Instabilities driven by electron cloud: Summary Outline

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Instabilities driven by electron cloud Summary
Outline

• Principal observations
• Single bunch effects
• Coupled bunch effects
• Analytical models
• Assume some existing electron cloud distribution
• Based on impedance models
• Simulation codes
• PEHTS
• HEADTAIL
• QuickPIC
• BEST
• CSEC/NCSEC
• Towards a predictive theory

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What are the principal observations?

• General characteristics and criteria
• Observed effects in positron beams and not in
  electron beams
• Correlation of vacuum pressure with time
  structure
• Correlation of instabilities with vacuum pressure
• Effect of suppression techniques e.g. solenoids
  on/off
• Direct observations of electrons
• Tune shifts along bunch trains (B Factories, SPS)
•  
• Single bunch
• Beam-size blow up
• Time scales ???
• Differences in horizontal and vertical planes
• Dependence on betatron tune (KEK-B)
• Dependence on chromaticity (sometimes)
• Effect of octupoles (BEPC)
• Trailing edge multipacting
• In long, flat-topped bunches, tail becomes
  unstable first
• Centroid motion (uncorrelated from bunch-to-bunch)

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KEKB e beam blow up, 2000 (H. Fukuma, et al.)
IP spot size
threshold of fast vertical blow up
slow growth below threshold?
beam current
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calculated measured head-tail phase
difference for an LHC bunch train in the SPS
start of train
additional e- cloud wake field with wavelength
of 0.3-0.5 bunch length can reproduce measurement
end of train
K. Cornelis, 2002
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centroid motion bunch size tilt by
KEKB streak camera preliminary, October
2002 J. Flanagan, H. Fukuma, S. Hiramatsu, H.
Ikeda, T. Mitsuhashi
tail bunches blown up, slight evidence for tilt
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Evolution of PSR instability, beam current,
stripline difference signal, electron flux at
wall. From R.J. Macek
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Fast ion instability in the recycler ring?
?Transverse emittances took a jump and lost about
1E10 of beam. Before jump intensity was
about 126E10. Bunch length 7.3
ms. ?Usually, the growth is triggered by a
change in the cycling of the Main Injector
underneath the Recycler.
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What are the principal observations? (continued)

• Coupled bunch (the usual suspects)
• Growth in oscillations along bunch train
• Differences in horizontal and vertical planes

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• Izawa et.al., Phys. Rev. Lett. 74, 5044 (1995).
• (Photon Factory)

BPM spectrum for V motion.
Electron 354 mA Positron 324 mA 240 mA
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BEPC mode spectra by Single Path Beam Position
Monitor (measurement)

• Positron electron

Guo, et al, PRST (2002).
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Analytical models

• General characteristics
• Assume existence of cloud at particular
  density/distribution
• Pinch effect
• Based on linear perturbation theories (assume
  superposition)
• Beam break-up
• For growth times ltlt synchrotron period
• Fast head-tail (TMCI Resonator Model)
• Ohmi, Zimmermann, Perevedentsev
• Derive expression for the wake broad band
  resonator
• Apply standard theory
• Valid for ?c?t lt 1 ??? transition to coasting
  beam theory?
• Coupled bunch
• Derive expression for the wake, and apply
  standard theory
• Simulations indicate superposition ok, linearity
  for first few bunches
• Effect of solenoid characteristic frequency
  cyclotron frequency

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Pinch Effect
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generalization of transverse impedance

• must consider wake W1(z,z), not W1(z-z)

2-dimensional Fourier transform
(E. Perevedentsev, ECLOUD02)

• the wake W1(z,z) can be obtained from
• simulations

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(G. Rumolo)
extracting the 2-dimensional wake
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Smooth transverse distribution with 8 uC

• Electron density
• Same voltage between pipe center and wall as in
  previous case
• Effective frequency is lower than small amplitude
  value.
• 9 turns plotted for electron density (in beam)
  and wakefield

