Transport Of Solar Energetic Particles Research Articles

Modeling the Transport of Solar Energetic Particles in a Corotating Interaction Region

We present a new three-dimensional (3D) magnetohydrodynamic (MHD) model and a new 3D energetic particle transport (EPT) model. The 3D MHD model numerically solves the ideal MHD equations using the relaxing total variation diminishing scheme. In the 3D MHD simulations, we use simple boundary conditions with a high-speed flow, and we can clearly identify a corotating interaction region (CIR) with the characteristics of forward shock and reverse shock. The 3D EPT model solves the Fokker–Planck transport equation for the solar energetic particles (SEPs) using backward stochastic processes, with the magnetic field and solar wind velocity field from MHD results. For comparison, the 3D EPT model results with Parker fields are also obtained. We investigate the transport of SEPs with particle sources and observers in different positions in MHD fields with a CIR, and we compare the results with those in the Parker fields. Our simulation results show that the compression region with local enhancement of the magnetic field, i.e., CIR, can act as a barrier to scatter energetic particles back, and particles can struggle to diffuse through the strong magnetic field regions. Usually, a normal anisotropy profile is commonly present in SEP simulation results with Parker fields, and it is also typically present in that with MHD fields. However, because of the compression region of the magnetic field, energetic particles may exhibit anomalous anisotropy. This result may be used to replicate the spacecraft observation phenomena of the anomalous anisotropy.

Element abundance and the physics of solar energetic particles

The acceleration and transport of solar energetic particles (SEPs) cause their abundance, measured at a constant velocity, to be enhanced or suppressed as a function of the magnetic rigidity of each ion, and hence, of its atomic mass-to-charge ratio of A/Q. Ion charges, in turn, depend upon the source electron temperature. In small “impulsive” SEP events, arising from solar jets, acceleration during magnetic reconnection causes steep power-law abundance enhancements. These impulsive SEP events can have 1,000-fold enhancements of heavy elements from sources at ∼2.5 MK and similar enhancements of 3He/4He and of streaming electrons that drive type-III radio bursts. Gamma-ray lines show that solar flares also accelerate 3He-rich ions, but their electrons and ions remain trapped in magnetic loops, so they dissipate their energy as X-rays, γ-rays, heat, and light. “Gradual” SEPs accelerated at shock waves, driven by fast coronal mass ejections (CMEs), can show power-law abundance enhancements or depressions, even with seed ions from the ambient solar corona. In addition, shocks can reaccelerate seed particles from residual impulsive SEPs with their pre-existing signature heavy-ion enhancements. Different patterns of abundance often show that heavy elements are dominated by a source different from that of H and He. Nevertheless, the SEP abundance, averaged over many large events, defines the abundance of the corona itself, which differs from the solar photosphere as a function of the first ionization potential (FIP) since ions, with FIP <10 eV, are driven upward by forces of electromagnetic waves, which neutral atoms, with FIP >10 eV, cannot feel. Thus, SEPs provide a measurement of element abundance in the solar corona, distinct from solar wind, and may even better define the photosphere for some elements.

A Surrogate Model for Studying Solar Energetic Particle Transport and the Seed Population

AbstractThe high energy particles originating from the Sun, known as solar energetic particles (SEPs), contribute significantly to the space radiation environment, posing serious threats to astronauts and scientific instruments on board spacecraft. The mechanism that accelerates the SEPs to the observed energy ranges, their transport in the inner heliosphere, and the influence of suprathermal seed particle spectrum are open questions in heliophysics. Accurate predictions of the occurrences of SEP events well in advance are necessary to mitigate their adverse effects but prediction based on first principle models still remains a challenge. In this scenario, adopting a machine learning approach to SEP modeling and prediction is desirable. However, the lack of a balanced database of SEP events restrains this approach. We addressed this limitation by generating large data sets of synthetic SEP events sampled from the physics‐based model, Energetic Particle Radiation Environment Module (EPREM). Using this data, we developed neural networks‐based surrogate models to study the seed population parameter space. Our models, EPREM‐S, run thousands to millions of times faster (depending on computer hardware), making simulation‐based inference workflows practicable in SEP studies while providing predictive uncertainty estimates using a deep ensemble approach.

