Normalized averaged equations of the helical motion of relativistic electrons in gyroresonance regimes. I. II Quasiplane approximation
Abstract
The present study derives a normalized system of differential equations of the averaged magnetically guided motion of relativistic electrons in the field of a resonant electromagnetic wave (possibly hybrid and nonsinusoidal) propagating with arbitrary phase velocity. The normalization is performed by a set of dimensionless parameters of transversely weakly relativistic theory and one new parameter, which is a specific property of the essentially relativistic theory. In addition, a determination is made of the approximate reducibility of the averaged equations of the gyroresonant motion of electrons in the field of a nonplane electromagnetic wave to a simplified form corresponding to the planewave case. It is shown that the quasiplane approximation is valid only in a special narrow range of electron energy and wave phase velocity.
 Publication:

Radiotekhnika i Elektronika
 Pub Date:
 May 1984
 Bibcode:
 1984RaEl...29..956Z
 Keywords:

 Gyromagnetism;
 Particle Motion;
 Relativistic Electron Beams;
 Relativistic Theory;
 Approximation;
 Electromagnetic Radiation;
 Helical Inducers;
 Magnetic Resonance;
 Phase Velocity;
 Plane Waves;
 Electronics and Electrical Engineering