Modeling plasma dynamics is challenging. The computationally most efficient approach is magnetohydrodynamics (MHD), a fluid-type description extended with the induction equation for the magnetic field. MHD models are powerful tools to capture the large scales, for example the structure of the solar corona, or the magnetosphere.
On the other hand, MHD is not valid at the very small scales where kinetic physics dominates, for example where magnetic reconnection occurs. This physics can be captured by kinetic models that solve the Vlasov equations for the 6 dimensional phase space distribution and the full set of Maxwell equations. Even the most efficient semi-implicit particle-in-cell (PIC) model is orders of magnitude more expensive than the MHD model, so it is not feasible to use a kinetic model to simulate a large system.
In the last 7 years we have developed and implemented the magnetohydrodynamics with embedded particle-in-cell (MHD-EPIC) model. MHD-EPIC allows performing MHD simulations two-way coupled with local PIC simulations covering regions where kinetic effects are important, such as magnetic reconnection sites. We have improved the semi-implicit PIC algorithm to conserve energy and satisfy Gauss' law at the same time. We have also studied a technique of artificially increasing the kinetic scales by changing the mass per charge ratio for the ions and electrons, and found that the global solution remains essentially the same as long as the global and kinetic scales are reasonably well separated. Most recently, we developed the MHD with adaptively embedded PIC (MHD-AEPIC) algorithm and implemented it using a new PIC model, the Flexible Exascale Kinetic Simulation (FLEKS) and the BATS-R-US MHD model coupled by the Space Weather Modeling Framework (SWMF).
The combination of these new technologies and insights enables us to perform MHD-EPIC simulations for several magnetospheres, including Ganymede, Mercury, Mars, Earth and Saturn. A few representative results will be shown.
Our work is supported by the NSF INSPIRE and PRE-EVENTS grants.
