Propagation Of Solar Energetic Particles Research Articles

Solar Energetic Particle and the Heliospheric Current Sheet

The effect of the heliospheric current sheet (HCS) on the propagation of solar energetic particles (SEPs) remains poorly known. In this study we address this question by surveying energetic (∼2.0–9.6 MeV nucleon–1) helium data acquired by the energetic particle acceleration, composition, and transport (EPACT) sensor on board the Wind spacecraft. A superposed epoch analysis of 319 HCS crossings made by Wind reveals a sharp drop in the SEP fluxes at the HCS for the low-energy channels and little change across the HCS for the high-energy channels. To help understand the statistical result, we studied a total of 15 SEP flux dropout (a decrease of ∼50% or more) events that coincided with the crossing of the HCS. One of the common features of these SEP events is that they were initiated in the western hemisphere but far away from the longitude of HCS crossings, suggesting that the source of SEPs was well connected initially but was cut off later after Wind moved to the opposite hemisphere (e.g., HCS crossing). Further analysis of the events suggests that the percentage of flux dropouts decreases with increasing energy. It is suggested that a strong scattering of MeV helium may have occurred as the particle gyroradius is comparable to the thickness of the current sheet. This study clearly provides solid evidence for the HCS as a barrier to suppressing SEP flux of MeV energies from the onset hemisphere to the other.

Solar energetic particles propagation during solar events at the beginning of the 25th solar cycle

Space weather is induced by solar events like solar flares, solar wind, the solar cycle, and coronal mass ejections. These solar events have the potential to affect various aspects of Earth, including radio communications, electric power failures, and navigation signals, and pose risks to spacecraft and astronauts. Solar activity is more or less intense according to the solar cycle. We are currently in the 25th solar cycle, which began in 2019. This research studies the space weather at the beginning of the 25th solar cycle using the distribution data obtained from spacecraft including the explosion on the Sun’s surface, by analyzing the solar energetic particles (SEPs) propagation. The distribution of SEPs with flux; F is given by a power law for solar events on November 29, 2020, July 3, 2021, and April 22, 2022, with indices 6.2, 4.5, and 1.8 depending on energy. The propagation of the SEPs was studied using Ruffolo’s transport equation, which was solved using the Finite-differences method. We found that solar flares with higher X-ray intensity have a longer movement along the irregular magnetic field and arrive at Earth more quickly than those with lower X-ray intensity. The SEPs are weaker and have no impact on Earth, although both events generated coronal mass ejection. The M-class and X-class solar flares occurred during the beginning of the 25th solar cycle, the position of explosion and injection time of particles resulted in space weather with little impact on Earth.

A Data-driven, Physics-based Transport Model of Solar Energetic Particles Accelerated by Coronal Mass Ejection Shocks Propagating through the Solar Coronal and Heliospheric Magnetic Fields

In an effort to develop computational tools for predicting radiation hazards from solar energetic particles (SEPs), we have created a data-driven physics-based particle transport model to calculate the injection, acceleration, and propagation of SEPs from coronal mass ejection (CME) shocks traversing through the solar corona and interplanetary magnetic fields. The model runs on an input of corona and heliospheric plasma and magnetic field configuration from a magnetohydrodynamic model driven by solar photospheric magnetic field measurements superposed with observed CME shocks determined from coronagraph images. SEP source particles are injected at the shock using the result of diffusive shock acceleration formulation from a characteristic obliquity-dependent injection from a heated solar wind thermal tail population. With several advanced computation techniques involving stochastic simulation and integration, the model obtains the particle intensity at any location in interplanetary space through the rigorous solution to the time-dependent 5D focus transport equation in the phase space that includes perpendicular diffusion. We apply the model to the 2011 November 3 CME event. The calculation results reproduce multispacecraft SEP observations at Earth and STEREO-B reasonably well without normalization of particle flux. The observations at STEREO-A can be reproduced by rescaling particle energy or modified energy dependence of particle diffusion coefficients. This circumsolar SEP event seen by spacecraft at Earth, STEREO-A, and STEREO-B at widely separated longitudes can be explained by diffusive shock acceleration by a single CME shock with a moderate speed.

