Acceleration of Solar Energetic Particles in coronal shocks through self-generated turbulence

The acceleration of solar energetic particles (SEPs) by flares and coronal mass ejections (CMEs) has been a major topic of research for the solar-terrestrial physics and geophysics communities for decades. This thesis discusses theories describing first-order Fermi acceleration of SEPs through repeated crossings at a CME-driven shock. We propose that particle trapping occurs through self-generated Alfvén waves, leading to a turbulent trapping region in front of the shock. Decelerating coronal shocks are shown to be capable of efficient SEP acceleration, provided seed particle injection is sufficient. Quasi-parallel shocks are found to inject thermal particles with good efficiency. The roles of minimum injection velocities, cross-field diffusion, downstream scattering efficiency and cross-shock potential are investigated in detail, with downstream isotropisation timescales having a major effect on injection efficiency. Accelerated spectra of heavier elements up to iron are found to exhibit significantly harder spectra than protons. Accelerated spectra cut-off energies are found to scale proportional to (Q/A)1.5, which is explained through analysis of the spectral shape of amplified Alfvénic turbulence. Acceleration times to different threshold energies are found to be non-linear, indicating that self-consistent time-dependent simulations are required in order to expose the full extent of acceleration dynamics. The well-established quasilinear theory (QLT) of particle scattering is investigated by comparing QLT scattering coefficients with those found via full-orbit simulations. QLT is found to overemphasise resonance conditions. This finding supports the simplifications implemented in the presented coronal shock acceleration (CSA) simulation software. The CSA software package is used to simulate a range of acceleration scenarios. The results are found to be in agreement with well-established particle acceleration theory. At the same time, new spatial and temporal dynamics of particle population trapping and wave evolution are revealed.Siirretty Doriast

Solar energetic particle drifts and the energy dependence of 1 AU charge states

The event-averaged charge state of heavy ion Solar Energetic Particles (SEPs), measured at 1 AU from the Sun, typically increases with the ions’ kinetic energy. The origin of this behaviour has been ascribed to processes taking place within the acceleration region. In this paper we study the propagation through interplanetary space of SEP Fe ions, injected near the Sun with a variety of charge states that are uniformly distributed in energy, by means of a 3D test particle model. In our simulations, due to gradient and curvature drifts associated with the Parker spiral magnetic field, ions of different charge propagate with very different efficiencies to an observer that is not magnetically well connected to the source region. As a result we find that, for many observer locations, the 1 AU event-averaged charge state , as obtained from our model, displays an increase with particle energy E, in qualitative agreement with spacecraft observations. We conclude that drift-associated propagation is a possible explanation for the observed distribution of versus E in SEP events, and that the distribution measured in interplanetary space cannot be taken to represent that at injection

Modeling Solar Energetic Particle Transport near a Wavy Heliospheric Current Sheet

Understanding the transport of solar energetic particles (SEPs) from acceleration sites at the Sun into interplanetary space and to the Earth is an important question for forecasting space weather. The interplanetary magnetic field (IMF), with two distinct polarities and a complex structure, governs energetic particle transport and drifts. We analyze for the first time the effect of a wavy heliospheric current sheet (HCS) on the propagation of SEPs. We inject protons close to the Sun and propagate them by integrating fully 3D trajectories within the inner heliosphere in the presence of weak scattering. We model the HCS position using fits based on neutral lines of magnetic field source surface maps (SSMs). We map 1 au proton crossings, which show efficient transport in longitude via HCS, depending on the location of the injection region with respect to the HCS. For HCS tilt angles around 30 degrees-40 degrees, we find significant qualitative differences between A+ and A- configurations of the IMF, with stronger fluences along the HCS in the former case but with a distribution of particles across a wider range of longitudes and latitudes in the latter. We show how a wavy current sheet leads to longitudinally periodic enhancements in particle fluence. We show that for an A+ IMF configuration, a wavy HCS allows for more proton deceleration than a flat HCS. We find that A- IMF configurations result in larger average fluences than A+ IMF configurations, due to a radial drift component at the current sheet.Peer reviewe

Multi-spacecraft observations and transport simulations of solar energetic particles for the May 17th 2012 event

Context. The injection, propagation and arrival of solar energetic particles (SEPs) during eruptive solar events is an important and current research topic of heliospheric physics. During the largest solar events, particles may have energies up to a few GeVs and sometimes even trigger ground-level enhancements (GLEs) at Earth. These large SEP events are best investigated through multispacecraft observations. Aims.We study the first GLE-event of solar cycle 24, from 17th May 2012, using data from multiple spacecraft (SOHO, GOES, MSL, STEREO-A, STEREO-B and MESSENGER). These spacecraft are located throughout the inner heliosphere, at heliocentric distances between 0.34 and 1.5 astronomical units (au), covering nearly the whole range of heliospheric longitudes. Methods. We present and investigate sub-GeV proton time profiles for the event at several energy channels, obtained via different instruments aboard the above spacecraft. We investigate issues due to magnetic connectivity, and present results of three-dimensional SEP propagation simulations.We gather virtual time profiles and perform qualitative and quantitative comparisons with observations, assessing longitudinal injection and transport effects as well as peak intensities. Results. We distinguish different time profile shapes for well-connected and weakly connected observers, and find our onset time analysis to agree with this distinction. At select observers, we identify an additional low-energy component of Energetic Storm Particles (ESPs). Using well-connected observers for normalisation, our simulations are able to accurately recreate both time profile shapes and peak intensities at multiple observer locations. Conclusions. This synergetic approach combining numerical modelling with multi-spacecraft observations is crucial for understanding the propagation of SEPs within the interplanetary magnetic field. Our novel analysis provides valuable proof of the ability to simulate SEP propagation throughout the inner heliosphere, at a wide range of longitudes. Accurate simulations of SEP transport allow for better constraints of injection regions at the Sun, and thus, better understanding of acceleration processes

A semi-analytical foreshock model for energetic storm particle events inside 1 AU

We have constructed a semi-analytical model of the energetic-ion foreshock of a CME-driven coronal/interplanetary shock wave responsible for the acceleration of large solar energetic particle (SEP) events. The model is based on the analytical model of diffusive shock acceleration of Bell (1978), appended with a temporal dependence of the cut-off momentum of the energetic particles accelerated at the shock, derived from the theory. Parameters of the model are re-calibrated using a fully time-dependent self-consistent simulation model of the coupled particle acceleration and Alfv&eacute;n-wave generation upstream of the shock. Our results show that analytical estimates of the cut-off energy resulting from the simplified theory and frequently used in SEP modelling are overestimating the cut-off momentum at the shock by one order magnitude. We show also that the cut-off momentum observed remotely far upstream of the shock (e.g., at 1 AU) can be used to infer the properties of the foreshock and the resulting energetic storm particle (ESP) event, when the shock is still at small distances from the Sun, unaccessible to the in-situ observations. Our results can be used in ESP event modelling for future missions to the inner heliosphere, like the Solar Orbiter and Solar Probe Plus as well as in developing acceleration models for SEP events in the solar corona.</p

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

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

Asymmetries in the Earth's dayside magnetosheath : results from global hybrid-Vlasov simulations

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 Alfven 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 Alfven 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.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