Analytical and numerical treatment of a multidimensional fractional FEL equation

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.

Keywords:

• equation
• fractional integral and derivatives
• Hermite polynomials
• Laguerre polynomials

Acknowledgement^∗:The present research was supported by DFG (Deutsche Forschungsgemeinschaft).

Acknowledgement^∗:The present research was supported by DFG (Deutsche Forschungsgemeinschaft).

Notes

Acknowledgement^∗:The present research was supported by DFG (Deutsche Forschungsgemeinschaft).