Elias Métral, APC meeting, 02/02/2006 1/35 E. Métral, G. Arduini and G. Rumolo u Observations of fast instabilities in the SPS (1988 and 2002/3) and PS (2000) u Intensity threshold vs. beam/machine parameters u Analysis of the evolution in time of the instability  Measurements in the V- and H-planes (SPS )  Theories: BBU and HT&TMC  Simulations with the HEADTAIL code u The case of the PS instability u Conclusions and future work u Appendices: BB impedance model, FFT, spectrum analyzer, linear HT phase shift FAST VERTICAL SINGLE-BUNCH INSTABILITY AT SPS INJECTION

Elias Métral, APC meeting, 02/02/2006 2/35 Fast instability of positron bunches in the SPS  Gareyte & Brandt in 1988 (BBU analysis)

Elias Métral, APC meeting, 02/02/2006 3/35 ” Instability suppressed by increasing the chromaticity Fast vertical single-bunch instability with protons at the SPS injection in 2003

Elias Métral, APC meeting, 02/02/2006 4/35 Fast vertical single-bunch instability with protons at the PS near transition in 2000 ,  R,  V signals Time (10 ns/div) ~ 700 MHz  Instability suppressed by increasing the longitudinal emittance Head stable Tail unstable

Elias Métral, APC meeting, 02/02/2006 5/35 Scaling of the intensity threshold with beam&machine parameters The farther the transition energy the better (confirmed by the HEADTAIL code) As in the PSAs in the SPS It is not the energy which matters! !

Elias Métral, APC meeting, 02/02/2006 6/35 MEASUREMENTS IN THE VERTICAL PLANE (1/5) 1 st trace (in red) = turn 2Last trace = turn 150Every turn shown HeadTail  Travelling-wave pattern along the bunch

Elias Métral, APC meeting, 02/02/2006 7/35 MEASUREMENTS IN THE VERTICAL PLANE (2/5) 1 st trace (in red) = turn 2Last trace = turn 150Every turn shown

Elias Métral, APC meeting, 02/02/2006 8/35 MEASUREMENTS IN THE VERTICAL PLANE (3/5) 1 st trace (in red) = turn 2Last trace = turn 150Every turn shown

Elias Métral, APC meeting, 02/02/2006 9/35 Turn 99 shown Δt  1.25 ns  f  800 MHz Δt  1 ns  f  1 GHz Δt  1.1 ns  f  900 MHz MEASUREMENTS IN THE VERTICAL PLANE (4/5)

Elias Métral, APC meeting, 02/02/ /35 MEASUREMENTS IN THE VERTICAL PLANE (5/5) Betatron phase difference between different temporal slices with respect to the central slice (=centre of the bunch) Slice preceding the central one by 1 ns Slice following the central one by 1 ns Every 250 ps shown ~ Time of beam loss The phases are arranged for a coherent instability (the centre of mass changes along the bunch)

Elias Métral, APC meeting, 02/02/ /35 MEASUREMENTS IN THE HORIZONTAL PLANE (1/2) 1 st trace (in red) = turn 2Last trace = turn 150Every turn shown

Elias Métral, APC meeting, 02/02/ /35 MEASUREMENTS IN THE HORIZONTAL PLANE (2/2) Betatron phase difference between different temporal slices with respect to the central slice (=centre of the bunch) Slice preceding the central one by 1 ns Slice following the central one by 1 ns Every 250 ps shown The phases are not arranged for a coherent instability

Elias Métral, APC meeting, 02/02/ /35 BBU THEORY 1 st trace = turn 1Last trace = turn 115Every turn shown BB resonator impedance  Travelling-wave pattern along the bunch HeadTail

Elias Métral, APC meeting, 02/02/ /35 u The spectrum of mode mq (σ mq ) is peaked at and extend  2 modes with same q are peaked at the same frequency (same line density), and therefore have ~ the same sensitivity in the same frequency range. They however correspond to entirely different patterns in phase space  In the next 2 slides, the same plots as Laclare (CERN 87-03) are shown for a single (Head-Tail) mode, i.e. no TMC HT&TMC THEORY (1/10) with

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (2/10)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (3/10)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (4/10) Observations in the PS in 1999 (20 revolutions superimposed) Time (20 ns/div)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (5/10) 1 st trace = turn 1Last trace = turn 115Every turn shown Time evolution for HT mode -24 alone (no rise-time)  Standing-wave pattern

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (6/10) 1 st trace = turn 1Last trace = turn 115Every turn shown  Standing-wave pattern Time evolution for HT mode -24 alone (no rise-time)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (7/10) 1 st trace = turn 1Last trace = turn 115Every turn shown  Standing-wave pattern Time evolution for HT mode -35 alone (no rise-time)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (8/10) 1 st trace = turn 1Last trace = turn 115Every turn shown  Standing-wave pattern Time evolution for HT mode -35 alone (no rise-time)

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (9/10) 1 st trace = turn 1Last trace = turn 115Every turn shown TMC between modes -24 and -35  Complete theory not yet finished  Travelling-wave pattern along the bunch

Elias Métral, APC meeting, 02/02/ /35 HT&TMC THEORY (10/10) Instability rise-time from MOSES

Elias Métral, APC meeting, 02/02/ /35 HEADTAIL SIMULATIONS (1/5) 1 st trace = turn 1Last trace = turn 50Every turn shown Flat chamber  Travelling-wave pattern along the bunch HeadTail

Elias Métral, APC meeting, 02/02/ /35 HEADTAIL SIMULATIONS (2/5) Turn 38 shown Δz/2  16 cm  f  0.94 GHz

Elias Métral, APC meeting, 02/02/ /35 HEADTAIL SIMULATIONS (3/5) 1 st trace = turn 1Last trace = turn 50Every turn shown Round chamber  Travelling-wave pattern along the bunch

