Kinetic theory of very high-frequency and high-pressure continuous atomic discharges

We derive the analytical solution of the Boltzmann equation for the stationary electron distribution function that is reached in a plasma generated on the application of a uniform very high-frequency electric field in an atomic gas. The theory includes all excitation transitions: ionization and electronic transitions. The analytic solution is also extended to continuous discharges with low electric field or high pressure in the gas. Then the electron rate coefficient for excitation of the first state (which is the most significant) is calculated analytically. We apply the results to the modelling of very high-frequency argon discharges and to high-pressure continuous discharges in argon and in sodium. The results are compared with numerical results of Ferreira and co-workers for argon and of LaVerne for sodium: in both cases we find good agreement between numerical and analytical approaches.