Particle drift in the Earth's plasma sheet

We generalize the derivation of the average gradient/curvature-drift for a flux tube filled with an isotropic distribution of particles at specified kinetic energy. The present treatment is restricted to a two-dimensional magnetic field with zero electric field, but it includes all chaotic and Speiser orbits, which do not correspond to the simple picture of gradient/curvature drift. We assume that particles are evenly distributed throughout the regions of phase space allowed by their energy and canonical momentum. This assumption is closely related but not exactly equivalent to the assumption of isotropic pitch-angle distribution. Our derivation assumes that the maximum Larmor radius is small compared to the scale length for equatorial variations in the flux tube volume, but it does not involve any restrictions on the curvature of the field line. The resulting expression for the drift rate is valid for situations where the particle drift velocity is comparable to the thermal speed in some regions. The apparent implication of this generalized treatment is that the existence of very complex non-adiabatic particle trajectories in the plasma sheet may not invalidate previous estimates of the average rate of particle drift out the sides of the tail, estimates that were made under the assumption of simple guiding-center drifts.