CSR-DrivenLongitudinal Instability – Comparison of Theoretical

CSR-Driven Longitudinal Instability –

Comparison of

Theoretical

and Experimental Results

Peter Kuske, Helmholtz-Zentrum Berlin, Germany

3rd Low Emittance Ring Workshop, 8th-10th July, 2013, Oxford, UK


Content of the Talk

I. Introduction - Detection of CSR and Signals of Unstable Beams

II. Theoretical Predictions

III. Comparison of Predictions with Observations

IV. Summary

2


I.1 Observation of CSR @ BESSY II

K. H

olldack, et al., TH

PK

F013, E

PA

C‘04


I.2 Observation of CSR @ ANKA, MLS, ATF, …

Hot Electron Bolometer

A.-S. Müller, et al., TU5RFP027, PAC‘09

S. De Santis, et al., THPCH067, EPAC‘06


I.3 Observation of CSR @ Diamond

G. R

ehm, et al., T

UP

D32,D

IPA

C‘09


I.4 Observations @ DiamondR

. Bartolini, et al., T

HP

C068, IP

AC

‘11


I.5 Observations @ ANKA by V. Judin, et al.


I.6 Observations @ MLS

G. W

üstefeld, et al., WE

PA

015, IPA

C‘10

3rd Low Emittance Ring Workshop, 7th-10th July, 2013, Oxford, UK99

I.7 Observations @ BESSY II

BESSY II, Fsyno=1 kHz, o~1.5 ps

Many modes visible in the Fourier transformed CSR


II.1 Shielded CSR-Impedance

R.L. Warnock, PAC'91, PAC1991_1824, http://www.JACoW.org

Broad band resonator with low Q:

ANKA: Fres ~ 127 GHz

BESSY II: Fres ~ 100 GHz

MLS: Fres ~ 44 GHz

2/32/124/ hcFres

d=2h, plate separation


II.2 Theoretical Result


II.3 Shielded CSR-Wake – BESSY II

3/40

3/1 )(2

cNr

Ss

ecsr

2/32/124/ hcFres

Scsr ~ 0.5 + 0.12·X (Bane, et al., IPAC’10)


II.3 Shielded CSR-Wake – BESSY II

3/40

3/1 )(2

cNr

Ss

ecsr

2/32/124/ hcFres


II.4 Shielded CSR-Wake


II.5 Frequency of First Unstable Mode vs. norm. 0

BBR-Wake:

variation of Fres with constant o and

Shielded CSR-Wake:

Fres given by geometry and variation of o through α


II.6 Bunch Length, inst, at Instability Threshold

Broad-Band-Resonator Impedance Shielded CSR Impedance


II.7 Frequency of First Unstable Mode vs. norm. inst


III.1 First Unstable Modes BESSY II

Slope agrees with resonance Fres~100 GHz


III.2 CSR-Threshold Currents for BESSY II

Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)

In fair agreement with predictions – bunch lengthening explains shift


III.3 CSR-Threshold Currents for the MLS

Solid black line: K.L. Bane, et al., Phys. Rev. ST-AB 13, 104402 (2010)


Observation at ANKA: Stability between 45 μA and 60 μA, below and above the beam is longitudinally unstable

III.4 CSR-Threshold Currents Observed at ANKA


Shielded CSR-Impedance at ANKA

Decscription of the code: P. Kuske, “CSR-DRIVEN LONGITUDINAL SINGLE BUNCH INSTABILITY THRESHOLDS”, WEOAB102, IPAC’13, Shanghai, China

RMS bunch length: σ = 1.953 psBending radius: ρ = 5.593 mHeight of dipole chamber: 2·h = 0.032 mEnergy: E = 1.3 GeVMomentum compaction factor: α = 2.033 10-4

Accelerating voltage: Vrf = 1.8 MVLongitudinal damping time: Τlong = 10.6 msSynchrotron frequency: Fsyn = 7.8 kHzDamping/excitation parameter: β = 1.93 10-3

CSR-impedance has first maximum at: Fres = c·(/24)1/2·ρ1/2·h-3/2 = 126.7 GHz

Shielding parameter (à la Bane, et al.): Χ = c·σ·ρ1/2·h-3/2 = 0.684 or 2Fres·σ = 1.555

III.5 Parameters for ANKA


Beam is longitudinally stable below 20 μA and between ~48 μA and ~59 μA

III.6 Result of the Simulation


Stability – thin lines, normalized energy spread = 1.0Oscillations – thick lines, normalized energy spread > 1.0

Bursts – more or less regular, saw tooth instability

III.7 Result of the Simulation:Normalized Energy Spread vs. Time


60 μA

III.8 Result of the Simulation:CSR-Signal


48 μA

III.8 Result of the Simulation:CSR-Signal


Very good agreement between the observations at ANKA and the results of the numerical solution of the VFP-equation:

• Correct predictions for the regions of longitudinal stability and instability

Correct predictions for the dominant mode of the longitudinal instability:

• Dipole mode at 20 μA, above ~36 μA quadrupole mode with a shift to lower frequencies as the current is increased

• Quadrupole mode above 60 μA shifting upwards with increasing bunch charge

IV.1 Summary of the Results for ANKA


IV.2 Status of CSR-Driven Longitudinal Instability

2/32/124/ hcFres

3/40

3/1 )(2

cNr

Ss

ecsr

Example for ANKA: 0=5.5 ps, Fsyn=8.5 kHz, Vrf=0.7 MV (E=1.3 GeV, α=6.24e-4):

2Fres·0 = 4.38 Finst ~4.5·Fsyn~ 38 kHz

Scsr ~ 0.8, Ithr ~ 0.32 mA

V. Judin, et al., TUPPP010, IPAC’12


IV.3 Observations @ ANKA by V. Judin, et al.


•Predictions using the shielded CSR-wake are in surprisingly good agreement with measurements at BESSY II, MLS, ANKA, and other storage rings.

•If the bunch length is known then we can estimate the shielding parameter or normalized resonance frequency and predict the threshold current.

•The observed resonance-like features show the importance of the vertical gap of the dipole vacuum chamber.

•Increasing the cavity voltage gradient will not necessarily lead to higher threshold currents for shorter bunches – consequences for BESSY-VSR.

•CSR-driven longitudinal single bunch instability thresholds are of no concern for low emittance rings – coupled multi bunch instabilities could be an issue because of the tube-like vacuum chambers.

•If bunch length and Finst are known then we can determine the dominant

frequency of the impedance.

•Longitudinal modes below the instability thresholds can be observed - with sensitive detectors.

•The support of Dennis Engel is acknowledged. 31

IV.4 Summary

CSR-DrivenLongitudinal Instability – Comparison of Theoretical

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