‘‘Phase mixing’’ of bunches and decrease of negative-mass instability increments in cyclotron resonance masers

Abstract

Negative-mass (space-charge) instability in magnetized electron beams is considered for a flat, thin (having a thickness about the cyclotron diameter) beam of weakly relativistic electrons oscillators. Pitch angle and energy spreads of particles, as well as magnetic tapering are investigated on the base of averaged differential-integral equations of electron motion. For the energy spread, the phenomenon of ‘‘phase mixing’’ of particles rotating with different frequencies limits the number of cyclotron harmonics taking part in the instability and significantly decreases the increments. For the magnetic tapering, this effect leads to linear saturation at the length comparable with the characteristic scale of the tapering.