HEADTAIL simulation during the accelerating ramp in the PS S. Aumon - EPFL & CERN Acknowledgement to B. Salvant, G. Rumolo

TMC Instability measurements without gamma jump Instability believed to be an TMCI Instability during the acceleration around transition Instrumentation: wide band pickup, band width 2.5MHz-1GHz (See the “A 1.5 GHz wide-band beam position and intensity monitor for the electron-positron accumulator (EPA)”) 10MHz RF cavity height 145kV instead of 200kV (ToF beam) Vertical Longitudinal

TMC Instability measurements without gamma jump: chromaticity settings The chromaticity is not measurable around 15 ms both side of transition Programmed Obtained?

Instability simulations HEADTAIL code Broad band impedance model Flat chamber No longitudinal and transverse space charge Acceleration No higher orders in momentum compaction. Chromaticity as in measurements 1 kick per turn Parameters PS - nToF R [m]100 ρ [m]70 Bdot [T/s]2.2 Vrf [kV]145 harmonic8 el [eVs] Nb [e10 p/b] Є [1σ norm] μm Betax=betay[m]16 Pipe [cmxcm]7x3.5 Qt6.22 Hor. & Vert. ξ0/0-varying Gamma transition6.08 Acceleration46 GeV/c/s

TMCI simulation without chromaticity Benchmark the rise time of the instability with/without chromaticity Systematic offset of 30 turns in the measurements compared to the simulations

TMCI simulation without chromaticity Set a broad band impedance model in HEADTAIL Rs=1.4MOhm/m, fr=1 GHz, Q=1 No coupling, no resistive wall (length set to 0) Vertical chromaticity set to 0 MeasurementsHEADTAIL

TMCI simulation without chromaticity Before transition 1000 turns before Before transition 400 turns 200 turns after transition

TMCI simulation without chromaticity Spectrum 2 frequencies 600MHz and 800MHz Look like two interfering waves

TMCI simulation without chromaticity – Static bucket Simulation in a stationary bucket (no acceleration) Same bunch length at a given energy before transition with the same bunch length and momentum spread as initial condition as in the accelerating bucket No node

TMCI simulations with chromaticity Routine implementation in HEADTAIL which change the vertical chromaticity (Qprime). Not a very elegant way The chromaticity is printed in the inph file

TMCI simulations with chromaticity After transition (200 turns) Through transitionBefore transition

TMCI simulation with chromaticity Eta= (below transition) ~100 turns before transition xiV=0.02 More we go far from transition (below), more the rise time of headtail instability is increasing Rise time (s) Mode m Rise time: Mode 0 : 0.9ms Mode 1: 1.7ms Mode 2: 2.6 ms Mode 3: 3.3 ms

TMCI simulation: tune shift FFT with sussix not suitable with acceleration since the bunch length is changing, how many turns? Try with a sliding windows and 700 turns (not enough for a FFT). Any idea, suggestion? Qy

TMCI simulation: tune shift Sliding windows Qy ??

Gamma jump in headtail Crossing Transition in the CERN PS Asymmetrical gamma jump In the past, avoid 'negative mass instability' and longitudinal space charge effect on bunch length. Doublets and triplets (combined doublets) quadrupoles in non zero dispersion locations. Designed for a Qx,y=6.25 with no tune shift. Δγt=-1.24 in 500μs RF stable phase jump at transition to keep the longitudinal focusing after transition energy

Gamma jump in headtail no chromaticity Implementation of gamma jump in headtail with interpolation equation by part (eta/ gammatranstion as a function of the energy) NOT elegant at all… If In this case, it would be nice to have a passerelle between MAD and headtail

Outlooks Strange nodes in hdtl file which are not present in the static bucket and no chromaticity (not headtail mode) Any suggestion/idea/help is very welcome (thanks already to Benoit, Elena for their suggestions) Is this phenomena appears in the simulations with gamma jump? …sometimes the documentation is not up to date..