## FANDOM

155 Pages

In general, the diffusion coefficient is roughly equal to the product of the velocity at which a particle moves between collisions, and the mean free path between collisions. In the case of a plasma, the velocity at which particles move is the thermal velocity

$v_{th} \approx \sqrt{\frac{k T}{m}}$

where $k$ is the Boltzmann constant, $T$ is the temperature and $m$ is the mass of the particles. The mean free path can be estimated in the following way. If we assume only interaction between neighbouring particles, and we imagine particles with charge $q$ flying next to each other with impact parameter $b$, then the impact parameter at which the deflection angle is of order unity is

$b_{c} \approx \frac{q^2}{k T}$

The mean free path for such an interaction is

$l \approx \frac{k^2 T^2}{q^4 n}$

where $n$ is the particle number density. The diffusion coefficient is therefore

$D \approx \sqrt{\frac{k T}{m}} \frac{k^2 T^2}{q^4 n}$

We note that the assumption of interaction from nearest neighbours is not entirely justified. At a larger distance the electric field decreases on the one hand, but the number of particle increases, so that different radii have similar contribution, and this introduces a logarithmic correction to cross section.