Abstract
The Free Electron Laser (FEL) integral equation is derived from the complete set of coupled Lorentz-Maxwell equations. Its rules the evolution of the field amplitude in different regions: small-signal, longitudinal and transverse mode dynamics as well. The goal of this paper is to derive generalizations of a multidimensional FEL equation in the context of fractional calculus. The considerations are based on the perturbative approach, yielding closed-form expressions for the solution, which are suitable for numerical treatment.
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