Physical Limitations of Empirical Field Models: Force Balance and Plasma Pressure

Abstract

In this paper, we study whether the magnetic field of the T96 empirical model can be in force balance with an isotropic plasma pressure distribution. Using the field of T96, we obtain values for the pressure P by solving a Poisson-type equation {del}{sup 2}P = {del} {center_dot} (J x B) in the equatorial plane, and 1-D profiles on the Sun-Earth axis by integrating {del}P = J x B. We work in a flux coordinate system in which the magnetic field is expressed in terms of Euler potentials. Our results lead to the conclusion that the T96 model field cannot be in equilibrium with an isotropic pressure. We also analyze in detail the computation of Birkeland currents using the Vasyliunas relation and the T96 field, which yields unphysical results, again indicating the lack of force balance in the empirical model. The underlying reason for the force imbalance is likely the fact that the derivatives of the least-square fitted model B are not accurate predictions of the actual magnetospheric field derivatives. Finally, we discuss a possible solution to the problem of lack of force balance in empirical field models.