The Transition from Free to Ambipolar Diffusion

Abstract

In gas discharge plasmas with very low charge densities, the charged particles diffuse freely in directions perpendicular to the applied electric field because the space-charge field is negligible. At high charge densities, the space-charge field saturates and gives rise to a combination of diffusive and mobility flow termed ambipolar. The transition between these limits is examined theoretically for the case of plasmas maintained through ionization by electron impact. The ionization frequency per electron, one of the principal parameters of the transition, can be re-expressed in terms of an effective diffusion coefficient; it falls from a high value at the free diffusion limit to a low value at the ambipolar limit as the electron density increases over many orders of magnitude. The trnasition is accompanied by changes in the charge distributions and by the development of a positive ion sheath. The current equations determining the process are examined, and approximate solutions are obtained. Second approximations are obtained for the case where the ratio of electron to ion energies is much greater than unity. Machine solutions are presented both for the above case and for an isothermal plasma in which this ratio equals unity. An application to the afterglow is shown.