Calculation of the Greenʹs function for an axisymmetric diaphragm focusing line

A novel type of an FEL amplifier with diaphragm focusing line (periodically spaced absorbing screens with holes) has perspective to be used for application where high average and peak radiation power is required. In this paper we present the derivation of the Greenʹs function for diaphragm focusing line. The approach to obtain the Greenʹs function is based on the using of impedance boundary conditions proposed by Veinstein, Open Resonators and Waveguides, Sovetskoe Radio, Moscow, 1996. This algorithm of electromagnetic field calculations can be implemented in linear and nonlinear codes for simulation of the FEL amplifier with diaphragm focusing line.