Intense relativistic nonneutral E-layers—Equilibrium theory

Equilibrium properties of intense relativistic nonneutral E layers are studied within the framework of the steady-state Vlasov-Maxwell equations. The analysis is carried out for an infinitely long E layer aligned parallel to a uniform magnetic field B0êz, assuming that the E layer is thin (radial thickness is small in comparison with the mean radius R0) and ν/γ0 ≪ 1 (ν is Budker's parameter, and γ0mc2 is the electron energy). Equilibrium properties are calculated for the class of thin E-layer equilibria in which all electrons have the same canonical angular momentum Pθ, but an arbitrary distribution in energy H, i.e., fe0 (H, Pθ) = R0F (H + eφ¯) δ (Pθ − P0), where R0, φ¯0, and P0 are constants. One of the most important features of the analysis is that the influence of equilibrium self-fields on the radial thickness of the E layer can be large, even though ν/γ0 ≪ 1 is assumed and the self-field corrections to the mean radius of the E layer are small.