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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 driven longitudinal instability comparison of theoretical

CSR-DrivenLongitudinal 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

Content of the Talk

Introduction - Detection of CSR and Signals of Unstable Beams

Theoretical Predictions

Comparison of Predictions with Observations

IV.Summary

2


I 1 observation of csr @ bessy ii

I.1Observation of CSR @ BESSY II

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


I 2 observation of csr @ anka mls atf

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 3 observation of csr @ diamond

I.3Observation of CSR @ Diamond

G. Rehm, et al., TUPD32,DIPAC‘09


I 4 observations @ diamond

I.4Observations @ Diamond

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


I 5 observations @ anka by v judin et al

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


I 6 observations @ mls

I.6Observations @ MLS

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


Csr driven longitudinal instability comparison of theoretical

I.7Observations @ BESSY II

BESSY II, Fsyno=1 kHz, o~1.5 ps

Many modes visible in the Fourier transformed CSR

9

9


Csr driven longitudinal instability comparison of theoretical

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

10


Ii 2 theoretical result

II.2Theoretical Result


Ii 3 shielded csr wake bessy ii

II.3Shielded CSR-Wake – BESSY II

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


Ii 3 shielded csr wake bessy ii1

II.3Shielded CSR-Wake – BESSY II


Ii 3 shielded csr wake bessy ii2

II.3Shielded CSR-Wake – BESSY II


Csr driven longitudinal instability comparison of theoretical

II.4Shielded CSR-Wake


Ii 5 frequency of first unstable mode vs norm 0

II.5Frequency 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

II.6 Bunch Length, inst, at Instability Threshold

Broad-Band-Resonator Impedance Shielded CSR Impedance


Csr driven longitudinal instability comparison of theoretical

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


Csr driven longitudinal instability comparison of theoretical

III.1First Unstable Modes BESSY II

Slope agrees with resonance Fres~100 GHz

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19


Csr driven longitudinal instability comparison of theoretical

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)

20

20


Csr driven longitudinal instability comparison of theoretical

III.3CSR-Threshold Currents for the MLS

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

21

21


Csr driven longitudinal instability comparison of theoretical

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


Shielded csr impedance at anka

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

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


Beam is longitudinally stable below 20 a and between 48 a and 59 a

III.6Result of the Simulation

Beam is longitudinally stable below 20 μA

and between ~48 μA and ~59 μA


Csr driven longitudinal instability comparison of theoretical

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


Csr driven longitudinal instability comparison of theoretical

III.8Result of the Simulation:

CSR-Signal

60 μA


Csr driven longitudinal instability comparison of theoretical

III.8Result of the Simulation:

CSR-Signal

48 μA


Csr driven longitudinal instability comparison of theoretical

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

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 3 observations @ anka by v judin et al

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


Csr driven longitudinal instability comparison of theoretical

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.

IV.4Summary

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