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 35x24px , 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 [cm^{2}/s] | [cm^{2} sec 53x28px | ||
height12pt width0pt H_{2} | 70x28px | 0.34 | 13.0 | ||
He | 70x28px | 0.26 | 10.2 | ||
Ar | 70x28px | 0.04 | 1.7 | ||
O_{2} | 70x28px | 0.06 | 2.2 | ||
H_{2}O | 70x28px | 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.