Solar energetic particle event onsets at different heliolongitudes: The effect of turbulence in Parker spiral geometry

Context. Solar energetic particles (SEPs), accelerated during solar eruptions, are observed to rapidly reach a wide heliolongitudinal range in the interplanetary space. Turbulence-associated SEP propagation across the mean Parker spiral direction has been suggested to contribute to this phenomenon. Aims. We study SEP propagation in turbulent magnetic fields to evaluate SEP spatial distribution in the heliosphere, their path lengths, and the overall evolution of SEP intensities at 1 au. Methods. We use full-orbit test particle simulations of 100-MeV protons in a novel analytic model of the turbulent heliospheric magnetic field, where the turbulence is dominated by modes that are transverse and 2D with respect to the Parker spiral direction. Results. We find that by propagating along meandering field lines, SEPs reach a 60°-wide heliolongitudinal range at 1 au within an hour of their injection for the turbulence parameters considered. The SEP onset times are asymmetric with respect to the location connected to the source along the Parker spiral, with the earliest arrival times being 15° westwards from the well-connected Parker spiral longitude. The inferred path length of the first arriving particles is 1.5−1.8 au within 30° of the well-connected longitude; 20−30% longer than the length of the random-walking field lines, increasing monotonously at longitudes further away; and 30−50% longer than the Parker spiral. The global maximum intensity is reached 15° west from the well-connected longitude an hour after the SEP injection. Subsequently, the SEP distribution broadens, consistent with diffusive spreading of SEPs across the field lines. Conclusions. Our results indicate that magnetic field line meandering can explain rapid access of SEPs to wide longitudinal ranges, as well as several other features of SEP event intensity evolution.

High resolution finite volume method for kinetic equations with Poisson brackets

Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral relation for Poisson brackets to solve the Liouville equation, the most fundamental kinetic equation. The proposed scheme conserves the number of particles, maintains the total-variation-diminishing (TVD) property, and provides high-quality numerical results. Other types of kinetic equations may be also formulated in terms of Poisson brackets and solved with the proposed method including the transport equations describing the acceleration and propagation of Solar Energetic Particles (SEPs), which is of practical importance, since the high energy SEPs produce radiation hazards. The proposed scheme is demonstrated to be accurate and efficient, which makes it applicable to global simulation systems analyzing space weather.

Influence of Large-scale Interplanetary Structures on the Propagation of Solar Energetic Particles: The Multispacecraft Event on 2021 October 9

An intense solar energetic particle (SEP) event was observed on 2021 October 9 by multiple spacecraft distributed near the ecliptic plane at heliocentric radial distances R ≲ 1 au and within a narrow range of heliolongitudes. A stream interaction region (SIR), sequentially observed by Parker Solar Probe (PSP) at R = 0.76 au and 48° east from Earth (ϕ = E48°), STEREO-A (at R = 0.96 au, ϕ = E39°), Solar Orbiter (SolO; at R = 0.68 au, ϕ = E15°), BepiColombo (at R = 0.33 au, ϕ = W02°), and near-Earth spacecraft, regulated the observed intensity-time profiles and the anisotropic character of the SEP event. PSP, STEREO-A, and SolO detected strong anisotropies at the onset of the SEP event, which resulted from the fact that PSP and STEREO-A were in the declining-speed region of the solar wind stream responsible for the SIR and from the passage of a steady magnetic field structure by SolO during the onset of the event. By contrast, the intensity-time profiles observed near Earth displayed a delayed onset at proton energies ≳13 MeV and an accumulation of ≲5 MeV protons between the SIR and the shock driven by the parent coronal mass ejection (CME). Even though BepiColombo, STEREO-A, and SolO were nominally connected to the same region of the Sun, the intensity-time profiles at BepiColombo resemble those observed near Earth, with the bulk of low-energy ions also confined between the SIR and the CME-driven shock. This event exemplifies the impact that intervening large-scale interplanetary structures, such as corotating SIRs, have in shaping the properties of SEP events.

