The effects of pressure anisotropy on birkeland currents in dipole and stretched magnetospheres

Abstract

The expression for the Birkeland current density in an anisotropic P⊥, P∥ plasma derived in a companion paper (Birmingham, this issue) is simplified by linearization: for purposes of computing j∥ the magnetic configuration is assumed to be axisymmetric, either a dipole or a dipole stretched by the field arising from an azimuthal current sheet. The anisotropy is that of a bi‐Maxwellian and characterized by equatorial values P⊥ (s0) and r, the equatorial temperature (pressure) ratio. Parameter j∥ is proportional to the azimuthal derivatives of P⊥ (s0) and r, with coefficients that are integral functions along the background B of the pressure and field strength from the equator s0, where there is (by assumption) no Birkeland current, to the point of reference. Values of j∥ at the ionosphere are compared between the two magnetic models for 0.1 < r < 10., a range that assuredly spans anisotropy ratios likely to be encountered in planetary magnetospheres. The effect of the anisotropy is modest, amounting to a factor of roughly 10 (larger or smaller depending on whether r < 1 or vice versa) for a stretched field line crossing the equator at r0 = 20, less than half this amount for the comparable dipole line. Parameter j∥ grows, owing to the diversion of perpendicular currents, rapidly away from the equator, significantly more so for a pressure anisotropy favoring P⊥ (r > 1) than for one favoring P∥(r < 1). The growth away from the equator is particularly steep in the stretched model because of the strong curvature of the field lines, especially at large r0: plasma is trapped in the weak equatorial field, confined on either side by the strong B which arises from the azimuthal current sheet.