current (assuming quasineutrality of the plasma). In the context of special relativity, in the frame moving with this velocity, the electric field vanishes. The value of the drift velocity is given by Nonuniform E If the electric field is not uniform, the above formula is modified to read Nonuniform B Guiding center drifts may also result not only from external forces but also from non-uniformities in the magnetic field. It is convenient to express these drifts in terms of the parallel and perpendicular kinetic energies In that case, the explicit mass dependence is eliminated. If the ions and electrons have similar temperatures, then they also have similar, though oppositely directed, drift velocities. Grad-B drift When a particle moves into a larger magnetic field, the curvature of its orbit becomes tighter, transforming the otherwise circular orbit into a cycloid. The drift velocity is Curvature drift In order for a charged particle to follow a curved field line, it needs a drift velocity out of the plane of curvature to provide the necessary centripetal force. This velocity is where is the radius of curvature pointing outwards, away from the center of the circular arc which best approximates the curve at that point. where is the unit vector in the direction of the magnetic field. This drift can be decomposed into the sum of the curvature drift and the term In the important limit of stationary magnetic field and weak electric field, the inertial drift is dominated by the curvature drift term. Curved vacuum drift In the limit of small plasma pressure, Maxwell's equations provide a relationship between gradient and curvature that allows the corresponding drifts to be combined as follows For a species in thermal equilibrium, can be replaced by ( for and for ). The expression for the grad-B drift above can be rewritten for the case when is due to the curvature. This is most easily done by realizing that in a vacuum, Ampere's Law is . In cylindrical coordinates chosen such that the azimuthal direction is parallel to the magnetic field and the radial direction is parallel to the gradient of the field, this becomes Since is a constant, this implies that and the grad-B drift velocity can be written Polarization drift A time-varying electric field also results in a drift given by Obviously this drift is different from the others in that it cannot continue indefinitely. Normally an