Re. Robson, THE STEADY-STATE TOWNSEND EXPERIMENT - COMPARISON OF BOLTZMANN-EQUATION AND DIFFUSION EQUATION ANALYSIS, Australian journal of physics, 48(3), 1995, pp. 347-356
A general solution of the diffusion equation corresponding to an ideal
ised swarm experiment in infinite plane-parallel electrode geometry is
given and the result is then specialised to the steady state Townsend
experiment. The role of the 'dispersion relation' generated by the-di
ffusion equation is discussed, and the physical meaning of its two zer
os explored. It is found that the smaller zero generally allows adequa
te representation of the electron density distribution downstream of t
he source, but the larger zero must be found from the full Boltzmann e
igenvalue equation in order that the upstream region be represented ev
en qualitatively correctly. The results of a numerical calculation for
electrons in water vapour are presented. The procedure adopted by Tag
ashira et al. (1994) to obviate this difficulty is discussed.