No abstract

The fundamental questions of the formation of the electron distribution function are investigated by numerically solving the Boltzmann kinetic equation in sinusoidal modulated fields for two limiting cases; domination of either elastic or inelastic energy loss in the electron energy balance. The role of non-local effects is demonstrated in the formation of both the distribution function and macroscopic properties, such as electron density and average energy, excitation and ionization rates. The phase shifts of these parameters are considered, which are responsible for the propagation of the ionization wave. Stratification mechanisms differ considerably for these two cases and are determined by the peculiarities of the electron non-local kinetics, whereas the fluid models of striations are inapplicable. Precise calculations are carried out for a discharge in neon for two cases observed in real experiments at low and intermediate pressures and small currents.

A formalism of the self-consistent solution of the kinetic equation and the field equation is described for the positive plasma column in an inert gas discharge. The model considers the presence of electrons trapped in the potential well transfering the discharge current and of free electrons which reach the walls in a free diffusion regime supporting the required ionization level in the discharge. The calculations have been carried out for neon. In the model application range the comparison is made with experimental data of axial fields, wall potentials, wall currents and in some cases with distribution functions. A good correspondence takes place.

A general multiterm representation of the phase space electron distribution function in terms of spherical tensors is used to solve the Boltzmann kinetic equation in crossed electric and magnetic fields. The problem is formulated for an axisymmetric cylindrical magnetron discharge with the homogeneous magnetic field being directed axially and the electric field between the coaxial cathode and anode varying in radius only. A spherical harmonic representation of the velocity distribution function in Cartesian coordinates becomes especially cumbersome in the presence of the magnetic field. In contrast, the employment of a spherical tensor representation leads to a compact hierarchy of equations that accurately take into account the spatial inhomogeneities and anisotropy of the plasma in crossed fields. To describe the spatially inhomogeneous plasma the hierarchy of the kinetic equations is formulated in terms of the total energy and the radial coordinate. Appropriate boundary conditions at the electrodes for the tensor expansion coefficients are obtained.