Threedimensional numerical simulations of FEL's by the transverse mode spectral method
Abstract
A numerical method is presented for solving a threedimensional radiation field by decomposing the radiation field into transverse modes that satisfy the free space wave equation and the boundary conditions. The formalism includes betatron oscillations in a realizable wiggler, finite emittance, and energy spread in an amplifier or oscillator configuration. This formalism can be generalized to calculate sidebands resulting from the synchrotron oscillations. The transverse mode spectral method is compared to the finite difference method, spectral method, and transform spectral method. Examples from a computer code using GaussianHermite expansion are given. Selffocusing of the radiation beam due to gain and refraction of the FEL is shown.
 Publication:

IEEE Journal of Quantum Electronics
 Pub Date:
 July 1985
 DOI:
 10.1109/JQE.1985.1072764
 Bibcode:
 1985IJQE...21..970T
 Keywords:

 Free Electron Lasers;
 Laser Outputs;
 Radiation Distribution;
 Betatrons;
 Energy Conservation;
 Finite Difference Theory;
 Self Focusing;
 Sidebands;
 Spectral Methods;
 Wave Equations;
 Wiggler Magnets;
 Lasers and Masers