Gain and modecoupling in a threedimensional freeelectron laser  A generalization of Madey's theorem
Abstract
A generalized formulation of Madey's theorem, giving a relation between spontaneous emission and gain of an undulator, is proved to hold in a threedimensional, multimode context. This formulation is then used to obtain an expression of the full transition matrix representing the smallsignal gain and mode coupling of an undulator, both in the planewave and Gaussianmode representations. On this basis, several approximate results are obtained, showing how this approach is able to take into account the finite section and divergence of the electron as well as the laser beam and to give simple explanation of the operation of a widebeam FEL and of the ACO modecoupling measurements.
 Publication:

IEEE Journal of Quantum Electronics
 Pub Date:
 July 1985
 DOI:
 10.1109/JQE.1985.1072770
 Bibcode:
 1985IJQE...21..952L
 Keywords:

 Coupled Modes;
 Electrodynamics;
 Free Electron Lasers;
 Laser Outputs;
 Power Gain;
 Spontaneous Emission;
 Electromagnetic Interactions;
 Electron Energy;
 Electron Scattering;
 Hamiltonian Functions;
 Matrices (Mathematics);
 Plane Waves;
 Reciprocity Theorem;
 Storage Rings (Particle Accelerators);
 Wiggler Magnets;
 Lasers and Masers