Transcript Document 7188146

Longitudinal
Dynamics in High
Intensity / Bunch
Cécile Limborg
SSRL / SLAC
5/20/2016
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Introduction
• Light sources
 Energy spread minimum (high Intensity spectral lines Und.)
 Short bunches: subps desired
Time resolved experiments
High Î for SRFEL
Coherent Synchrotron Radiation
•Damping Rings
 Large Energy oscillations undesirable @ injection in linac
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Nature of instability
• Usually no beam loss
transverse instabilities fix Ithr
• “Instability” = Threshold of energy widening
• 2 regimes :
- potential well
lengthening, no energy widening
- microwave instability
lengthening, energy widening
Coherent signals (+fs, +2 fs, +3 fs …) pop up
(saturation or sawtooth)
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Strong Bunch lengthening
•Natural bunch length
 E3
 o 
 rf Vrf
@ I  0 mA
•Quasi-isochronous tuning
•Demonstrated @ (SuperAco, ESRF, ALS, UVSOR…)
@ high current bunch length independent of  and Energy
• Slope of assymptotic curve for each ring determined by
|Z/n|effective of the ring
•At high currents,
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
follows
 Z
I

n eff

  rf Vrf

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




4
Measurements
• ESRF, Super-Aco, ALS, APS, Daphne, HER, ATF, NSLS
VUV,Elettra  strong lengthening
• Some signs of bunch shortening
SPEAR I ,CESR , LEP (before SC cavities)
• Threshold of microwave instability
Strong coherent signals on sync. Sidebands
Ex: SLC DR, ALS, SuperAco
Microwave Instability Threshold in number of particles
ESRF
APS
Elettra
ALS
1.1.1011
1.8.1011
3.2.1010
2.87.1010 7.6.1010
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Super-Aco
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Measurements
Elettra To the courtesy of E.Karantzoulis
Daphne To the courtesy of A.Ghigo
SuperAco EPAC 98 Nadji et al.
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ALS To the courtesy of J.Byrd
Measurements
Energy Spread
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Measurements
Vrf=0.84 MV
Vrf=1.68 MV
Vrf=3.36MV
SPEAR C.Limborg- J.Sebek 98
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Signs of bunch shortening, but at
low currents
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Models & Methods
 Evolution of distribution of particles in phase space (,) with
increasing current in the presence of short range wakefields
• Vlasov equation conservation of charges + radiation = Fokker-Planck
Stationary solution = Haissinski equation
 o ( p, q ) 
1
exp(  p 2 2) f o (q)
2

f o (q)  A exp   q 2 2  I 
 
q


q'
f o (q' ' )W (q'q' ' )dq' dq' ' 

Linearized form Vlasov  mode coupling theory
 Non-linearized  numerical solvers (Warnock, Novokhatski
See Warnock &Al. submitted submitted Word Scientific Feb 26 -00
• Multiparticle Tracking codes
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Impedance models
• Impedance from codes
Wakefield extracted from codes
(ABCI-TBCI- MAFIA- GdFidl- Urmel...)
 Computing Limitations for the high frequencies
• Analytical Impedance models:
- SPEAR model 1st attempt to fit impedance (P.Wilson)
- Broadband RLC
- Heifets-Bane
Z // 
Rs
1  jQ(  r   r  )
(A.Hofmann)
Z //  jL  Rs  B(1  j sgn(  ))   A
1  j sgn(  )

Zotter review
see http://www-project.slac.stanford.edu/lc/wkshp/talks
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Academic case of Z//=jL
• Haissinski equation with purely inductive Z//:
fo ' 
 xfo
1  f o
with  
2 I L

Vrf  rf cos  s ( o    )3
 so
There exists a solution  >0
for  > 0, stable NO  increase
 No solution for < -1.55
for  < 0, Negative mass instability STRONG  increases
• Interest of Purely inductive impedance
Fits bunch lengthening curves
Good benchmark for test numerical noise (tracking code & solvers)
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Broadband impedance
• Handy model analytically (Rs, fr, Q=1)
•Tracking code
RF Voltage -losses
Radiation Damping
Fluctuations
 eV (  )  U o 

