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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.

Solar wind charge exchange produces emissions in the soft X-ray energy range which can enable the study of near-Earth space regions such as the magnetopause, the magnetosheath and the polar cusps by remote sensing techniques. The Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) and Lunar Environment heliospheric X-ray Imager (LEXI) missions aim to obtain soft X-ray images of near-Earth space thanks to their Soft X-ray Imager (SXI) instruments. While earlier modeling works have already simulated soft X-ray images as might be obtained by SMILE SXI during its mission, the numerical models used so far are all based on the magnetohydrodynamics description of the space plasma. To investigate the possible signatures of ion-kinetic-scale processes in soft X-ray images, we use for the first time a global hybrid-Vlasov simulation of the geospace from the Vlasiator model. The simulation is driven by fast and tenuous solar wind conditions and purely southward interplanetary magnetic field. We first produce global X-ray images of the dayside near-Earth space by placing a virtual imaging satellite at two different locations, providing meridional and equatorial views. We then analyze regional features present in the images and show that they correspond to signatures in soft X-ray emissions of mirror-mode wave structures in the magnetosheath and flux transfer events (FTEs) at the magnetopause. Our results suggest that, although the time scales associated with the motion of those transient phenomena will likely be significantly smaller than the integration time of the SMILE and LEXI imagers, mirror-mode structures and FTEs can cumulatively produce detectable signatures in the soft X-ray images. For instance, a local increase by 30% in the proton density at the dayside magnetopause resulting from the transit of multiple FTEs leads to a 12% enhancement in the line-of-sight- and time-integrated soft X-ray emissivity originating from this region. Likewise, a proton density increase by 14% in the magnetosheath associated with mirror-mode structures can result in an enhancement in the soft X-ray signal by 4%. These are likely conservative estimates, given that the solar wind conditions used in the Vlasiator run can be expected to generate weaker soft X-ray emissions than the more common denser solar wind. These results will contribute to the preparatory work for the SMILE and LEXI missions by providing the community with quantitative estimates of the effects of small-scale, transient phenomena occurring on the dayside.

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.

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.

The foreshock located upstream of Earth's bow shock hosts a wide variety of phenomena related to the reflection of solar wind particles from the bow shock and the subsequent formation of ultra-low-frequency (ULF) waves. In this work, we investigate foreshock cavitons, which are transient structures resulting from the non-linear evolution of ULF waves, and spontaneous hot flow anomalies (SHFAs), which are thought to evolve from cavitons as they accumulate suprathermal ions while being carried to the bow shock by the solar wind. Using the global hybrid-Vlasov simulation model Vlasiator, we have conducted a statistical study in which we track the motion of individual cavitons and SHFAs in order to examine their properties and evolution. In our simulation run where the interplanetary magnetic field (IMF) is directed at a sunward–southward angle of 45∘, continuous formation of cavitons is found up to ∼11 Earth radii (RE) from the bow shock (along the IMF direction), and caviton-to-SHFA evolution takes place within ∼2 RE from the shock. A third of the cavitons in our run evolve into SHFAs, and we find a comparable amount of SHFAs forming independently near the bow shock. We compare the properties of cavitons and SHFAs to prior spacecraft observations and simulations, finding good agreement. We also investigate the variation of the properties as a function of position in the foreshock, showing that transients close to the bow shock are associated with larger depletions in the plasma density and magnetic field magnitude, along with larger increases in the plasma temperature and the level of bulk flow deflection. Our measurements of the propagation velocities of cavitons and SHFAs agree with earlier studies, showing that the transients propagate sunward in the solar wind rest frame. We show that SHFAs have a greater solar wind rest frame propagation speed than cavitons, which is related to an increase in the magnetosonic speed near the bow shock.

