longitudinal stability of short bunches at bessy peter kuske,

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, ...)


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.


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))


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


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


CSR-wake (J. B. Murphy, et al. Part. Acc. 1997, Vol. 57, pp 9-64)


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


3.2 Haissinski Equation:


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


3.2 Solution of the Haissinski Equation and CSR-Spectra

stationary distribution function stable coherent SR spectrum


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


3.3 Vlasov-Fokker-Planck (VFP) Equation


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.


3.3 VFP- Results for 1ps Bunch and > 0 - only CSR-wake


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.


3.3 Bursting VFP - Results for 1ps Bunch and < 0 – only CSR-wake


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


3.3 Bursting VFP - Results for 1ps Bunch – Vacuum chamber and CSR-wake


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


3.4 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


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:


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


4.2 Turbulent Instability

time dependent CSR-bursts observed in frequency domain:

0=14 ps, nom. optics, with 7T-WLS


Spectrum of the CSR-signal:

CSR-bursting threshold

Stable, time independent CSR


4.2 Turbulent Instability


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


5. Other „Instabilities“

5.2 Multi Bunch Instability at Small Negative Alpha

experimental conditions: Fsyn ~ 300 Hz, 2 mA in 200 buckets


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


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

longitudinal stability of short bunches at bessy peter kuske,

Documents

importance of short

bunch length o0

multi bunch instability

appearance of csr

bessypeter kuske

spectrometer bunch shape

time domain

longitudinal damping