Unusually long path length for a nearly scatter-free solar particle event observed by Solar Orbiter at 0.43 au

Context. After their acceleration and release at the Sun, solar energetic particles (SEPs) are injected into the interplanetary medium and are bound to the interplanetary magnetic field (IMF) by the Lorentz force. The expansion of the IMF close to the Sun focuses the particle pitch-angle distribution, and scattering counteracts this focusing. Solar Orbiter observed an unusual solar particle event on 9 April 2022 when it was at 0.43 astronomical units (au) from the Sun. Aims. We show that the inferred IMF along which the SEPs traveled was about three times longer than the nominal length of the Parker spiral and provide an explanation for this apparently long path. Methods. We used velocity dispersion analysis (VDA) information to infer the spiral length along which the electrons and ions traveled and infer their solar release times and arrival direction. Results. The path length inferred from VDA is approximately three times longer than the nominal Parker spiral. Nevertheless, the pitch-angle distribution of the particles of this event is highly anisotropic, and the electrons and ions appear to be streaming along the same IMF structures. The angular width of the streaming population is estimated to be approximately 30 degrees. The highly anisotropic ion beam was observed for more than 12 h. This may be due to the low level of fluctuations in the IMF, which in turn is very probably due to this event being inside an interplanetary coronal mass ejection The slow and small rotation in the IMF suggests a flux-rope structure. Small flux dropouts are associated with very small changes in pitch angle, which may be explained by different flux tubes connecting to different locations in the flare region. Conclusions. The unusually long path length along which the electrons and ions have propagated virtually scatter-free together with the short-term flux dropouts offer excellent opportunities to study the transport of SEPs within interplanetary structures. The 9 April 2022 solar particle event offers an especially rich number of unique observations that can be used to limit SEP transport models.

Energetic particle dynamics in a simplified model of a solar wind magnetic switchback

Context.Recent spacecraft observations in the inner heliosphere have revealed the presence of local Alfvénic reversals of the magnetic field, while the field magnitude remains almost constant. These are called magnetic switchbacks (SBs) and are very common in the plasma environment close to the Sun explored by the Parker Solar Probe satellite.Aims.A simple numerical model of a magnetic field reversal with constant magnitude is used in order to explore the influence of SBs on the propagation of energetic particles within a range of energy typical of solar energetic particles.Methods.We model the reversal as a region of space of adjustable size bounded by two rotational discontinuities. By means of test particle simulations, beams of mono-energetic particles can be injected upstream of the SB with various initial pitch- and gyro-phase angles. In each simulation, the particle energy may also be changed.Results.Particle dynamics is highly affected by the ratio between the particle gyroradius and the size of the SB, with multiple pitch-angle scatterings occurring when the particle gyroradius is of the order of the SB size. Further, particle motion is extremely sensitive to the initial conditions, implying a transition to chaos; for some parameters of the system, a large share of particles is reflected backwards upstream as they interact with the SB. These results could have a profound impact on our understanding of solar energetic particle transport in the inner heliosphere, and therefore possible comparisons with in situ spacecraft data are discussed.

