Variational approach for coupled backward and forward wave excitation in free-electron lasers

In a recent paper [1] we have described a novel variational formulation for the propagation and generation of radiation in wave-guides The work underlines calculation of modal amplitude evolution rather than the calculation of the modal shapes, which is common in previous art. Modal amplitude evolution is important in electron devices such as free electron lasers and gyrotrons. The present paper deals with a variational derivation of a numerical scheme that can be used to study the build up of radiation in free electron lasers in the linear approximation.