Effect of axial momentum spread on radiation growth rates in a spatiotemporally gyrating electron beam

Summary form only given, as follows. In previous work, a stability analysis was made of an electron beam propagating along and gyrating about a uniform magnetic field for the case of a spatiotemporal distribution in the phase angle of the transverse electron momentum component. A result of that work was that the beam may emit stimulated radiation at frequencies far in excess of the Doppler shifted electron cyclotron frequency. However, in that work it was assumed that the beam was cold (i.e., that the axial and transverse momentum components have definite magnitudes). In the present work, an analysis is made of the influence of a Lorentzian axial momentum spread on the stability properties of the beam. It is found that, for a sufficiently narrow momentum spread, the integral equations that relate electromagnetic field amplitude can be approximated by a set of algebraic relations, so that a dispersion relation is obtained. Numerical examples of the effect of axial momentum spread on radiation growth rates are presented.