Return-current-driven instabilities of propagating electron beams

A stability analysis is performed for the first nine transverse modes (azimuthal mode number plus radial mode number < or =3) of a self-pinched relativistic electron beam propagating in a collisional plasma. Only frequencies ω in the range ωtau/sub d/<<1 are considered, where tau/sub d/ is the dipole magnetic decay length. For such modes, the presence of plasma return current is the only destabilizing mechanism. Paraxial flow, space charge neutrality, and a flat radial profile of beam density are also assumed. Within these limitations, an exact analysis of the linearized Vlasov stability problem is carried out in closed form. For each mode, the instability threshold, growth rate, and conditions for oscillatory versus pure growth are determined. For beams with a moderate return current fraction, the hose, sausage, and axial hollowing modes appear to be particularly dangerous