Selfconsistent kinetic description of the free electron laser instability in a planar magnetic wiggler
Abstract
The linearized VlasovMaxwell equations are used to investigate detailed free electron laser (FEL) stability properties for a tenuous relativistic electron beam propagating in the zdirection through the planar wiggler magnetic field. The theoretical model neglects longitudinal perturbations and transverse spatial variations. For low or moderate electron energy, there can be a sizeable modulation of beam equilibrium properties by the wiggler field and a concomitant coupling of the k'th Fourier component of the wave to the components k + or  2k0, k + or  4k0,... in the matrix dispersion equation. In the diagonal approximation, investigations of detailed stability behavior range from the regime of strong instability (monoenergetic electrons) to weak resonant growth (sufficiently large energy spread). In the limit of ultrarelativistic electrons and very low beam density, the kinetic dispersion relation is compared with the dispersion relation obtained from a linear analysis of the conventional Comptonregime FEL equations. Finally, assuming ultrarelativistic electrons and a sufficiently broad spectrum of amplifying waves, the quasilinear kinetic equations appropriate to the planar wiggler configuration are presented.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 May 1985
 Bibcode:
 1985STIN...8616568D
 Keywords:

 BoltzmannVlasov Equation;
 Coupling;
 Free Electron Lasers;
 Kinetic Theory;
 Maxwell Equation;
 Plasmas (Physics);
 Relativistic Electron Beams;
 Self Consistent Fields;
 Stability;
 Wiggler Magnets;
 Compton Effect;
 Electron Beams;
 Fourier Series;
 Liouville Equations;
 Magnetic Fields;
 Lasers and Masers