1. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 1 CHESS / LEPP New tool for beam break-up analysis y z y x EB injected beam 2 nd pass deflected beam Reasons for writing a new code: TDBBU weaknesses need for new features need for an ‘in-house’ code TM 110

2. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 2 CHESS / LEPP bi - ‘beam instability’ code Features: allows any ERL topology cleaner algorithm than TDBBU (very likely a personal bias) written in C++ (compiles with GNU GCC, i.e. all major OS) faster than TDBBU (a single 5 GeV ERL run takes less than a minute; execution time is estimated to be 7-9 times faster than TDBBU when no coupling is present; with coupling it is estimated to be at least 4 times faster) easier to use

3. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 3 CHESS / LEPP Basic algorithm Expand beam line into a consecutive list of cavities (pointers) in the same order a bunch sees them in its lifetime (from injection to dump); Link pointers to actual HOMs; Start filling beam line with bunch train; Determine which pointer sees a bunch next; Update wake-field in HOM which is pointed by the pointer; Push the bunch to next pointer, store its coordinates until they are needed by any bunch that will reach this point next; consecutive list of cavities: actual HOMs (n  N): hom 1 hom 2 … hom (n – 1) hom n 123…N – 2N – 1N

4. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 4 CHESS / LEPP Wake arithmetics Wake function due to single bunch: Electrons in “test” bunch will get a kick: Same for “test” bunch trailing behind a bunch train {q n, d n }:  “e”“t”

5. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 5 CHESS / LEPP Horner’s trick Problem: evaluate polynomial: a n x n + a n–1 x n–1 + … + a 1 x + a 0 Correct answer: (…(a n x + a n–1 ) x + a n–2 ) x + … ) x + a 0 In the same vein: Introduce complex kick from HOM: CPU expenses then become linear with the size of the problem

6. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 6 CHESS / LEPP findbi – utility to find threshold Features: uses amplitude of complex kick due to HOM to determine whether case is stable uses bisection method to find threshold until derivative of wake amplitude growth rate vs. beam current stabilizes, then uses Newton-like method finds threshold with 0.1 % accuracy in a typical  8 iteration calls moving average LSM

7. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 7 CHESS / LEPP Calibration: single HOM recirculator 1 st order perturbation approach fails

8. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 8 CHESS / LEPP HOM frequency randomization (fixed current) rms = 0 Hzrms = 33 kHz rms = 42 kHz rms = 46 Hzrms = 53 kHz rms = 67 kHz

9. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 9 CHESS / LEPP Simulation example: ‘ERL in CESR tunnel’ single “worst” HOM: R/Q = 51.5 , Q = 50000, f = 2575 MHz frequency spread applied (rms):3 MHz smallest threshold found so far:163 mA (linac lattice DCS, 04/01/03, max beta 80 m)

10. Ivan Bazarov, New Tool for Beam Break-up Simulations, SRF mtg, 9 April 2003 10 CHESS / LEPP HOM displacement effect 5.6 mm (rms) 2.8 mm (rms) no displacement No change in threshold due to displacement errors is observed. There is emittance growth when operating near the threshold. Average kick amplitude grows.