We present a description of free-electron laser (FEL) radiation in the high-gain, small-signal regime through an expansion of eigenmodes of a virtual dielectric waveguide. A set of coupled differential equations is derived for the slowly-varying mode expansion coefficients and the electron beam density modulation amplitudes. The equations are decoupled into an algebraic matrix equation for solutions of the self-similar FEL supermodes that propagate with a self-similar profile. For a suitable choice of the form of the virtual dielectric, this virtual dielectric waveguide expansion (VDE) approach has the advantage of describing gain-guided FEL radiation over many Rayleigh lengths in terms of a basis that parallels the standard gaussian modes of free-space paraxial optics.
|Number of pages||4|
|State||Published - 2007|
|Event||29th International Free Electron Laser Conference, FEL 2007 - Novosibirsk, Russian Federation|
Duration: 26 Aug 2007 → 31 Aug 2007
|Conference||29th International Free Electron Laser Conference, FEL 2007|
|Period||26/08/07 → 31/08/07|