Multipoint Interplanetary Coronal Mass Ejections Observed with Solar Orbiter, BepiColombo, Parker Solar Probe, Wind, and STEREO-A

Abstract We report the result of the first search for multipoint in situ and imaging observations of interplanetary coronal mass ejections (ICMEs) starting with the first Solar Orbiter (SolO) data in 2020 April–2021 April. A data exploration analysis is performed including visualizations of the magnetic-field and plasma observations made by the five spacecraft SolO, BepiColombo, Parker Solar Probe (PSP), Wind, and STEREO-A, in connection with coronagraph and heliospheric imaging observations from STEREO-A/SECCHI and SOHO/LASCO. We identify ICME events that could be unambiguously followed with the STEREO-A heliospheric imagers during their interplanetary propagation to their impact at the aforementioned spacecraft and look for events where the same ICME is seen in situ by widely separated spacecraft. We highlight two events: (1) a small streamer blowout CME on 2020 June 23 observed with a triple lineup by PSP, BepiColombo and Wind, guided by imaging with STEREO-A, and (2) the first fast CME of solar cycle 25 (≈1600 km s−1) on 2020 November 29 observed in situ by PSP and STEREO-A. These results are useful for modeling the magnetic structure of ICMEs and the interplanetary evolution and global shape of their flux ropes and shocks, and for studying the propagation of solar energetic particles. The combined data from these missions are already turning out to be a treasure trove for space-weather research and are expected to become even more valuable with an increasing number of ICME events expected during the rise and maximum of solar cycle 25.

Variable Ion Compositions of Solar Energetic Particle Events in the Inner Heliosphere: A Field Line Braiding Model with Compound Injections

Abstract We propose a model for interpreting highly variable ion composition ratios in solar energetic particle (SEP) events recently observed by the Parker Solar Probe (PSP) at 0.3–0.45 au. We use numerical simulations to calculate SEP propagation in a turbulent interplanetary magnetic field with a Kolmogorov power spectrum from large scales down to the gyration scale of energetic particles. We show that when the source regions of different species are offset by a distance comparable to the size of the source regions, the observed energetic particle composition He/H can be strongly variable over more than two orders of magnitude, even if the source ratio is at the nominal value. Assuming a 3He/4He source ratio of 10% in impulsive 3He-rich events and the same spatial offset of the source regions, the 3He/4He ratio at observation sites also vary considerably. The variability of the ion composition ratios depends on the radial distance, which can be tested by observations made at different radial locations. We discuss the implications of these results on the variability of ion composition of impulsive events and on further PSP and Solar Orbiter observations close to the Sun.

The study of the strongest solar event on a minimum of the 24th solar cycle

The strongest solar flares of the 24th solar cycle erupted on September 6, 2017, and it was the 8th strongest solar flare recorded since 1996. This extreme solar flare occurred at the minimum of the 24th solar cycle. The active region is located in the Western Hemisphere and produced the violent explosion of class X9.3 and X2.2 on September 6, X1.3 on September 7, and X8.2 on September 10, 2017. The injection duration of the solar energetic particles of the solar event was 17 minutes. All data for this solar event was collected from the Advanced Composition Explorer and simulated for particles’ motion using the transport equation and solved by the numerical technique. We obtained the injection time of the solar energetic particle propagation by comparing fitting between the simulation results and the spacecraft data. Injection time taken by high-energy particles to travel from the Sun to the Earth was found to be in the range of 39 to 743 minutes. At the peak of this solar flare, the coronal mass ejection was detected, which increased the injection time. The Kp-index of this solar flare was 4; thus, there was no effect on the Earth. The Kp-index value increased to 8 on September 7-8, 2017, due to another solar event from the same sunspot region, indicating the effect of solar flare and CME, which resulted in the appearance of aurora.

