Theoretical study of a weakly ionised gas in a uniform constant electric field

The collision operators of the Boltzmann equation are expressed in terms of the transition probabilities for a Lorentz gas and inelastic type collisions in the case of conservation and non-conservation of the initial number of particles. These operators are approximately expressed when the mass ratio of the present particles is weak. The expressions obtained are valid for any particle distribution functions. A series expansion in spherical harmonics is effected for these operators. The Boltzmann equation is then solved for the case of a steady homogeneous medium when the electric field effect is lower than that of collisions. A resolving method is then proposed for the case where the electric field and collisions play comparable roles. Analytical expressions are given for the distribution functions in terms of asymptotic solutions valid for any type of cross section. A steady heterogenous medium is then studied by a direct numerical solution of the Boltzmann equation, for high values of the electric field/ pressure ratio. The existence of a single lattice of characteristic directions is established as well as a distribution function representing in phase space a band structure characteristic of the presence of inelastic collisions. The electron motion is simulated using a Monte-Carlo method. The calculations being effected in helium, a bibliography of the cross sections for this gas is given