Transport Of Solar Energetic Particles Research Articles

Modeling solar energetic particle transport in 3D background solar wind: Influences of the compression regions

In modeling the transport process of solar energetic particles (SEPs) in the heliosphere, previous simulation works often simplify the solar wind velocity as radial and constant, and treat the magnetic field as Parker spiral. In order to fully understand the effect of solar wind velocity and interplanetary magnetic field on the particles’ transport process, a realistic background solar wind and magnetic field is required. In this work, we use the focused transport model to investigate the transport of SEPs in the solar wind velocity and magnetic field generated by the 3D high-resolution MHD model with a six-component grid. We find that in the uncompressed solar wind, the time intensity profiles of energetic particles show similar trend in both the MHD background and the Parker magnetic field assumption. However, the simulated SEP flux displays an enhancement in the decay phase when a compression region sweeps past the local observer. Through investigating various effects, we find that the magnetic focusing effect is primarily responsible for the intensity enhancement, suggesting that the magnetic focusing effect has an important influence on the transport of SEPs. Further, we show that the magnetic focusing could also be effective in large heliocentric distances.

Effects of Coronal Magnetic Field Structures on the Transport of Solar Energetic Particles

Abstract This Letter presents a model calculation of solar energetic particle (SEP) transport to test the sensitivity of the distribution of escaped SEPs in interplanetary space and dependence upon the details of the magnetic field structure in the corona. It is applied to a circumsolar event on 2011 November 3, in which SEPs are observed promptly after the solar event eruption by three spacecraft (the twin Solar TErrestrial RElations Observatories (STEREO-A and STEREO-B) and ACE) separated by more than 100° in longitude from each other. The corona magnetic field reconstructed from photosphseric field measurements using the PFSS method changes substantially before and after the solar eruption, especially around the active region. The locations of open field regions, separatrix surfaces including the heliospheric current sheet, and footpoints of magnetic field lines connected to the spacecraft location have shifted substantially. We inject 100 keV energetic electrons on the open field lines at 1.5 R s within the size of observed coronal mass ejections (CMEs) and follow their propagation in the corona and the interplanetary space. We find that with a perpendicular diffusion due to field line random walk equal to 10% of the supergranular diffusion rate, the overall distribution of escaped SEPs does not change much even though the region of open field lines from SEPs has changed. The result suggests that detailed small-scale coronal magnetic field structures and the exact magnetic field connection are not crucially important for observing SEPs in the interplanetary space.

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 multi-spacecraft observations. Aims. We aim to 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 investigated issues caused by magnetic connectivity, and present results of three-dimensional SEP propagation simulations. We gathered virtual time profiles and perform qualitative and quantitative comparisons with observations, assessed 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.

Modeling Solar Energetic Particle Transport near a Wavy Heliospheric Current Sheet

Abstract 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°–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.

The effect of turbulence strength on meandering field lines and Solar Energetic Particle event extents

Insights into the processes of Solar Energetic Particle (SEP) propagation are essential for understanding how solar eruptions affect the radiation environment of near-Earth space. SEP propagation is influenced by turbulent magnetic fields in the solar wind, resulting in stochastic transport of the particles from their acceleration site to Earth. While the conventional approach for SEP modelling focuses mainly on the transport of particles along the mean Parker spiral magnetic field, multi-spacecraft observations suggest that the cross-field propagation shapes the SEP fluxes at Earth strongly. However, adding cross-field transport of SEPs as spatial diffusion has been shown to be insufficient in modelling the SEP events without use of unrealistically large cross-field diffusion coefficients. Recently, Laitinen et al. [ApJL 773 (2013b); A&A 591 (2016)] demonstrated that the early-time propagation of energetic particles across the mean field direction in turbulent fields is not diffusive, with the particles propagating along meandering field lines. This early-time transport mode results in fast access of the particles across the mean field direction, in agreement with the SEP observations. In this work, we study the propagation of SEPs within the new transport paradigm, and demonstrate the significance of turbulence strength on the evolution of the SEP radiation environment near Earth. We calculate the transport parameters consistently using a turbulence transport model, parametrised by the SEP parallel scattering mean free path at 1 AU, λ∥*, and show that the parallel and cross-field transport are connected, with conditions resulting in slow parallel transport corresponding to wider events. We find a scaling σφ,max∝(1/λ∥*)1/4 for the Gaussian fitting of the longitudinal distribution of maximum intensities. The longitudes with highest intensities are shifted towards the west for strong scattering conditions. Our results emphasise the importance of understanding both the SEP transport and the interplanetary turbulence conditions for modelling and predicting the SEP radiation environment at Earth.