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average wake
wake on axis
factor 20 difference! dependence on z!
(G. Rumolo, F.Z., PRST-AB 5, 121002, 2002)
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in TMCI calculation pinch effect acts stabilizing!
no incoherent tune shift DQ0
real part
imaginary part
incoherent tune shift DQ(/-sz)/-2.5Qs
(E. Perevedentsev, ECLOUD02 see also V. Danilov
et al., PRST-AB, 1998)
head-tail mode tunes in units of synchrotron
tune vs. the cloud density in units of 1012 m-3
at Nb1011
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Round
The e-cloud makes the vertical impedance look
more than a round chamber.
Flat vertical
Flat vertical E-cloud
Flat horizontal
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Simulation Codes PEHTS

• Principles
• PIC code
• Based on beam-beam strong-strong simulation model
• Observations in simulations
• TMCI instability
• Benchmarking
• Comparison with observations at KEK-B
• Agreement with TMCI threshold 30
• with some assumption for cloud density
• Comparison with results from HEADTAIL

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Scaling of ns and cloud density

• In the theory of the strong head-tail
  instability, the instability should be scaled by
  the ratio of the wake strength (cloud density)
  and the synchrotron tune.

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Electron motion in the beam potential
Electron cloud instability in coasting proton beam

• Fixed coasting beam

beam position modulation of 1mm
Red fixed beam. Green 10 turn. Blue 100 turn
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Simulation Codes HEADTAIL

• Principles
• Single bunch instabilities
• Interaction between bunch/cloud at N points
  around ring
• Need large N to converge results
• Bunch sliced longitudinally cloud modeled by
  macroparticles
• Includes chromaticity, chamber boundary
  conditions etc.
• Observed effects in simulation
• Incoherent emittance growth
• Fast head-tail (with threshold for fast emittance
  growth)
• Effect of (large) chromaticity in suppressing
  instability for LHC
• Benchmarking
• Agreement within factor 2 with QuickPIC (in
  discrete interaction mode)
• Should be exact agreement for same physics
• Agreement with resonator model (for thresholds
  of fast head-tail)
• but without pinch enhancement

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Simulation Codes HEADTAIL (continued)

• Agreement with experimental observations
• Thresholds for fast blow-up in SPS and KEK-B
• Agreement with threshold in KEK-B within 30
• ...with some assumption for cloud density
• Effect of chromaticity in SPS
• Needed to suppress instability in the real
  machine
• Consistent with simulations if machine impedance
  included
• Other examples?

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Resonator Model (1)
Reson r 9 1011 m-3
Reson r 6 1011 m-3
Reson r 3 1012 m-3

• Emittance growth for different electron cloud
  density
• comparison between the Resonator Model and
  HEADTAIL PIC module

Reson r 15 1011 m-3
PIC r 9 1011 m-3
PIC r 3 1012 m-3
Vertical emittance m
PIC r 15 1011 m-3
PIC r 6 1011 m-3
PIC r 4 1011 m-3
Reson r 4 1011 m-3
Time s
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Benchmark with QuickPIC code
Collaboration with Ali Ghalam and Tom Katsouleas
QuickPIC
HEADTAIL
Horizontal Beam Size m
Vertical Beam Size m
HEADTAIL
QuickPIC
Time s
Time s

• Horizontal (right) and vertical (left) beam size
  vs. time.
• For purpose of comparison in both HEADTAIL and
  QuickPIC the electron cloud has been modeled
  using 1 IP per turn.

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Simulation Codes QuickPIC

• Principles
• Plasma code, adapted for electron cloud
• Single bunch instabilities
• Continuous interaction around ring
• Constant focusing lattice (at present)
• PIC code, 3D, parallel
• Quasi-static approximation
• Bunch dynamics slow compared to e cloud dynamics
• Observed effects in simulation
• Fast head-tail
• Stabilizing effect of the pinch enhancement
• Consistent with Perevedentsev calculation
• Tune shifts
• Is the physics the same in QuickPIC and HEADTAIL?

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Growth rate changes with number of kicks
Green 4 Kicks/Turn Blue 2
Kicks/Turn Red 1Kick/Turn Aqua 16Kicks/Turn
QuickPIC Results for LHC

• Growth rate changes with the
• number of kicks!

HEAD-TAIL results for LHC
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Effects of Dipole Magnets on Beam-cloud
Interactions

• CERN_SPS Ring Specifications
• 750 bending of length 6.26m.
• 70 percent bending sections.
• Straight sections 9m.
• Dipole Strength 0.117T.

