Nonlinear Debye-Onsager-Relaxation-Effect

The quantum kinetic equation for charged particles in strong electric fields is used to derive the nonlinear particle flux. The relaxation field is calculated quantum mechanically up to any order in the applied field provided a given Maxwellian plasma. The classical limit is given in analytical form. In the range of weak fields the deformation of the screening cloud is responsible for the Debye-Onsager relaxation effect. High field transport has become a topic of current interest in various fields of physics. Especially, the nonlinear current or the electrical conductivity gives access to properties of dense nonideal plasmas. At low fields we expect the linear response regime to be valid. Then the contribution of field effects to the conductivity can be condensed into the DebyeOnsager relaxation effect [1–5] which was first derived within the theory of electrolytes [6–8]. Debye has given a limiting law of electrical conductivity which stated that the external electric field E on a charge e is diminished by the amount δE = E (1 − κe 6ǫ0T )where κ is the inverse screening radius of the screening cloud. Later it has been shown by Onsager that this result has to be corrected if the dynamics of ions is considered. In this paper we will give the complete result beyond linear response for the static case E (1 − κe 6ǫ0T F (E))similar to the theoretical explanation of the Wien effect [8]. We start from the kinetic equation derived with the help of the gauge invariant formulation of Green’s function, [9,10] ∂ ∂t fa + eE∇kafa = ∑ b Iab Iab = 2 h̄ ∫ dk a dkbdk ′ b (2πh̄)6 V 2 ab(ka − k′a)δ (ka + kb − k′a − k′b) × ∞ ∫