Formulation of normalized nonlinear free electron laser equations
Abstract
The general nonlinear selfconsistent equations describing the Free electron laser (FEL) in the steady state amplifying configuration is derived with the space charge effects and all the efficiency enhancement schemes: (1) a spatially varying wiggler amplitude and/or period and (2) a d.c. electric field E sub DC (z) = ((del phi sub DC)/del z)ecarat sub z. All the efficiency enhancement schemes are shown to be somewhat equivalent. For a variable period magnetic wiggler, the FEL equations can be appropriately normalized to a three parameter set of coupled equations. All operating regimes are covered by these normalized equations. The condition for space charge to be unimportant is given. In the absence of the space charge effects, the three parameter set of equations reduces to a two parameter set. The inclusion of additional efficiency enhancement schemes increases the number of parameters to describe the FEL. Curves showing the efficiency, radiation amplitude and growth rate will be presented.
 Publication:

Naval Research Lab. Report
 Pub Date:
 December 1981
 Bibcode:
 1981nrl..reptW....T
 Keywords:

 Free Electrons;
 Laser Applications;
 Nonlinear Equations;
 Phase Shift;
 Charged Particles;
 Electric Fields;
 Lorentz Force;
 Magnetic Pumping;
 Wiggler Magnets;
 Lasers and Masers