Indirect methods for wake potential integration

The development of the modern accelerator and free-electron laser projects requires to consider wake fields of very short bunches in arbitrary three dimensional structures. To obtain the wake numerically by direct integration is difficult, since it takes a long time for the scattered fields to catch up to the bunch. On the other hand no general algorithm for indirect wake field integration is available in the literature so far. In this paper we review the known indirect methods to compute wake potentials in rotationally symmetric and cavity-like three dimensional structures. For arbitrary three dimensional geometries we introduce several new techniques and test them numerically.