1. Ion Trapping Experiments and Single Kicker Injection Studies
CSR-driven Longitudinal Instability Thresholds with Negative Momentum Compaction Factor
An Alternative Experimental Determination of the Effective Transverse Impedance
Ion Trapping Experiments and Single Kicker Injection Studies
Peter Kuske, Helmholtz-Zentrum Berlin, Germany
4th Low Emittance Rings Workshop, INFN-LNF, Frascati, Italy

2. IV. Is Ion-Trapping an Issue for the MAXIV 3 GeV Ring?
Content of the Talk
I. General Remarks on CSR Driven Single Bunch Instability – with Positive Momentum Compaction Factor, α > 0
II. Theoretical Predictions for α < 0, Comparison with Experimental Results, Difficulties Encountered in the Calculations. Work in Progress – Preliminary Results only.
III. Alternative Experimental Determination of the Effective Transverse Impedance – A Failure
IV. Is Ion-Trapping an Issue for the MAXIV 3 GeV Ring?
V. Single Kicker Injection Studies – Off-Momentum Injection Experiment at BESSY II
VI. Summary 2

3. I.1 CSR-Driven Single Bunch Instability
Modeling the interaction of electrons via CSR which is shielded by conducting infinite parallel plates 2 h apart (J. B. Murphy, et al., Part. Acc. 1997, Vol. 57, pp 9-64)
Impact on particle distribution analyzed by
Numerical solution of the Vlasov-Fokker-Planck-equation (see my contribution to TWIICE 2014 Workshop, January, 2014, Soleil, France)
Multi particle tracking
General scaling laws exist for the following dimensionless parameters (K. Bane’s and Y. Cai’s contribution to TWIICE 2014 Workshop):
either the “shielding factor”:
or the “normalized resonance frequency” (K. Oide and K. Yokoya, KEK Preprint 90-10, April 1990) with the frequency given by (R.L. Warnock, PAC'91, PAC1991_1824,
with
and the strength parameter: 3 3

4. I.2 Theoretical Result for >0

5. I.3 CSR-Driven Longitudinal Instability for >0
Threshold current depends on
Π > 1: Scsr ~ ·Π
2Fres·o > 5: Finst/Fsyno= 2Fres·o

6. I.4 Summary of Results for >0
Threshold current for the CSR-driven longitudinal single bunch instability depends on shielding factor or normalized resonance frequency and the ratio of Tsyn to Tlong, the damping per synchrotron period. For 2 Fres 0 <2 the instability is weak.
For larger values of the normalized frequency the instability is strong and the threshold current is independent of =Tsyn/Tlong/2 and is given for by:
For longer bunches the frequency of the first unstable mode, Finst, is given by: ,
where inst is the bunch length at the onset of the instability.
Many experimental observations agree very well with these theoretical predictions.
As predicted stable islands at higher beam currents and above unstable regions have been observed. 6

7. II.1 Parameters for the Calculations
Calculations have been performed for the Metrology Light Source (PTB) because experimental results are available (M. Ries, PhD-thesis)
Parameter
MLS
Energy, E0/MeV
629
Bending radius, /m
1.528
Momentum compaction, α
variable
Cavity voltage, Vrf/kV
20, 100, 500
Accelerating frequency, rf/MHz
2 500
Revolution time, T0/ns
160
Natural energy spread, E
Zero current bunch length, 0/ps
Longitudinal damping time, l/ms
11.1
Synchrotron frequency, s/kHz
Height of the dipole chamber, 2h/cm
4.2 7 7

8. II.2 Scaling Laws for <0
Bunch length vs. bunch current, Haissinski solutions up to the instability thresholds (shown for the MLS with Fres = 44.1 GHz):
With increasing bunch current short bunches get lengthened and long bunches get shortened first and lengthened at higher bunch current.
With positive alpha it is the other way round. 8 8

9. II.3 Preliminary Results for <0
Vrf is fixed and bunch length varied via α. There is no simple linear scaling law. For all parameters studied the threshold depends on the damping per synchrotron period. Red solid line: threshold for >0. 9 9

