Rotor Equilibria of Non-Neutral Plasmas

Equilibria are considered within a Vlasov-Maxwell model for an electron gas column rotating about an axis parallel to a uniform external magnetic field B0. A condition is derived which restricts the values of ωR (angular speed of mean rotation), Ωc (electron cyclotron frequency), and ωp (electron plasma frequency on axis) in order that the general class of rigid-rotor distributions f0(H⊥ − ωRL, pz) corresponds to radially confined equilibria in the nonrelativistic, nondiamagnetic case. It is demonstrated that rigid-rotor distributions have the property that a specification of the radial equilibrium density profile n0(r) uniquely determines the distribution ∫ dpzf0(H⊥ − ωRL, pz) of electrons perpendicular to B0. Explicit examples in this regard are discussed in both the nonrelativistic, and relativistic, diamagnetic cases. This can serve as a useful experimental diagnostic whereby a determination of n0(r) yields the perpendicular distribution ∫ dpzf0(H⊥ − ωRL, pz).