Simulations of the coupled ionosphere–magnetosphere system are a key tool to understand geospace and its response to space weather. For the most part, they are based on fluid descriptions of plasma (magnetohydrodynamics, MHD) formalism, coupled to an electrostatic ionosphere. Kinetic approaches to modeling the global magnetosphere with a coupled ionosphere system are still a rarity. We present an ionospheric boundary model for the global near-Earth plasma simulation system Vlasiator. It complements the magnetospheric hybrid-Vlasov simulations with an inner boundary condition that solves the ionospheric potential based on field-aligned current and plasma quantities from the magnetospheric domain. This new ionospheric module solves the ionospheric potential in a height-integrated approach on an unstructured grid and couples back to the hybrid-kinetic simulation by mapping the resulting electric field to the magnetosphere's inner boundary. The solver is benchmarked against a set of well-established analytic reference cases, and we discuss the benefits of a spherical Fibonacci mesh for use in ionospheric modeling. Preliminary results from coupled global magnetospheric–ionospheric simulations are presented, showing formation of both Region 1 and Region 2 current systems.

We explore the three-dimensional structure of ion-kinetic instabilities in a thin current layer using a hybrid-Vlasov simulation of the Earth's magnetosphere. The simulation shows the simultaneous growth of tearing and kinking instabilities, which develop in the Sun-Earth and dawn-dusk directions, respectively, within the magnetotail current sheet. The formation of flux ropes indicates the development of the tearing instability, while flapping-type cross-tail oscillations arise from the kink instability. We consider both instabilities as independent polarizations, albeit sharing a common source: demagnetized ions forming crescent-shape distributions at the center of the current layer. These oscillations exhibit spatiotemporal characteristics within the proton-scale range, featuring a growth time on the order of 40-80 proton gyroperiods and a wavelength of approximately 15-30 proton skin depths.

When plasma and magnetic field discontinuities in the solar wind interact with Earth’s magnetic field, they can significantly alter the properties and dynamics of Earth’s bow shock, magnetosheath, and magnetopause. In this study, we investigate magnetosheath dynamic pressure enhancements generated by the interaction between a solar wind rotational discontinuity with Earth’s bow shock in a 2D simulation run of the global magnetospheric hybrid-Vlasov model Vlasiator. We find that as the discontinuity is advected into the bow shock, several fast-mode pulses associated with enhanced dynamic pressure are launched toward the Earth. In addition, the interaction between discontinuity and shock generates transient enhancements of dynamic pressure at the bow shock that move Earthward together with the discontinuity. We find that the fast-mode pulses are able to traverse the magnetosheath and disturb the magnetopause. This finding differs from the results of previous studies using 2D and 3D MHD simulations as well as spacecraft measurements, which concluded that magnetopause disturbances should be caused by the rotational discontinuity itself and the dynamic pressure enhancement associated with it.

Magnetic reconnection is a crucially important process for energy conversion in plasma physics, with the substorm cycle of Earth's magnetosphere and solar flares being prime examples. While 2D models have been widely applied to study reconnection, investigating reconnection in 3D is still, in many aspects, an open problem. Finding sites of magnetic reconnection in a 3D setting is not a trivial task, with several approaches, from topological skeletons to Lorentz transformations, having been proposed to tackle the issue. This work presents a complementary method for quasi-2D structures in 3D settings by noting that the magnetic field structures near reconnection lines exhibit 2D features that can be identified in a suitably chosen local coordinate system. We present applications of this method to a hybrid-Vlasov Vlasiator simulation of Earth's magnetosphere, showing the complex magnetic topologies created by reconnection for simulations dominated by quasi-2D reconnection. We also quantify the dimensionalities of magnetic field structures in the simulation to justify the use of such coordinate systems.