We present results of noon–midnight meridional plane global hybrid-Vlasov simulations of the magnetotail ion dynamics under a steady southward interplanetary magnetic field using the Vlasiator model. The simulation results show magnetotail reconnection and formation of earthward and tailward fast plasma outflows. The hybrid-Vlasov approach allows us to study ion velocity distribution functions (VDFs) that are self-consistently formed during the magnetotail evolution. We examine the VDFs collected by virtual detectors placed along the equatorial magnetotail within earthward and tailward outflows and around the quasi-steady X line formed in the magnetotail at X≈-14RE. This allows us to follow the evolution of VDFs during earthward and tailward motion of reconnected flux tubes as well as study signatures of unmagnetized ion motion in the weak magnetic field near the X line. The VDFs indicate actions of Fermi-type and betatron acceleration mechanisms, ion acceleration by the reconnection electric field, and Speiser-type motion of ions near the X line. The simulated VDFs are compared and show good agreement with VDFs observed in the magnetotail by the Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Acceleration, Reconnection, Turbulence and Electrodynamics of Moon's Interaction with the Sun (ARTEMIS) spacecraft. We find that the VDFs become more gyrotropic but retain transverse anisotropy and counterstreaming ion beams when being convected earthward. The presented global hybrid-Vlasov simulation results are valuable for understanding physical processes of ion acceleration during magnetotail reconnection, interpretation of in situ observations, and for future mission development by setting requirements on pitch angle and energy resolution of upcoming instruments.

Magnetosheath jets are regions of high dynamic pressure, which can traverse from the bow shock towards the magnetopause. Recent modelling efforts, limited to a single jet and a single set of upstream conditions, have provided the first estimations about how the jet parameters behave as a function of position within the magnetosheath. Here we expand the earlier results by doing the first statistical investigation of the jet dimensions and parameters as a function of their lifetime within the magnetosheath. To verify the simulation behaviour, we first identify jets from Magnetosphere Multiscale (MMS) spacecraft data (6142 in total) and confirm the Vlasiator jet general behaviour using statistics of 924 simulated individual jets. We find that the jets in the simulation are in quantitative agreement with the observations, confirming earlier findings related to jets using Vlasiator. The jet density, dynamic pressure, and magnetic field intensity show a sharp jump at the bow shock, which decreases towards the magnetopause. The jets appear compressive and cooler than the magnetosheath at the bow shock, while during their propagation towards the magnetopause they thermalise. Further, the shape of the jets flatten as they progress through the magnetosheath. They are able to maintain their flow velocity and direction within the magnetosheath flow, and they end up preferentially to the side of the magnetosheath behind the quasi-parallel shock. Finally, we find that Vlasiator jets during low solar wind Alfvén Mach number MA are shorter in duration, smaller in their extent, and weaker in terms of dynamic pressure and magnetic field intensity as compared to the jets during high MA.

Modern investigations of dynamical space plasma systems such as magnetically complicated topologies within the Earth's magnetosphere make great use of supercomputer models as well as spacecraft observations. Space plasma simulations can be used to investigate energy transfer, acceleration, and plasma flows on both global and local scales. Simulation of global magnetospheric dynamics requires spatial and temporal scales currently achievable through magnetohydrodynamics or hybrid-kinetic simulations, which approximate electron dynamics as a charge-neutralizing fluid. We introduce a novel method for Vlasov-simulating electrons in the context of a hybrid-kinetic framework in order to examine the energization processes of magnetospheric electrons. Our extension of the Vlasiator hybrid-Vlasov code utilizes the global simulation dynamics of the hybrid method whilst modelling snapshots of electron dynamics on global spatial scales and temporal scales suitable for electron physics. Our eVlasiator model is shown to be stable both for single-cell and small-scale domains, and the solver successfully models Langmuir waves and Bernstein modes. We simulate a small test-case section of the near-Earth magnetotail plasma sheet region, reproducing a number of electron distribution function features found in spacecraft measurements.

Kinetically driven plasma waves are fundamental for a description of the thermodynamical properties of the Earth's magnetosheath. The most commonly observed ion-scale instabilities are generated by temperature anisotropy of the ions, such as the mirror and proton cyclotron instabilities. We investigate here the spatial resolution dependence of the mirror and proton cyclotron instabilities in a global hybrid-Vlasov simulation using the Vlasiator model; we do this in order to find optimal resolutions and help future global hybrid-Vlasov simulations to save resources when investigating those instabilities in the magnetosheath. We compare the proton velocity distribution functions, power spectra and growth rates of the instabilities in a set of simulations with three different spatial resolutions but otherwise identical set-up. We find that the proton cyclotron instability is absent at the lowest resolution and that only the mirror instability remains, which leads to an increased temperature anisotropy in the simulation. We conclude that the proton cyclotron instability, its saturation and the reduction of the anisotropy to marginal levels are resolved at the highest spatial resolution. A further increase in resolution does not lead to a better description of the instability to an extent that would justify this increase at the cost of numerical resources in future simulations. We also find that spatial resolutions between 1.32 and 2.64 times the inertial length in the solar wind present acceptable limits for the resolution within which the velocity distribution functions resulting from the proton cyclotron instability are still bi-Maxwellian and reach marginal stability levels. Our results allow us to determine a range of spatial resolutions suitable for the modelling of the proton cyclotron and mirror instabilities and should be taken into consideration regarding the optimal grid spacing for the modelling of these two instabilities, within available computational resources.