Solar Energetic Particles (SEP) and Galactic Cosmic Rays (GCR) as tracers of solar wind conditions near Saturn: Event lists and applications

The lack of an upstream solar wind monitor poses a major challenge to any study that investigates the influence of the solar wind on the configuration and the dynamics of Saturn’s magnetosphere. Here we show how Cassini MIMI/LEMMS observations of Solar Energetic Particle (SEP) and Galactic Cosmic Ray (GCR) transients, that are both linked to energetic processes in the heliosphere such us Interplanetary Coronal Mass Ejections (ICMEs) and Corotating Interaction Regions (CIRs), can be used to trace enhanced solar wind conditions at Saturn’s distance. SEP protons can be easily distinguished from magnetospheric ions, particularly at the MeV energy range. Many SEPs are also accompanied by strong GCR Forbush Decreases. GCRs are detectable as a low count-rate noise signal in a large number of LEMMS channels. As SEPs and GCRs can easily penetrate into the outer and middle magnetosphere, they can be monitored continuously, even when Cassini is not situated in the solar wind. A survey of the MIMI/LEMMS dataset between 2004 and 2016 resulted in the identification of 46 SEP events. Most events last more than two weeks and have their lowest occurrence rate around the extended solar minimum between 2008 and 2010, suggesting that they are associated to ICMEs rather than CIRs, which are the main source of activity during the declining phase and the minimum of the solar cycle. We also list of 17 time periods ( > 50 days each) where GCRs show a clear solar periodicity ( ∼ 13 or 26 days). The 13-day period that derives from two CIRs per solar rotation dominates over the 26-day period in only one of the 17 cases catalogued. This interval belongs to the second half of 2008 when expansions of Saturn’s electron radiation belts were previously reported to show a similar periodicity. That observation not only links the variability of Saturn’s electron belts to solar wind processes, but also indicates that the source of the observed periodicity in GCRs may be local. In this case GCR measurements can be used to provide the phase of CIRs at Saturn. We further demonstrate the utility of our survey results by determining that: (a) Magnetospheric convection induced by solar wind disturbances associated with SEPs is a necessary driver for the formation of transient radiation belts that were observed throughout Saturn’s magnetosphere on several occasions during 2005 and on day 105 of 2012. (b) An enhanced solar wind perturbation period that is connected to an SEP of day 332/2013 was the definite source of a strong magnetospheric compression which led to open flux loading in the magnetotail. Finally, we propose how the event lists can define the basis for single case studies or statistical investigations on how Saturn and its moons (particularly Titan) respond to extreme solar wind conditions or on the transport of SEPs and GCRs in the heliosphere.

A Hitch-hiker’s Guide to Stochastic Differential Equations

In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the literature and at the same time introduce key principles of the SDE approach via “toy models”. Using these examples, we hope to provide an easy way for newcomers to the field to use such methods in their own research. Aspects covered are the solar modulation of cosmic rays, diffusive shock acceleration, galactic cosmic ray propagation and solar energetic particle transport. We believe that the SDE method, due to its simplicity and computational efficiency on modern computer architectures, will be of significant relevance in energetic particle studies in the years to come.

Perpendicular Diffusion of Solar Energetic Particles: Model Results and Implications for Electrons

Abstract The processes responsible for the effective longitudinal transport of solar energetic particles (SEPs) are still not completely understood. We address this issue by simulating SEP electron propagation using a spatially 2D transport model that includes perpendicular diffusion. By implementing, as far as possible, the most reasonable estimates of the transport (diffusion) coefficients, we compare our results, in a qualitative manner, to recent observations at energies of 55–105 keV, focusing on the longitudinal distribution of the peak intensity, the maximum anisotropy, and the onset time. By using transport coefficients that are derived from first principles, we limit the number of free parameters in the model to (i) the probability of SEPs following diffusing magnetic field lines, quantified by , and (ii) the broadness of the Gaussian injection function. It is found that the model solutions are extremely sensitive to the magnitude of the perpendicular diffusion coefficient and relatively insensitive to the form of the injection function as long as a reasonable value of a = 0.2 is used. We illustrate the effects of perpendicular diffusion on the model solutions and discuss the viability of this process as a dominant mechanism by which SEPs are transported in longitude. Lastly, we try to quantity the effectiveness of perpendicular diffusion as an interplay between the magnitude of the relevant diffusion coefficient and the SEP intensity gradient driving the diffusion process. It follows that perpendicular diffusion is extremely effective early in an SEP event when large intensity gradients are present, while the effectiveness quickly decreases with time thereafter.