The Kelvin-Helmholtz instability (KHI), characterized by vortices forming at a perturbed velocity shear layer, is a prominent candidate mechanism for mass, momentum, and energy transport across boundaries with velocity shear in various space plasma environments. It is of particular interest at the flanks of Earth's magnetopause, which separates the plasma of the magnetosphere from the adjacent shocked solar wind flow in the magnetosheath. In the present study, we use local hybrid-Vlasov simulations to investigate the ion velocity distribution functions (VDFs) associated with KHI in a magnetopause-like, transverse velocity shear layer setting (magnetic field perpendicular to the shear plane). We look for signatures of ion finite Larmor radius (FLR) effects, which could be utilized in spacecraft measurements to recognize when such effects are active, influencing KHI evolution and driving plasma mixing. We show that when a density/temperature asymmetry exists across the shear layer, FLR effects produce a heat flux along the vortex edges. With a magnitude (greater than or similar to 0.1 mW m-2) that is a significant fraction of the total magnetosheath energy flux, the heat flux provides a distinct signature that could be measured with a single spacecraft. During the late nonlinear stage of KHI, mixed non-Maxwellian ion VDFs are additionally found within the vortices. Our results are also valid in the presence of a small magnetic shear across the magnetopause.

Abstract Flux transfer events (FTEs) are transient magnetic flux ropes at Earth's dayside magnetopause formed due to magnetic reconnection. As they move across the magnetopause surface, they can generate disturbances in the ultralow frequency (ULF) range, which then propagate into the magnetosphere. This study provides evidence of ULF waves in the Pc2 wave frequency range (>0.1 Hz) caused by FTEs during dayside reconnection using a global 3D hybrid‐Vlasov simulation (Vlasiator). These waves resulted from FTE formation and propagation at the magnetopause are particularly associated with large, rapidly moving FTEs. The wave power is stronger in the morning than afternoon, showing local time asymmetry. In the pre and postnoon equatorial regions, significant poloidal and toroidal components are present alongside the compressional component. The noon sector, with fewer FTEs, has lower wave power and limited magnetospheric propagation.

Kinetic Alfvén wave (KAW) is the kinetic extension of shear Alfvén wave (SAW) where the perpendicular wavelength with respect to the magnetic field becomes comparable to the ion scale. It has been suggested theoretically that mode conversion from incident compressional waves to KAWs at the magnetopause leads to the plasma transport. Existence of KAWs has been identified from in-situ observations and shown to be closely related to the Hall field from magnetic reconnection. In this study, we investigate the properties of KAWs using the hybrid-Vlasov model Vlasiator. Local runs of tangential discontinuities with parameters relevant to Earth’s magnetopause are performed to look at the mode conversion from fast waves to Alfvén waves. Signatures of KAWs are identified from both local and global simulations, which provide insights into the nonlinear plasma transport process in the magnetosphere.

Flapping waves are large-scale oscillations of the Earth's magnetotail current layer propagating in a cross-tail direction. In the current study, we investigate the plasma sheet flapping waves observed in a global 6D hybrid-Vlasov simulation of the Earth’s magnetosphere obtained with the Vlasiator code. Applying the timing analysis for 4 virtual spacecraft located in the near tail around X=-14 Re (where Re=6371 km is the Earth radius), we find that the phase velocity of the waves is directed duskwards and has a magnitude comparable to the ion drift velocity in the current sheet centre. We analyse the spatio-temporal characteristics of the waves by the ad-hoc technique of current sheet extremum tracing and we find that the average period of the flapping waves is T~40 s, and the typical wavelength λ=1.6 Re. The necessity to develop a specific technique arises from the large inaccuracy of the timing analysis output for the different positions of the virtual spacecraft constellation. We clearly observe that the area of most intense growth of the flapping oscillations coincides with the vicinity of the ion diffusion region of magnetic reconnection. In order to clarify the origin of the flapping waves, we calculate the dispersion relation for the ion-kink instability, taking the parameters of different ion distributions observed nearby with the reconnection X-line at the different time steps. Notably, the ion distribution has a specific crescent-type shape revealing the meandering motion of ions in the reconnecting current sheet that we identify as ions carrying the non-adiabatic current which is required for the development of the current layer instabilities. The agreement between the predicted values of the frequency and wave vectors and those observed in the simulation gives us evidence that flapping waves in the global hybrid-Vlasov simulation arise due to the development of the ion kink instability in the reconnecting current layer.

