Gradient and curvature drifts in magnetic fields with arbitrary spatial variation

It is shown that, for a magnetic field of arbitrary spatial variation, a nearly isotropic distribution of charged particles drifts with a velocity given by the usual first-order orbit theory drifts averaged over pitch angle. It is assumed that the near-isotropy brought about by scattering, but conclusions concerning drift are insensitive to the details of the scattering process. It is found that this drift velocity is correct even for arbitrarily large ratios of particle gyroradius to magnetic spatial scale, although this velocity must, like all drift effects, be viewed on a scale larger than a gyroradius. Hence for many astrophysical applications, such as cosmic rays, where anisotropies are small, the usual drift velocities provide a valid approximation to convective motions even if the magnetic field scales are very small.