Comment on "Electron diffusion under the influence of an electric field near absorbing boundaries." I

A simple rigorous proof is given of the complementarity theorem introduced by Lowke, Parker, and Hall (LPH) to relate electron back diffusion to forward diffusion. It provides additional insight from which we conclude (i) that the theorem does not strictly apply to the situation discussed by LPH, and (ii) that for certain types of Monte Carlo simulations of electron-swarm behavior, the relaxation distance of the injected electrons can be minimized by injecting them into the forward hemisphere with a mean energy substantially higher than the anticipated equilibrium value. The Monte Carlo simulation data of Braglia and Lowke provide an interesting example of the effects discussed, and an improved version of this type of simulation is proposed. It employs an ideal source, having the same velocity distribution as the electrons arriving at an absorbing anode. In the steady-state distribution generated by such a source all the electrons carry useful information, even when the source is placed arbitrarily close to an absorbing anode.