THE STEADY-STATE TOWNSEND EXPERIMENT - COMPARISON OF BOLTZMANN-EQUATION AND DIFFUSION EQUATION ANALYSIS

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.