Three-dimensional magnetotail equilibria with prescribed boundary shapes

[1] Three-dimensional magnetotail equilibrium configurations are presented that are derived from a prescribed outer flux surface, equivalent to a closed magnetopause. The explicit solutions neglect the effects of field-aligned currents, closely associated with a bending of field lines in the x, y plane, but include tail flaring in y and z. Most of the solutions are derived for an axisymmetric boundary, approximately consistent with force balance between the unperturbed solar wind and the magnetosphere at a closed magnetopause (Newtonian approximation). This force balance is used to relate the downtail variation of the tail radius to that of the total interior magnetotail pressure, equivalent to the lobe magnetic pressure. However, these properties are not sufficient to determine the tail configuration. We demonstrate this by deriving solutions with identical boundaries and identical variation of the total pressure along the tail but different amounts of field line flaring in the x, y plane. Under these conditions, stronger field line flaring is associated with a reduction of the magnetotail plasma pressure near midnight and an increase of the plasma sheet thickness from midnight toward the tail flanks. A reduction of the tail boundary flaring leads to an increase of the plasma sheet thickness near the Earth but does not significantly affect the cross-tail variation. Nonuniform boundary flaring with a flattening of the tail, corresponding to a more significant increase of the tail radius in y, can reduce the plasma sheet thickening from midnight to the tail flanks or even reverse it to a thinning. The explicit solutions illustrate the effects on the tail structure of both the instantaneous force balance between the magnetosphere and the solar wind and the history of this interaction, which affects the plasma and magnetic flux distribution inside the magnetotail.