Mean field kinetic theory of a classical electron gas in a periodic potential. III. The high-temperature limit in two dimensions

The Vlasov-like mean field kinetic equation for a classical electron plasma in the periodic field of an ionic lattice is solved in the high-temperature limit in two dimensions. The predictions for the one-electron density, the static structure factor, and the long-wavelength charge fluctuation spectrum are compared to the results of extensive molecular dynamics simulations. The predicted shift and damping of the plasma oscillation mode are in reasonable agreement with the simulation data at intermediate couplings (=e ²/k _B T1), but the agreement deteriorates as the temperature or the density is lowered, because mean field theory does not lead to the expected Kosterlitz-Thouless transition to the dielectric phase where electrons are localized.