Theory of scan plane flux anisotropies

When a spacecraft detector measures particle flux as a function of look direction in a plane (the scan plane) anisotropy is often seen. This anisotropy is caused by spatial gradients, by E × B particle drift, and by various spectral and geometric effects. This paper treats all of these effects systematically, starting from the nonrelativistic Vlasov equation. The general analysis is applied to a simple model of an anisotropic distribution to give a relation between the E × B drift, the gradient and the experimentally observed first, second, and third harmonics of the flux as a function of angle in the scan plane. Even with an assumed model, anisotropy observations in one plane alone do not suffice to determine the E × B drift velocity and the spatial gradient independently. If one is assumed, the other follows. If the E × B velocity is assumed (e.g., the corotational velocity in a rotating planetary magnetosphere), the spatial gradient may be deduced, and from it the time rate of change of flux in a nonrotating frame of reference.