Ion transport theory for a slightly ionized rarefied gas in a strong electric field. II.

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Abstract
Solutions to the initial-value problem of a weakly ionized rarefied gas in a uniform electrostatic field are found explicitly for the lowest three hydrodynamic levels indicated by a moment method previously described. The resulting sets of equations are solved by a completely implicit Crank-Nicholson scheme. For very light ions, or moderately inelastic electrons, a Monte Carlo solution is also found and compared to the moment solutions delineating their range of validity. The deviation of the higher-order theory from the diffusion theory is mapped on a parametric plane bounding the region of validity of the diffusion equation as derivable from the Boltzmann equation. The Hornbeck experiment is analyzed neglecting a cathode boundary, thus illustrating the effects of large initial density gradients on the transient current.