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Context. On 2022 January 20, the Energetic Particle Detector (EPD) on board Solar Orbiter measured a solar energetic particle (SEP) event showing unusual first arriving particles from the anti-Sun direction. Near-Earth spacecraft separated 17° in longitude to the west from Solar Orbiter measured classic antisunward-directed fluxes. STEREO-A and MAVEN, separated 18° to the east and 143° to the west from Solar Orbiter respectively, also observed the event, suggesting that particles spread over at least 160° in the heliosphere. Results. Solar Orbiter was embedded in a MC erupting on 16 January from the same active region as the one related to the SEP event on 20 January. The SEP event is related to a M5.5 flare and a fast CME-driven shock of 1433 km/s, which injected particles within and outside the MC. The hard SEP spectra, the presence of a Type II radio burst, and the co-temporal Type III radio bursts being observed from 80 MHz that seems to emanate from the Type II, points to the shock as the relevant accelerator of the particles. Conclusions. The detailed analysis of the SEP event strongly suggest that the energetic particles are injected mainly by a CME-driven shock into and outside of a previous MC present in the heliosphere at the time of the particle onset. The sunward propagating SEPs measured by Solar Orbiter are produced by the injection of particles along the longer (western) leg of the MC still connected to the Sun at the time of the release of the particles. The determined electron propagation path length inside the MC is around 30% longer than the estimated length of the loop leg of the MC itself (based on the graduated cylindrical shell model) consistent with a low number of field line rotations.

On 2022 January 20, the Energetic Particle Detector on board Solar Orbiter detected a solar energetic particle (SEP) event showing unusual sunward-directed fluxes. Near-Earth spacecraft separated by 17° in longitude from Solar Orbiter measured classic antisunward-directed fluxes. Parker Solar Probe and MAVEN, separated by 130° and 216° respectively from Solar Orbiter, observed the particle event as well, suggesting a widespread event of nearly 360° in the heliosphere. The SEP event was associated with an M5-class X-ray flare and a CME with a speed of 1400 km/s. The energetic particles reached 3 MeV and 100 MeV energies for electrons and protons, respectively. The aim of this study is to disentangle how the particles are able to spread throughout the heliosphere and how the local heliospheric conditions affect the acceleration and transport of the particles at different spacecraft locations. This work presents the observations and analyses that lead to a scenario in which the solar source injected energetic particles into the solar wind and within a preceding interplanetary coronal mass ejection (ICME) that was already present in the heliosphere at the time of the SEP event onset. In particular, Solar Orbiter measured the particles injected along the longest leg of an ICME still connected to the Sun at the time of the particle release.

Solar Energetic Particles (SEPs), accelerated during solar eruptions, are observed using instruments onboard spacecraft in interplanetary space, at a large distance from their source. As SEPs propagate in the solar wind, they are guided by the interplanetary magnetic field (IMF), which consists of a large-scale Parker spiral magnetic field superposed by turbulent fluctuations. The turbulence causes the SEPs to scatter along the magnetic field lines, resulting in some cases in delayed arrival of SEPs to spacecraft in interplanetary space. It also gives rise to meandering of field lines, which helps to spread SEPs across heliolongitudes, and eventually results in diffusive cross-field propagation of the particles. To investigate how turbulence affects SEP propagation and arrival to observing spacecraft in different locations in the heliosphere, we have developed a novel analytical model of the IMF, where the Parker spiral is superposed with Fourier modes that represent the turbulence. Unlike any previous models, our description reproduces the observed geometry for the main mode of turbulence, the so-called 2D mode, with both the magnetic field disturbance vector and the wavenumber vector normal to the background Parker spiral field. We use 3D test particle simulations to study the propagation of energetic protons in our new turbulent IMF description. Particles are injected close to the Sun and observables derived at different radial distances and heliolongitudes, representing the locations of near-Earth spacecraft as well as locations accessible to Solar Orbiter and Parker Solar Probe. We compare the SEP onset times obtained from our simulations to those obtained with a 1D focused transport model. We find that the turbulence prolongs the field lines, and thus when particle are simulated in our new IMF model, the SEP intensity onsets are delayed compared to those obtained by using a 1D focused transport model. Further, we find that onset delay depends on the longitudin

