The steady‐state Vlasov‐Maxwell equations are used to study the equilibrium properties of a nonneutral E layer confined both axially and radially, by a static external mirror field, mirror field, B0ext(x). Equilibrium properties are calculated for the electron distribution function fe0 (H , P θ) in which all electrons have the same total energy (H) and the same canonical angular momentum (P θ), i.e., fe0 (H , P θ) = N0δ(H − H0)δ(Pθ − P0), where N 0, H 0, and P 0 are positive constants. For a low‐density E layer, the electrostatic potential energy of an electron, − e ϕ0(r , z ), is small in comparison with H 0. Neglecting terms of order ∣e ϕ0(r , z)/ H 0∣, a closed zero‐order expression for the r ‐ z boundary of the E layer is obtained. Iterating, the equilibrium electrostatic potential ϕ0(r , z) is then computed to lowest order, together with O [e ϕ0(r , z) / H0] corrections to the boundary of the E layer. Computer simulation experiments are used to investigate electrostatic stability properties for the case of azimuthally symmetric perturbations (∂/∂θ = 0). The code allows only r and z spatial variations but self‐consistently follows the three velocity components of 6264 macroparticles. When the electrons are initially loaded close to the equilibrium state described by fe0(H , Pθ) = N 0δ(H − H 0)δ(P θ − P 0), the E layer is observed to achieve a stable quasisteady configuration in about 15 ωp e−1 with negligible particle loss out the mirrors.