Stability Properties of Coherently Gyrating Relativistic Electron Beams

An investigation is made of the effects of nongyrotropic equilibrium distributions in the phase angle of pj on the stability properties of a relativistic electron beam propagating along and gyrating about an applied uniform magnetic field. Perturbations are assumed to vary spatially only in the direction of the applied magnetic field, so that generated electromagnetic and longitudinal electric fields propagate parallel to the applied field. The two equilibrium distributions considered are the time-dependent distribution fo(p_, p, ) with = q ct/-y and the axial-dependent distribution fo (pi, pz, () with C = mQcz/pz. A Vlasov-Maxwell analysis leads to integral equations relating the field Fourier components. These equations reduce to algebraic equations when no spread in -y is present in the time-dependent equilibrium distribution and when no spread in pz is present in the axial-dependent distribution. Numerical computations for these special cases show that a rich variety of stability properties are obtained by changing the distributions in and c. a) Permanent Address: Department of Physics, Clark University, Worcester, Massachusetts 01610 1