Plasma current density is defined as $\textbf{j}=-\mathrm{e}n_e\textbf{u}_e$ where $\mathrm{e}$ is electron charge, $n_e$ is electron concentration and $\textbf{u}_e$ is electron velocity. What exactly causes polarization current density and why we do not consider other types of current densities (free-charge current density, magnetization current density) in plasma?
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A polarization current can be driven by something that causes a time-varying electric field, like a gradient drift which forces positive and negative charges to drift in opposite directions. This can be similar to a displacement current, but it is generally driven by bulk particle motion.
Side Note:
The current density is not just due to the electron drift. Currents are also not a Lorentz invariant. The current density in the macroscopic sense is defined by:
$$
\mathbf{j} = \sum_{s} \ n_{s} \ q_{s} \ \mathbf{v}_{s}
$$
where $n_{s}$ is the number density, $q_{s}$ is the electric charge, and $\mathbf{v}_{s}$ is the bulk flow velocity of particle species $s$. So as you can see, the current density is not just derived from the electron flow, though electrons often do carry currents due to their higher mobility than ions.
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