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.

Fluid models that approximate kinetic effects have received attention recently in the modelling of large-scale plasmas such as planetary magnetospheres. In three-dimensional reconnection, both reconnection itself and current sheet instabilities need to be represented appropriately. We show that a heat flux closure based on pressure gradients enables a 10-moment fluid model to capture key properties of the lower-hybrid drift instability (LHDI) within a reconnection simulation. Characteristics of the instability are examined with kinetic and fluid continuum models, and its role in the three-dimensional reconnection simulation is analysed. The saturation level of the electromagnetic LHDI is higher than expected, which leads to strong kinking of the current sheet. Therefore, the magnitude of the initial perturbation has significant impact on the resulting turbulence.

<p>The electromagnetic branch of the lower-hybrid drift instability (LHDI) can lead to kinking of current sheets and fluctuations in the magnetic field and is present for example in Earth’s magnetosphere. Previous particle-in-cell studies suggested that the electromagnetic LHDI’s saturation is at a moderate level and that strong current sheet kinking is only caused by slower kink-type modes. Here, we present kinetic continuum simulations that show strong kinking and high saturation levels of the B-field fluctuations. Has the impact of the electromagnetic LHDI been underestimated? The capability of the LHDI to produce x-lines and turbulence in 3D reconnection is discussed at the example of ten-moment multi-fluid simulations.</p>

In many plasmas, for example, the space plasma around the Earth and the sun and plasmas in fusion devices, collisions are rare. Therefore kinetic methods are necessary to accurately model these plasmas. Kinetic continuum Vlasov simulations provide an accurate and noise-free representation of velocity space, but solve the Vlasov equation on a phase space grid which is numerically challenging. In order to avoid unphysical negative values for the particle distribution function, positivity preserving limiters can be introduced. These, however, lead to numerical heating of the plasma so that conservation of total energy is violated. Vlasov solvers that conserve energy, on the other hand, do not prevent the distribution function from taking negative values. While numerical oscillations can in general occur at steep gradients, negative values of the distribution function are the primary cause of numerical oscillations in continuum Vlasov methods. In consequence, the usability of solvers that do not preserve positivity can be limited over longer time-spans in simulations with prominent non-linear effects. Both numerical heating and non-positivity become more problematic at low resolutions/large cell sizes in velocity space.

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