Solar Energetic Particle Transport Near a Heliospheric Current Sheet

Abstract 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 analyze the implications that a flat Heliospheric Current Sheet (HCS) has on proton propagation from SEP release sites to the Earth. We simulate proton propagation by integrating fully 3D 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 interpretations of observations. We find that variation of the current sheet thickness within a realistic parameter range has little effect on particle propagation. We show that the IMF configuration strongly affects the 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.

Calculation of the SEP Flux at 1 au and Comparison with Multi-Satellite Observations

The SEP (Solar Energetic Particles) flux at 1au is an important index of space weather. Based on the parameterized Green function of the two-step SEP transport equation, we have simulated the SEP event on 2012 September 28, and calculated for the first time the SEP flux profiles observed by the GOES and STEREO double satellites for the same event. At the positions of GOES and STEREO-A, the calculated SEP peak value Imax and the time to reach the peak value tmax are well consistent with the observations. However, at the position of STEREO-B, there is a certain difference between our calculation and the observation, due to a large angular distance between the observed position and the SEP source, as well as the effect of unknown solar activities on the backside of the Sun.

Energy spectra of 3He-rich solar energetic particles associated with coronal waves

In addition to their anomalous abundances, 3He-rich solar energetic particles (SEPs) show puzzling energy spectral shapes varying from rounded forms to power laws where the later are characteristics of shock acceleration. Solar sources of these particles have been often associated with jets and narrow CMEs, which are the signatures of magnetic reconnection involving open field. Recent reports on new associations with large-scale EUV waves bring new insights on acceleration and transport of 3He-rich SEPs in the corona. We examined energy spectra for 32 3He-rich SEP events observed by ACE at L1 near solar minimum in 2007-2010 and compared the spectral shapes with solar flare signatures obtained from STEREO EUV images. We found the events with jets or brightenings tend to be associated with rounded spectra and the events with coronal waves with power laws. This suggests that coronal waves may be related to the unknown second stage mechanism commonly used to interpret spectral forms of 3He-rich SEPs.

Solar energetic particle access to distant longitudes through turbulent field-line meandering

Context. Current solar energetic particle (SEP) propagation models describe the effects of interplanetary plasma turbulence on SEPs as diffusion, using a Fokker-Planck (FP) equation. However, FP models cannot explain the observed fast access of SEPs across the average magnetic field to regions that are widely separated in longitude within the heliosphere without using unrealistically strong cross-field diffusion. Aims. We study whether the recently suggested early non-diffusive phase of SEP propagation can explain the wide SEP events with realistic particle transport parameters. Methods. We used a novel model that accounts for the SEP propagation along field lines that meander as a result of plasma turbulence. Such a non-diffusive propagation mode has been shown to dominate the SEP cross-field propagation early in the SEP event history. We compare the new model to the traditional approach, and to SEP observations. Results. Using the new model, we reproduce the observed longitudinal extent of SEP peak fluxes that are characterised by a Gaussian profile with $\sigma=30-50^\circ$, while current diffusion theory can only explain extents of 11$^\circ$ with realistic diffusion coefficients. Our model also reproduces the timing of SEP arrival at distant longitudes, which cannot be explained using the diffusion model. Conclusions. The early onset of SEPs over a wide range of longitudes can be understood as a result of the effects of magnetic field-line random walk in the interplanetary medium and requires an SEP transport model that properly describes the non-diffusive early phase of SEP cross-field propagation.

