Electron and Ion Runaway in a Fully Ionized Gas. I

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Abstract
Hydrodynamic equations are used to describe the flow of the electrons and ions of a fully ionized gas under the action of an electric field, E, of arbitrary magnitude. The dynamical friction force exerted by the electrons and ions upon each other through the agency of two-body Coulomb encounters is evaluated. In this connection the electrons and ions have been assigned Maxwellian velocity distributions which are displaced from each other by their relative drift velocity. This treatment yields a dynamical friction force which maximizes when the relative drift velocity is equal to the sum of the most probable random electron and ion speeds. For relative drift velocities in excess of this value the friction force decreases rapidly. As a consequence, it is found that a fully ionized gas cannot exhibit the steady-state behavior characterized by time independent drift velocities which has previously been accredited to it by other authors. Instead, it is shown that the electron and ion currents flowing parallel to the existing magnetic fields increase steadily in time (i.e., runaway) as long as a component of the electric field persists along the magnetic field. Drift velocities which greatly exceed the random speeds of the plasma particles can be created in this manner.