Magnetotail equilibrium theory: The general three‐dimensional solution

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Abstract
We have reduced the general magnetostatic equilibrium problem for the geomagnetic tail to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self‐consistent magnetotail equilibrium field from the knowledge of four functions of two space variables, x and y: the neutral sheet location zo (x,y), the total pressure , the magnetic field strength Bo (x,y), and the z component of the magnetic field Bzo (x,y) at the neutral sheet. The self‐consistency of the equilibrium problem thus reduces the effort to construct a tail model from empirical knowledge of four functions (Bx, By, Bz, and p) of three space coordinates to four functions of two coordinates only. All functions can be (and are in fact to a large extent) obtained from observations. The basic assumption of the quasi‐static theory with isotropic pressure is that spatial variations in the x and y directions can be treated as small in comparison with variations in the z direction perpendicular to the plasma sheet. This assumption restricts the validity of the theory to average, quiet configurations of the interior tail excluding, in particular, regions of fast flow and strong y gradients such as the plasma mantle and the low‐latitude boundary layer. The theory allows one to include the effects of field‐aligned currents and distortions due to an average cross‐tail By field (in addition to an antisymmetric By of a flaring tail) not present in earlier models.