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CSR-DrivenLongitudinal Instability – Comparison of Theoretical and Experimental Results. Peter Kuske, Helmholtz-Zentrum Berlin, Germany. 3 rd Low Emittance Ring Workshop, 8 th -10 th July, 2013, Oxford, UK. Content of the Talk.

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CSR-DrivenLongitudinal Instability – Comparison of Theoretical

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CSR-DrivenLongitudinal Instability –

Comparison of


and Experimental Results

Peter Kuske, Helmholtz-Zentrum Berlin, Germany

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

Content of the Talk

Introduction - Detection of CSR and Signals of Unstable Beams

Theoretical Predictions

Comparison of Predictions with Observations



I.1Observation of CSR @ BESSY II

K. Holldack, et al., THPKF013, EPAC‘04

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

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

Hot Electron Bolometer

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

I.3Observation of CSR @ Diamond

G. Rehm, et al., TUPD32,DIPAC‘09

I.4Observations @ Diamond

R. Bartolini, et al., THPC068, IPAC‘11

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

I.6Observations @ MLS

G. Wüstefeld, et al., WEPA015, IPAC‘10

I.7Observations @ BESSY II

BESSY II, Fsyno=1 kHz, o~1.5 ps

Many modes visible in the Fourier transformed CSR



II.1Shielded CSR-Impedance

d=2h, plate separation

Broad band resonator with low Q:

ANKA: Fres ~ 127 GHz

BESSY II: Fres ~ 100 GHz

MLS: Fres ~ 44 GHz

R.L. Warnock, PAC'91,

PAC1991_1824, http://www.JACoW.org


II.2Theoretical Result

II.3Shielded CSR-Wake – BESSY II

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

II.3Shielded CSR-Wake – BESSY II

II.3Shielded CSR-Wake – BESSY II

II.4Shielded CSR-Wake

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


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

III.1First Unstable Modes BESSY II

Slope agrees with resonance Fres~100 GHz



III.2CSR-Threshold Currents for BESSY II

In fair agreement with predictions – bunch lengthening explains shift

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



III.3CSR-Threshold Currents for the MLS

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



III.4 CSR-Threshold Currents Observed at ANKA

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

III.5Parameters for ANKA

RMS bunch length: σ = 1.953 ps

Bending radius: ρ = 5.593 m

Height of dipole chamber: 2·h = 0.032 m

Energy:E = 1.3 GeV

Momentum compaction factor: α = 2.033 10-4

Accelerating voltage: Vrf = 1.8 MV

Longitudinal damping time: Τlong = 10.6 ms

Synchrotron frequency: Fsyn = 7.8 kHz

Damping/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 2Fres·σ = 1.555

Shielded CSR-Impedance at ANKA


III.6Result of the Simulation

Beam is longitudinally stable below 20 μA

and between ~48 μA and ~59 μA

III.7Result of the Simulation:

Normalized Energy Spread vs. Time

Stability – thin lines, normalized energy spread = 1.0

Oscillations – thick lines, normalized energy spread > 1.0

Bursts – more or less regular, saw tooth instability

III.8Result of the Simulation:


60 μA

III.8Result of the Simulation:


48 μA

IV.1Summary of the Results for ANKA

  • 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.2 Status of CSR-Driven Longitudinal Instability

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

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

 Scsr ~ 0.8, Ithr ~ 0.32 mA

V. Judin, et al., TUPPP010, IPAC’12

IV.3Observations @ 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.



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