The presence of a velocity shear layer in a plasma can lead to the development of the Kelvin-Helmholtz instability (KHI). KHI is characterised by the growth of waves that roll up to form non-linear vortices. An example of such velocity shear layer is found at either flank of Earth's magnetopause, where KHI acts a driver of mass and energy transfer from the solar wind into the magnetosphere. Within the rolled-up vortices, kinetic length scales may be attained, allowing vortex-induced magnetic reconnection and kinetic-scale diffusion to operate. In the present study, we have considered the realistic case of a density/temperature jump across the magnetopause and modelled the development of the KHI using a local hybrid-Vlasov simulation with the Vlasiator code. For a case with a northward directed magnetic field, we find that an enhanced ion heat flux arises at vortex boundaries whose thickness approaches the ion gyroscale. Furthermore, the direction of the heat flux vector closely follows the direction of the vortex boundary tangent vector. As such, this signature could provide observational evidence of ion diffusion occurring within KHI, and also information on vortex boundary geometry with single spacecraft data. To validate our results, we compare our simulation run with data from the Magnetospheric Multiscale Mission.

Pitch-angle diffusion is one of the main processes of isotropisation of ions in the Earth's magnetosheath. It results from the proton cyclotron and mirror instabilities, arising from temperature anisotropy in the magnetosheath, and is governed by the pitch-angle diffusion coefficient Dμμ. We have previously developed a sub-grid model to describe pitch-angle diffusion in global-hybrid Vlasov simulations when coarse spatial grid resolution leads to a lack of diffusion. In this study, we present an analytical solution for a pitch-angle diffusion coefficient derived from bi-Maxwellian velocity distribution functions in order to apply this solution to the sub-grid model. This will allow us to model accurately the isotropisation of the distribution functions and to reduce the temperature anisotropy of the plasma while saving computational resources.

Vlasiator, the global hybrid-Vlasov model of the terrestrial magnetosphere, now features a coupled ionosphere model replacing the previous, perfectly conducting inner boundary. Following a well-established approach, densities, temperatures and field-aligned currents are mapped along the geomagnetic dipole field down to an ionospheric grid. Height-integrated Hall and Pedersen conductivities are computed using a model atmospheric profile based on the NRLMSIS model in order to solve for the ionospheric potential. Its gradient is then mapped back to the hybrid-Vlasov simulation domain, yielding an electric field and a resulting EXB drift affecting the plasma at the boundary.We present an overview of this new coupled ionosphere module as well as highlights from the first large-scale magnetospheric simulation runs performed with it. In particular, we compare the global behaviour of the magnetosphere under steady southward interplanetary magnetic field driving using the perfectly conducting or coupled ionosphere boundary models.

Sub-grid models are key tools to accurately describe the physical processes at play in a system when high-resolution simulations are not feasible. We previously developed a sub-grid model for pitch-angle diffusion in hybrid-Vlasov simulations of Earth's magnetosphere. However, a more precise description of the pitch-angle diffusion coefficient is required to apply this model to global simulations. In this study, we use an existing method to parametrize pitch-angle diffusion coefficients from monotonic distribution functions and adapt it to bi-Maxwellian distributions. We determine these coefficients for various values of the ion temperature anisotropy and plasma β∥. We use these newly parametrized coefficients in our sub-grid model and show that it accurately models reduction of temperature anisotropy in both local simulations and global simulations of the Earth's magnetosphere, while using minimal computational resources.

