Preliminary Simulation Results for Stormtime Ring Current in a Self-Consistent Magnetic Field Model

The stormtime ring current generates a strong and time-dependent perturbation of the magnetospheric ěc{B} field, and this magnetic-field perturbation can have important feedback on the dynamics of ring current particles themselves. In particular, the modification of ěc{B} can significantly alter the gradient-curvature drifts of ring current particles, and the induced electric field associated with ∂ ěc{B}/∂ t can inhibit ring current particle injection and energization. Thus, in order to accurately simulate the stormtime ring current, we need a self-consistent magnetic field model that takes into account effects of the ring current on the particles that produce it. This study is our first attempt to address this issue. We assume for simplicity a model for ěc{B} (= ∇ α ×∇ β ) such that magnetic field lines lie in meridional planes and satisfy the generic equation r = La(1+0.5r^{3/b^3)sin ^2θ} , where r is the radial distance from the point dipole, θ is the magnetic colatitude, a is the radius of the Earth, L is a dimensionless field-line label inversely proportional to the Euler potential α = -μ _E/La, β is the magnetic local time, and the parameter b (a function of L and β ) controls the amount by which a field line is stretched. The special case of constant b yields Dungey's model magnetosphere (dipole field plus uniform southward Δ B), in which the limit b->∞ corresponds to a purely dipolar B field (Δ B = 0). More generally, we now let the value of b varies from field line to field line so as to account also for the ring current's contribution to equatorial Δ B as a function of r and β . The self-consistent magnetic field should satisfy the force balance, as specified by the equation μ _{0^{-1}ěc{B}×(∇ ×ěc{B})} = -∇ ṡěc{ěc{P}}, where μ ₀ is the permeability of free space and ěc{ěc{P}} is the pressure tensor. Under these assumptions, the radial component of the left-hand side of the force balance equation in the equatorial plane can be expressed via an ordinary differential equation in L or in r₀, where r₀ is the geocentric radial distance in the equatorial plane (related to L by solving the equation of a field line for r at θ = π /2). Given the plasma pressure in the equatorial plane as a function of r₀ and β as a result of our bounce-averaged guiding center simulations of representative ring-current particles, we can thus solve the pressure-balance equation to obtain the self-consistent magnetic field. We will show some preliminary results found by applying this method to actual ring-current plasma simulations.