The 17 April 2021 widespread solar energetic particle event

Context.A complex and long-lasting solar eruption on 17 April 2021 produced a widespread solar energetic particle (SEP) event that was observed by five longitudinally well-separated observers in the inner heliosphere that covered distances to the Sun from 0.42 to 1 au: BepiColombo, Parker Solar Probe, Solar Orbiter, STEREO A, and near-Earth spacecraft. The event was the second widespread SEP event detected in solar cycle 25, and it produced relativistic electrons and protons. It was associated with a long-lasting solar hard X-ray flare that showed multiple hard X-ray peaks over a duration of one hour. The event was further accompanied by a medium-fast coronal mass ejection (CME) with a speed of 880 km s−1that drove a shock, an extreme ultraviolet wave, and long-lasting and complex radio burst activity that showed four distinct type III burst groups over a period of 40 min.Aims.We aim to understand the reason for the wide spread of elevated SEP intensities in the inner heliosphere as well as identify the underlying source regions of the observed energetic electrons and protons.Methods.We applied a comprehensive multi-spacecraft analysis of remote-sensing observations and in situ measurements of the energetic particles and interplanetary context to attribute the SEP observations at the different locations to the various potential source regions at the Sun. We used an ENLIL simulation to characterize the complex interplanetary state and its role in the energetic particle transport. The magnetic connection between each spacecraft and the Sun was determined using ballistic backmapping in combination with potential field source surface extrapolations in the lower corona. Using also a reconstruction of the coronal shock front, we then determined the times when the shock establishes magnetic connections with the different observers. Radio observations were used to characterize the directivity of the four main injection episodes, which were then employed in a 2D SEP transport simulation to test the importance of these different injection episodes.Results.A comprehensive timing analysis of the inferred solar injection times of the SEPs observed at each spacecraft suggests different source processes being important for the electron and proton events. Comparison among the characteristics and timing of the potential particle sources, such as the CME-driven shock or the flare, suggests a stronger shock contribution for the proton event and a more likely flare-related source for the electron event.Conclusions.In contrast to earlier studies on widespread SEP events, we find that in this event an important ingredient for the wide SEP spread was the wide longitudinal range of about 110° covered by distinct SEP injections, which is also supported by our SEP transport modeling.

Modeling the 2020 November 29 solar energetic particle event using EUHFORIA and iPATH models

Aims.We present the implementation of a coupling between EUropean Heliospheric FORcasting Information Asset (EUHFORIA) and improved Particle Acceleration and Transport in the Heliosphere (iPATH) models. In this work, we simulate the widespread solar energetic particle (SEP) event of 2020 November 29 and compare the simulated time-intensity profiles with measurements at Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A, SOlar and Heliospheric Observatory (SOHO), and Solar Orbiter. We focus on the influence of the history of shock acceleration on the varying SEP time-intensity profiles and investigate the underlying causes in the origin of this widespread SEP event.Methods.We simulated a magnetized coronal mass ejection (CME) propagating in the data-driven solar wind with the EUHFORIA code. The CME was initiated by using the linear force-free spheromak module of EUHFORIA. The shock parameters and a 3D shell structure were computed from EUHFORIA as inputs for the iPATH model. Within the iPATH model, the steady-state solution of particle distribution assuming diffuse shock acceleration is obtained at the shock front. The subsequent SEP transport is described by the focused transport equation using the backward stochastic differential equation method with perpendicular diffusion included.Results.We examined the temporal evolution of shock parameters and particle fluxes during this event and we find that adopting a realistic solar wind background can significantly impact the expansion of the shock and, consequently, the shock parameters. Time-intensity profiles with an energetic storm particle event at PSP are well reproduced from the simulations. In addition, the simulated and observed time-intensity profiles of protons show a similar two-phase enhancement at STA. These results illustrate that modeling a shock using a realistic solar wind is crucial in determining the characteristics of SEP events. The decay phase of the modeled time-intensity profiles at Earth is in good agreement with the observations, indicating the importance of perpendicular diffusion in widespread SEP events. Taking into account the possible large curved magnetic field line connecting to Solar Orbiter, the modeled time-intensity profiles show a good agreement with the observation. We suggest that the broadly distorted magnetic field lines, which are due to a stream interaction region, may be a key factor in helping to improve our understanding of the observed SEPs at Solar Orbiter for this event.