10. II.4 Experimental Results from M. Ries for <0
MLS-experiments: alpha fixed and Vrf varied 10 10

11. II.5 Experimental Results from M. Ries for <0
MLS-experiments: alpha fixed and Vrf varied 11 11

12. II.6 Experimental and Theoretical Results for <0
MLS-experiments: alpha fixed and Vrf varied 12 12

13. II.7 Experimental and Theoretical Results for <013 13

14. II.8 Some Observations and Difficulties
4ps with 20 kV, Fsyn=813Hz, ß= 14 14

15. II.9 Some Observations and Difficulties
4ps with 20 kV, Fsyn=813Hz, ß= 15 15

16. II.10 Some Observations and Difficulties
4ps with 20 kV, Fsyn=813Hz, ß=
Comparison of different calculations: numerical solution of the VFP-equation (red), particle tracking with different number of tracked particles, the length of tracking, and the resolution for the determination of the induced voltage. 16 16

17. II.11 Some Observations and Difficulties
4ps with 20 kV, Fsyn=813Hz, ß=
Usually tracking calculations start at I=0 from a bi-Gaussian particle distribution. For higher currents (I+ΔI) the calculation continues with the previously found distribution (I). If instead the Haissinski solution at 60 µA is used as initial distribution the black results are obtained – there appears a quite stable island between 50 and 70 µA. 17 17

18. II.12 Some Observations and Difficulties
40 µA µA µA µA
Between 50 and 70µA there exist two “more or less stable” (top and bottom) particle distributions in the longitudinal phase space. In the low current unstable region (20 – 50 µA) the particle distribution rotates very regularly in the longitudinal phase space. Above 50µA the bunches are “boiling” or can be quite “silent” up to 70µA (bottom). 18 18

19. II.13 Summary of Preliminary Results for <0
The CSR-driven longitudinal single bunch instability thresholds seem to depend always on the ratio between Tsyn and Tlong.
There is no simple scaling law relating the strength at which the instability sets in and the shielding parameter (or the normalized resonance frequency).
For short bunches my numerical solution of the VFP-equation does not yield meaningful instability thresholds – importance of shot noise?
Had to use particle tracking for shorter bunches 20 kV)
Thresholds depend on the number of tracked particles – the more the higher is the threshold.
Only for long bunches particular spectral features in the spectra of the low frequency CSR-power indicate the onset of the instability directly. Even in this region no linear relationship between the dominant frequency and 2 ·Fres·o was found (Vrf=20kV).
Only the increase in energy spread can be used for the shortest bunches as an indication for the instability. 19 19

20. III. Alternative Experimental Determination of the Effective Transverse Impedance?
smaller alpha:
beam current is lost and
filling becomes very regular
important for stable CSR
 ~
 ~
 ~ 20

21. III. Alternative Experimental Determination of the Effective Transverse Impedance?
Threshold current for the transverse mode coupling instability (according to R. Nagaoka and K. Bane):
Threshold current should be linear proportional to the momentum compaction factor, alpha. The experimental study revealed a very non-linear dependence:
Better explanation provided by Markus Ries: the smaller alpha the more the bunches are longitudinally unstable and the larger is the momentum spread. With the smaller alpha the energy acceptance is reduced substantially. This is like longitudinal scraping with reduced cavity voltage. 21

22. IV. Could Ion Trapping Limit MAX IV Performance?
MAX IV ring will use harmonic cavities in order to lengthen the bunches
Filling of all buckets foreseen in order to keep phase transients small
In the following I quote from A. Wolski‘s lecture on „Electron Cloud and Ion Effects“, 4th International Accelerator School for Linear Colliders, Beijing, September 2009:
There will be no gap in the MAX IV ring – will there be ion trapping? 22

23. IV. Could Ion Trapping Limit MAX IV Performance?
A. Wolski‘s lecture on „Electron Cloud and Ion Effects“, 4th International Accelerator School for Linear Colliders, Beijing, September 2009: 23

24. IV. Could Ion Trapping Limit MAX IV Performance?
A. Wolski‘s lecture on „Electron Cloud and Ion Effects“, 4th International Accelerator School for Linear Colliders, Beijing, September 2009:
We want to kick out ions and thus require: sbk > 2 24