Elias Métral, APC meeting, 02/02/ /35 HEADTAIL SIMULATIONS (4/5) u Round chamber u Flat chamber  The intensity threshold is increased in a flat chamber by - The vertical Yokoya factor in the y-plane - Slightly more than the horizontal Yokoya factor in the x-plane (it is not suppressed! and the effect of the detuning impedance, if any, seems small and in the plane of higher threshold)  This is the starting point for our study on the effect of linear coupling y-Yokoya factor x-Yokoya factor

Elias Métral, APC meeting, 02/02/ /35 HEADTAIL SIMULATIONS (5/5) u The role of space charge and longitudinal mismatch has also been studied in detail in a recently published paper “Simulations of the fast transverse instability in the SPS”, G. Rumolo, V. G. Vaccaro and E. Shaposhnikova (CERN-AB RF) u Emittance blow-up in space charge regime below TMCI threshold! LHC beam !

Elias Métral, APC meeting, 02/02/ /35 THE CASE OF THE PS INSTABILITY (1/4) MEASUREMENTS IN 2000 BBU THEORY AFTER 90 TURNS (~ 200 μs)  Seem very close except head and tail exchanged!!! It may start only for the maximum peak intensity, i.e. in the middle…  Try to produce the same movie with measurements next year (as we did for the SPS fast instability at injection)  Slide from APC 08/12/05

Elias Métral, APC meeting, 02/02/ /35 THE CASE OF THE PS INSTABILITY (2/4) HEADTAIL SIMULATION 1 st trace = turn 1Last trace = turn 130Every turn shown Flat chamber HeadTail

Elias Métral, APC meeting, 02/02/ /35 THE CASE OF THE PS INSTABILITY (3/4) Turn 130 shown Δz  40 cm  f  750 MHz Δz  120 cm  f  250 MHz HEADTAIL SIMULATION

Elias Métral, APC meeting, 02/02/ /35 THE CASE OF THE PS INSTABILITY (4/4) HEADTAIL SIMULATION Same simulation for a flat bunch (same density as the Gaussian peak density) 1 st trace = turn 1Last trace = turn 100Every turn shown

Elias Métral, APC meeting, 02/02/ /35 u Using the classical BB impedance model of the SPS machine (Q~1, ~1 GHz, ~10-20 MΩ/m), the evolution in time of the instability can be reasonably reproduced (  Travelling-wave pattern along the bunch) using either the BBU or TMC formalism u The instability starts near the middle of the bunch, i.e. at the maximum of the peak intensity (and even on flat bunches)  Local phenomenon  This is why the intensity threshold is the same as the one for coasting beams with peak values  Transverse microwave instability CONCLUSIONS AND FUTURE WORK (1/3)

Elias Métral, APC meeting, 02/02/ /35 u Measured pictures very close to the simulated ones Head HEADTAIL SIMULATION MEASUREMENT CONCLUSIONS AND FUTURE WORK (2/3) Head Tail HeadTail SPS PS Head

Elias Métral, APC meeting, 02/02/ /35 CONCLUSIONS AND FUTURE WORK (3/3) u Future work: Try to better estimate the impedance (and aperture) of the machine  Produce the movies of the evolution in time of the coherent motion (instability) AND the beam intensity AND the transverse beam sizes (measurements and HEADTAIL code)  At which turn do we lose and where (BLM) and how?  Repeat the same measurements with larger transverse emittances to see the effect of space charge  Analysis of the relative difference between 2003/2004 and 2006 (4 new MKE kickers installed)  We proposed to measure the transverse impedances of these MKE kickers (without and with coating) as was done in the PS for new kickers to be installed for the new CT (the resonance frequency seems to be lower than predicted by 2D theory  Worse for TMCI)  Simulations with MAFIA by Bruno Spataro (Frascatti) of the BPM impedances (108 BPH and 108 BPV)  Ongoing

Elias Métral, APC meeting, 02/02/ /35 APPENDIX 1 : THE BB IMPEDANCE MODEL u It is a single-bunch instability  Short-range wake field  BB impedance u Measured impedances of the PS kickers for the new CT very close to BB impedances. Predictions for the MKE also u BB impedance model deduced from Head-Tail growth/decay rate u Intensity threshold vs. quality factor (from MOSES) Resonator impedance

Elias Métral, APC meeting, 02/02/ /35 APPENDIX 2 : MEASURED FFT IN V- & H-PLANE 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 μs are acquired

Elias Métral, APC meeting, 02/02/ /35 APPENDIX 3 : SPECTRUM ANALYZER IN V- & H-PLANE Transverse pick-ups (BPWA31901 for V and BPWB32101 for H) in the Faraday Cage have been connected to a Spectrum Analyzer  Wide- band directional couplers with exponential coupling, optimized for the studies of instabilities in the frequency domain

Elias Métral, APC meeting, 02/02/ /35 APPENDIX 4 : Time evolution for the linear HT phase shift (1/4) 1 st trace = turn 1 Last trace = turn 308 Every turn shown Head and Tail remain in phase LHC Project Report 602 (Fartoukh&Jones)

Elias Métral, APC meeting, 02/02/ /35 1 st trace = turn 1 Last trace = turn 308 Every turn shown LHC Project Report 602 (Fartoukh&Jones) APPENDIX 4 : Time evolution for the linear HT phase shift (2/4)

Elias Métral, APC meeting, 02/02/ /35 turn 2 Head and Tail in phase APPENDIX 4 : Time evolution for the linear HT phase shift (3/4)

Elias Métral, APC meeting, 02/02/ /35 turn 150 ~ Maximum phase difference between Head and Tail APPENDIX 4 : Time evolution for the linear HT phase shift (4/4)