On the Electrical Conductivity of a Weakly Ionized Turbulent Plasma I

Abstract

On the basis of the magnetohydrodynamic equations, the effect of density fluctuations on the frequency dependent electrical conductivity of a weakly ionized isothermal plasma is investigated. Only the case in which the magnetic field is static and homogeneous and in which the external electric field is parallel to the magnetic field is considered. The density fluctuations or waves are assumed to be formed by a certain driving force which acts either only on the electrons or only on the ions. The approximations involved are i) the neglect of the inertia term, ii) the neglect of the mode-mode coupling term except when it acts as a driving force and iii) the neglect of the response of the driving force to the external electric field. Some special cases are considered in detail. In particular, when a 6tatic density fluctuation is formed by a driving force acting only on the ions, the d. c. conductivity becomes the same as was obtained by Yoshikawaa¹⁾ using a more intuitive argument. In general, in the absence of a magnetic field, the effect of fluctuations on the conductivity depends little on whether the driving force is acting on the electrons or on the ions, provided that the characteristic frequencies are much samaller than the electron plasma frequency, but much larger than the ion collision frequency. A difference arises, however, when the magnetic field dependence is considered, i.e. the dependence of the d. c. current on the magnetic field takes place through the electron cyclotron frequency when the driving force is acting on the ions and through the on cyclotron frequency when it is acting on the electrons. This difference, however, disappears at high frequencies at which the ions can no longer follow the variation of the external electric field; in this case the magnetic field dependence takes place only through the electrcn cyclotron frequency.