Solar energetic particles (SEPs), accelerated during solar eruptions, are observed to rapidly reach a wide heliolongitudinal range in the interplanetary space. To access these locations, the SEPs must have either been accelerated at a wide particle source, or propagated across the mean Parker spiral magnetic field. We study the propagation of SEPs in a new model of heliospheric turbulence which takes the spiral geometry of the average magnetic field into account, to evaluate how this improved description affects the SEP path lengths and the overall evolution of SEP intensities at 1~au. We use full-orbit test particle simulations of 100-MeV protons in a turbulence model dominated by modes that are transverse and 2D with respect to the Parker spiral. We find that the SEPs spread along the meandering field lines to arrive at a 60∘ heliolongitudinal range at 1~au within an hour of their injection at the Sun, consistent with the extent of the meandering field lines. The SEP onset times are asymmetric with respect to the location connected to the source along the Parker spiral, with westward locations seeing earlier arrival and higher peak intensity. The inferred path length of the first-arriving SEPs is 1.5-1.7~au, 30-50\% longer than the Parker spiral, and 20\% longer than the length of the meandering field lines. Subsequently, the SEP distribution broadens, consistent with diffusive spreading of SEPs across the field lines. Our results indicate that SEPs can propagate rapidly across the mean Parker Spiral field to arrive at wide range of longitudes, even without a wide particle source. The modelled SEP onset times, the peak intensity and subsequent heliolongitudinal evolution replicate several observed SEP event features. Further studies are be required to investigate the relative importance of interplanetary transport and source size in different turbulence environments.

The forecasting of solar energetic particles (SEPs) is a prominent area of space weather research. Numerous forecasting models exist that predict SEP event properties at proton energies <100 MeV. One of these models is the Solar Particle Radiation SWx (SPARX) system, a physics-based forecasting tool that calculates >10 and >60 MeV flux profiles within minutes of a flare being detected. This work describes SPARX−H, the extension of SPARX to forecast SEP events above 300 MeV. SPARX−H predicts fluxes in three high energy channels up to several 100 MeV. Correlations between SEP peak flux and peak intensity of the associated solar flare are seen to be weak at high energies, but improved when events are grouped based on the field polarity during the event. Initial results from this new high energy forecasting tool are presented here and the applications of high energy forecasts are discussed. Additionally, the new high energy version of SPARX is tested on a set of historic SEP events. We see that SPARX−H performs best when predicting peak fluxes from events with source locations in well-connected regions, where many large SEP events tend to originate.

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random-walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotically slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60$^\circ$ heliolongitudinal and -latitudinal range at 1~au, with standard deviation of the angular spread of the field lines $14^\circ$. Small source regions map to an intermittent range of longitudes and latitudes at 1~au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17~au up to 1.6~au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk centre. We discuss the implications of our findings on understanding charged particle propagation, and the importance of understanding the turbulence properties close to the Sun.

Context. Corotation of particle-filled magnetic flux tubes is generally thought to have a minor influence on the time-intensity profiles of gradual Solar Energetic Particle (SEP) events. For this reason many SEP models solve the focussed transport equation within the corotating frame, thus neglecting corotation effects. Aims. We study the effects of corotation on gradual SEP intensity profiles at a range of observer longitudinal positions relative to the solar source. We study how corotation affects the duration and decay time constant of SEP events and the variation of peak intensity with observer position. Methods. We use a 3D full-orbit test particle code with time-extended SEP injection via a shock-like source. Unlike with focussed transport models, the test particle approach enables us to switch corotation on and off easily. While shock acceleration is not modelled directly, our methodology allows us to study how corotation and the time-varying observer-shock magnetic connection influence intensity profiles detected at several observers. Results. We find that corotation strongly affects SEP intensity profiles, for a monoenergetic population of 5 MeV protons, being a dominant influence during the decay phase. Simulations including corotation display dramatically shortened durations for western events, compared to those which do not include it. When corotation effects are taken into account, for both eastern and western events the decay time constant is reduced and its dependence on the value of the scattering mean free path becomes negligible. Corotation reduces the SEP peak intensity for western events and enhances it for eastern ones, thus making the east-west asymmetry in peak intensity stronger, compared to the no-corotation case. Modelling SEP intensity profiles without carefully accounting for the effects of corotation leads to artificially extended decay phases during western events, leading to profiles with a similar shape regardless of observer longitud

