Correction to the adiabatic approximation for variable parameter freeelectron lasers
Abstract
The limits of validity of the adiabatic approximation commonly used in onedimensional theories of variable parameter freeelectron lasers (FEL) are obtained by formulating a Lietransform perturbation theory in which the zerothorder problem is the adiabatic approximation, modified to include any secular effects due to the nonadiabatic part of the Hamiltonian. It is shown that secular effects are absent in first order, and that the secondorder secular terms can be neglected in practical FEL calculations. The lowest order nonsecular effects are evaluated by perturbation theory and are shown to yield small terms which can easily be included in Maxwell's equations for the signal field.
 Publication:

IEEE Journal of Quantum Electronics
 Pub Date:
 August 1981
 DOI:
 10.1109/JQE.1981.1071291
 Bibcode:
 1981IJQE...17.1469G
 Keywords:

 Adiabatic Conditions;
 Approximation;
 Error Analysis;
 Free Electron Lasers;
 Perturbation Theory;
 Correction;
 Fourier Series;
 Hamiltonian Functions;
 Lie Groups;
 Liouville Equations;
 Maxwell Equation;
 Wiggler Magnets;
 Lasers and Masers