THE BOUNDARY-VALUE PROBLEM OF MAGNETOTAIL EQUILIBRIUM

The equilibrium problem for the Earth's magnetotail is discussed under the assumption that the boundary of the tail can be prescribed or derived from the force balance with the solar wind. A general solution of this problem is presented for the two-dimensional case, where the dependence on the y coordinate and the presence of B(y) axe neglected. These solutions axe further generalized to include the y dependence (but no B(y)) and an open magnetopause. In this formulation, a solution can be obtained by integration when the magnetopause boundary a(x, y), the total pressure function p(x), and the magnetic flux distribution A(b)(x, y) at the magnetopause are prescribed. Certain restrictions, however, may limit the free choice of these functions to yield physically reasonable, real solutions. When the interaction with the solar wind is included, the boundary location can no longer be chosen freely but follows from the force balance of the magnetotail with the solar wind. For a simplified description of this force balance a differential equation for the boundary location is derived, which general an earlier result by Coroniti and Kennel (1972). It is shown that solutions of this differential equation are bounded by a maximum tail width if the plasma sheet thickness is limited. Several explicit solutions are presented, illustrating cases with and without tail flaring in the z direction, and including the restrictions of the force balance with the solar wind and of the conservation laws of adiabatic convection in a steady configuration.