Thermal equilibrium properties of nonneutral plasma in the weak coupling approximation

Abstract

Thermal equilibrium properties are calculated for a cylindrical, pure electron plasma confined radially by a uniform axial magnetic field B0ez. In the weak coupling approximation (e2/n̂e−1/3 ≪kBTe), the one‐particle thermal equilibrium distribution function is feq(H,Pθ)=const.. ×exp{−(H‐ωrPθ)/ kBTe}, where H is the energy, Pθ is the canonical angular momentum, Te is the temperature, and ωr is the equilibrium angular rotation velocity of an electron fluid element. The self‐consistent equilibrium density profile neq(r)=Fd3p feq is characterized over a wide range of values of the on‐axis electron density (n̂e), electron temperature (Te), and confining field strength (BO).Closed analytical expressions are derived for the mean‐square radius 〈r2〉eq of the plasma column and the angular rotation velocity ωr, expressed in terms of the nonlinear conservation constraints, Ne=∫d2x∫d3p Pθfe(x, p, t)=const. and 〈Pθ〉=Ne−1∫d2x∫d3p Pθfe(x,p,t)=const., which correspond to the total number of electrons per unit axial length and the total canonical angular momentum per unit axial length, respectively. Finally, an exact power‐series solution is derived for the thermal equilibrium density profile neq(r) as a function of the radial distance r from the axis of the plasma column.