Physics: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 File:Hepb img193.gif , 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	[cm]	D [cm2/s]	[cm2 sec File:Hepb img195.gif
	height12pt width0pt H2	File:Hepb img196.gif	0.34	13.0
	He	File:Hepb img197.gif	0.26	10.2
	Ar	File:Hepb img198.gif	0.04	1.7
	O2	File:Hepb img198.gif	0.06	2.2
	H2O	File:Hepb img198.gif	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.