Astron E-layer equilibria formed by injection

A study is made of the collisionless E-layer equilibria which are formed by the injection and trapping of a relativistic electron beam in a cylindrical conducting vessel. Assuming axisymmetry, information about the general E-layer equilibria is derived from the conservation of canonical angular momentum. Of particular interest for the design of experiments is the range of radial thicknesses and the average radius of the layers as a function of layer strength ζ. Under certain conditions there is shown to be a maximum radial thickness Δrmax, dependent only on ζ. For a number of practical cases Δrmax/r¯ ≈ ζ1/2, where r¯ is the average radius. The balance of axial pressures and over-all energy conservation are imposed as constraints on the general equilibria. For most of the cases studied these constraints are incompatible with the assumption of a radially thin E layer. In such cases the thin-layer equilibria are inaccessible, but it is expected that the thick-layer equilibria are accessible.