A Multi-Event Study of Early-Stage SEP Acceleration by CME-Driven Shocks—Sun to 1 AU

The solar corona between below 10 solar radii is an important region for early acceleration and transport of solar energetic particles (SEPs) by coronal mass ejection-driven shock waves. There, these waves propagate into a highly variable dynamic medium with steep gradients and rapidly expanding coronal magnetic fields, which modulates the particle acceleration near the shock/wave surfaces, and the way SEPs spread into the heliosphere. We present a study modeling the acceleration of SEPs in global coronal shock events in the corona, as well as their transport to 1 au, based on telescopic observations coupled with dynamic physical models. As part of the project Solar Particle Radiation Environment Analysis and Forecasting—Acceleration and Scattering Transport (SPREAdFAST), we model the interaction of observed off-limb coronal bright fronts (CBF) with the coronal plasma from synoptic magnetohydrodynamic (MHD) simulations. We then simulate the SEP acceleration in analytical diffusive shock acceleration (DSA) model. The simulated fluxes are used as time-dependent inner boundary conditions for modeling the particle transport to 1 au. Resulting flux time series are compared with 1 au observations for validation. We summarize our findings and present implications for nowcasting SEP acceleration and heliospheric connectivity.

Transport of Solar Energetic Particles along Stochastic Parker Spirals

Abstract It was recently shown that, owing to the turbulent nature of the solar wind, the interplanetary magnetic field lines can be well described by stochastic Parker spirals. These are realizations of Brownian diffusion on a sphere of increasing radius, superimposed on the angular drift due to the solar rotation. In this work, we present a model for the transport of solar energetic particles along stochastic Parker spirals in the inner heliosphere. The transport model is governed by a set of four stochastic differential equations for the heliographic position ( r , α = cos θ , ϕ ) of the guiding centers and the cosine of the pitch angle between the velocity vector and the Parker field. The model accounts for the role played by the combination of pitch angle scattering and magnetic focusing in the interplanetary medium. The effects of the dynamical evolution of the turbulence are included in the model by taking the field line angular diffusivity to be a function of the radial distance from the Sun. The heliolongitudinal distribution of particles propagating along stochastic Parker spirals is given by the wrapped Gaussian distribution. This angular distribution can also well be represented by the von Mises distribution that interpolates between the Gaussian distribution at small angular spread and the uniform distribution at large distances from the acceleration region of energetic particles in the aftermath of a solar eruption.

On the Turbulent Reduction of Drifts for Solar Energetic Particles

Abstract Particle drifts perpendicular to the background magnetic field have been proposed by some authors as an explanation for the very efficient perpendicular transport of solar energetic particles (SEPs). This process, however, competes with perpendicular diffusion caused by magnetic turbulence, which can also disrupt the drift patterns and reduce the magnitude of drift effects. The latter phenomenon is well known in cosmic-ray studies, but not yet considered in SEP models. Additionally, SEP models that do not include drifts, especially for electrons, use turbulent drift reduction as a justification of this omission, without critically evaluating or testing this assumption. This article presents the first theoretical step for a theory of drift suppression in SEP transport. This is done by deriving the turbulence-dependent drift reduction function with a pitch-angle dependence, as is applicable for anisotropic particle distributions, and by investigating to what extent drifts will be reduced in the inner heliosphere for realistic turbulence conditions and different pitch-angle dependencies of the perpendicular diffusion coefficient. The influence of the derived turbulent drift reduction factors on the transport of SEPs are tested, using a state-of-the-art SEP transport code, for several expressions of theoretically derived perpendicular diffusion coefficients. It is found, for realistic turbulence conditions in the inner heliosphere, that cross-field diffusion will have the largest influence on the perpendicular transport of SEPs, as opposed to particle drifts.