Magnetosheath jets are plasma structures that are characterised by enhanced dynamic pressure and/or plasma velocity. In this study, we investigate the formation of magnetosheath jets in four two-dimensional simulation runs of the global magnetospheric hybrid-Vlasov model Vlasiator. We focus on jets whose origins were not clearly determined in a previous study using the same simulations (Suni et al., 2021) to have been associated with foreshock structures of enhanced dynamic pressure and magnetic field. We find that these jets can be divided into two categories based on their direction of propagation, either predominantly antisunward or predominantly toward the flanks of the magnetosphere. As antisunward-propagating jets can potentially impact the magnetopause and have effects on the magnetosphere, understanding which foreshock and bow shock phenomena are associated with them is important. The antisunward-propagating jets have properties indistinguishable from those of the jets found in the previous study. This indicates that the antisunward jets investigated in this paper belong to the same continuum as the jets previously found to be caused by foreshock structures; however, due to the criteria used in the previous study, they did not appear in this category before. These jets together make up 86 % of all jets in this study. The flankward-propagating jets make up 14 % of all jets and are different, showing no clear association with foreshock structures and exhibiting temperature anisotropy unlike the other jets. We suggest that they could consist of quasi-perpendicular magnetosheath plasma, indicating that these jets could be associated with local turning of the shock geometry from quasi-parallel to quasi-perpendicular. This turning could be due to bow shock reformation at the oblique shock caused by foreshock ultralow-frequency (ULF) wave activity.

The precipitation of charged particles from the magnetosphere into the ionosphere is one of the crucial coupling mechanisms between these two regions of geospace and is associated with multiple space weather effects, such as global navigation satellite system signal disruption and geomagnetically induced currents at ground level. While precipitating particle fluxes have been measured by numerous spacecraft missions over the past decades, it often remains difficult to obtain global precipitation patterns with a good time resolution during a substorm. Numerical simulations can help to bridge this gap and improve the understanding of mechanisms leading to particle precipitation at high latitudes through the global view they offer on the near-Earth space system. We present the first results on auroral (0.5-50 keV) proton precipitation within a 3-dimensional simulation of the Vlasiator hybrid-Vlasov model. The run is driven by southward interplanetary magnetic field conditions with constant solar wind parameters. We find that on the dayside, cusp proton precipitation exhibits the expected energy-latitude dispersion and takes place in the form of successive bursts associated with the transit of flux transfer events formed through dayside magnetopause reconnection. On the nightside, the precipitation takes place within the expected range of geomagnetic latitudes, and it appears clearly that the precipitating particle injection is taking place within a narrow magnetic local time span, associated with fast Earthward plasma flows in the near-Earth magnetotail. Finally, the simulated precipitating fluxes are compared to observations from Defense Meteorological Satellite Program spacecraft during driving conditions similar to those in the simulation and are found to be in good agreement with the measurements.

Rapid plasma eruptions explosively release energy within Earth’s magnetosphere, at the Sun and at other planets. At Earth, these eruptions, termed plasmoids, occur in the magnetospheric nightside and are associated with sudden brightening of the aurora. The chain of events leading to the plasmoid is one of the longest-standing unresolved questions in space physics. Two competing paradigms have been proposed to explain the course of events. The first asserts that magnetic reconnection changes the magnetic topology in the tail, severing a part of the magnetosphere as plasmoid. The second employs kinetic instabilities that first disrupt the current sheet supporting the magnetotail and launch waves that trigger the topological change to eject the plasmoid. Here we numerically simulate Earth’s magnetosphere at realistic scales using a model that captures the physics underlying both paradigms. We show that both magnetic reconnection and kinetic instabilities are required to induce a global topological reconfiguration of the magnetotail, thereby combining the seemingly contradictory paradigms. Our results help to understand how plasma eruptions may take place, guide spacecraft constellation mission design to capture these ejections in observations and lead to improved understanding of space weather by improving the predictability of the plasmoids.

Vlasiator is a high‐performance ion‐kinetic code that is now conducting 3D hybrid‐Vlasov simulations of the global magnetosphere. We use Vlasiator to investigate the impact of a pressure pulse with southward‐oriented magnetic field on the Earth's magnetosphere. The simulation driving parameters are comparable to conditions that have led to geomagnetic storms. Our pressure pulse simulation reproduces many physical effects, namely the expansion of the auroral oval, the development of field‐aligned currents, enhanced particle precipitation near the open/closed field line boundary, and compression of Earth's magnetopause. This demonstrates the effectiveness of the hybrid‐Vlasov approach for moderate driving conditions. Our investigation of the time‐dependent magnetopause compression motivates a generalization of the existing theory. Specifically, we find that accounting for the finite transition time of the solar wind dynamic pressure improves the model's description of the magnetopause oscillations.

