longitudinal stability of short bunches at bessy peter kuske,
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Longitudinal Stability of Short Bunches at BESSY Peter Kuske, M. Abo-Bakr, W. Anders, J. Feikes, K. Holldack, U. Schade, G. Wüstefeld (BESSY) H.-W. Hübers (DLR) ICFA Mini-Workshop on „Frontiers of Short Bunches in Storage Rings“ INFN-LNF, Frascati, 7- 8 November 2005. Content. - PowerPoint PPT PresentationTRANSCRIPT
Longitudinal Stability of Short Bunches at BESSYPeter Kuske,
M. Abo-Bakr, W. Anders, J. Feikes, K. Holldack, U. Schade, G. Wüstefeld (BESSY)
H.-W. Hübers (DLR)
ICFA Mini-Workshop on
„Frontiers of Short Bunches in Storage Rings“
INFN-LNF, Frascati, 7- 8 November 2005
Content
1. Introduction
2. Experimental Techniques 2.1 Streak Camera 2.2 Observation of CSR 3. Theoretical Approaches 3.1 Impedance Model 3.2 Haissinski Equation 3.3 Vlasov-Fokker-Planck Equation 3.4 Instability Thresholds
4. Comparison of Experiment and Theory 4.1 Bunch Length 4.2 Turbulent Instability
5. Other “Instabilities” 5.1 Timing Jitter 5.2 Multi Bunch Instability at Small Negative Alpha
6. Summary
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
1. Introduction
BESSY:
3rd generation light source, in operation since 1998
Importance of short bunches: Table: BESSY parameter Investigation of fast phenomena Coherent synchrotron radiation (CSR) Accademic interest
History of short bunches at BESSY: 1984 Isochronous SR based FEL project at BESSY I (D. Deacon, A. Gaupp) since 1999 more seriously persued at BESSY II (G. Wüstefeld, ...)
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Energy 1.72 GeV
Natural energy spread / 810-4
Longitudinal damping time lon 7.7 ms
Momentum compaction factor 510-5 .. + 10-4
Bunch length o 0.5 … 15 ps
Accellerating voltage Vrf 1.4 MV
RF-frequency rf 5002 MHz
Gradient of RF-Voltage Vrf/t 4.63 kV/ps
Circumference C 240 m
Revolution time To 800 ns
Number of electrons 5106 per µA
2. Experimental Techniques
2.1 Streak Camera:
Dual sweep SC model C5680 with fast sweep=250 MHz, ±1mrad bending magnet radiation, for “direct” bunch length measurements - PAC ’03: “Bunch Length Measurements at BESSY”, M. Abo-Bakr, et al.
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Results of bunch length measurements as a function of the synchrotron frequency Fsyn
Bunch length as a function of beam current for three different momentum compaction factors
2
..
2
.
2
resstatnoisephmeasact
ph.noise 2.4 psstat.res. 1.5 ps
2. Experimental Techniques
2.2 Observation of CSR Suppression due to shielding and finite acceptance angles
Detector: InSb-FIR detector HDL-5 (QMC Instrum. Ltd.) most sensitive around 20 cm-1, very fast – revolution frequency resolved
Time-dependence of CSR-signal indicates instability, CSR-spectra (Martin-Puplett-spectrometer) bunch shape (K. Holldack, et al., Phys. Rev ST-AB 8, 040704 (2005))
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Appearance of CSR-bursts measured in time domain (left) and the corresponding Fourier transformation (right)
Current dependence of the 1.25 MHz- CSR-component as a function of single bunch current
3. Theoretical Approaches
Observations:
Streak Camera and CSR
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Current below threshold Current above threshold
Long. particle distribution Stationary (non-Gaussian)
Non-Gaussian, time dependent
Momentum distribution Stationary, Gaussian with natural spread
Time dependent, non-Gaussian with increasing spread
Theory Potential well distortion Turbulent bunch lengthening (energy widening), longitudinal mode mixing-, µ-wave-, CSR-instability
Consequences:
3.1 Impedance Model
Inductive impedance: (I) prop. I1/3
Assumption for chamber: Z﴾﴿ ≈ R -
iL
with R = 850 Ω
Lo = 0.2 ... 0.35 Ω
o ≤ 2 ps ... 13 ps
3. Theoretical Approaches
CSR-wake (J. B. Murphy, et al. Part. Acc. 1997, Vol. 57, pp 9-64)
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Assumption: R = 850 Ω, 0L ≈ 0.2 Ω valid for ≈ 1 ps, unshielded CSR-wake can be added
3.1 Impedance Model
Short bunch – 1 ps rms-bunch length
Radiation wake field
3. Theoretical Approaches
3.2 Haissinski Equation:
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Exception is the purely inductive impedance with negative momentum compaction:
Potential well distortion due to CSR-wake in comparison with results of K. Bane, et al. AIP Conf. Proc. 367, p. 191
Potential well distortion due to CSR- and vacuum chamber impedance (<0)
> 0 < 0
t
indrf
dVV
tKtI
)(
1
2exp)(
20
20
2
1)( dttI
dItWtILtIRTItV CSRind )()()()()( 00induced voltage per turn:
Analytical solutions only in some cases numerical approaches requiredSolutions exist in most cases, if none can be found use relaxation technique (N. Towne, Phys. Rev. ST-AB Vol 4, 114401 (2001)) - usually numerical difficulties have nothing to do with instability
3. Theoretical Approaches
3.2 Solution of the Haissinski Equation and CSR-Spectra
stationary distribution function stable coherent SR spectrum
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Distortorted shapes of short bunches just below instability thresholds and their “free space” CSR-spectra.The strong enhancement of CSR at frequencies>3 THz with <0 could not be observed ( J. Lee, G. Wüstefeld)
22 )()( dttIeS ti
CSR
3. Theoretical Approaches
3.3 Vlasov-Fokker-Planck (VFP) Equation
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Numerical solution based on R.L. Warnock, J.A. Ellison, SLAC-PUB-8404, March 2000 S. Novokhatski, EPAC 2000 and SLAC-PUB-11251, May 2005
p
fpf
ptp
ffqFq
q
fp
f
dsc
2),,(
ts
zzq / EEp /
RF focusing Collective Force Damping Quantum Excitation
My code:
limited to 127x127 mesh pointsand CPU-time500-2000 time steps per ωs
simulation of 200 Tsyn
(M. Venturini)
Bunch shape at end of simulation: 1ps bunch with R, L-impedance and CSR-wake.
