Nonlinear thermal diffusion of electrons in ionized gases

The authors have obtained a solution of Boltzmann's transfer equation for electrons in a slightly ionized gas and a simple model semiconductor, in the presence of a high temperature gradient. An explicit expression for f₀(the isotropic part of the electron velocity distribution function) correct to terms involving the square of the temperature gradient has been obtained. Using this solution, explicit expressions for non-linear electric and thermal current densities due to high temperature gradient have been obtained.