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New tool for beam break-up analysis

New tool for beam break-up analysis. TM 110. y. y. 2 nd pass deflected beam. z. x. injected beam. E. B. Reasons for writing a new code: TDBBU weaknesses need for new features need for an ‘in-house’ code. bi - ‘beam instability’ code. Features: allows any ERL topology

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New tool for beam break-up analysis

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  1. New tool for beam break-up analysis TM110 y y 2nd pass deflected beam z x injected beam E B • Reasons for writing a new code: • TDBBU weaknesses • need for new features • need for an ‘in-house’ code

  2. 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. 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: 1 2 3 … N – 2 N – 1 N actual HOMs (n  N): hom 1 hom 2 … hom (n – 1) hom n

  4. 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 {qn, dn}: “t” “e” t

  5. Horner’s trick Problem: evaluate polynomial: an xn + an–1 xn–1 + … + a1 x + a0 Correct answer: (…(anx + an–1) x + an–2) x + … ) x + a0 In the same vein: Introduce complex kick from HOM: CPU expenses then become linear with the size of the problem

  6. moving average LSM 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

  7. Calibration: single HOM recirculator 1st order perturbation approach fails

  8. HOM frequency randomization (fixed current) rms = 0 Hz rms = 33 kHz rms = 42 kHz rms = 46 Hz rms = 53 kHz rms = 67 kHz

  9. 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. no displacement 2.8 mm (rms) 5.6 mm (rms) HOM displacement effect • No change in threshold due to displacement errors is observed. • There is emittance growth when operating near the threshold. • Average kick amplitude grows.

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