Daring to think of the impossible : The story of Vlasiator

Vlasiator is the world's first global Eulerian hybrid-Vlasov simulation code, going beyond magnetohydrodynamics in the solar wind-magnetosphere-ionosphere system. This paper gives the story of Vlasiator. An important enabler of Vlasiator is the rapid increase of computational resources over the last decade, but also the open-minded, courageous forerunners, who have embraced this new opportunity, both as developers but also as co-authors of our papers. Typically, when starting a new coding project, people think about the presently available resources. But when the development continues for multiple years, the resources change. If instead, one targets to upcoming resources, one is always in possession of a code which does not contain large legacy parts that are not able to utilize latest resources. It will be interesting to see how many modelling groups will take the opportunity to benefit from the current high-performance computing trends, and where are we in the next 10 years. In the following, a simulation that directly handles and manipulates the phase space density f(r,v,t) is referred to as a Vlasov approach, whereas a simulation system that traces phase space samples by their kinetic characteristics of motion is a Particle-in-Cell approach. This terminology is consistent with its use in the magnetospheric simulation community.Peer reviewe

On the Importance of Spatial and Velocity Resolution in the Hybrid-Vlasov Modeling of Collisionless Shocks

In hybrid-Vlasov plasma modeling, the ion velocity distribution function is propagated using the Vlasov equation while electrons are considered a charge-neutralizing fluid. It is an alternative to particle-in-cell methods, one advantage being the absence of sampling noise in the moments of the distribution. However, the discretization requirements in up to six dimensions (3D position, 3V velocity) make the computational cost of hybrid-Vlasov models higher. This is why hybrid-Vlasov modeling has only recently become more popular and available to model large-scale systems. The hybrid-Vlasov model Vlasiator is the first to have been successfully applied to model the solar-terrestrial interaction. It includes in particular the bow shock and magnetosheath regions, albeit in 2D-3V configurations so far. The purpose of this study is to investigate how Vlasiator parameters affect the modeling of a plasma shock in a 1D-3V simulation. The setup is similar to the Earth's bow shock in previous simulations, so that the present results can be related to existing and future magnetospheric simulations. The parameters investigated are the spatial and velocity resolution, as well as the phase space density threshold, which is the key parameter of the so-called sparse velocity space. The role of the Hall term in Ohm's law is also studied. The evaluation metrics used are the convergence of the final state, the complexity of spatial profiles and ion distributions as well as the position of the shock front. In agreement with previous Vlasiator studies it is not necessary to resolve the ion inertial length and gyroradius in order to obtain kinetic phenomena. While the code remains numerically stable with all combinations of resolutions, it is shown that significantly increasing the resolution in one space but not the other leads to unphysical results. Past a certain level, decreasing the phase space density threshold bears a large computational weight without clear physical improvement in the setup used here. Finally, the inclusion of the Hall term shows only minor effects in this study, mostly because of the 1D configuration and the scales studied, at which the Hall term is not expected to play a major role.In hybrid-Vlasov plasma modeling, the ion velocity distribution function is propagated using the Vlasov equation while electrons are considered a charge-neutralizing fluid. It is an alternative to particle-in-cell methods, one advantage being the absence of sampling noise in the moments of the distribution. However, the discretization requirements in up to six dimensions (3D position, 3V velocity) make the computational cost of hybrid-Vlasov models higher. This is why hybrid-Vlasov modeling has only recently become more popular and available to model large-scale systems. The hybrid-Vlasov model Vlasiator is the first to have been successfully applied to model the solar-terrestrial interaction. It includes in particular the bow shock and magnetosheath regions, albeit in 2D-3V configurations so far. The purpose of this study is to investigate how Vlasiator parameters affect the modeling of a plasma shock in a 1D-3V simulation. The setup is similar to the Earth's bow shock in previous simulations, so that the present results can be related to existing and future magnetospheric simulations. The parameters investigated are the spatial and velocity resolution, as well as the phase space density threshold, which is the key parameter of the so-called sparse velocity space. The role of the Hall term in Ohm's law is also studied. The evaluation metrics used are the convergence of the final state, the complexity of spatial profiles and ion distributions as well as the position of the shock front. In agreement with previous Vlasiator studies it is not necessary to resolve the ion inertial length and gyroradius in order to obtain kinetic phenomena. While the code remains numerically stable with all combinations of resolutions, it is shown that significantly increasing the resolution in one space but not the other leads to unphysical results. Past a certain level, decreasing the phase space density threshold bears a large computational weight without clear physical improvement in the setup used here. Finally, the inclusion of the Hall term shows only minor effects in this study, mostly because of the 1D configuration and the scales studied, at which the Hall term is not expected to play a major role.In hybrid-Vlasov plasma modeling, the ion velocity distribution function is propagated using the Vlasov equation while electrons are considered a charge-neutralizing fluid. It is an alternative to particle-in-cell methods, one advantage being the absence of sampling noise in the moments of the distribution. However, the discretization requirements in up to six dimensions (3D position, 3V velocity) make the computational cost of hybrid-Vlasov models higher. This is why hybrid-Vlasov modeling has only recently become more popular and available to model large-scale systems. The hybrid-Vlasov model Vlasiator is the first to have been successfully applied to model the solar-terrestrial interaction. It includes in particular the bow shock and magnetosheath regions, albeit in 2D-3V configurations so far. The purpose of this study is to investigate how Vlasiator parameters affect the modeling of a plasma shock in a 1D-3V simulation. The setup is similar to the Earth's bow shock in previous simulations, so that the present results can be related to existing and future magnetospheric simulations. The parameters investigated are the spatial and velocity resolution, as well as the phase space density threshold, which is the key parameter of the so-called sparse velocity space. The role of the Hall term in Ohm's law is also studied. The evaluation metrics used are the convergence of the final state, the complexity of spatial profiles and ion distributions as well as the position of the shock front. In agreement with previous Vlasiator studies it is not necessary to resolve the ion inertial length and gyroradius in order to obtain kinetic phenomena. While the code remains numerically stable with all combinations of resolutions, it is shown that significantly increasing the resolution in one space but not the other leads to unphysical results. Past a certain level, decreasing the phase space density threshold bears a large computational weight without clear physical improvement in the setup used here. Finally, the inclusion of the Hall term shows only minor effects in this study, mostly because of the 1D configuration and the scales studied, at which the Hall term is not expected to play a major role.Peer reviewe

