  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.
