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New tool for longitudinal BBU simulations

monopole ( m = 0). TM 01 -like. y. y. z. x. E. B. high losses, no kick. New tool for longitudinal BBU simulations. R 56. 2 nd pass deflected beam. injected beam. Longitudinal BBU interaction with monopole modes through arc’s R 56 worst case threshold is given by.

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New tool for longitudinal BBU simulations

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  1. monopole (m = 0) TM01-like y y z x E B high losses, no kick New tool for longitudinal BBU simulations R56 2nd pass deflected beam injected beam • Longitudinal BBU • interaction with monopole modes through arc’s R56 • worst case threshold is given by

  2. Implementation of the code Features: • allows any ERL topology • arbitrary bunch pattern • implemented by using Standard Template Library (STL) of C++ Performance • surprisingly fast (0.1 ms of 5 GeV ERL takes ~ 1 min on my 800 MHz laptop) • clear and concise code

  3. Benchmarking E = 30 MeV, (R/Q) = 100, Q = 10000, R56 = –10 m, tr = 10t0 tracking formula threshold current [mA] HOM frequency [GHz]

  4. Some features of the longitudinal instability I = 22.0 mA • similar to transverse BBU in its scaling:  [(R/Q)Q]–1, E • “bad” frequencies (n +¼)0 • does not grow exponentially, but saturates I = 22.1 mA arrival time difference [ps] I = 23.0 mA bunch #

  5. Instability vs. Resonance I = 23.0 mA 13.0325 GHz HOM-induced energy difference [eV] 13.0 GHz bunch #

  6. Outlook • have all the necessary in-house tools to simulate long-range HOM interaction with the beam in ERL (e.g cumulative effects, multipass BBU) • useful to simulate transients (ion gap, start-up), beam induced power, etc. • study of possible feedback remedy for BBU • full longitudinal–dipole–quadrupole wake interaction (e.g. through dispersion in the linac) recirculation time induced energy at the last HOM [eV] beam is on for 20 s time [s]

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