Markus Battarbee

Heavy-ion acceleration and self-generated waves in coronal shocks

Context. Acceleration in coronal mass ejection driven shocks is currently considered the primary source of large solar energetic particle events. Aims. The solar wind, which feeds shock-accelerated particles, includes numerous ion populations, which offer much insight into acceleration processes. We present first simulations of shock-accelerated minor ions, in order to explore trapping dynamics and acceleration timescales in detail. Methods. We have simulated diffusive shock acceleration of minor ions (3He2+, 4He2+, 16O6+ and 56Fe14+) and protons using a Monte Carlo method, where self-generated Alfvenic turbulence allows for repeated shock crossings and acceleration to high energies. Results. We present the effect of minor ions on wave generation, especially at low wavenumbers, and show that it is significant. We find that maximum ion energy is determined by the competing effects of particle escape due to focusing in an expanding flux tube and trapping due to the amplified turbulence. We show the dependence of cut-off energy on the particle charge to mass ratio to be approximately (Q/A)1.5. Conclusions. We suggest that understanding the acceleration of minor ions at coronal shocks requires simulations which allow us to explore trapping dynamics and acceleration timescales in detail, including evolution of the turbulent trapping boundary. We conclude that steady-state models do not adequately describe the acceleration of heavy ions in coronal shocks.

Injection of thermal and suprathermal seed particles into coronal shocks of varying obliquity

Context. Diffusive shock acceleration in the solar corona can accelerate solar energetic particles to very high energies. Acceleration efficiency is increased by entrapment through self-generated waves, which is highly dependent on the amount of accelerated particles. This, in turn, is determined by the efficiency of particle injection into the acceleration process. Aims. We present an analysis of the injection efficiency at coronal shocks of varying obliquity.We assessed injection through reflection and downstream scattering, including the effect of a cross-shock potential. Both quasi-thermal and suprathermal seed populations were analysed. We present results on the effect of cross-field diffusion downstream of the shock on the injection efficiency. Methods. Using analytical methods, we present applicable injection speed thresholds that were compared with both semi-analytical flux integration and Monte Carlo simulations, which do not resort to binary thresholds. Shock-normal angle θBn and shock-normal velocity Vs were varied to assess the injection efficiency with respect to these parameters. Results. We present evidence of a significant bias of thermal seed particle injection at small shock-normal angles. We show that downstream isotropisation methods affect the θBn-dependence of this result. We show a non-negligible effect caused by the crossshock potential, and that the effect of downstream cross-field diffusion is highly dependent on boundary definitions. Conclusions. Our results show that for Monte Carlo simulations of coronal shock acceleration a full distribution function assessment with downstream isotropisation through scatterings is necessary to realistically model particle injection. Based on our results, seed particle injection at quasi-parallel coronal shocks can result in significant acceleration efficiency, especially when combined with varying field-line geometry.

Particle scattering in turbulent plasmas with amplified wave modes

High-energy particles stream during coronal mass ejections or flares through the plasma of the solar wind. This causes instabilities, which lead to wave growth at specific resonant wave numbers, especially within shock regions. These amplified wave modes influence the turbulent scattering process significantly. In this paper, results of particle transport and scattering in turbulent plasmas with excited wave modes are presented. The method used is a hybrid simulation code, which treats the heliospheric turbulence by an incompressible magnetohydrodynamic approach separately from a kinetic particle description. Furthermore, a semi-analytical model using quasilinear theory (QLT) is compared to the numerical results. This paper aims at a more fundamental understanding and interpretation of the pitch-angle scattering coefficients. Our calculations show a good agreement of particle simulations and the QLT for broad-band turbulent spectra; for higher turbulence levels and particle beam driven plasmas, the QLT approximation gets worse. Especially the resonance gap at μ = 0 poses a well-known problem for QLT for steep turbulence spectra, whereas test-particle computations show no problems for the particles to scatter across this region. The reason is that the sharp resonant wave-particle interactions in QLT are an oversimplification of the broader resonances in test-particle calculations, which result from nonlinear effects not included in the QLT. We emphasise the importance of these results for both numerical simulations and analytical particle transport approaches, especially the validity of the QLT. Appendices A-D are available in electronic form at http://www.aanda.org

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 Earths 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 Ohms 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.

Vlasov methods in space physics and astrophysics

This paper reviews Vlasov-based numerical methods used to model plasma in space physics and astrophysics. Plasma consists of collectively behaving charged particles that form the major part of baryonic matter in the Universe. Many concepts ranging from our own planetary environment to the Solar system and beyond can be understood in terms of kinetic plasma physics, represented by the Vlasov equation. We introduce the physical basis for the Vlasov system, and then outline the associated numerical methods that are typically used. A particular application of the Vlasov system is Vlasiator, the world’s first global hybrid-Vlasov simulation for the Earth’s magnetic domain, the magnetosphere. We introduce the design strategies for Vlasiator and outline its numerical concepts ranging from solvers to coupling schemes. We review Vlasiator’s parallelisation methods and introduce the used high-performance computing (HPC) techniques. A short review of verification, validation and physical results is included. The purpose of the paper is to present the Vlasov system and introduce an example implementation, and to illustrate that even with massive computational challenges, an accurate description of physics can be rewarding in itself and significantly advance our understanding. Upcoming supercomputing resources are making similar efforts feasible in other fields as well, making our design options relevant for others facing similar challenges.

