51%6$,25-( ( K))$*$/,%#( )%*%(8%3"(&"",( *%H",(0$*8(JGE( TGE( ILGE( %,)(IUG,5( 51%6$,2E( &4*(4,7/!*4,%*"#'E( *8"( !"54#*5( 8%3"( 1!/3",( )$77$64#*( */($,*"!1!"*-( ( >*( $5( 8/1")( *8%*( *8"( +/!"( %)3%,6")( %,%#'5$5(*"68,$<4"5( +",*$/,")( %&/3"( 0$##( %##/0( 45( */( $,*"!1!"*(*8"5"()%*%-((C4!*8"!(+"%54!"+",*5(%!"(1#%,,")(%5(,"")")-(
./+"%/'0!(1+%2+#3%)%(+#$%#,1,)!%(+,(/+,4*%$#)!%(+A8"( 5$+4#%*$/,5( )"56!$&")( %&/3"( 45"( *8"( 18/*/,(
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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
University of Chicago
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
January 4, 2016 University of Chicago 46
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
January 4, 2016 University of Chicago 47
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
9785 macroparticles, 15496088 e- at T=434.046 ns
00.00250.0050.00750.010.01250.0150.01750.02
9830 macroparticles, 15560880 e- at T=434.097 ns
00.00250.0050.00750.010.01250.0150.01750.020.0225
9961 macroparticles, 15752340 e- at T=434.149 ns
00.0050.010.0150.020.025
10258 macroparticles, 16256958 e- at T=434.2 ns
00.0050.010.0150.020.0250.030.0350.04
10918 macroparticles, 17291198 e- at T=434.252 ns
00.010.020.030.040.05
12061 macroparticles, 19094100 e- at T=434.304 ns
00.010.020.030.040.050.060.07
13516 macroparticles, 21367112 e- at T=434.355 ns
00.0050.010.0150.020.0250.030.0350.040.045
14956 macroparticles, 23683380 e- at T=434.407 ns
00.0050.010.0150.020.0250.030.0350.04
15966 macroparticles, 25243816 e- at T=434.458 ns
00.0050.010.0150.020.0250.03
16517 macroparticles, 536 e- at T=434.51 ns
-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
January 4, 2016 University of Chicago
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
January 4, 2016 University of Chicago 49
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
January 4, 2016 University of Chicago 50
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
0
2
4
6
8
10
420.1 420.20
0.51
1.52
2.53
3.54
420.1 420.20
2
4
6
8
10
420.1 420.2
0
2
4
6
8
10
448.1 448.20
0.51
1.52
2.53
3.54
448.1 448.20
2
4
6
8
10
448.1 448.2
0
2
4
6
8
10
504.10
0.51
1.52
2.53
3.54
504.10
2
4
6
8
10
504.1
0
2
4
6
8
10
616.1 616.20
0.51
1.52
2.53
3.54
616.1 616.20
2
4
6
8
10
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
4
6
8
10
420.1 420.20
0.51
1.52
2.53
3.54
420.1 420.20
2
4
6
8
10
420.1 420.2
0
2
4
6
8
10
448.1 448.20
0.51
1.52
2.53
3.54
448.1 448.20
2
4
6
8
10
448.1 448.2
0
2
4
6
8
10
504.10
0.51
1.52
2.53
3.54
504.10
2
4
6
8
10
504.1
0
2
4
6
8
10
616.1 616.20
0.51
1.52
2.53
3.54
616.1 616.20
2
4
6
8
10
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
4
6
8
10
420.1 420.20
0.51
1.52
2.53
3.54
420.1 420.20
2
4
6
8
10
420.1 420.2
0
2
4
6
8
10
448.1 448.20
0.51
1.52
2.53
3.54
448.1 448.20
2
4
6
8
10
448.1 448.2
0
2
4
6
8
10
504.10
0.51
1.52
2.53
3.54
504.10
2
4
6
8
10
504.1
0
2
4
6
8
10
616.1 616.20
0.51
1.52
2.53
3.54
616.1 616.20
2
4
6
8
10
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
4
6
8
10
420.1 420.20
0.51
1.52
2.53
3.54
420.1 420.20
2
4
6
8
10
420.1 420.2
0
2
4
6
8
10
448.1 448.20
0.51
1.52
2.53
3.54
448.1 448.20
2
4
6
8
10
448.1 448.2
0
2
4
6
8
10
504.10
0.51
1.52
2.53
3.54
504.10
2
4
6
8
10
504.1
0
2
4
6
8
10
616.1 616.20
0.51
1.52
2.53
3.54
616.1 616.20
2
4
6
8
10
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
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
January 4, 2016 University of Chicago
Witness bunch measuements
52 January 4, 2016 University of Chicago
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
January 4, 2016 University of Chicago
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
January 4, 2016 University of Chicago
Electron Cloud Summary
January 4, 2016 University of Chicago 55
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
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The weak-strong model has promise. We plan to further develop the model and compare predictions with measurements
Sources of Emittance Growth Summary
January 4, 2016 University of Chicago 56
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
January 4, 2016 University of Chicago 57
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