Diffusion in Gases

  During the drift in electric fields, charged particles diffuse according to a Gaussian distribution

where

It is convenient to define a reduced drift velocity, the mobility at atmospheric pressure

with

From classical arguments it can be shown that the diffusion coefficient is given by the Nernst-Einstein relation

with

The mobility depends on the energy distribution, the mean free path and the inelasticity , i.e. the fraction of energy lost on each impact.

For positive ions, the following table gives some values for the mean free path and the diffusion coefficients D for different molecules under normal conditions (from [Schultz77] and [Sauli91]):

height12pt width0pt Gas D [cm²/s]

height12pt width0pt H₂ 0.34 13.0

He 0.26 10.2

Ar 0.04 1.7

O₂ 0.06 2.2

H₂O 0.02 0.7

For electrons, the neutralization by ions and the attachment by molecules with electron affinity must be considered. Except for very low fields the mobility of electrons is not a constant; the mean free path varies in some gases with the electric field (Ramsauer effect), all resulting in a diffusion coefficient dependent on the electric field.

Note that the limiting accuracy is not given by the standard deviation from f_t(x), but depends on the number of electrons necessary to trigger the shift-line electronics. If n electrons are produced and k electrons are needed to overcome the electronics threshold, the following formula holds:

For more details, [Piuz83], [Breskin84], [Charpak84], [Peisert84], [Amendolia86], [Sauli91].