1. Observation of Transverse Mode Coupling Instability at the PS and SPS
TMC Instability simulations and benchmarking G. Rumolo, work done with G. Arduini, H. Burkhardt, E. Métral, F. Ruggiero, E. Shaposhnikova, F. Zimmermann
Introduction
Observation of Transverse Mode Coupling Instability at the PS and SPS
HEADTAIL simulations of TMCI thresholds
Estimation of the SPS impedance, influence of space charge
TMCI with broad-band and narrow-band resonators
Impedance diagnostics techniques using TMCI
Conclusions
Darmstadt,
Giovanni Rumolo

2. Some general features of the Transverse Mode Coupling Instability
TMCI is a strong single bunch instability driven by wake fields, which sets in above a certain current threshold.
TMCI develops on a fast time scale, typically shorter than the synchrotron period.
Unlike regular head-tail instabilities, TMCI does not directly depend on the sign of chromaticity, even if positive chromaticity can help to raise its threshold.
TMCI causes coherent motion: the D signal along a bunch during a TMCI has a specific travelling wave pattern, whose shape depends on the impedance that drove the instability
The onset of TMCI corresponds to the point of merging of transverse coherent modes of oscillation of a bunch.
Darmstadt,
Giovanni Rumolo

3. , R, V signals Time (10 ns/div) ~ 700 MHz
Observation of a fast vertical single-bunch instability near transition (~ 6 GeV) in the CERN-PS
, R, V signals
Time (10 ns/div)
~ 700 MHz
Darmstadt,
Giovanni Rumolo

4. Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
Darmstadt,
Giovanni Rumolo

5. Beam: MESPS on MD segment of supercycle 950
Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
Beam: MESPS on MD segment of supercycle 950
Measurements at injection momentum 26 GeV/c.
Nbunch =1.1 x 1011 p
Bunch length (4)=3.9 ns (measured in the PS just before extraction)
L=0.176 eVs (2)
p/p (2  – before rotation in the PS)=0.414 x10-3
Chromaticity settings in the SPS:
’H =+0.2 (control settings) – (measured)
’V =+0.1 (control settings) – (measured)
200 MHz RF voltage=0.57 MV (measured in the Faraday cage)
Qy=26.14 – Qx=26.18
Darmstadt,
Giovanni Rumolo

6. Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
S (left) and D (right) signals provided by the HT monitor (vertical plane) triggered just before injection. The first trace refers to turn 2. The last trace refers to turn 192 (i.e. ~4.4 ms after injection). The time interval between two traces is 10 turns (i.e. turn 2,12,22…etc are shown)
Darmstadt,
Giovanni Rumolo

7. Chromaticity settings in the SPS were changed:
Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
Chromaticity settings in the SPS were changed:
’H =+0.2 (control settings) – (measured)
’V =+0.5 (control settings) – this should correspond to (measured)
Rest unchanged:
200 MHz RF voltage=0.57 MV (measured in the Faraday cage)
Qy=26.14 – Qx=26.18.
The beam parameters should be also unchanged
Nbunch =1.1 x 1011 p
Bunch length (4)=3.9 ns (measured in the PS just before extraction)
L=0.176 eVs (2)
p/p (2  – before rotation in the PS)=0.414 x 10-3
Darmstadt,
Giovanni Rumolo

8. Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
S (left) and D (right) signals provided by the HT monitor (vertical plane) triggered just before injection. The first trace refers to turn 2. The last trace refers to turn 192 (i.e. ~4.4 ms after injection). The time interval between two traces is 10 turns (i.e. turn 2,12,22…etc are shown)
Darmstadt,
Giovanni Rumolo

9. Chromaticity settings in the SPS:
Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
Chromaticity settings in the SPS:
’H =+0.3 (control settings) – (measured)
’V =+2.0 (control settings) – this should correspond to (measured)
Rest unchanged:
200 MHz RF voltage=0.57 MV (measured in the Faraday cage)
Qy =26.14 – Qx=26.18.
The beam parameters should be also unchanged
Nbunch =1.1 x 1011 p
Bunch length (4)=3.9 ns (measured in the PS just before extraction)
L=0.176 eV.s (2)
p/p (2  – before rotation in the PS)=0.414 x 10-3
Darmstadt,
Giovanni Rumolo