25. IV. Could Ion Trapping Limit MAX IV Performance?
Experiment at BESSY II together with Simon Leemann (MAXLab): filling of every fifth RF-bucket in order to simulate the filling pattern of MAX IV
Parameter
BESSY II Ring
MAX IV 3GeV Ring
Energy/GeV
1.72
3.0
Circumference/m
240
528
RF/MHz
500
100
Harmonic number
400
176
Imax/mA
300
Emittance/nm·rad 6
0.3
Coupling/%
0.5 – 1
a few
227 corresponds to 500 IV 3 GeV ring
(204 mA equivalent to 450 mA) 25

26. IV. Ion-Trapping at the MAX IV 3 GeV ring?
Initially stable beam without transverse feedback systems – chromaticity slightly increased
After ~ 10 minutes beam starts to blow up 26

27. IV. Ion-Trapping in the MAX IV 3 GeV ring?
beam current 227 mA
beam loss monitors
vertical beam size 27
 min 

28. IV. Ion-Trapping in the MAX IV 3 GeV ring?
slow increase of beam size clear indication of ion trapping
beam current 227 mA
vertical beam size
 2 min  28

29. IV. Ion-Trapping in the MAX IV 3 GeV ring?
beam loss monitor
beam current 204 mA
vertical beam size
skew quadrupole current 29
 min 

30. IV. No Ion-Trapping in the MAX IV 3 GeV ring!
With the comparatively large beam sizes at BESSY II (and our well conditioned vacuum chamber) a current of 204 mA and filling every fifth bucket is stable over longer times without any ion clearing gap
Transversely enlarged beam will trap ions – in agreement with theoretical expectations
At BESSY beam is unstable and does trap ions if all 500 MHz-bucket are filled – gap of ~100 ns required
Based on this observation no ion-trapping to be expected for the MAX IV 3 GeV ring – the larger distance between bunches and the stronger kicks due to the much smaller emittance will kick ions away from the electron beam. 30

31. V. Single Kicker Injection Studies at BESSY II: together with O
V. Single Kicker Injection Studies at BESSY II: together with O. Dressler and S. Leemann (MAX-lab)
Beam injected into the BESSY II ring without any injection kicker – 7 turns before beam gets lost at the injection septum: 31

32. V. Single Kicker Injection Studies at BESSY II: together with O
V. Single Kicker Injection Studies at BESSY II: together with O. Dressler and S. Leemann (MAX-lab)
Horizontal diagnostics kicker (~193m downstream of injection point, half sinusoidal pulse with a full width of 1.3 s ) fired at the right time and with the right amplitude:
Not quite yet on-axis injection, however, beam can be accumulated with close to 100% efficiency with this single kicker! If the pulse duration would be 2ns than only the bunch which is topped-up would perform horizontal oscillations. 32

33. Injected beam still in phase with the storage ring RF-bucket
V. Single Kicker Injection Studies at BESSY II: together with O. Dressler and S. Leemann (MAX-lab)
Close to on-axis injection achieved by storage ring tune and amplitude adjustments of the kicker:
Injected beam still in phase with the storage ring RF-bucket 33

34. Theoretical studies required.
V. Single Kicker Injection Studies at BESSY II: together with O. Dressler and S. Leemann (MAX-lab)
Bunch injected 1 ns (half the RF-period) shifted in time – try out off-momentum injection:
Beam can only be accumulated very slowly by an additional energy mismatch between synchrotron and storage ring. In our case a rather low storage ring cavity voltage is necessary in order to cope with the large bunch length of the injected beam.
Theoretical studies required. 34

35. VI. Summary
Theoretical results for the CSR-driven longitudinal single bunch instability have been reviewed for positive momentum compaction factors
Preliminary theoretical results were given for negative momentum compaction factors - thresholds seem to depend always on the ratio between Tsyn and Tlong. Experimental results from the MLS (M. Ries) are in fair agreement with predictions.
Opposite to positive alpha there appears to be no simple scaling law.
It is a longitudinal and not the TMC-instability which leads to an equal population of buckets – the effective transverse impedance is not involved and can not be determined.
It was shown that Ion-trapping will most likely not degrade the performance of the MAXIV 3Gev ring operated without any ion clearing gap.
At BESSY II single kicker injection can be performed with very high injection efficiency.
At BESSY II the off-momentum injection efficiency suffers from the very long injected bunches – this additional longitudinal mismatch hampers the injection process. 35 35