2.2 High-latitude
potential
We use a Python version of REMIX, which is the electrostatic potential
solver in the Grid Agnostic MHD with Extended Research Applications
(GAMERA) global magnetosphere model (Sorathia et al., 2020). REMIX is a
redeveloped version of the Magnetosphere-Ionosphere Coupler-Solver (MIX)
developed originally by Merkin and Lyon (2010). In the application
presented here, we solve for the high-latitude potential using
field-aligned currents from AMPERE (Anderson et al., 2000, 2014, 2021)
and the SAMI3 conductances described above. The underlying solution is
based on the current continuity equation presented by Wolf (1983)
and Goodman (1995), which is analogous to Ohm’s Law. This is
shown in Equation 1 (note that \(\delta\) is the magnetic dip angle).
\(\nabla_{\bot}\bullet\par
\begin{bmatrix}\end{bmatrix}\bullet\nabla_{\bot}\psi=\ j_{||}\text{cos\ δ}\) (1)
The solver operates in Solar Magnetic (SM) coordinates with the pole
boundary based on the regularity constraint (Lewis & Bellan, 1991;
Merkin & Lyon, 2010) and the lower latitude boundary condition setting
Ψ=0 at 40o MLAT.
Figure 3 shows an example REMIX potential solution (right) calculated
from AMPERE field-aligned currents (left) and the SAMI3 conductances
from Figure 2. The solver produces the expected two-cell convection
pattern directly from the observed currents and modeled conductances,
without relying on a background potential model.