Thermal equilibrium properties are calculated for a cylindrical, pure electron plasma confined radially by a uniform axial magnetic field B 0 e z . In the weak coupling approximation (e 2/n̂ e −1/3 ≪k B T e ), the one‐particle thermal equilibrium distribution function is f eq (H,P θ)=const.. ×exp{−(H‐ω r P θ)/ k B T e }, where H is the energy, P θ is the canonical angular momentum, T e is the temperature, and ω r is the equilibrium angular rotation velocity of an electron fluid element. The self‐consistent equilibrium density profile n eq(r)=F d 3 p f eq is characterized over a wide range of values of the on‐axis electron density (n̂ e ), electron temperature (T e ), and confining field strength (B O). Closed analytical expressions are derived for the mean‐square radius 〈r 2〉 eq of the plasma column and the angular rotation velocity ω r , expressed in terms of the nonlinear conservation constraints, N e =∫d 2 x∫d 3 p Pθf e (x, p, t)=const. and 〈P θ〉=N e − 1∫d2 x∫d3 p P θ f e (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 eq (r) as a function of the radial distance r from the axis of the plasma column.