EUROTeV-Report-2007-029 Cockcroft-07-20 COLLIMATOR WAKEFIELDS: FORMULAE AND SIMULATION ∗

The effect of a leading particle on a trailing particle due to resistive and geometric wakefields in collimators can be described by expanding in a series of angular mode po-tentials Wm(s). Several formulae for these are given in the literature. We compare these formulae with numerical predictions from codes that solve the EM field equations. We also show how the EM code results can be used to nu-merically obtain angular mode potentials suitable for use in tracking codes. WAKE FIELDS IN COLLIMATORS In the collimation system of the ILC the beams pass very close to the collimator edges, which may lead to significant wakefield effects. Collimators, unlike cavities, are not basi-cally resonant structures, so the behaviour is not dominated by resonant modes. Long range inter-bunch wakefields are therefore unimportant, whereas short range intra-bunch ef-fects can be significant. Because parts of the beam are near the edge of the conductor, high order angular modes can become important. Effects from transverse wakefields are believed to be more important than longitudinal ones. The study of these effects continues[1, 2]. BUNCH WAKES AND DELTA WAKES A particle going through an aperture induces charges and currents which produce electromagnetic fields (wake fields) that act on later particles. The simulation programs need to know the effect that a leading particle with some transverse co-ordinate ~r ′ has on some particle with trans-verse co-ordinate ~r trailing by some distance s. For axially symmetric apertures the transverse dependence is taken care of by a sum over modes m = 0, 1, 2.. leaving the wake functions Wm(s). These functions for individual particles are termed the delta wakes. The effect on the trailing particle comes not only from this particular leading particle but from all particles in the bunch which are ahead of it. This aggregated wake func-tions are termed the bunch wakes. Bunch wakes can be determined from delta wakes by summation or integration. The question addressed here is how to obtain knowledge of the delta wakes from the bunch wakes. ∗Work supported by the EU Framework VI program, contract 01189