CME Magnetic Structure and IMF Preconditioning Affecting SEP Transport

AbstractCoronal mass ejections (CMEs) and solar energetic particles (SEPs) are two phenomena that can cause severe space weather effects throughout the heliosphere. The evolution of CMEs, especially in terms of their magnetic structure, and the configuration of the interplanetary magnetic field (IMF) that influences the transport of SEPs are currently areas of active research. These two aspects are not necessarily independent of each other, especially during solar maximum when multiple eruptive events can occur close in time. Accordingly, we present the analysis of a CME that erupted on May 11, 2012 (SOL2012‐05‐11) and an SEP event following an eruption that took place on May 17, 2012 (SOL2012‐05‐17). After observing the May 11 CME using remote‐sensing data from three viewpoints, we evaluate its propagation through interplanetary space using several models. Then, we analyze in‐situ measurements from five predicted impact locations (Venus, Earth, the Spitzer Space Telescope, the Mars Science Laboratory en route to Mars, and Mars) in order to search for CME signatures. We find that all in‐situ locations detect signatures of an SEP event, which we trace back to the May 17 eruption. These findings suggest that the May 11 CME provided a direct magnetic connectivity for the efficient transport of SEPs. We discuss the space weather implications of CME evolution, regarding in particular its magnetic structure, and CME‐driven IMF preconditioning that facilitates SEP transport. Finally, this work remarks the importance of using data from multiple spacecraft, even those that do not include space weather research as their primary objective.

On the Correlation between Energy Spectra and Element Abundances in Solar Energetic Particles

In solar energetic particle (SEP) events, the physical processes of both shock acceleration and scattering during transport can cause energy-spectral indices to be correlated with enhancement or suppression of element abundances versus mass-to-charge ratios A/Q. We observe correlations for those “gradual” SEP events where shock waves accelerate ions from the ambient coronal plasma, but there are no such correlations for “impulsive” SEP events produced by magnetic reconnection in solar jets, where abundance enhancement in different events vary from (A/Q)^{+2} to (A/Q)^{+8}, nor are there correlations when shock waves reaccelerate these residual impulsive ions. In the latter events the abundances are determined separately, prior to the accelerated spectra. Events with correlated spectra and abundances show a wide variety of interesting behavior that has not been described previously. Small and moderate gradual SEP events, with relative abundances typically depending approximately upon (A/Q)^{-1} and the spectra upon energy E^{-2.5}, vary little with time. Large SEP events show huge temporal variations skirting the correlation line; in one case O spectra vary with time from E^{-1} to E^{-5} while abundances vary from (A/Q)^{+1} to (A/Q)^{-2} during the event. In very large events, streaming-limited transport through proton-generated resonant Alfvén waves flattens the spectra and enhances heavy ion abundances prior to local shock passage, then steepens the spectra and reduces enhancements afterward, recapturing the typical correlation. Systematic correlation of spectra and element abundances provide a new perspective on the “injection problem” of ion selection by shocks and on the physics of SEP acceleration and transport.

Perpendicular diffusion of solar energetic particles: When is the diffusion approximation valid?

Multi-spacecraft observations of widespread solar energetic particle (SEP) events indicate that perpendicular (to the mean field) diffusion is an important SEP transport mechanism. However, this is in direct contrast to so-called spike and drop-out events, which indicate very little lateral transport. To better understand these seemingly incongruous observations, we discuss the recent progress made towards understanding and implementing perpendicular diffusion in transport models of SEP electrons. This includes a re-derivation of the relevant focused transport equation, a discussion surrounding the correct form of the pitch-angle dependent perpendicular diffusion coefficient and what turbulence quantities are needed as input, and how models lead to degenerate solutions of the particle intensity. Lastly, we evaluate the validity of a diffusion approach to SEP transport and conclude that it is valid when examining a large number of (an ensemble of) events, but that individual SEP events may exhibit coherent structures related to the magnetic field turbulence at short timescales that cannot be accounted for in this modelling approach.

