Fields and characteristic impedances of dipole and quadrupole cylindrical stripline kickers

We present semi-analytical methods for calculating the electromagnetic field in dipole and quadrupole stripline kickers with curved plates of infinitesimal thickness. Two different methods are used to solve Laplace's equation by reducing it either to a single or to two coupled matrix equations; they are shown to yield equivalent results. Approximate analytic solutions for the lowest order fields (dipole or quadrupole) are presented and their useful range of validity are shown. The kickers plates define a set of coupled transmission lines and the characteristic impedances of modes relevant to each configuration are calculated. The solutions are compared with those obtained from a finite element solver and found to be in good agreement. Mode matching to an external impedance determines the kicker geometry and this is discussed for both kicker types. We show that a heuristic scaling law can be used to determine the dependence of the characteristic impedance on plate thickness. The solutions found by semi-analytical methods can be used as a starting point for a more detailed kicker design.