Kinetic description of negative-mass instability in an intense relativistic nonneutral <i>E</i> layer

Abstract

The negative-mass stability properties of a relativistic nonneutral E layer are investigated within the framework of the Vlasov–Maxwell equations. It is assumed that the E layer is thin with radial thickness (2a) much smaller than the mean radius (R0), and that ν/γ0≪1, where ν is Budker’s parameter and γ0mc2 is the electron energy. The equilibrium electron charge is partially neutralized by a positive ion background with density n0i(r) =fn0e(r), where f=const=fractional charge neutralization. Moreover, no a priori restriction is made to low beam density (ω2p≪ω2c is not assumed), and the stability analysis is carried out for perturbations about the electron equilibrium f0e= (N0/2Δ) δ (U−γ̂mc2) ⊕[Δ2−(Pϑ−P0)2], where N0, Δ, γ̂, and P0 are constants, U is an effective energy variable, and Pϑ is the canonical angular momentum. The negative-mass growth rate is calculated including the effects of (a) equilibrium self-fields, (b) transverse magnetic perturbations (δB≠0), (c) the presence of inner and outer cylindrical conductors, and (d) a spread in canonical angular momentum (2Δ). All of these effects are shown to have an important influence on stability behavior.