ANALYTICAL TREATMENT OF THE HIGH-GAIN FREE-ELECTRON LASER EQUATION

Exact solutions are obtained for the monodimensional and higher dimens ional Free Electron Laser high-gain equations. These equations, which belong to the class of integrodifferential Volterra equations are trea ted within the context of a perturbative approach, yielding suitable c losed-form expressions for the relevant solutions. The proposed method allows to obtain a unified analytical formalism for the full FEL dyna mics. Numerical results are given for the one-dimensional case where a suitable expression has been derived for the solution in terms of eas ily computable functions. Copyright (C) 1996 Elsevier Science Ltd.