1. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 1 CHESS / LEPP New tool for longitudinal BBU simulations injected beam 2 nd pass deflected beam Longitudinal BBU interaction with monopole modes through arc’s R 56 worst case threshold is given by monopole (m = 0) TM 01 -like y z EB x y high losses, no kick R 56

2. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 2 CHESS / LEPP 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. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 3 CHESS / LEPP Benchmarking HOM frequency [GHz] threshold current [mA] tracking formula E = 30 MeV, (R/Q) = 100, Q = 10000, R 56 = –10 m, t r = 10t 0

4. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 4 CHESS / LEPP Some features of the longitudinal instability similar to transverse BBU in its scaling:  [(R/Q)Q  ] –1,  E “bad” frequencies (n +  ¼)  0 does not grow exponentially, but saturates bunch # arrival time difference [ps] I = 22.0 mA I = 23.0 mA I = 22.1 mA

5. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 5 CHESS / LEPP Instability vs. Resonance bunch # HOM-induced energy difference [eV] I = 23.0 mA 13.0325 GHz 13.0 GHz

6. Ivan Bazarov, New Tool for Longitudinal BBU Simulations, SRF mtg, 7 October 2003 6 CHESS / LEPP 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) time [  s] induced energy at the last HOM [eV] recirculation time beam is on for 20  s