When forces are applied to a plasma (or any fluid) in the presence of a damping force (viscosity, friction, collisions, etc), the plasma achieves a steady-state velocity (i.e. terminal velocity).

$\left< v \right> = \text{constant} * \frac{F_{orces}}{e} $. If the forces are electromagnetic, the process is called electrical conductivity. If the forces are pressures and density gradients, the process is called diffusion. The two cases can also be mixed.

Terminal velocities associated with electromagnetic forces is called electrical conductivity.

In terms of current, it has the form

$J= n \mu F_{orces} = \sigma \frac{F_{orces}}{e} $

where $\mu$ (the mobility) is a collection of constants (mass, viscosity, charge, etc) and $\sigma$ is the electrical conductivity (constant or tensor).

Electrostatic form,

$ J = \sigma E $

Electromagnetic form,

$ J = \sigma \left( E + v x B \right) $ callen_ch6

Diffusion is the terminal velocity due to pressure and density gradients.

$\Gamma = n v = D \nabla n$

where $\Gamma$ is the flux and $D$ is the set of constants that make up the diffusion coefficient.