Ohm's Law in Multicomponent Nonisothermal Plasmas with Temperature and Pressure Gradients

A closed set of transport equations with collision terms evaluated by the 13-moment approximation is used, under well-defined assumptions, to derive a generalized Ohm's law in multicomponent nonisothermal plasmas as a function of the electric and magnetic fields and the temperature and pressure gradients. The nine coefficients defining this dependence are obtained in two successive approximations and are expressed in terms of component properties for any number N of components in the plasma, each component having its own temperature. The matrixes and determinants involved in these expressions are of order N. Results obtained for N = 4 and 5 allow the investigation of new effects that cannot be studied with the available 3-fluid expressions. It is shown that the only temperature gradient that needs to be considered in Ohm's law is that of the electrons and that all plasma properties, except those that describe or include interactions between heavy components, must be determined at the electron temperature. It is concluded that interactions between heavy particles cannot always be neglected in favor of electron-heavy particle interactions and that the results of this study may be used for a more general evaluation of all the coefficients of Ohm's law in multicomponent nonisothermal plasmas. The results are valid for any degree of ionization greater than approximately 10−7 and are presented in a form useful for many applications.