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 analyse 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∘−40∘, 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.

Solar Energetic Particle Transport Near a Heliospheric Current Sheet

Solar Energetic Particles (SEPs), a major component of space weather, propagate through the interplanetary medium strongly guided by the Interplanetary Magnetic Field (IMF). In this work, we analyse the implications a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP release sites to the Earth. We simulate proton propagation by integrating fully 3-D trajectories near an analytically defined flat current sheet, collecting comprehensive statistics into histograms, fluence maps and virtual observer time profiles within an energy range of 1--800 MeV. We show that protons experience significant current sheet drift to distant longitudes, causing time profiles to exhibit multiple components, which are a potential source of confusing interpretation of observations. We find that variation of current sheet thickness within a realistic parameter range has little effect on particle propagation. We show that IMF configuration strongly affects deceleration of protons. We show that in our model, the presence of a flat equatorial HCS in the inner heliosphere limits the crossing of protons into the opposite hemisphere.

Foreshock Properties at Typical and Enhanced Interplanetary Magnetic Field Strengths: Results From Hybrid‐Vlasov Simulations

In this paper, we present a detailed study of the effects of the interplanetary magnetic field (IMF) strength on the foreshock properties at small and large scales. Two simulation runs performed with the hybrid-Vlasov code Vlasiator with identical setup but with different IMF strengths, namely, 5 and 10 nT, are compared. We find that the bow shock position and shape are roughly identical in both runs, due to the quasi-radial IMF orientation, in agreement with previous magnetohydrodynamic simulations and theory. Foreshock waves develop in a broader region in the higher IMF strength run, which we attribute to the larger growth rate of the waves. The velocity of field-aligned beams remains essentially the same, but their density is generally lower when the IMF strength increases, due to the lower Mach number. Also, we identify in the regular IMF strength run ridges of suprathermal ions which disappear at higher IMF strength. These structures may be a new signature of the foreshock compressional boundary. The foreshock wave field is structured over smaller scales in higher IMF conditions, due to both the period of the foreshock waves and the transverse extent of the wave fronts being smaller. While the foreshock is mostly permeated by monochromatic waves at typical IMF strength, we find that magnetosonic waves at different frequencies coexist in the other run. They are generated by multiple beams of suprathermal ions, while only a single beam is observed at typical IMF strength. The consequences of these differences for solar wind-magnetosphere coupling are discussed. Plain Language Summary Our solar system is filled with a stream of particles escaping from the Sun, called the solar wind. The Earth is shielded from these particles by its magnetic field, which creates a magnetic bubble around our planet, the magnetosphere. Because the solar wind flow is supersonic, a bow shock forms in front of the magnetosphere to slow it down. The outermost region of the near-Earth space is called the foreshock. It is a very turbulent region, filled with particles reflected off the Earth’s bow shock, and with a variety of magnetic waves. These waves can be transmitted inside the magnetosphere and create disturbances in the magnetic field on the Earth’s surface. In this work, we use supercomputer simulations to study how the foreshock changes when the solar magnetic field, carried by the solar wind, intensifies. This happens in particular during solar storms, which create stormy space weather at Earth and can have adverse consequences on, for example, spacecraft electronics and power grids. We find that the foreshock properties are very different during these events compared to normal conditions and that these changes may have consequences in the regions closer to Earth.

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

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. 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. 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. 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. This synergetic approach combining numerical modeling 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.

Particle acceleration and foreshock evolution in heliospheric shocks from self-consistent Monte Carlo simulations

Self-consistent Monte Carlo simulations have been a fruitful approach to model particle acceleration dynamically coupled with the foreshock development in quasi-parallel shocks. There is the global Coronal Shock Acceleration (CSA) Monte Carlo simulation code that is capable of modelling self-consistent shock acceleration from the inner corona to the solar wind. However, in CSA, the resonant interactions of particles with the foreshock Alfvén waves are not modelled using the full resonance condition. The used simplified condition implies that particles of a given energy interact with only one particular spectral component of the wave spectrum. In contrast, the exact (within quasi-linear theory) treatment implies that such particles due to scattering in pitch angle can interact with different wave spectrum components. This changes the modelled particle acceleration efficiency of the shock and the wave spectrum evolution in the foreshock. We have developed a new self-consistent Monte Carlo simulation code, in which we overcome the previous simplification, and applied the two codes to model acceleration of protons in a parallel coronal shock. We also used the new code to simulate proton acceleration in an interplanetary shock. Due to the choice of the plasma and shock parameters, this simulation is applicable to quasi-parallel bow shock of the Earth. Comparison of the results shows that the resonant wave-particle interactions governed by the full resonance condition yield less efficient particle acceleration at the shock and the opposite energy dependence of the proton mean free path in the foreshock than the simplified treatment. Moreover, the Alfvén wave intensity spectrum resulting from the new code exhibits a k−2 dependence at large wavenumbers, characteristic for both the coronal shock and the interplanetary one. This result is in agreement with that of a hybrid-Vlasov simulation (Vlasiator) of the foreshock evolution of the Earth’s bow shock.