• Modeling bending sections/Magnets on QuickPIC
• Effect of magnetic field on cloud dynamics is
  significant
• Resolving the spatial profile of the magnets
  increases the run time by a factor of ten.
• Assume average B on the whole ring

B 0
B 0.117T
Vertical Plane
Horizontal Plane
Shallow Cloud Compression
Severe Cloud Compression
Cloud Density in Horizontal Plane
3D cloud density with magnetic field
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Simulation Codes BEST

• Principles
• Vlasov-Maxwell solver for two-stream instability
• Numerical evaluation of perturbation to
  stationary distribution (delta-f)
• Observations in simulations
• Unstable modes
• Benchmarking
• Comparison with data from PSR
• Good agreement for instability mode structure and
  frequency
• Poor agreement for saturation
• Stronger effects observed in machine than in
  simulation

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Simulation of instability with CSEC/NCSEC

• The effective electron density as a function of
  bunch/gap length is crucial.
• How do we dead-reckon this? (Compare pink and
  red!)
• Threshold estimates for future machines require
  caution.

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Simulation Codes Coupled Bunch Effects

• Results for KEK-B presented by Ohmi-san
• Excellent agreement with data
• Mode structure frequencies and amplitude
• Effects of solenoids
• some assumptions needed about cloud distribution
• Longitudinal wake may also drive coupled-bunch
  instability

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KEKB
Solenoid-Off
Su Su Win et al,(EC2002)
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Wake force and unstable mode caused by electron
cloud for KEKB

• Very rapid growth time (10 turn for KEKB at 2.6
  A, 5000 bunch)
• Broad mode spectrum

Dy1 mm 2 mm
KEKB design report (1996 or 7)
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Longitudinal wake force
Shifted bunch
Super KEKB sz3mm, N1.17E11, L3016m, h2E-4,
ns0.02
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Predictions for future machines

• LHC
• Is requirement set by heat load or slow emittance
  growth?
• To avoid emittance growth, present estimate
  iscloud density lt 31010 m-3
• SNS
• Using linear models for uniform cloud density
• Accumulator ring still looks like it will be
  stable
• GLC/NLC
• For TMCI, threshold 1012 m-3, but
• outside regime for rho/Qs scaling (other
  instability modes important)
• Coupled bunch growth times few hundred us
• TESLA
• Work in progress
• JPARC
• Should be stable (for pressure lt 10-6 Torr)

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Towards a Predictive Theory

• Input parameters are important, but not always
  well known
• Materials science ? cloud development ? beam
  dynamics
• Still some way from self-consistent model
• Observations are often difficult to interpret
• e.g. current limits in DA?NE
• Coupled bunch instabilities
• Some success already shown for analysis of KEK-B
  results
• More data already available, to be analyzed and
  understood
• APS, PSR, SPS
• Feedback systems provide powerful diagnostics
• But what are the conditions? i.e. what is the
  cloud distribution?
• Analytical models in relatively good shape
• IF linearity and superposition are good enough

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Towards a Predictive Theory (continued)

• Single bunch instabilities
• Possible to measure emittance growth, tune
  shifts
• Possible to observe head-tail modes
• Streak camera data
• Quantitative measurements are difficult
• Analytical treatments based on perturbation
  theory
• May provide reasonable estimates for thresholds
• Not able to predict detailed dynamics
• Simulations need to push parameters for results
  to converge
• Number of interaction points/turn, number of
  bunch slices
• Computationally expensive

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Comments

• Need to include all sources of tune spread
• May reduce number of kicks per turn needed in
  simulations?
• Small number of kicks may (anomalously) lead to
  chaotic behavior
• Do we know how far existing preventive measures
  will work?
• Solenoids in high current B-factories

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Directions for Developments

• Various effects to be included
• Real magnetic field profiles
• Beta function variations
• Pipe impedance
• Boundary conditions
• Develop useful reduced models
• Ability to make fast simulations of long-term
  behavior, possibly using parameters found from
  more detailed simulation
• Several possibilities
• Some good ideas and studies needed
• Find scaling laws to access long timescales
• E.g. rho/Qs (Ohmi-san)
• E.g. Apply many kicks per turn, but all in one
  betatron period
• Aims
• Reliable simulation of LHC behavior over 2000
  turns
• Reliable simulation of LHC behavior over 30
  minutes