Advances in Solving the 3D Quasineutral Potential Equation

A useful model of the ionospheric density irregularities that lead to radio scintillation requires a robust and efficient solution method for the electrostatic potential.

Gradients in E-region plasma density on the order of kilometers or more drive fluid instabilities that cascade to smaller scales. In the same plasma, differences in electron and ion drifts drive kinetic or semi-kinetic instabilities that cascade to larger scales. At the intersection of these two wavelength regimes are the ionospheric density irregularities that produce radio scintillation. Hybrid particle-in-cell (PIC) models have been successful in simulating the coupling between kilometer-scale fluid instabilities and meter-scale kinetic instabilities by virtue of a compromise between fluid and particle physics.

The hybrid version of the Electrostatic Parallel Particle-in-Cell (EPPIC) simulator has replicated remote and in-situ observations of meter-scale plasma-density irregularities driven by, and feeding back to, a kilometer-scale wave. However, it currently only supports 2D systems that are periodic in both directions. The most significant restriction preventing hybrid EPPIC from supporting 3D systems -- thereby unlocking valuable knowledge of the instabilities that cause scintillation -- has thus far been the potential solver. Much of the difficulty in implementing a robust and efficient potential solver comes from the same differences in electron and ion mobility that produce meter-scale E-region irregularities. This presentation will describe recent advances in upgrading hybrid EPPIC to 3D by extending the solution method for the electrostatic potential to the dimension parallel to the ambient magnetic field. It will include comparison of numerical methods, theoretical analysis of the governing equation, and preliminary results.