Flux-tube-dependent propagation of Alfvén waves in the solar corona

Context. Alfven-wave turbulence has emerged as an important heating mechanism to accelerate the solar wind. The generation of this turbulent heating is dependent on the presence and subsequent interaction of counter-propagating Alfven waves. This requires us to understand the propagation and evolution of Alfven waves in the solar wind in order to develop an understanding of the relationship between turbulent heating and solar-wind parameters. Aims. We aim to study the response of the solar wind upon injecting monochromatic single-frequency Alfven waves at the base of the corona for various magnetic flux-tube geometries. Methods. We used an ideal magnetohydrodynamic model using an adiabatic equation of state. An Alfven pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. Results. Alfven waves were found to be reflected due to the development of the parametric decay instability (PDI). Further investigation revealed that the PDI was suppressed both by efficient reflections at low frequencies as well as magnetic flux-tube geometries.Peer reviewe

Energy Flux Through the Magnetopause During Flux Transfer Events in Hybrid-Vlasov 2D Simulations

Solar wind-magnetosphere coupling drives magnetospheric dynamic phenomena by enabling energy exchange between magnetospheric and solar wind plasmas. In this study, we examine two-dimensional noon-midnight meridional plane simulation runs of the global hybrid-Vlasov code Vlasiator with southward interplanetary magnetic field driving. We compute the energy flux, which consists of the Poynting flux and hydrodynamic energy flux components, through the Earth's magnetopause during flux transfer events (FTEs). The results demonstrate the spatiotemporal variations of the energy flux along the magnetopause during an FTE, associating the FTE leading (trailing) edge with an energy injection into (escape from) the magnetosphere on the dayside. Furthermore, FTEs traveling along the magnetopause transport energy to the nightside magnetosphere. We identify the tail lobes as a primary entry region for solar wind energy into the magnetosphere, consistent with results from global magnetohydrodynamic simulations and observations.Peer reviewe

