Theory of the resistive hose instability in relativistic electron beams

A Vlasov-Maxwell theory of the resistive hose instability is developed for an infinitely long relativistic electron beam propagating parallel to an applied axial magnetic field. Complete space charge neutralization by the ambient plasma, and paraxial flow (p(z)p:2 p(r)p:2 + p(theta)2 mu) are assumed. The analysis is performed for rigid-rotor and cold laminar flow equilibria. An integro-differential eigenvalue equation is obtained for the general case, and is reduced to an ordinary differential equation in either the cold laminar flow limit or the case of a square beam density profile. Using a variational technique, an approximate dispersion relation is found for arbitrary density profile, and evaluated in closed form for either the Bennett or square profile. Stability properties are illustrated and discussed in detail for a square profile, including the influence of the applied magnetic field (stabilizing), proximity to a conducting guide (stabilizing), and partial current neutralization (destabilizing).