Abstract
Collisionless plasmas, mostly present in astrophysical and space environments, often require a kinetic treatment as given by the Vlasov equation. Unfortunately, the six-dimensional Vlasov equation can only be solved on very small parts of the considered spatial domain. However, in some cases, e.g. magnetic reconnection, it is sufficient to solve the Vlasov equation in a localized domain and solve the remaining domain by appropriate fluid models. In this paper, we describe a hierarchical treatment of collisionless plasmas in the following way. On the finest level of description, the Vlasov equation is solved both for ions and electrons. The next courser description treats electrons with a 10-moment fluid model incorporating a simplified treatment of Landau damping. At the boundary between the electron kinetic and fluid region, the central question is how the fluid moments influence the electron distribution function. On the next coarser level of description the ions are treated by an 10-moment fluid model as well. It may turn out that in some spatial regions far away from the reconnection zone the temperature tensor in the 10-moment description is nearly isotopic. In this case it is even possible to switch to a 5-moment description. This change can be done separately for ions and electrons. To test this multiphysics approach, we apply this full physics-adaptive simulations to the Geospace Environmental Modeling (GEM) challenge of magnetic reconnection.
Highlights
One of the most important challenges in astrophysical, space and fusion plasmas is the treatment of different spatial and temporal scales and the correct physical description on each of these different scales.In order to give a rough estimate for different plasma systems, let us first consider the warm ionized phase in the interstellar medium
We showed that the proposed multiphysics coupling hierarchy can give excellent results even when only a small part of computational domain near the reconnection zone is captured with a kinetic model
The multiphysics coupling strategy should be formulated as an asymptotic preserving scheme [40, 41]
Summary
One of the most important challenges in astrophysical, space and fusion plasmas is the treatment of different spatial and temporal scales and the correct physical description on each of these different scales. It is not possible to carry out simulations which represent all scales with the finest level (kinetic equations) of the physical description Most of these plasmas can be considered as collisionless, since collision times are orders of magnitude larger than time scales relevant for the dynamical evolution of the plasma. In future studies we will try to include the coupling of the 5moment model to magnetohydrodynamic (MHD) models (with generalized Ohms law) which would represent the last step in this hierarchy With this multiphysics strategy, these codes can be applied to problem sizes that are otherwise impossible to reach with kinetic simulations and the understanding of the impact of small scale phenomena on the dynamics on global scales is in reach. We will study the Geospace Environmental Modeling (GEM) reconnection setup [24] and perform comparisons to pure kinetic and pure fluid simulations
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