Cross-field transport and pitch-angle anisotropy of solar energetic particles in MHD turbulence

Abstract. Recent modelling of solar energetic particles (SEPs) propagation through the heliospheric turbulence, also discussed in this workshop, has investigated the role of the pitch-angle scattering and the perpendicular transport in spreading particles in heliolongitude, as shown by multi-spacecraft measurements (STEREO A/B, ACE, SOHO, etc.) at 1 AU in various energy ranges. In some events the first-order pitch-angle anisotropy of the particles distribution is not-negligible. We calculate the average perpendicular displacement due to the gradient/curvature drift in an inhomogeneous turbulence accounting for pitch-angle dependence for two MHD turbulence models: (a) 3-D isotropic, (b) anisotropic as conjectured by Goldreich-Sridhar. We find in both cases that the drift scales as (1 − μ2)2 with the cosine of pitch-angle μ, in contrast with previous models for transport of SEPs. This result can impact the models of propagation of SEPs through the heliosphere.

Interplanetary particle transport simulation for warning system for aviation exposure to solar energetic particles

Solar energetic particles (SEPs) are one of the extreme space weather phenomena. A huge SEP event increases the radiation dose received by aircrews, who should be warned of such events as early as possible. We developed a warning system for aviation exposure to SEPs. This article describes one component of the system, which calculates the temporal evolution of the SEP intensity and the spectrum immediately outside the terrestrial magnetosphere. To achieve this, we performed numerical simulations of SEP transport in interplanetary space, in which interplanetary SEP transport is described by the focused transport equation. We developed a new simulation code to solve the equation using a set of stochastic differential equations. In the code, the focused transport equation is expressed in a magnetic field line coordinate system, which is a non-orthogonal curvilinear coordinate system. An inverse Gaussian distribution is employed as the injection profile of SEPs at an inner boundary located near the Sun. We applied the simulation to observed SEP events as a validation test. The results show that our simulation can closely reproduce observational data for the temporal evolution of particle intensity. By employing the code, we developed the WArning System for AVIation Exposure to Solar energetic particles (WASAVIES).

DRIFT-INDUCED DECELERATION OF SOLAR ENERGETIC PARTICLES

We investigate the deceleration of Solar Energetic Particles (SEPs) during their propagation from the Sun through interplanetary space, in the presence of weak to strong scattering in a Parker spiral configuration, using relativistic full orbit test particle simulations. The calculations retain all three spatial variables describing particles' trajectories, allowing to model any transport across the magnetic field. Large energy change is shown to occur for protons, due to the combined effect of standard adiabatic deceleration and a significant contribution from particle drift in the direction opposite to that of the solar wind electric field. The latter drift-induced deceleration is found to have a stronger effect for SEP energies than for galactic cosmic rays. The kinetic energy of protons injected at 1 MeV is found to be reduced by between 35 and 90% after four days, and for protons injected at 100 MeV by between 20 and 55%. The overall degree of deceleration is a weak function of the scattering mean free path, showing that, although adiabatic deceleration plays a role, a large contribution is due to particle drift. Current SEP transport models are found to account for drift-induced deceleration in an approximate way and their accuracy will need to be assessed in future work.

NUMERICAL STUDY OF THE LONGITUDINALLY ASYMMETRIC DISTRIBUTION OF SOLAR ENERGETIC PARTICLES IN THE HELIOSPHERE

Solar energetic particles (SEPs) affect the solar-terrestrial space environment and become a very important aspect in space weather research. In this work, we numerically investigate the transport processes of SEPs in three-dimensional interplanetary magnetic field, with an emphasis on the longitudinal distribution of SEPs in the heliosphere. We confirm our previous finding that there exists an east-west longitudinal asymmetry in the SEP intensities, i.e., with the same longitude separations between the solar source centers and the magnetic footpoint of the observer, the fluxes of SEP events originating from solar sources located on the eastern side of the nominal magnetic footpoint of the observer are systematically larger than those of the SEP events originating from sources located on the western side. We discuss the formation mechanism of this phenomenon, and conclude that the longitudinally asymmetric distribution of SEPs results from the east-west azimuthal asymmetry in the topology of the heliospheric magnetic field as well as the effects of perpendicular diffusion on the transport of SEPs in the heliosphere. Our results will be valuable to understanding Sun-Earth relations and useful for space weather forecasting.

