This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov system, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world’s first global hybrid-Vlasov simulation for the Earth’s magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator’s parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation and physical results is included. The purpose of the paper is to present the Vlasov system and introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics can be rewarding in itself and significantly advance our understanding. Upcoming supercomputing resources are making similar efforts feasible in other fields as well, making our design options relevant for others facing similar challenges.
For decades, monochromatic large‐scale ultralow frequency (ULF) waves with a period of about 30 s have been observed upstream of the quasi‐parallel bow shock. These waves typically propagate obliquely with respect to the interplanetary magnetic field (IMF), while the growth rate for the instability causing the waves is maximized parallel to the magnetic field. It has been suggested that the mechanism for the oblique propagation concerns wave refraction due to the spatial variability of the suprathermal ions, originating from the E × B drift component. We investigate the ULF foreshock under a quasi‐radial IMF with Vlasiator, which is a newly developed global hybrid‐Vlasov simulation solving the Vlasov equation for protons, while electrons are treated as a charge‐neutralizing fluid. We observe the generation of the 30 s ULF waves and compare their properties to previous literature and multipoint Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft observations. We find that Vlasiator reproduces the foreshock ULF waves in all reported observational aspects. We conclude that the variability of the density and velocity of the reflected back streaming ions determines the large‐scale structure of the foreshock, which affects the wave frequency, wavelength, and oblique propagation. We conclude that the wave refraction may also be at work for radial IMF conditions, which has earlier been thought of as an exception to the refraction mechanism due to the small E × B drift component. We suggest that additional refraction may be caused by the large‐scale spatial variability of the density and velocity of the back streaming ions.
Contrary to previous simulation results on the existence of amorphous intergranular films at high-angle twist grain boundaries (GBs) in elemental solids such as silicon, recent experimental results imply structural order in some high-angle boundaries. With a novel protocol for simulating twist GBs, which allows the number of atoms at the boundary to vary, we have found new low-energy ordered structures. We give a detailed exposition of the results for the simplest boundary. The validity of our results is confirmed by first-principles calculations.
We present results from a first study of the local reconnection rate and reconnection site motion in a 2D‐3V global magnetospheric self‐consistent hybrid‐Vlasov simulation with due southward interplanetary magnetic field. We observe magnetic reconnection at multiple locations at the dayside magnetopause and the existence of magnetic islands, which are the 2‐D representations of flux transfer events. The reconnection locations (the X lines) propagate over significant distances along the magnetopause, and reconnection does not reach a steady state. We calculate the reconnection rate at the location of the X lines and find a good correlation with an analytical model of local 2‐D asymmetric reconnection. We find that despite the solar wind conditions being constant, the reconnection rate and location of the X lines are highly variable. These variations are caused by magnetosheath fluctuations, the effects of neighboring X lines, and the motion of passing magnetic islands.
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