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Magnetospheric ultra-low frequency (ULF) waves are known to cause radial diffusion and transport of hundreds-keV to few-MeV electrons in the radiation belts, as the range of drift frequencies of such electrons overlaps with the frequencies of the waves, leading to resonant interactions. Numerous expressions have been derived to quantitatively describe radial diffusion, so that they can be incorporated in global models of radiation belt electrons; however, most expressions of the radial diffusion rates are derived only for equatorially mirroring electrons, and are based on estimates of the power of ULF waves that are obtained either from spacecraft close to the equatorial plane or from the ground. Recent studies using the Van Allen Probes and Arase have shown that the wave power in magnetic fluctuations is significantly enhanced away from the magnetic equator, consistent with models simulating the natural modes of oscillation of magnetospheric field lines. This has significant implications for the estimation of radial diffusion rates, as higher pitch angle electrons will experience considerably higher ULF wave fluctuations than equatorial electrons. In this talk, we present recent results on the distribution of the magnetic field wave power as a function of magnetic latitude in different local time sectors and under different solar and geomagnetic conditions. Furthermore, using analytic functions of wave amplitudes in 3D test particle simulations, we simulate the change in L over time for particles of different pitch angles; this change in L can be translated to novel analytic diffusion coefficients with pitch-angle, L and energy dependence. In this talk we discuss the potential implications for the radial diffusion rates as currently estimated.

Numerical simulations play a central role in modern sciences. The trade-off between the accuracy of the physical processes described and the cost of computational resources is often the main limiting factor in these simulations. In global hybrid-Vlasov simulations, such as Vlasiator, lowering the spatial resolution in order to save on resources can lead to key processes being unresolved. A previous study has shown how insufficient resolution of the proton cyclotron instabilities leads to a misrepresentation of ion dynamics. This leads to larger temperature anisotropy and loss-cone shaped velocity distribution functions. In this study, we present a numerical model to introduce pitch-angle diffusion in velocity space, at a spatial resolution where this process was previously not correctly resolved. We test two different methods to enable pitch-angle diffusion in the 3D cartesian velocity space of Vlasiator. We show that we are successfully able to isotropise loss-cone shaped velocity distribution functions, and that this method could be applied to large simulations in order to save computational resources and still correctly model the Earth's magnetosheath.

Numerical simulations are widely used in modern space physics and are an essential tool to understand or discover new phenomena which cannot be observed using spacecraft measurements. However, numerical simulations are limited by the space grid resolution of the system and the computational costs of having a high spatial resolution. Therefore, some physics may be unresolved in part of the system due to its low spatial resolution. We have previously identified, using Vlasiator, that the proton cyclotron instability is not resolved for grid cell sizes larger than four times the inertial length in the solar wind, for waves in the downstream of the quasi-perpendicular shock in the magnetosheath of a global hybrid-Vlasov simulation. This leads to unphysically high perpendicular temperature and a dominance of the mirror mode waves. In this study, we use high-resolution simulations to measure and quantify how the proton cyclotron instability diffuses and isotropizes the velocity distribution functions. We investigate the process of pitch-angle scattering during the development of the instability and propose a method for the sub-grid modelling of the diffusion process of the instability at low resolution. This allows us to model the isotropization of the velocity distribution functions and to reduce the temperature anisotropy in the plasma while saving computational resources.

Numerical simulations are key in modern space physics, as they can be used as 1) context to data, 2) predict future behaviour of the system, 3) understand the system using unforeseen boundary conditions, and increasingly also in 4) discovering new phenomena that are hard to be observed using point-wise satellite measurements. Especially, the discovery of new phenomena pertains to global systems, where phenomena of interest may be initiated far away from the point of observations. The most typical method of simulating the global solar wind - magnetosphere - ionosphere system is based on magnetohydrodynamics (MHD), which is however not representing the actual plasma behaviour in locations where kinetic physics becomes important. Such regions are e.g., the foreshock - magnetosheath interaction, reconnection, and the inner magnetosphere.Vlasiator is the world’s first and so far the only global simulation based on the hybrid-Vlasov approach that simulates the ion distributions accurately without noise. The simulation has, for computational reasons, been so far executed in 2D real space. Even so, the global 5D Vlasiator results have shown without a doubt that ion-kinetic effects cannot be neglected from the large scales, as small-scale phenomena affect large scales and vice versa. This scale coupling leads to phenomena that are not predicted using local simulations without proper boundary conditions, or with spacecraft measurements lacking the global context.Here, we present the world’s first global 6-dimensional ion-kinetic global magnetospheric simulation run, accurate both locally and globally. The simulation box extends from the dayside to the nightside, and includes global dynamics and both dayside and nightside reconnection regions. We will investigate unambiguously for the first time the dayside magnetopause reconnection as driven by the kinetic variations in the magnetosheath, and tail reconnection as driven by magnetic flux from the dayside.

The foreshock, extending upstream of the quasi-parallel shock and populated with shock-reflected particles, is home to intense wave activity in the ultra-low frequency range. The most commonly observed of these waves are the “30 s” waves, fast magnetosonic waves propagating sunward in the plasma rest frame, but carried earthward by the faster solar wind flow. These waves are thought to be the main source of Pc3 magnetic pulsations (10 – 45 s) in the dayside magnetosphere. A handful of case studies with suitable spacecraft conjunctions have allowed simultaneous investigations of the wave properties in different geophysical regions, but the global picture of the wave transmission from the foreshock through the magnetosheath into the magnetosphere is still not known. In this work, we use global simulations performed with the hybrid-Vlasov model Vlasiator to study the Pc3 wave properties in the foreshock, magnetosheath and magnetosphere for different solar wind conditions. We find that in all three regions the wave power peaks at higher frequencies when the interplanetary magnetic field strength is larger, consistent with previous studies. While the transverse wave power decreases with decreasing Alfvén Mach number in the foreshock, the compressional wave power shows little variation. In contrast, in the magnetosheath and the magnetosphere, the compressional wave power decreases with decreasing Mach number. Inside the magnetosphere, the distribution of wave power varies with the IMF cone angle. We discuss the implications of these results for the propagation of foreshock waves across the different geophysical regions, and in particular their transmission through the bow shock.