Statistical Survey of Reservoir Phenomenon in Energetic Proton Events Observed by Multiple Spacecraft

Abstract In this work, reservoir phenomenon in the decay phase of gradual solar energetic particle (SEP) events are investigated with two Helios and the IMP 8 spacecraft from 1976 January to 1980 March and two STEREO and the SOHO spacecraft from 2010 January to 2014 September. Using these data, 62 reservoir events of solar energetic protons were identified, and the effects of perpendicular diffusion and magnetic mirroring on the formation of the reservoir phenomenon have been studied. We find that the reservoir events could be observed in almost all longitudes in the ecliptic at 1 au; thus, the perpendicular diffusion in interplanetary space is an important mechanism to explain the uniform distribution of SEPs. Furthermore, in the 1976 April 30 event, the effects of magnetic mirroring associated with an interplanetary coronal mass ejection were observed during the reservoir phenomenon. Therefore, the effects of magnetic mirroring could also help to form the reservoir phenomenon. This study could improve the understanding of the propagation of SEPs in interplanetary space.

Observations of Energetic-particle Population Enhancements along Intermittent Structures near the Sun from the Parker Solar Probe

Abstract Observations at 1 au have confirmed that enhancements in measured energetic-particle (EP) fluxes are statistically associated with “rough” magnetic fields, i.e., fields with atypically large spatial derivatives or increments, as measured by the Partial Variance of Increments (PVI) method. One way to interpret this observation is as an association of the EPs with trapping or channeling within magnetic flux tubes, possibly near their boundaries. However, it remains unclear whether this association is a transport or local effect; i.e., the particles might have been energized at a distant location, perhaps by shocks or reconnection, or they might experience local energization or re-acceleration. The Parker Solar Probe (PSP), even in its first two orbits, offers a unique opportunity to study this statistical correlation closer to the corona. As a first step, we analyze the separate correlation properties of the EPs measured by the Integrated Science Investigation of the Sun (IS⊙IS) instruments during the first solar encounter. The distribution of time intervals between a specific type of event, i.e., the waiting time, can indicate the nature of the underlying process. We find that the IS⊙IS observations show a power-law distribution of waiting times, indicating a correlated (non-Poisson) distribution. Analysis of low-energy (∼15 – 200 keV/nuc) IS⊙IS data suggests that the results are consistent with the 1 au studies, although we find hints of some unexpected behavior. A more complete understanding of these statistical distributions will provide valuable insights into the origin and propagation of solar EPs, a picture that should become clear with future PSP orbits.

Propagation of Solar Energetic Particles in the Outer Heliosphere: Interplay between Scattering and Adiabatic Focusing

Abstract The turbulence and spatial nonuniformity of the guide magnetic field cause two competitive effects, namely, the scattering effect and the adiabatic focusing effect, respectively. In this work, we numerically solve the five-dimensional Fokker–Planck transport equation to investigate the radial evolutions of these important effects undergone by the solar energetic particles (SEPs) propagating through interplanetary space. We analyze the interplay process between the scattering and adiabatic focusing effects in the context of three-dimensional propagation, with special attention to the scenario of the outer heliosphere, in which some peculiar SEP phenomena are found and explained. We also discuss the radial dependence of the SEP peak intensities from the inner through the outer heliosphere, and conclude that it cannot be simply described by a single functional form such as R −α (R is radial distance), which is often used.

Time intermittency in nondiffusive transport regimes of suprathermal ions in turbulent plasmas

Intermittent phenomena have long been studied in the context of nondiffusive transport across a variety of fields. In the TORPEX device, the cross-field spreading of an injected suprathermal ion beam by electrostatic plasma turbulence can access different nondiffusive transport regimes. A comprehensive set of suprathermal ion time series has been acquired, and time intermittency quantified by their skewness. Values distinctly above background level are found across all observed transport regimes. Intermittency tends to increase toward quasi- and superdiffusion and for longer propagation times of the suprathermal ions. The specific prevalence of intermittency is determined by the meandering motion of the instantaneous ion beam. We demonstrate the effectiveness of an analytical model developed to predict local intermittency from the time-average beam. This model might thus be of direct interest for similar systems, e.g., in beam physics, or meandering flux-rope models for solar energetic particle propagation. More generally, it illustrates the importance of identifying the system-specific sources of time-intermittent behavior when analyzing nondiffusive transport.