Radial diffusion coefficients quantify non-adiabatic transport of energetic particles by electromagnetic field fluctuations in planetary radiation belts. Theoretically, radial diffusion occurs for an ensemble of particles that experience irreversible violation of their third adiabatic invariant, which is equivalent to a change in their Roederer L* parameter. Thus, the Roederer L* coordinate is the fundamental quantity from which radial diffusion coefficients can be computed. In this study, we present a methodology to calculate the Lagrangian derivative of L* from global magnetospheric simulations, and test it with an application to Vlasiator, a hybrid-Vlasov model of near-Earth space. We use a Hamiltonian formalism for particles confined to closed drift shells with conserved first and second adiabatic invariants to compute changes in the guiding center drift paths due to electric and magnetic field fluctuations. We investigate the feasibility of this methodology by computing the time derivative of L* for an equatorial ultrarelativistic electron population travelling along four guiding center drift paths in the outer radiation belt during a 5 minute portion of a Vlasiator simulation. Radial diffusion in this simulation is primarily driven by ultralow frequency waves in the Pc3 range (10–45 s period range) that are generated in the foreshock and transmitted through the magnetopause to the outer radiation belt environment. Our results show that an alternative methodology to compute detailed radial diffusion transport is now available and could form the basis for comparison studies between numerical and observational measurements of radial transport in the Earth’s radiation belts.

Bounded by the bow shock and the magnetopause, the magnetosheath forms the interface between solar wind and magnetospheric plasmas and regulates solar wind–magnetosphere coupling. Previous works have revealed pronounced dawn–dusk asymmetries in the magnetosheath properties. The dependence of these asymmetries on the upstream parameters remains however largely unknown. One of the main sources of these asymmetries is the bow shock configuration, which is typically quasi-parallel on the dawn side and quasi-perpendicular on the dusk side of the terrestrial magnetosheath because of the Parker spiral orientation of the interplanetary magnetic field (IMF) at Earth. Most of these previous studies rely on collections of spacecraft measurements associated with a wide range of upstream conditions which are processed in order to obtain average values of the magnetosheath parameters. In this work, we use a different approach and quantify the magnetosheath asymmetries in global hybrid-Vlasov simulations performed with the Vlasiator model. We concentrate on three parameters: the magnetic field strength, the plasma density, and the flow velocity. We find that the Vlasiator model reproduces the polarity of the asymmetries accurately but that their level tends to be higher than in spacecraft measurements, probably because the magnetosheath parameters are obtained from a single set of upstream conditions in the simulation, making the asymmetries more prominent. A set of three runs with different upstream conditions allows us to investigate for the first time how the asymmetries change when the angle between the IMF and the Sun–Earth line is reduced and when the Alfvén Mach number decreases. We find that a more radial IMF results in a stronger magnetic field asymmetry and a larger variability of the magnetosheath density. In contrast, a lower Alfvén Mach number leads to a reduced magnetic field asymmetry and a decrease in the variability of the magnetosheath density, the latter likely due to weaker foreshock processes. Our results highlight the strong impact of the quasi-parallel shock and its associated foreshock on global magnetosheath properties, in particular on the magnetosheath density, which is extremely sensitive to transient quasi-parallel shock processes, even with the perfectly steady upstream conditions in our simulations. This could explain the large variability of the density asymmetry levels obtained from spacecraft measurements in previous studies.

The foreshock is a region of space upstream of the Earth's bow shock extending along the interplanetary magnetic field (IMF). It is permeated by shock-reflected ions and electrons, low-frequency waves, and various plasma transients. We investigate the extent of the He2+ foreshock using Vlasiator, a global hybrid-Vlasov simulation. We perform the first numerical global survey of the helium foreshock and interpret some historical foreshock observations in a global context. The foreshock edge is populated by both proton and helium field-aligned beams, with the proton foreshock extending slightly further into the solar wind than the helium foreshock and both extending well beyond the ultra-low frequency (ULF) wave foreshock. We compare our simulation results with Magnetosphere Multiscale (MMS) Hot Plasma Composition Analyzer (HPCA) measurements, showing how the gradient of suprathermal ion densities at the foreshock crossing can vary between events. Our analysis suggests that the IMF cone angle and the associated shock obliquity gradient can play a role in explaining this differing behaviour. We also investigate wave–ion interactions with wavelet analysis and show that the dynamics and heating of He2+ must result from proton-driven ULF waves. Enhancements in ion agyrotropy are found in relation to, for example, the ion foreshock boundary, the ULF foreshock boundary, and specular reflection of ions at the bow shock. We show that specular reflection can describe many of the foreshock ion velocity distribution function (VDF) enhancements. Wave–wave interactions deep in the foreshock cause de-coherence of wavefronts, allowing He2+ to be scattered less than protons.

