Electron and Ion Runaway in a Fully Ionized Gas. II

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The treatment presented in an earlier paper is extended to give a more exact estimate of the particle runaway rate in a fully ionized gas under the action of a weak applied electric field. By analyzing the motion of particles in various regions of velocity space, it is shown that in any weak applied electric field some particles will always run away. The rate at which this occurs is determined by the flow of particles from the collision-dominated to the electric-field-dominated region of velocity space. The probability, $Q(\ensuremath{\tau})$, of electron runaway as a function of time is calculated with the help of the Boltzmann-Fokker-Planck equation and can be expressed in the form $Q(\ensuremath{\tau})=1\ensuremath{-}\mathrm{exp}(\ensuremath{-}{\ensuremath{\lambda}}_{1}\ensuremath{\tau})$. The runaway rate, ${\ensuremath{\lambda}}_{1}$, is presented as a function of applied electric field, and the plasma temperature and density. It exceeds by several orders of magnitude the rate recently proposed by Harrison. The runaway rate for positive ions is shown to be exceedingly small compared to ${\ensuremath{\lambda}}_{1}$, in the circumstances usually encountered.A brief discussion is devoted to the experimental evidence, the effects of magnetic fields, and the excitation of plasma instabilities. The correction which particle runaway introduces in the equation of pressure balance is presented for the case of a static pinched discharge.