## FANDOM

167 Pages

We would like to calculate the mobility of electrons in a radiative plasma, where the braking mechanism is collisions between photons and electrons. The relevant density of scattering centers is not the photon density, but rather the ratio between the radiation energy density and rest mass energy of an electron $n_s = \frac{u_{\gamma}}{m_e c^2}$. This is because a single collision with a low energy photon cannot alter the trajectory of the electron considerably. Multiple collisions are required for that, and the number of such collisions is simply the ratio between the rest mass energy of an electron and the energy of a photon. The mean free path for collisions is therefore

$l = \frac{1}{\sigma_T n_s} = \frac{m_e c^2}{\sigma_T u_{\gamma}}$

where $\sigma_T$ is the Thomson cross section. The photons are assumed to move much faster than the electrons, the mean free time is

$\tau = \frac{l}{c} = \frac{m_e c}{\sigma_T u_{\gamma}}$

The mobility is therefore given by

$\mu = \frac{q}{m_e} \tau = \frac{q c}{\sigma_T u_{\gamma}}$

where $q$ is the elementary charge. The resistivity is given by

$\eta = \frac{1}{n_e q \mu} = \frac{\sigma_T u_{\gamma}}{n_e q^2 c}$