## Abstract

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.

Original language | English |
---|---|

Pages | 65-68 |

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

Conference | 29th International Free Electron Laser Conference, FEL 2007 |
---|---|

Country/Territory | Russian Federation |

City | Novosibirsk |

Period | 26/08/07 → 31/08/07 |