10. Observation of a fast vertical single-bunch instability at injection (26 GeV) in the CERN-SPS
S (left) and D (right) signals provided by the HT monitor (vertical plane) triggered just before injection. The first trace refers to turn 2. The last trace refers to turn 192 (i.e. ~4.4 ms after injection). The time interval between two traces is 10 turns (i.e. turn 2,12,22…etc are shown)
Darmstadt,
Giovanni Rumolo

11. Darmstadt,
Giovanni Rumolo

12. Darmstadt,
Giovanni Rumolo

13. Darmstadt,
Giovanni Rumolo

14. Predictions of TMCI thresholds: MOSES
TMCI thresholds can be evaluated using the Transverse Mode Coupling theory. Given a resonator impedance, the MOSES code predicts at which bunch intensity the first mode coupling occurs. The growth time of the resulting instability (as a function of the bunch intensity above threshold) is also an output of the code.
First mode coupling associated to a weak instability
Second mode coupling: strong instability
Darmstadt,
Giovanni Rumolo

15. Predictions of TMCI thresholds: HEADTAIL
HEADTAIL does particle tracking for a bunch that interacts at each turn with a known impedance (resonator, resistive wall, collimators).
 The TMCI threshold is inferred by the sudden change from a stable to an unstable regime, in which the coherent motion of the bunch centroid exhibits exponential growth.
Advantages of HEADTAIL:
It allows for full simulations of flat geometries by using dipole and quadrupole wakes appropriately scaled by the Yokoya factors.
It allows for simulation of longitudinally unmatched bunches
It allows for combined impedance-space charge simulations.
It gives as an output the full bunch dynamics in the unstable regime.
Darmstadt,
Giovanni Rumolo

16. Benchmarking MOSES and HEADTAIL
E. Métral et al.
„Transverse Mode Coupling Instability in the CERN-SPS“
ICFA-HB2004, Bensheim, Germany, 18-22/10/2004
The agreement between HEADTAIL and MOSES is excellent for low longitudinal emittances.
The agreement is worse but still keeps within a factor less than 2 for high longitudinal emittances.
Darmstadt,
Giovanni Rumolo

17. The case of the PS instability with HEADTAIL - I
Darmstadt,
Giovanni Rumolo

18. The case of the PS instability with HEADTAIL - II
Darmstadt,
Giovanni Rumolo

19.  Space charge seems to play a significant role at 26 GeV.
Trying to extrapolate the SPS transverse impedance from TMCI measurements (fitting with a broad-band resonator) - I
“Simulations of the fast transverse instability in the SPS”,
G. Rumolo, E. Shaposhnikova and V.G. Vaccaro (CERN-AB RF)
We use a broad-band resonator (Q=1) with a resonance frequency of wr =2 p x 1.3 GHz, and change the Rs value to fit the observed thresholds.
 Space charge seems to play a significant role at 26 GeV.
Darmstadt,
Giovanni Rumolo

20. Trying to extrapolate the SPS transverse impedance from TMCI measurements (fitting with a broad-band resonator) - II
HEADTAIL results
LHC beam
If the installation of 5 new MKE kickers into the SPS raises the impedance by ~3MW/m, the nominal LHC beam is only stable when captured in a 2 MV bucket.
Darmstadt,
Giovanni Rumolo

21. Trying to extrapolate the SPS transverse impedance from TMCI measurements (fitting with a broad-band resonator) - III
Space charge seems beneficial since it raises the TMCI threshold but...
 Effect of space charge below TMCI threshold: given the initial small beam transverse sizes, impedance + space charge cause fast emittance blow up before instability
Darmstadt,
Giovanni Rumolo

22. Darmstadt,
Giovanni Rumolo

23. Vertical impedance per BPM bx (m) by (m) fr (GHz) R (MW/m) Q
Could the main impedance source be the BPM‘s? - I
From B. Spataro‘s MAFIA study of the SPS BPM‘s 4 dangerous transverse trapped modes are found (2 for the horizontal BPM‘s and 2 for vertical ones):
Vertical impedance per BPM
bx (m)
by (m)
fr (GHz)
R (MW/m) Q
BPH
103 21
0.537
4.6
1951
1.836
2.35
3367
BPV 22
101
0.786
1.67
2366
2.27
2.05
5880
# of BPM‘s  108 (H) (V)
Darmstadt,
Giovanni Rumolo