Stochastic Propagation of Solar Energetic Particles in Coronal and Interplanetary Magnetic Fields

This paper describes a method of simulating solar energetic particle propagation through the magnetic fields of the solar corona and interplanetary medium. The simulation code is based on the focus transport equation of energetic particles in 3-d magnetic fields, which contains all the particle transport mechanisms, including streaming, convection, gradient/curvature drift, adiabatic focusing, pitch angle scattering by Alfvénic magnetic field fluctuations and perpendicular diffusion due to the random walk of field lines. In the simulation, particles are injected at their source in the corona, and their guiding center trajectories are calculated using stochastic differential equations. Because of the vastly different time scales of particle transport mechanisms included in the equation, we use the 4-th order Runge-Kutta method to integrate the particle streaming and adiabatic focusing terms, while the stochastic terms of pitch angle scattering and perpendicular diffusion are integrated with the Euler scheme. The model is applied to the 2017 September 10 solar energetic particle event. With perpendicular diffusion, we are able to explain SEP observations from Earth and STEREO-A. A pattern of SEP precipitation on the solar surface is also predicted.

Solar Energetic Particle Propagation in Wave Turbulence and the Possibility of Wave Generation

Abstract A complete theory for the complex interaction between solar energetic particles (SEPs) and the turbulent interplanetary magnetic field remains elusive. In this work we aim to contribute to such a theory by modeling the propagation of SEP electrons in plasma wave turbulence. We specify a background turbulence spectrum, as constrained through observations, calculate the transport coefficients from first principles, and simulate the propagation of these electrons in the inner heliosphere. We have also, for the first time, included dynamical effects into the perpendicular diffusion coefficient. We show that such a “physics-first” approach can lead to reasonable results, when compared qualitatively to observations. In addition, we include the effect of wave growth/damping due to streaming electrons and show that these particles can significantly alter the turbulence levels close to the Sun for the largest events.

Relativistic Proton Levels from Region AR 12673 (GLE #72) and the Heliospheric Current Sheet as a Sun–Earth Magnetic Connection

On 2017 September 10 Neutron Monitors (NMs) apparatus located at ground level and high latitudes detected an increase in the counting rate associated to solar energetic particles (SEPs) emission from X8.2-class solar flare and its associated CME. This was the second-highest flare of the current solar cycle. The origin was the active region AR 12673 when it was located at the edge of the west solar disk, magnetically poorly connected with Earth. However, there was a peculiar condition: the solar protons accelerated by the CME shocks were injected within a heliospheric current sheet (HCS) region when Earth was crossing this region. We show that often HCS and SEPs propagation are closely related. If the source locations of SEPs are within or close to HCS, the HCS play the role of a Sun–Earth magnetic connection. SEPs drift around HCS paths, and SEPs are also drift in a wide range of longitudes by the HCSs. In some cases, and especially when Earth crosses the HCS sector, a fraction of these particles can reach Earth with a harder energetic particle flux, triggering a ground-level enhancement (GLE). The blast on 2017 September 10, which triggered the GLE #72, was the second in the current solar cycle. We show that the two GLEs, including all sub-GLEs observed in the current solar cycle, comes from solar explosions that happened within an HCS structure; this behavior is also observed in the GLEs of the previous solar cycle. In general, solar explosions from active regions poorly connected with Earth can trigger GLEs, through the mechanism described above. In all cases, the SEPs drift processes by HCS structures provides an efficient particle transport, allowing the observation of these solar transient events.

The effect of solar eruption promulgation on the propagation of solar energetic particles

Solar eruption events investigated for the period from 2000 to 2014. These events associated with solar energetic particles (SEPs) that composed of halo-type coronal mass ejections (CMEs) and accompanying with intense flares. The incline of the time intensity profile are computing by analysing the eastern and western events through the CMEs source regions. This study shows that the incline angle for west events is smaller than Eastern Events. The western events are seem to be sharper in the acceleration phase than the eastern event. Considerate these phenomena is important to relate the space weather environment near Earth and other destinations in the solar system.

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.