The impact on global magnetohydrodynamic simulations from varying initialisation methods : results from GUMICS-4

We investigate the effects of different initialisation methods of the GUMICS-4 global magnetohydrodynamic (MHD) simulation to the dynamics in different parts of the Earth's magnetosphere and hence compare five 12 h simulation runs that were initiated by 3 h of synthetic data and followed by 9 h of solar wind measurements using the OMNI data as input. As a reference, we use a simulation run that includes nearly 60 h of OMNI data as input prior to the 9 h interval examined with different initialisations. The selected interval is a high-speed stream event during a 10-day interval (12-22 June 2007). The synthetic initialisations include stepwise, linear and sinusoidal functions of the interplanetary magnetic field with constant density and velocity values. The results show that the solutions converge within 1 h to give a good agreement in both the bow shock and the magnetopause position. However, the different initialisation methods lead to local differences which should be taken into consideration when comparing model results to satellite measurements.Peer reviewe

Non-locality of Earth's quasi-parallel bow shock : injection of thermal protons in a hybrid-Vlasov simulation

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.Peer reviewe

Hybrid-Vlasov simulation of auroral proton precipitation in the cusps : Comparison of northward and southward interplanetary magnetic field driving

Particle precipitation is a central aspect of space weather, as it strongly couples the magnetosphere and the ionosphere and can be responsible for radio signal disruption at high latitudes. We present the first hybrid-Vlasov simulations of proton precipitation in the polar cusps. We use two runs from the Vlasiator model to compare cusp proton precipitation fluxes during southward and northward interplanetary magnetic field (IMF) driving. The simulations reproduce well-known features of cusp precipitation, such as a reverse dispersion of precipitating proton energies, with proton energies increasing with increasing geomagnetic latitude under northward IMF driving, and a nonreversed dispersion under southward IMF driving. The cusp is also found more polewards in the northward IMF simulation than in the southward IMF simulation. In addition, we find that the bursty precipitation during southward IMF driving is associated with the transit of flux transfer events in the vicinity of the cusp. In the northward IMF simulation, dual lobe reconnection takes place. As a consequence, in addition to the high-latitude precipitation spot associated with the lobe reconnection from the same hemisphere, we observe lower-latitude precipitating protons which originate from the opposite hemisphere's lobe reconnection site. The proton velocity distribution functions along the newly closed dayside magnetic field lines exhibit multiple proton beams travelling parallel and antiparallel to the magnetic field direction, which is consistent with previously reported observations with the Cluster spacecraft. In both runs, clear electromagnetic ion cyclotron waves are generated in the cusps and might further increase the calculated precipitating fluxes by scattering protons to the loss cone in the low-altitude cusp. Global kinetic simulations can improve the understanding of space weather by providing a detailed physical description of the entire near-Earth space and its internal couplings.Peer reviewe

Phase space density analysis of outer radiation belt electron energization and loss during geoeffective and nongeoeffective sheath regions

Coronal mass ejection driven sheath regions are one of the key drivers of drastic outer radiation belt responses. The response can however be significantly different based on the sheath properties and the associated inner magnetospheric wave activity. We performed two case studies on the effects of sheaths on outer belt electrons of various energies using data from the Van Allen Probes. One sheath caused a major geomagnetic disturbance and the other had only a minor impact. We especially investigated the phase space density (PSD) of seed, core, and ultrarelativistic electrons to determine the dominant energization and loss processes taking place during the events. Both sheaths produced substantial variation in the electron fluxes from tens of kiloelectronvolts up to ultrarelativistic energies. The responses were however the opposite: the geoeffective sheath mainly led to enhancement, while the nongeoeffective one caused a depletion throughout most of the outer belt. The case studies highlight that both inward and outward radial transport driven by ultra-low frequency waves played an important role in both electron energization and loss. Additionally, PSD radial profiles revealed a local peak that indicated significant acceleration to core energies by chorus waves during the geoeffective event. The distinct responses and different mechanisms in action during these events were related to the timing of the peaked solar wind dynamic pressure causing magnetopause compression, and the differing levels of substorm activity. The most remarkable changes in the radiation belt system occurred in key sheath sub-regions near the shock and the ejecta leading edge.Peer reviewe