Self‐consistent magnetotail theory: Equilibrium structures including arbitrary variation along the tail axis

The self‐consistent theory of the quiet magnetotail is extended to two‐dimensional static equilibrium configurations with arbitrary variations in two cartesian space dimensions. For the case of negligible pressure anisotropy and small plasma flow velocities, self‐consistent theory leads to a nonlinear equation which is solved numerically and analytically for several special cases. To define boundary conditions we use the weakly two‐dimensional magnetotail theory by Birn et al. [1975] to fit the tail region to the entire magnetosphere. We investigate the influence of boundary conditions and find that small changes of boundary values cause the equilibrium to form oscillatory structures with magnetic islands in the plasma sheet. This model is able to explain structures observed in the quiet magnetotail as equilibrium phenomena. Besides these taillike solutions, there exists another class of equilibria which is stable against all two‐dimensional perturbations. These solutions have one neutral point; they contain less energy than the taillike solution, the difference of energy being of the same order as the energy release in a magnetospheric substorm.