A virtual dielectric eigenmode expansion of high-gain FEL radiation for study of paraxial wave mode coupling

An expansion of guided free-electron laser radiation is presented in terms of eigenmodes of a transversely varying dielectric waveguide. For a particular quadratic distribution of the refractive index, the constituent eigenmode expansion basis is equivalent to a free-space paraxial basis evaluated at the mode waist, which facilitates investigations of guided coupling to naturally diffracting Gaussian modes over many Rayleigh lengths. A set of coupled differential equations is derived for the slowly varying field mode amplitude coefficients and the longitudinal electron density bunching in the cold-beam fluid approximation. Preliminary results calculated in this formulation show that selective amplification of dominant higher-order modes, particularly azimuthal modes, can be achieved by seeding with higher-order spatial modes and by selective density pre-bunching of the electron beam.