## FANDOM

157 Pages

The conductivity of plasma can be related to its microscopic properties using the Drude model

$\sigma \approx \frac{n q^2}{m \omega}$

where $n$ is the number density, $q$ is the elementary charge, $m$ is the mass of the electron and $\omega$ is the collision rate. The latter is given by

$\omega \approx n \Sigma v$

where $\Sigma$ is the cross section for collisions and $v$ is the thermal velocity. To calculate the cross section, we note the impact parameter below which a scattering angle between an electron and a proton will be of order unity

$b \approx \frac{q^2}{m v^2}$

so

$\Sigma \approx b^2 \approx \frac{q^4}{m^2 v^4}$

Finally, the resistivity is given by

$\eta = \frac{1}{\sigma} \approx \frac{m}{n q^2} n v \frac{q^4}{m^2 v^4} \approx \frac{q^2}{m v^3} \approx \frac{q^2 \sqrt{m}}{\left(k T \right )^{3/2}}$

where $T \,$ is the temperature and $k$ is the Boltzmann constant.