The Harris (1962) model, which is consistent with local thermodynamic equilibrium (LTE) does not represent the earth's magnetotail, which has a magnetic field component normal to the equatorial plane. However, inclusion of a normal magnetic B\sbz component can be made without violating the slow-flow MHD approximation, under the condition B\sbzB\sbx≪1. A procedure is developed for constructing a family of two-dimensional asymptotic equilibrium solutions that are ordered with respect to the magnetic disturbance index K\sbp and based on fitting to a three-dimensional magnetospheric model magnetotail. The low quality of fits for magnetically active configurations is indicative of their consistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere are ruled by different thermodynamic conditions than those associated with LTE.