[en] Two-dimensional solutions to the equilibrium equation for finite temperature, low density pure electron plasmas confined on magnetic surfaces [T. S. Pedersen and A. H. Boozer, Phys. Rev. Lett. 88, 205002 (2002)] are presented for the first time. These equilibria are not maximum energy states, in contrast to Penning trap equilibria [J. Notte et al., Phys. Rev. Lett. 69, 3056 (1992)]. By varying the number of Debye lengths in the plasma, a/λ_D, from 0.1 to 10, we explore both relatively warm and relatively cold plasma equilibria. The effects of different boundary conditions and the implications for collisional transport rates are discussed