An Energy Conserving Vlasov Solver That Tolerates Coarse Velocity Space Resolutions: Simulation of MMS Reconnection Events

Abstract

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.

Coupling multi-fluid dynamics equipped with Landau closures to the particle-in-cell method

“…However, they may lead to misleading results in multiscale simulations, where multiple characteristic damping lengths are present and depend on the estimate of . For example, Allmann-Rahn, Lautenbach & Grauer (2022) show a case where ion and electron heating intensities are switched qualitatively.…”