A wave equation describing the generation of field-aligned current in the magnetosphere

Abstract

A wave equation describing the generation of field-aligned current (FAC) in the magnetosphere is derived. The equation has four source terms. The first and second terms represent the effects of inhomogeneous Alfvén speed (V_A) and curvilinear magnetic field line, respectively. The perpendicular perturbation inertial current produces the perturbation FAC via these effects. Around the magnetic equator in the region of dipolar magnetic field where V_A is inversely proportional to the power of the radial distance from the Earth’s center, the first and second terms have magnitudes of the same order and their signs are identical. The first term dominates over the second one around the region where the gradient of V_A is sharp and vice versa around the position where the stretched field line intersects the magnetic equator. The third and fourth terms are related to the diamagnetic current. When the unperturbed magnetic pressure has an inhomogeneous distribution, the perpendicular diamagnetic current due to the perturbation of the plasma pressure yields the perturbation FAC (third term). When the perpendicular diamagnetic current flows in the unperturbed state, the perturbations of the magnetic and plasma pressures also bring about the perturbation FAC (fourth term). In the case of β ∼ 1, the third and fourth terms have magnitudes of the same order. If the disturbance bears a diamagnetic property, this would be especially the case. However, if the disturbance propagates perpendicularly to the ambient magnetic field, the perturbation FAC would be little generated by the fourth term.