E×B Drift

E×B Drift

When a plasma particle moves in crossed electric and magnetic fields, it undergoes a E×B drift — a bulk drift perpendicular to both E and B.

E×B Drift Velocity

For electric field E perpendicular to magnetic field B, the drift velocity magnitude is:

$v_{E \times B} = \frac{E}{B}$

This drift is species-independent: electrons and ions drift at the same velocity in the same direction. This is a key feature that distinguishes E×B drift from other drifts.

Grad-B Drift

When the magnetic field has a spatial gradient, particles also drift due to the varying Larmor radius:

$v_{\nabla B} = \frac{v_{\perp}^2}{2} \cdot \frac{m}{q B^2} \cdot \nabla B$

Here (v_{\perp}) is the perpendicular velocity, (m) is the particle mass, (q) is the charge, and (\nabla B) is the magnitude of the magnetic field gradient.

Unlike E×B drift, grad-B drift is charge-dependent — electrons and ions drift in opposite directions, generating a current.

Polarization Drift

When the electric field changes in time, there is an additional polarization drift:

$v_{pol} = \frac{m}{q B^2} \frac{dE}{dt}$

This drift is also charge-dependent and is important in time-varying fields.

Physical Intuition

• E×B drift: The particle gains energy from E on one half of its orbit and loses it on the other. The net effect is a sideways drift.
• Grad-B drift: The Larmor radius is larger where B is weaker, so the orbit is asymmetric and the particle drifts.
• Polarization drift: A changing E field shifts the guiding center in the direction of E.