3. Theoretical Approaches
3.3 VFP- Results for 1ps Bunch and > 0 - only CSR-wake
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Results of the VFP-calculations in comparison with solution of Haissinski equation. Threshold for energy widening is at 7 A. Instability starts with bunch shape oscillations at 1.8·Fsyn. Shown are the moments of the momentum distribution as a function of time at the end of the numerical calculation.
3. Theoretical Approaches
3.3 Bursting VFP - Results for 1ps Bunch and < 0 – only CSR-wake
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Results of the VFP-calculations in comparison with solution of Haissinski equation. Threshold for energy widening is at 25 A. -wave-type instability with density modulation accompanied by a small increase of the momentum spread. Well above threshold random bursts at a rate small compared to Fsyn.
Some moments of the particle distribution as a function of time
3. Theoretical Approaches
3.3 Bursting VFP - Results for 1ps Bunch – Vacuum chamber and CSR-wake
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Unstable longitudinal particle distribution and their projections just above threshold - periodic bursts of coherent radiation.
Results of the VFP-calculations in comparison with solution of Haissinski equation.
Burst rate in units of the synchrotron frequency as a function of intensity
3. Theoretical Approaches
3.4 Instability Thresholds
Stupakov & Heifets applied coasting beam instability analysis with CSR-impedance to bunched beams (Phys. Rev. ST-AB 5, 054402)
Results are in agreement with observations if the wavelength of the perturbation = 0 chosen
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Good agreement despite:
Vacuum chamber ignored - except for perfectly conducting infinite par. plates
Discrepancy for <0 between this theory and the VFP-calculations and
observed thresholds < thresholds with >0
Comparison of observed and simulated bursting thresholds. At BESSY a 1 ps-long bunch would have Fsyn~500 Hz.
4. Comparison of Experimental and Theoretical Results
4.1 Bunch Length:
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Comparison of measured and calculated bunch lengths
Chosen vacuum chamber impedance leads to:
very good agreement with the observations in the region of potential well distortion
VFP-simulation give too high thresholds and too small energy widening
4. Comparison of Experimental and Theoretical Results
4.2 Turbulent Instability
time dependent CSR-bursts observed in frequency domain:
0=14 ps, nom. optics, with 7T-WLS
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Spectrum of the CSR-signal:
CSR-bursting threshold
Stable, time independent CSR
4. Comparison of Experimental and Theoretical Results
4.2 Turbulent Instability
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
CSR-signal as a function of time at Isb=160 A
Fourier spectra of the time dependent CSR-signals as a function of single bunch current
With short bunches strong signal at 3·Fsyn
appearance of additional sidebands
with <0 1st and 2nd synchrotron sidebands at small Isb
5. Other „Instabilities“
5.1 Timing Jitter- Technical Imperfections?
Streak Camera measurements at Fsyn=1.7 kHz and Isb=0.85 mA
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
5. Other „Instabilities“
5.2 Multi Bunch Instability at Small Negative Alpha
experimental conditions: Fsyn ~ 300 Hz, 2 mA in 200 buckets
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Horizontal beam position in the straight section (BPM 1) and in the center of the bending region (BPM 2). There are large energy oscillations at Fsyn and much larger sporadic and slower energy variations. In this case the energy increases at a rate of ~12 Hz.
6. Summary
Longitudinal Stability of Short Bunches at BESSY, Peter Kuske, 7 November 2005
Rather short, intensity limited bunches can be produced in storage rings
Potential well distortion can lead to enhanced emission of stable CSR
Problems with threshold predictions – inclusion of vacuum chamber effects
In the region of turbulence our understanding is limited and further studies are required
Numerical solution of the VFP equation in combination with more realistic wakes or impedances is certainly a way to go
Threshold for energy widening usually accompanied by non-stationary bunch shapes and time dependent CSR emission
Observation of CSR leads to information on small scale variations and fluctuations of the particle density
Diagnostic power of CSR
There remain technical and intellectual challenges for the production of short bunches in storage rings – timing jitter and “orbit” stability