We study the interaction of solar wind protons with Earth's quasi-parallel bow shock using a hybrid-Vlasov simulation. We employ the global hybrid model Vlasiator to include effects due to bow shock curvature, tenuous upstream populations, and foreshock waves. We investigate the uncertainty of the position of the quasi-parallel bow shock as a function of several plasma properties and find that regions of non-locality or uncertainty of the shock position form and propagate away from the shock nose. Our results support the notion of upstream structures causing the patchwork reconstruction of the quasi-parallel shock front in a non-uniform manner. We propose a novel method for spacecraft data to be used to analyse this quasi-parallel reformation. We combine our hybrid-Vlasov results with test-particle studies and show that proton energization, which is required for injection, takes place throughout a larger shock transition zone. The energization of particles is found regardless of the instantaneous non-locality of the shock front, in agreement with it taking place over a larger region. Distortion of magnetic fields in front of and at the shock is shown to have a significant effect on proton injection. We additionally show that the density of suprathermal reflected particles upstream of the shock may not be a useful metric for the probability of injection at the shock, as foreshock dynamics and particle trapping appear to have a significant effect on energetic-particle accumulation at a given position in space. Our results have implications for statistical and spacecraft studies of the shock injection problem.

Particle precipitation plays a key role in the coupling of the terrestrial magnetosphere and ionosphere by modifying the upper atmospheric conductivity and chemistry, driving field-aligned currents, and producing aurora. Yet quantitative observations of precipitating fluxes are limited, since ground-based instruments can only provide indirect measurements of precipitation, while particle telescopes aboard spacecraft merely enable point-like in situ observations with an inherently coarse time resolution above a given location. Further, orbit timescales generally prevent the analysis of whole events. On the other hand, global magnetospheric simulations can provide estimations of particle precipitation with a global view and higher time resolution. We present the first results of auroral (∼1–30 keV) proton precipitation estimation using the Vlasiator global hybrid-Vlasov model in a noon–midnight meridional plane simulation driven by steady solar wind with a southward interplanetary magnetic field. We first calculate the bounce loss-cone angle value at selected locations in the simulated nightside magnetosphere. Then, using the velocity distribution function representation of the proton population at those selected points, we study the population inside the loss cone. This enables the estimation of differential precipitating number fluxes as would be measured by a particle detector aboard a low-Earth-orbiting (LEO) spacecraft. The obtained differential flux values are in agreement with a well-established empirical model in the midnight sector, as are the integral energy flux and mean precipitating energy. We discuss the time evolution of the precipitation parameters derived in this manner in the global context of nightside magnetospheric activity in this simulation, and we find in particular that precipitation bursts of  min duration can be self-consistently and unambiguously associated with dipolarising flux bundles generated by tail reconnection. We also find that the transition region seems to partly regulate the transmission of precipitating protons to the inner magnetosphere, suggesting that it has an active role in regulating ionospheric precipitation.

We use a global hybrid-Vlasov simulation for the magnetosphere, Vlasiator, to investigate magnetosheath high-speed jets. Unlike many other hybrid-kinetic simulations, Vlasiator includes an unscaled geomagnetic dipole, indicating that the simulation spatial and temporal dimensions can be given in SI units without scaling. Thus, for the first time, this allows investigating the magnetosheath jet properties and comparing them directly with the observed jets within the Earth's magnetosheath. In the run shown in this paper, the interplanetary magnetic field (IMF) cone angle is 30°, and a foreshock develops upstream of the quasi-parallel magnetosheath. We visually detect a structure with high dynamic pressure propagating from the bow shock through the magnetosheath. The structure is confirmed as a jet using three different criteria, which have been adopted in previous observational studies. We compare these criteria against the simulation results. We find that the magnetosheath jet is an elongated structure extending earthward from the bow shock by ∼ 2.6 RE, while its size perpendicular to the direction of propagation is ∼ 0.5 RE. We also investigate the jet evolution and find that the jet originates due to the interaction of the bow shock with a high-dynamic-pressure structure that reproduces observational features associated with a short, large-amplitude magnetic structure (SLAMS). The simulation shows that magnetosheath jets can develop also under steady IMF, as inferred by observational studies. To our knowledge, this paper therefore shows the first global kinetic simulation of a magnetosheath jet, which is in accordance with three observational jet criteria and is caused by a SLAMS advecting towards the bow shock.

