# What's the difference between a convection and a polarization electric field?

In the ionosphere and magnetosphere communities, studies frequently refer to the "convection electric field" and the "polarization electric field". What is the relationship between them, and what are some of the differences?

The convective field is just a Lorentz transformation in the non-relativistic limit where: $$\mathbf{E} = - \mathbf{v}_{bulk} \times \mathbf{B} \tag{1}$$
In contrast, the polarization electric field is the macroscopic extension of the displacement current. It causes oppositely charged species to separate and has a stronger effect on heavier particles. Further, the polarization current is proportional to the time-derivative of the electric field because the separation of oppositely charged particles increases the field. Eventually the field saturates due to the electric field caused by the charge separation. The field is given by: $$\frac{ \partial \mathbf{E} }{ \partial t } = \frac{ \gamma \ m_{s} }{ q_{s} \ B^{2} } \ \mathbf{v}_{pol} \tag{2}$$ where $$\gamma$$ is the Lorentz factor, $$m_{s}$$ is the mass of species $$s$$, $$q_{s}$$ is the charge of species $$s$$, $$\mathbf{v}_{pol}$$ is the polarization drift velocity (i.e., the drift between the oppositely charged particles generating the time-varying electric field), and $$B$$ is the quasi-static magnetic field magnitude.