Mechanisms for formation of the electron distribution function in the positive column of discharges under Langmuir-paradox conditions

The form of the electron distribution function in the positive column of lo w-pressure discharges is examined under conditions such that the electron m ean free path exceeds the vessel radius. Its formation is analyzed taking a ll major factors into account, including elastic and inelastic collisions, radial and axial electric fields, and the loss of fast electrons to the wal l. It is shown that the main mechanism controlling the fast part of the dis tribution function is the loss of electrons to the wall, which is determine d by the scattering of electrons into a comparatively small loss cone that depends on the relationship between the axial and radial components of the velocity. Since the elastic collision rate for all elements has a weak depe ndence on the energy beyond the ionization threshold, ultimately the high-e nergy part of the electron energy distribution function in the positive col umn of low-pressure discharges is nearly Maxwellian. The subthreshold porti on of the distribution function, in turn, is determined by the energy diffu sion, in a comparatively strong field, of Maxwellian electrons which arrive after inelastic collisions. The final electron distribution function is we ll approximated by an exponential with a single slope over the entire energ y range. Only within a narrow range of scattering angles is the electron di stribution function strongly depleted by the loss of electrons to the vesse l walls. In the end, it is concluded that this phenomenon, like the Langmui r paradox, may be related to aspects of the physics of the formation of the electron distribution function owing to a combination of already known mec hanisms, rather than to a hypothetical mechanism for thermalization of the electrons, as assumed up to now in the literature. A comparison of solution s of the model kinetic equation given here with published Monte Carlo calcu lations and experimental data shows that they are in good agreement. (C) 19 99 American Institute of Physics. [S1063- 7842(99)00711-4].