Warning Time Analysis From SEP Simulations of a Two‐Tier REleASE System Applied to Mars Exploration

AbstractThe sudden exposure to energetic protons from solar energetic particle (SEP) events beyond the Earth's magnetosphere and en route to and from Mars can, in extreme cases, lead to acute radiation sickness, an impairing, mission‐endangering condition for astronauts. Timely warnings of their impending occurrence may significantly reduce radiation exposure by allowing astronauts sufficient time to move to a radiation shelter. The Relativistic Electron Alert System for Exploration (REleASE) has been developed to provide such early warnings for the Earth‐Moon system by exploiting the time difference of the arrival of SEP electrons and ions at 1 AU. This study explores the effectiveness of REleASE in a scenario that assumes a two‐element system, one placed at Earth‐Sun L1 and the other at Mars‐Sun L1. This system would exploit the Hohmann‐Parker effect, the circumstance that a spacecraft remains close to the heliospheric magnetic field lines that connect Earth and/or Mars with the Sun while in the Hohmann transfer orbit. We investigate whether the two‐element REleASE system would provide advance warnings for all phases of a mission to and from Mars. In the absence of adequate long‐term SEP measurements beyond Earth orbit, we employ 2‐D modeling of SEP injection and transport for SEP exposure scenarios, in which the best magnetic connections and thus most rapid flux increases of protons occur at exploration vehicle. We show the relative timing of alert occurrence and arrival of harmful ions at the spacecraft throughout a round‐trip human mission to Mars.

The effect of drifts on the decay phase of SEP events

Aims. We study the effect of the magnetic gradient and curvature drifts on the pitch-angle dependent transport of solar energetic particles (SEPs) in the heliosphere, focussing on ∼3–36 MeV protons. By considering observers located at different positions in the heliosphere, we investigate how drifts may alter the measured intensity-time profiles and energy spectra. We focus on the decay phase of solar energetic proton events in which a temporal invariant spectrum and disappearing spatial intensity gradients are often observed; a phenomenon known as the “reservoir effect” or the “SEP flood”. We study the effects of drifts by propagating particles both in nominal and non-nominal solar wind conditions. Methods. We used a three-dimensional (3D) particle transport model, solving the focused transport equation extended with the effect of particle drifts in the spatial term. Nominal Parker solar wind configurations of different speeds and a magnetohydrodynamic (MHD) generated solar wind containing a corotating interaction region (CIR) were considered. The latter configuration gives rise to a magnetic bottle structure, with one bottleneck at the Sun and the other at the CIR. We inject protons from a fixed source at 0.1 AU, the inner boundary of the MHD model. Results. When the drift induced particle net-flux is zero, the modelled intensity-time profiles obtained at different radial distances along an IMF line show the same intensity fall-off after the prompt phase of the particle event, which is in accordance with the SEP flood phenomenon. However, observers magnetically connected close to the edges of the particle injection site can experience, as a result of drifts, a sudden drop in the intensities occurring at different times for different energies such that no SEP flood phenomenon is established. In the magnetic bottle structure, this effect is enhanced due to the presence of magnetic field gradients strengthening the nominal particle drifts. Moreover, anisotropies can be large for observers that only receive particles through drifts, illustrating the importance of pitch-angle dependent 3D particle modelling. We observe that interplanetary cross-field diffusion can mitigate the effects of particle drifts. Conclusions. Particle drifts can substantially modify the decay phase of SEP events, especially if the solar wind contains compression regions or shock waves where the drifts are enhanced. This is, for example, the case for our CIR solar wind configuration generated with a 3D MHD model, where the effect of drifts is strong. A similar decay rate in different energy channels and for different observers requires the mitigation of the effect of drifts. One way to accomplish this is through interplanetary cross-field diffusion, suggesting thus a way to determine a minimum value for the cross-field diffusion strength.

The soft X-ray Neupert effect as a proxy for solar energetic particle injection

The acceleration and injection of solar energetic particles (SEPs) near the Sun is one of the major unsolved problems in contemporary SEP transport modeling efforts. Here, we establish a new approach to the injection problem by utilizing a correlation between the soft X-ray thermal emission in solar flares, and their hard X-ray counterpart, the so-called Neupert effect, which is indicative of the presence of non-thermal particles. We show that the resulting injection function, in the initial phase of the flare, is similar to those inferred from inverting the transport problem based on in-situ observations. For few cases, we find early injections with no in-situ correspondence, that can be caused by particles accelerated before there is a magnetic connection between the source and the spacecraft. The method has limitations for long-duration injections, since it is not applicable to the decay phase of the flare where particle trapping might play a role. For a sample of SEP events in 1980, observed with the Helios-1 and IMP8 spacecraft, we show the results of a 2D SEP transport model based on this approach. We discuss that, with this method, a physics-based, real-time operational SEP now-cast model for the heliosphere is feasible.