T
T
  A I W  f o ( n )  o  n  2 o Rn 
 n1   n   rf
Eo
Tdamp
Tdamp 


Variation Energy
Wakefield
 n1   n  2 Qso n1
Variation Path Length
Bunch Spectrum vs Resonant frequency
16 000 particles in 200 cells over  7 o
I = 3mA  =150ps
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fr = 30 GHz,  = 5 r
fr = 15 GHz,  = 2.5 r
fr = 7 GHz,  = 0.9 r
fr = 3.5 GHz,  = 0.5 r
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Mode Coupling theory
• A.Mosnier proved good agreement of thresholds between
tracking and mode coupling theory;
p.w distorsion from Haissinski for stationary distribution
uses Oide-Yokoya radial step function expansion
for determining the stability of modes
compares threshold with tracking code results (good agreement)
fr>1, azimuthal mode coupling before radial
fr<1, radial mode coupling, sub-bunches
- spread in fs
- eventual presence of 2 bunchlets
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• K.Bane simulations
exhibit quadrupole form
of perturbation
(but 3% of total intensity)
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A Few other mechanisms
•Dyachkov-Baartman model of sawtooth
1stable fixed point 1 unstable fixed point
diffusion from u. to s.
followed by collapse of the 2
•A controlled instability:
Modulation of RF voltage
Byrd-Zimmerman experimentHuang- Li et al PhysRev
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Observe enhanced emission from NSLS VUV ring at 7 mm
wavelength To the courtesy of J.Murphy
Beam current dependence
•
•
I2 dependence beyond threshold.
threshold depends on operating parameters (E, bunch length, ).
Detector signal [mV]
1000
2
S
~
I
100
Emission occurs after a
current threshold Ith is
exceeded, grows as (I - Ith)2.
10
I
S~
1
10
100
Beam current [ma]
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Submitted to PRL (2/2000): G.L. Carr, S.L. Kramer, J.B. Murphy, NSLS - BNL
BIW Physics
MarchDep’t.
13-15
2000
R.P.S.M. Lobo,ESRF
D.B. Tanner,
- Univ.
Florida
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•Emission is not continuous, but occurs in quasi-periodic bursts.
period ~ 1 to 10 ms; rise/fall times faster than synchrotron damping time.
Emission bursts
• Quasi-periodic bursts
• T ~ 1 to 10 ms
• detector-limited fall time
• Duration < 100 ms for  =  o
• increases with decreasing 
4
f s =12kHz
Detector Signal [arb.]
Detector Signal [arb.]
20
15
10
5
0
0
20
40
60
80
100
f s = 1kHz
3
2
1
0
0.0
0.5
Time [ms]
1.0
1.5
2.0
Time [ms]
Submitted to PRL (2/2000): G.L. Carr, S.L. Kramer, J.B. Murphy, NSLS - BNL
R.P.S.M. Lobo, D.B. Tanner, Physics Dep’t. - Univ. Florida
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Ith varies linearly (quadratically) with (fs0).
Threshold dependence on fs0
Keil-Schnell
100
>0
<0
eI ave
Zn
n
£ 2E E2
I th µ  ~ f s20
Boussard
Threshold current [ma]
(coasting / unbunched beam)
2
I th
~ f s0
10
3
1
~
I th
f s0
0.1
replace Iave with Ipeak
1
10
Synchrotron frequency [kHz]
Ith µ  3 / 2 ~ f s30
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Submitted to PRL (2/2000): G.L. Carr, S.L. Kramer, J.B. Murphy, NSLS - BNL
R.P.S.M. Lobo, D.B. Tanner, Physics Dep’t. - Univ. Florida
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For discussion in W.G
• Quadrupole feedback at Super-Aco
+ Stabilization with FEL operation
• Effect of bunch lengthening cavities on Ith (J.Jacob, A.Mosnier)
Do Harmonic cavities help for
- Pushing the threshold of energy widening?
- Improve the B̂ better than in I 2/3 ?
• Computing Limitations of e.m structures codes
• How many Broadband resonator for a realistic wakefield?
• Probing high frequencies on existing rings:3mm  100 GHz
(limit of S.Analyzers and strong problem of attenuation along cables)
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References
Longitudinal Dynamics
Hofmann “ Single-beam collective phenomena- Longitudinal” CERN 77-13 CAS lectures
Besnier “Longitudinal Stability” PhD thesis, Rennes 1978
Laclare “Bunched beam coherent Instabilities” CERN 87-03 CAS lectures
Oide-Yokoya “Longitudinal Single Bunch Instability in e storage rings” KEK Preprint 90-10
Mosnier “Microwave Instability and impedance model” PAC 99
Bane “
Low and Negative Momentum Compaction:
C.Pellegrini, D.Robin “Quasi-Isochronous storage Rings” Nucl.Inst.&Methods A301,2736,1991
Nadji- Level ”Experiments with low and <0  with Super-Aco” EPAC 96
Limborg “A Review of Diffculties in Achieving Short Bunches in Storage Rings” EPAC 98
Limborg “Ultimate Brilliance of Storage Ring Based Synchrotron Radiation Facilities of the
3rd Generation- Potential of Storage Ring Based Sources in the production of Short and Intense
X-ray Pulses” PhD ESRF, Grenoble, 1996
Sawtooth Instability:
Dyachkov-Baartman “simulaiton of sawtooth Instability” PAC 95
Bane “Simulations of the Longitudinal Instability in the SLC Damping Rings” PAC 93
Podobedov “Longitudinal Dynamics in The SLC Damping Rings” PhD Dec 1999
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References
Non-Linear Dynamics:
Byrd “Non-linear Longitudinal studies at ALS”PAC99
Huang et al. “Experimental determination of the Hamiltonian for synchrotorn motion with RF
phase modulation” Phys Rev.E Vol48, Num.6 Dec 93
Vlasov equation Solvers:
Warnock-Ellison “ A general method for propagation of the phase space distribution, with
application to the sawtooth instability” Submitted to World Scientific Feb 26 2000
Novokhatski “SLC ring simulations” Proceedings Impedance Workshop SLAC Feb 2000
Impedances:
Hofmann “ Improved impedance models for High Enrgy Accelerator” CERN, LEP Note 1979
Zotter- Kheifets “ Impedance and Wakes in High-Energy Particle Accelerator” World
Scientific Publishing 1998
Palumbo-Vaccaro “Wakefields, Impedances and Green’function” CERN 87-03 CAS lectures
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Acknowledgements
ESRF (Nagaoka- Farvacque- Revol- Ropert- Gunzel- Besnier…)
CEA ( Mosnier- Laclare…)
Super-Aco (Nadji, Level, Couprie, Flynn…)
Elettra (Karantzoulis…)
APS (Harkay, Lumpkin, Emery …)
NSLS (Murphy, Podobedov…)
ALS (Byrd…)
SLAC (Heifets- Bane- Krejcik…)
CERN (Hofmann- Zotter…)
SSRL (Sebek)
Daphne (Ghigo)
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Mode Coupling ambiguities
Radial-Azimuthal modes not well suited for some
impedance models
Too Small perturbations w.r.t streak camera data
Does not exhibit the importance of synchrotron motion
and damping in mechanisms
REMOVE THIS SLIDE, FOR W.G
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