24. Could the main impedance source be the BPM‘s? - II
Flag_for_bunch_particles_(1->protons_2->positrons_3&4->ions): 1
Number_of_particles_per_bunch: e+12
Bunch_length_(rms_value)_[m]:
Horizontal_beam_size_(rms_value)_[m]:
Vertical_beam_size_(rms_value)_[m]:
Longitudinal_momentum_spread:
Momentum_compaction_factor:
Ring_circumference_length_[m]:
Relativistic_gamma:
Number_of_kick_sections:
Number_of_turns:
Longitud_extension_of_the_bunch_(+/-N*sigma_z)
Horizontal_tune:
Vertical_tune:
Horizontal_chromaticity:
Vertical_chromaticity:
Flag_for_synchrotron_motion:
Switch_for_wake_fields:
Switch_for_pipe_geometry_(0->round_1->flat):
Flag_for_the_tune_spread_(0->no_1->space_charge_2->random):
Flag_for_the_e-field_calc_method_(0->no_1->soft_Gauss_2->PIC): 0
x-kick_amplitude_at_t=0_[m]:
y-kick_amplitude_at_t=0_[m]:
Switch_for_amplitude_detuning:
Number_of_turns_between_two_bunch_shape_acquisitions:
Cavity_voltage_[V]: e+6
Cavity_harmonic_number:
Bunch total length 2.67 ns
Chosen to be matched to the given length for the given voltage
Means only a vertical impedance
No space charge and no e-cloud
Darmstadt,
Giovanni Rumolo

25. Could the main impedance source be the BPM‘s? - III
Nominal tune
Looking for the threshold we do a scan in increasing bunch current values.
Tune shift with current:
The main tune line shifts to lower values (as expected)
The amplitude of the secondary line (m=-2) increases and the line shifts, too.
The instability seems to appear left of the line m=-2 as result of merging of the shifting lines.
Darmstadt,
Giovanni Rumolo

26. Could the main impedance source be the BPM‘s? - IV
The threshold for TMCI is found to sit at around 1.0 x 1012 ppb
Below threshold in the range x 1012 ppb, a coherent motion on the Dy signal along the bunch is visible, but not leading eventually to an instability.
Nb=0.7 x 1012 ppb
Nb=1.1 x 1012 ppb
Darmstadt,
Giovanni Rumolo

27. Can we reconstruct the impedance from the TMCI signal? - I
From measurements
FFT of the HT monitor signals applied over the full acquisition depth (372 turns ~ 8.6 ms). The peaks at 40 MHz are due to the fact that at each turn only 25 ns out of the full revolution period of 23.1 ms are acquired
Darmstadt,
Giovanni Rumolo

28. Can we reconstruct the impedance from the TMCI signal? - II
From measurements
The transverse pick-ups in the Faraday Cage have been connected to a Spectrum Analyzer, which does an on-line the Fourier transform of the bunch signal. Frequency sweeps over 500 MHz are done to reconstruct the full signal up to 2.5 GHz.
Darmstadt,
Giovanni Rumolo

29. Can we reconstruct the impedance from the TMCI signal? - III
From simulations
fr=0.7 GHz
Using the short SPS bunches and a single broad-band resonator (Q=1) on different frequencies, we see peaks in the spectrum, but shifted at lower frequencies than that of the driving resonator
fr=1.0 GHz
fr=1.3 GHz
Darmstadt,
Giovanni Rumolo

30. Can we reconstruct the impedance from the TMCI signal? - IV
From simulations
Using the short SPS bunches and the 4 narrow-band resonators on different frequencies, we see only 1 peak in the spectrum, perhaps located at the frequency of the resonator that first determines the TMCI...
Using the long PS bunches and the a broad-band resonator, the spectrum is peaked exactly at the frequency of the resonator.
Darmstadt,
Giovanni Rumolo

31. Conclusions and outlook
SPS experiment
SPS simulation
PS simulation
PS experiment
Darmstadt,
Giovanni Rumolo

32. Conclusions and outlook
We have confidence in our simulation tools, MOSES and HEADTAIL, and their predictive power of the TMCI thresholds.
The TMCI threshold is certainly increased by space charge, but there is an emittance blow up below threshold that could degrade the beam.
The nominal LHC beam in the SPS could be unstable after the installation of the new 5 MKE kickers. Impedance needs to be controlled.
The source of the SPS transverse impedance is unlikely to be the BPM‘s alone, because the threshold due to their trapped modes would be much higher than the one observed.
Reconstruction of the impedance from the observed TMCI signal is not straightforward for short bunches (like in the SPS).
Measurements with longer (maybe debunching?) bunches should be pursued to gain information on the frequency content and possible sources of the machine transverse impedance.
Darmstadt,
Giovanni Rumolo