Indirect methods for wake potential integration

The development of modern accelerator and free-electron laser projects often requires one to consider wakefields of very short bunches in arbitrary three-dimensional structures. To obtain the wake numerically by direct integration of fields is difficult, since it can take a long time for fields scattered off the structure to catch up to the short bunch. On the other hand, no general algorithm for indirect wakefield integration exists in the literature. In this report we review the known indirect methods to compute wake potentials in rotationally symmetric and cavitylike three-dimensional structures. We present several extensions to the existing techniques and then derive a new general indirect method for arbitrary three-dimensional structures. Finally, the new method is numerically tested and applied to the problem of a rectangular collimator.