Resonant dynamics in presence of space charge G. Franchetti, GSI 8/5/2018 1 Giuliano Franchetti
Treatment of nonlinear dynamics 1) Amplitude dependent detuning Main effects of 2) Resonances (stable, unstable) Nonlinearities 3) DA and all stochastic seas Treatment R. Hagedorn, Report No. CERN 57–1, 1957. R. Hagedorn and A. Schoch, Report No. CERN 57–1 A. Schoch, Report No. CERN 57-23, 1958 G. Guignard, Report No. CERN 76–06, 1976. Analytic G. Guignard, Report No. CERN 78–11, 1978. 1) Perturbative 2) Normal form Numerical 1. Symplectic tracking 2. Early indicators (not so easy) 8/5/2018 2 Giuliano Franchetti
Popular tools Driving terms Measurement Resonance compensation Resonance driving terms Prediction of amplitude dependent detuning Interpolating Hamiltonian, Normal Form Note: DA still computed by brute force tracking 8/5/2018 3 Giuliano Franchetti
Space Charge (direct) Coherent Effects Incoherent Effects Space charge forces Space charge forces Feature acts only on particles create a collective beam like “external forces” response: Example • Amplitude dependent detuning Envelope oscillations • Tune-spread • Envelope instabilities • Modification of optics • Coherent tunes • Structure resonances • • .. Time scale Fast Fast Sometimes the distinction is ambiguous! Interplay: direct vs. indirect, coherent/incoherent subject of investigation 8/5/2018 4 Giuliano Franchetti
Space Charge in a circular accelerator Some issues 1) Space charge + resonances in coasting beams 2) Space charge + resonances in bunched beams 3) Collective beam response to direct space charge forces K. Schindl CAS 2003 8/5/2018 5 Giuliano Franchetti
Start of HB series 20th ICFA Advanced Beam Dynamic Workshop on High Intensity and High Brightness Hadron Beams, 8-12 April 2002, Fermilab, Chicago, USA. 8/5/2018 6 Giuliano Franchetti
Timeline Coherent coherent/ return of the Incoherent few % beam loss Vs core stability incoherent Incoherent Incoherent tuneshift Emittance preservation Particle core models Machines studies multiparticle simulations simulations codes CERN,GSI, J-PARC, SNS KV Sacherer’s theory Laslett machine modeling in codes long term tracking (frozen) coupling with EC, and other effects HB starts ~ 1985 ~ 1990 ~ 2000 Thanks to Shinji 7/11/15 7 G. Franchetti
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