Vlasov simulations

We present a novel algorithm for the numerical solution of the multi-species, non-relativistic, Vlasov-Maxwell system in the Gkeyll simulation framework, which uses high order discontinuous Galerkin finite elements to discretize the system on an upto a 3D-3V phase space grid. The resulting numerical method is robust and retains a number of important properties of the continuous system, such as conservation of mass and energy, yet the method is computationally efficient and performs well at scale on cutting edge high performance computational resources. We leverage the pristine phase space representation made possible by directly discretizing phase space to examine energy dissipation in a variety of systems relevant to space and astrophysical plasmas. Specifically, we employ the field-particle correlation technique and Fourier-Hermite decomposition in phase space to directly diagnose the exchange of energy between fields and particles and the flow of energy in phase space. We present results from a variety of simple systems, including magnetic pumping, resonant wave damping, and Langmuir turbulence, and we also apply the field-particle correlation technique to 2D-3V Vlasov-Maxwell simulations of reconnection and turbulence.

Recently MMS satellites measured a turbulent regime in the solar wind plasma, downstream of the Earth's bow shock, where magnetic reconnection acting in all the observed current sheets (at the electron skin depth scale) is completely ruled by electrons. These ``electron-only'' reconnection events are characterized by electron jets unaccompanied by ion outflows, contrary to the standard picture of magnetic reconnection. Hybrid-Vlasov-Maxwell simulations of magnetized plasma turbulence, including non-linear electron inertia effects in the generalized Ohm.s law, are able to reproduce this behavior as soon as the fluctuation energy is injected at scales close the ion-kinetic scales. In this case ions turn out to be de-magnetized over the whole numerical domain while electrons follow a nearly electron-magnetohydrodynamic evolution leading to electron-only reconnection. The injection scale seems to be the control parameter of this behavior: if energy is injected at larger scales ion outflows do form in reconnecting sheets.

Multi-dimensional Eulerian simulations of the hybrid Vlasov-Maxwell model[1] have been employed to investigate the role kinetic effects in turbulent plasmas at typical ion scales. Numerical results suggest that kinetic effects manifest through the deformation of the ion distribution function, with patterns of non-Maxwellian features being concentrated near regions of strong magnetic gradients. The velocity-space departure from Maxwellian of the ion velocity distributions has been also recovered in observational data from spacecraft. In a recent paper, Servidio et al.[2] investigated the velocity-space cascade process suggested by the highly structured shape of the ion velocity distribution detected by the NASA Magnetospheric Multiscale mission. Through a tree-dimensional Hermite transform, these authors pointed out a power-law distribution of moments and provided a theoretical prediction for the scaling, based on a Kolmogorov approach. Here, the possibility of a velocity-space cascade is investigated in the strongly magnetized case, in kinetic simulations of turbulence at ion scales. Through the Hermite decomposition of the ion velocity distribution from the simulations, we found that (i) the plasma displays spectral anisotropy in velocity space, due to the presence of the background magnetic field, (ii) the distribution of energy is in agreement with the prediction in Ref. [2] and (iii) the activity in velocity space shows a clear intermittent character in space, being enhanced close to coherent structures, such as the reconnecting current sheets produced by turbulence. Finally, in order to explore the possible role of inter-particle collisions, collisional and collisionless simulations of plasma turbulence have been compared using Eulerian Hybrid Boltzmann-Maxwell simulations, that explicitly model the proton-proton collisions through the nonlinear Dougherty operator.

This talk has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 776262 (AIDA, www.aida-space.eu)

[1] Valentini, F. et al., J. Comput. Phys. 225 2007, 753-770

[2] Servidio, S. et al., Phys. Rev. Lett. 119 2017, 205101