Computation of Electromagnetic Fields Generated by Relativistic Beams in Complicated Structures

We discuss numerical methods for computation of wake fields excited by short bunches in accelerators. The numerical methods to implement a low-dispersive scheme, conformal approximation of the boundaries, surface conductivity, and indirect wake potential integration are reviewed. The implementations of these methods in electromagnetic code ECHO for 2D and 3D problems are presented. Several examples of application of the code to important problems in the European Free Electron Laser project and in the Linac Coherent Light Source (LCLS) project are considered