Element Abundances of Solar Energetic Particles and the Photosphere, the Corona, and the Solar Wind

From a turbulent history, the study of the abundances of elements in solar energetic particles (SEPs) has grown into an extensive field that probes the solar corona and physical processes of SEP acceleration and transport. Underlying SEPs are the abundances of the solar corona, which differ from photospheric abundances as a function of the first ionization potentials (FIPs) of the elements. The FIP-dependence of SEPs also differs from that of the solar wind; each has a different magnetic environment, where low-FIP ions and high-FIP neutral atoms rise toward the corona. Two major sources generate SEPs: The small “impulsive” SEP events are associated with magnetic reconnection in solar jets that produce 1000-fold enhancements from H to Pb as a function of mass-to-charge ratio A/Q, and also 1000-fold enhancements in 3He/4He that are produced by resonant wave-particle interactions. In large “gradual” events, SEPs are accelerated at shock waves that are driven out from the Sun by wide, fast coronal mass ejections (CMEs). A/Q dependence of ion transport allows us to estimate Q and hence the source plasma temperature T. Weaker shock waves favor the reacceleration of suprathermal ions accumulated from earlier impulsive SEP events, along with protons from the ambient plasma. In strong shocks, the ambient plasma dominates. Ions from impulsive sources have T ≈ 3 MK; those from ambient coronal plasma have T = 1 – 2 MK. These FIP- and A/Q-dependences explore complex new interactions in the corona and in SEP sources.

An Improved Treatment of Neutral Sheet Drift in the Inner Heliosphere

Abstract Drifts due to the curvature and gradients in the heliospheric magnetic field, as well as along the heliospheric current sheet, have long been known to play a significant role in the transport of galactic cosmic rays. Recently, there has been greater interest in the role these drifts play in the transport of solar energetic particles. This study proposes an approach to modeling particle drift velocities in particle transport codes that, while being relatively simple to implement and computationally inexpensive, also models drift effects accurately across a broader range of energies than previous approaches.

Focused Transport of Solar Energetic Particles in Interplanetary Space and the Formation of the Anisotropic Beam-like Distribution of Particles in the Onset Phase of Large Gradual Events

Abstract In the onset phase of large gradual solar energetic particle (SEP) events, the first particles of a given rigidity to arrive at Earth are accelerated in the low corona, focused into a narrow cone of pitch angles by the diverging magnetic field, and transported from near the Sun to 1 au with minimal scattering. The effects of focused transport on the evolution of the beam-like SEPs are investigated analytically. The model assumes for simplicity a constant focusing length and a constant pitch-angle diffusion coefficient for SEPs at small pitch angles. Cross-field transport is ignored. This analytical approximation provides a reasonable representation of the spatial and pitch-angle distribution of the beam-like SEPs. Assuming an instantaneous injection of SEPs near the Sun, the model naturally reproduces several features of the SEP onset profiles observed at 1 au, including a spike-like time–intensity profile with rapid rising and declining edges that resemble a Reid–Axford profile. By assuming an extended injection profile with the shape of an isosceles triangle, we fit the onset phase data of the 2005 January 20 GLE event to our model. The derived mean free path (∼4 au) for relativistic protons is much larger than the theoretical prediction based on the standard quasilinear theory but consistent with our assumption of nearly scatter-free transport and can be explained by a reduced scattering rate, due to particles interacting with ambient turbulence with a Goldreich–Sridhar spectrum. Assuming that the SEPs that are scattered out of the beam are governed by spatial diffusive transport in interplanetary space, we perform an illustrative calculation to account for the nearly isotropic phase following the anisotropic onset as a natural result of the interplanetary transport of SEPs.

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.