Abstract

In a high gain FEL, the radius of the radiation field can remain approximately constant over many Rayleigh lengths due to the self-focusing phenomenon. Fully 3-D simulations of the FEL in this operating regime, including energy spread and finite emittance, can be costly. In this paper we present a technique that could reduce the computational requirements for a strongly self-focused FEL. The radiation field is expanded in a set of Hermite polynomials in which the arguments and coefficients are determined by the particular source term in the wave equation somewhat like a WKB expansion. In this novel formalism, the lowest-order terms are a good approximation to the exact solution. We present 3-D numerical results with this technique and compare them with the analytical results.

© 1986 Optical Society of America