We present methods and algorithms that allow the Vlasiator code to run global, three-dimensional hybrid-Vlasov simulations of Earth's entire magnetosphere. The key ingredients that make Vlasov simulations at magnetospheric scales possible are the sparse velocity space implementation and spatial adaptive mesh refinement. We outline the algorithmic improvement of the semi-Lagrangian solver for six-dimensional phase space quantities, discuss the coupling of Vlasov and Maxwell equations' solvers in a refined mesh, and provide performance figures from simulation test runs that demonstrate the scalability of this simulation system to full magnetospheric runs.

The Kelvin-Helmholtz instability (KHI) is a ubiquitous fluid instability in space plasmas. At the flanks of Earth's magnetopause, the KHI can typically develop during periods of northward interplanetary magnetic field, and it drives the solar wind-magnetosphere mass/energy transfer in the absence of dayside magnetic reconnection. We use local 2D-3V hybrid-Vlasov simulations to study the ion velocity distribution functions (VDFs) associated with the KHI in a magnetopause-like setup. Our results indicate that when the KHI enters the non-linear stage, the ion VDFs in the region perturbed by the instability become increasingly non-Maxwellian. The degree of non-Maxwellianity increases along with the magnitude of the density jump across the KHI boundary. We assess the impact of the non-Maxwellian ion VDFs on the development of the KHI, and compare the simulated VDFs with those observed by the Magnetospheric Multiscale Mission.

Among the most unpredictable phenomena within the near-Earth space are substorms, periods of energy loading and explosive release within the magnetospheric tail. Substorms are global, as energy is extracted from the solar wind via dayside reconnection, while the tail energy release takes place in a vast domain within a few tens of seconds. Due to the scarcity of space-borne observations, it has been difficult to conclusively separate between the onset scenarios that include magnetic reconnection and various ion-kinetic instabilities, which occur at mesoscales, and small scales. Another decades-long investigation concerns the flapping of the plasma sheet, occurring within a large area favouring the substorm growth phase, although it has been observed at other times as well. Mechanisms to explain the flapping are presently unknown. Modelling efforts have failed to explain the substorm onset either because all the required physics has not been included in the simulation, or the simulation does not cover the entire domain, thus possibly missing important drivers. Vlasiator is a model describing the global magnetosphere accurately at ion-kinetic scales, including the ion-kinetic effects that are absent in the fluid descriptions. Unlike many other kinetic simulations, Vlasiator extends the simulation domain to global scales and accurately represents the Earth’s unscaled magnetosphere from the dayside to the tail, in six dimensions including the 3D real space and 3D velocity space without noise that is present in the alternative PIC method. We present the first global 6D simulation encompassing the entire near-Earth space to simulate ion-kinetic magnetospheric dynamics self-consistently. We determine reconnection, ion-kinetic instabilities, plasma sheet flapping, and bursty bulk flows in the simulation domain, and show how they all contribute to the whole and work in concert in developing the substorm onset. Our results help to understand spacecraft measurements and the overall substorm process, which will significantly improve understanding space physics and eventually space weather. Our results can also be used in strategies to design a mission, which will finally and conclusively capture the substorm onset with in situ measurements.

The Earth's magnetosphere and its bow shock, which is formed by the interaction of the supersonic solar wind with the terrestrial magnetic field, constitute a rich natural laboratory enabling in situ investigations of universal plasma processes. Under suitable interplanetary magnetic field conditions, a foreshock with intense wave activity forms upstream of the bow shock. So-called 30 s waves, named after their typical period at Earth, are the dominant wave mode in the foreshock and play an important role in modulating the shape of the shock front and affect particle reflection at the shock. These waves are also observed inside the magnetosphere and down to the Earth's surface, but how they are transmitted through the bow shock remains unknown. By combining state-of-the-art global numerical simulations and spacecraft observations, we demonstrate that the interaction of foreshock waves with the shock generates earthward-propagating, fast-mode waves, which reach the magnetosphere. These findings give crucial insight into the interaction of waves with collisionless shocks in general and their impact on the downstream medium.