Thermal equilibrium properties of nonneutral plasma in the weak coupling approximation

Closed analytical expressions are derived for the mean-square radius left-angle r2 right-angle 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 left-angle Pθ right-angle=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 n at sign/deq(r) as a function of the radial distance r from the axis of the plasma column