Fast plasma flows produced as outflow jets from reconnection sites or X lines are a key feature of the dynamics in the Earth's magnetosphere. We have used a polar plane simulation of the hybrid-Vlasov model Vlasiator, driven by steady southward interplanetary magnetic field and fast solar wind, to study fast plasma sheet ion flows and related magnetic field structures in the Earth's magnetotail. In the simulation, lobe reconnection starts to produce fast flows after the increasing pressure in the lobes has caused the plasma sheet to thin sufficiently. The characteristics of the earthward and tailward fast flows and embedded magnetic field structures produced by multi-point tail reconnection are in general agreement with spacecraft measurements reported in the literature. The structuring of the flows is caused by internal processes: interactions between major X points determine the earthward or tailward direction of the flow, while interactions between minor X points, associated with leading edges of magnetic islands carried by the flow, induce local minima and maxima in the flow speed. Earthward moving flows are stopped and diverted duskward in an oscillatory (bouncing) manner at the transition region between tail-like and dipolar magnetic fields. Increasing and decreasing dynamic pressure of the flows causes the transition region to shift earthward and tailward, respectively. The leading edge of the train of earthward flow bursts is associated with an earthward propagating dipolarization front, while the leading edge of the train of tailward flow bursts is associated with a tailward propagating plasmoid. The impact of the dipolarization front with the dipole field causes magnetic field variations in the Pi2 range. Major X points can move either earthward or tailward, although tailward motion is more common. They are generally not advected by the ambient flow. Instead, their velocity is better described by local parameters, such that an X point moves in the direction of increasing reconnection electric field strength. Our results indicate that ion kinetics might be sufficient to describe the behavior of plasma sheet bulk ion flows produced by tail reconnection in global near-Earth simulations.

In this paper we present the first identification of foreshock cavitons and the formation of spontaneous hot flow anomalies (SHFAs) with the Vlasiator global magnetospheric hybrid-Vlasov simulation code. In agreement with previous studies we show that cavitons evolve into SHFAs. In the presented run, this occurs very near the bow shock. We report on SHFAs surviving the shock crossing into the downstream region and show that the interaction of SHFAs with the bow shock can lead to the formation of a magnetosheath cavity, previously identified in observations and simulations. We report on the first identification of long-term local weakening and erosion of the bow shock, associated with a region of increased foreshock SHFA and caviton formation, and repeated shock crossings by them. We show that SHFAs are linked to an increase in suprathermal particle pitch-angle spreads. The realistic length scales in our simulation allow us to present a statistical study of global caviton and SHFA size distributions, and their comparable size distributions support the theory that SHFAs are formed from cavitons. Virtual spacecraft observations are shown to be in good agreement with observational studies.

The origin of the flapping motions of the current sheet in the Earth's magnetotail is one of the most interesting questions of magnetospheric dynamics yet to be solved. We have used a polar plane simulation from the global hybrid-Vlasov model Vlasiator to study the characteristics and source of current sheet flapping in the center of the magnetotail. The characteristics of the simulated signatures agree with observations reported in the literature. The flapping is initiated by a hemispherically asymmetric magnetopause perturbation, created by subsolar magnetopause reconnection, that is capable of displacing the tail current sheet from its nominal position. The current sheet displacement propagates downtail at the same pace as the driving magnetopause perturbation. The initial current sheet displacement launches a standing magnetosonic wave within the tail resonance cavity. The travel time of the wave within the local cavity determines the period of the subsequent flapping signatures. Compression of the tail lobes due to added flux affects the cross-sectional width of the resonance cavity as well as the magnetosonic speed within the cavity. These in turn modify the wave travel time and flapping period. The compression of the resonance cavity may also provide additional energy to the standing wave, which may lead to strengthening of the flapping signature. It may be possible that the suggested mechanism could act as a source of kink-like waves that have been observed to be emitted from the center of the tail and to propagate toward the dawn and dusk flanks.