Influence of axial energy spread on the negative-mass instability in a relativistic nonneutral E layer

The influence of an axial energy spread on the negative-mass instability in a relativistic nonneutral E layer aligned parallel to a uniform axial magnetic field B0êz is investigated. The stability analysis is carried out within the framework of the linearized 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 mean electron energy. Stability properties are investigated for the choice of electron distribution function in which all electrons have the same value of canonical angular momentum (Pϑ=P0=const) and a step-function distribution in axial momentum pz. The negative-mass growth rate is calculated including the important stabilizing influence of axial energy spread (ΔE), and it is shown that a modest energy spread (ΔE/γ0mc2≈ a few percent) is sufficient to stabilize perturbations with axial wavenumber satisfying k2R20≳1.