ON ASPECTS PERTAINING TO THE PERPENDICULAR DIFFUSION OF SOLAR ENERGETIC PARTICLES

The multitude of recent multi-point spacecraft observations of solar energetic particle (SEP) events have made it possible to study the longitudinal distribution of SEPs in great detail. SEPs, even those accelerated during impulsive events, show a much wider than expected longitudinal extent, bringing into question the processes responsible for their transport perpendicular to the local magnetic field. In this paper we examine some aspects of perpendicular transport by including perpendicular diffusion into a numerical SEP transport model that simulates the propagation of impulsively accelerated SEP electrons in the ecliptic plane. We find that: (i) The pitch-angle dependence of the perpendicular diffusion coefficient is an important, and currently mainly overlooked, transport parameter. (ii) SEP intensities are generally asymmetric in longitude, being enhanced towards the west of optimal magnetic connection to the acceleration region. (iii) The maximum SEP intensity may also be shifted (parameter dependently) away from the longitude of best magnetic connectivity at 1 AU. We also calculate the maximum intensity, the time of maximum intensity, the onset time and the maximum anisotropy as a function of longitude at Earth's orbit and compare the results, in a qualitative fashion, to recent spacecraft observations.

PAMELA’S MEASUREMENTS OF MAGNETOSPHERIC EFFECTS ON HIGH-ENERGY SOLAR PARTICLES

The nature of particle acceleration at the Sun, whether through flare reconnection processes or through shocks driven by coronal mass ejections (CMEs), is still under scrutiny despite decades of research. The measured properties of solar energetic particles (SEPs) have long been modeled in different particle-acceleration scenarios. The challenge has been to disentangle to the effects of transport from those of acceleration. The Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) instrument, enables unique observations of SEPs including composition and the angular distribution of the particles about the magnetic field, i.e. pitch angle distribution, over a broad energy range (>80 MeV) -- bridging a critical gap between space-based measurements and ground-based. We present high-energy SEP data from PAMELA acquired during the 2012 May 17 SEP event. These data exhibit differential anisotropies and thus transport features over the instrument rigidity range. SEP protons exhibit two distinct pitch angle distributions; a low-energy population that extends to 90{\deg} and a population that is beamed at high energies (>1 GeV), consistent with neutron monitor measurements. To explain a low-energy SEP population that exhibits significant scattering or redistribution accompanied by a high-energy population that reaches the Earth relatively unaffected by dispersive transport effects, we postulate that the scattering or redistribution takes place locally. We believe these are the first comprehensive measurements of the effects of solar energetic particle transport in the Earth's magnetosheath.

THE DIFFUSION APPROXIMATION VERSUS THE TELEGRAPH EQUATION FOR MODELING SOLAR ENERGETIC PARTICLE TRANSPORT WITH ADIABATIC FOCUSING. I. ISOTROPIC PITCH-ANGLE SCATTERING

The diffusion approximation to the Fokker-Planck equation is commonly used to model the transport of solar energetic particles in interplanetary space. In this study, we present exact analytical predictions of a higher order telegraph approximation for particle transport and compare them with the corresponding predictions of the diffusion approximation and numerical solutions of the full Fokker-Planck equation. We specifically investigate the role of the adiabatic focusing effect of a spatially varying magnetic field on an evolving particle distribution. Comparison of the analytical and numerical results shows that the telegraph approximation reproduces the particle intensity profiles much more accurately than does the diffusion approximation, especially when the focusing is strong. However, the telegraph approximation appears to offer no significant advantage over the diffusion approximation for calculating the particle anisotropy. The telegraph approximation can be a useful tool for describing both diffusive and wavelike aspects of the cosmic-ray transport.

The telegraph equation for cosmic-ray transport with weak adiabatic focusing

Time-dependent solutions of a spatial diffusion equation are often used to describe the transport of solar energetic particles, accelerated in large solar flares. Approximate analytical solutions of the diffusion approximation can complement and guide detailed numerical solutions of the Fokker-Planck equation for the particle distribution function. The accuracy of the diffusion approximation is limited, however, because the signal propagation speed is infinite in the diffusion limit. An improved description of cosmic-ray transport is provided by the telegraph equation, characterised by a finite signal propagation speed. We derive the telegraph equation for the particle density, taking into account adiabatic focusing in a large-scale interplanetary magnetic field in a weak focusing limit. As an illustration, we calculate a propagating pulse solution of the telegraph equation, determine the rise time when the maximum particle intensity is reached at a given distance from the Sun, and compare the results with those obtained in the diffusion approximation. In comparison with the diffusion equation, the telegraph equation predicts an asymmetrical shape of the pulse and a shorter rise time. These potentially significant differences suggest that the more accurate telegraph equation should be used in analysis of the solar energetic particle data, at least to quantify the accuracy of the focused diffusion model.