Stimulated radiation from spatiotemporally gyrating relativistic electron beams

A stability analysis is made of an electron beam, propagating along and gyrating about a uniform magnetic field, for the case of a spatiotemporal equilibrium distribution in the phase angle of the transverse electron momentum component. The axial momentum component and the magnitude of the transverse momentum component are assumed to have definite values in the equilibrium distribution. The analysis is carried out by applying Lorentz transformations to previous results for nongyrotropic equilibrium distributions. The dispersion matrix, its eigenmodes (which relate field amplitudes), and the dispersion relation are obtained. Numerical results show that varying the spatiotemporal properties of a nongyrotropic equilibrium distribution has only a small effect on maximum growth rates of radiation, but has a strong effect on the frequencies and wavenumbers at which instability occurs. A novel mechanism is found by which electrons emit stimulated radiation at frequencies that, in principle, can be greater than the usual Doppler-shifted electron cyclotron frequency by orders of magnitude.