Context. Gamma-ray emission during long-duration gamma-ray flare (LDGRF) events is thought to be caused mainly by >300 MeV protons interacting with the ambient plasma at or near the photosphere. Prolonged periods of the gamma-ray emission have prompted the suggestion that the source of the energetic protons is acceleration at a coronal mass ejection (CME)-driven shock, followed by particle back-precipitation onto the solar atmosphere over extended times. Aims. We study the latter hypothesis using test particle simulations, which allow us to investigate whether scattering associated with turbulence aids particles in overcoming the effect of magnetic mirroring, which impedes back-precipitation by reflecting particles as they travel sunwards. Methods. The instantaneous precipitation fraction, P, the proportion of protons that successfully precipitate for injection at a fixed height, r_i, is studied as a function of scattering mean free path, lambda, and r_i. Upper limits to the total precipitation fraction, P_bar, were calculated for eight LDGRF events for moderate scattering conditions lambda=0.1 au). Results. We find that the presence of scattering helps back-precipitation compared to the scatter-free case, although at very low lambda values outward convection with the solar wind ultimately dominates. For eight LDGRF events, due to strong mirroring, P_bar is very small, between 0.56 and 0.93% even in the presence of scattering. Conclusions. Time-extended acceleration and large total precipitation fractions, as seen in the observations, cannot be reconciled for a moving shock source according to our simulations. Therefore, it is not possible to obtain both long duration gamma ray emission and efficient precipitation within this scenario. These results challenge the CME shock source scenario as the main mechanism for gamma ray production in LDGRFs.

There are many difficulties associated with forecasting high-energy solar particle events at Earth. One issue is understanding why some large solar eruptive events trigger ground level enhancement (GLE) events and others do not. In this work we perform 3D test particle simulations of a set of historic GLEs to understand more about what causes these powerful events. Particular focus is given to studying how the heliospheric current sheet (HCS) affects high-energy proton transport through the heliosphere following an event. Analysis of >M7.0 flares between 1976-2020 shows that active regions located closer to the HCS (<10deg) are more likely to be associated with a GLE event. We found that modelled GLE events where the source region was close to the HCS also led to increased heliospheric transport in longitude and higher count rates (when the Earth was located in the drift direction). In a model that does not include perpendicular diffusion associated with turbulence, the HCS is the dominant mechanism affecting heliospheric particle transport for GLE 42 and 69, and varying other parameters (e.g. a narrow, 10deg, or wider, 60deg, injection width) causes little change. Overall in our model, the HCS is relevant in 71% of our analysed GLEs and including it more accurately reproduces observed intensities near Earth. Our simulations enable us to produce model profiles at Earth that can be compared to existing observations by the GOES satellites and neutron monitors, as well as for use in developing future forecasting models.

Understanding the magnetic connections from the Sun to interplanetary space is crucial for linking in situ particle observations with the solar source regions of the particles. A simple connection along the large-scale Parker spiral magnetic field is made complex by the turbulent random-walk of field lines. In this paper, we present the first analytical model of heliospheric magnetic fields where the dominant 2D component of the turbulence is transverse to the Parker spiral. The 2D wave field is supplemented with a minor wave field component that has asymptotically slab geometry at small and large heliocentric distances. We show that turbulence spreads field lines from a small source region at the Sun to a 60$^\circ$ heliolongitudinal and -latitudinal range at 1~au, with standard deviation of the angular spread of the field lines $14^\circ$. Small source regions map to an intermittent range of longitudes and latitudes at 1~au, consistent with dropouts in solar energetic particle intensities. The lengths of the field lines are significantly extended from the nominal Parker spiral length of 1.17~au up to 1.6~au, with field lines from sources at and behind the west limb considerably longer than those closer to the solar disk centre. We discuss the implications of our findings on understanding charged particle propagation, and the importance of understanding the turbulence properties close to the Sun.

Solar Energetic Particles (SEPs) are known to be accelerated at Coronal Mass Ejection (CME)-driven interplanetary shocks. Traditionally their propagation has been described via focussed transport approaches, limited to 1 or 2 spatial dimensions. We use 3D test particle simulations, which naturally incorporate the effect of drifts, to simulate the propagation of SEPs from a moving shock-like source. We investigate the effect of an expanding shock-like source propagating through interplanetary space, as opposed to an SEP source within the corona, on the observable properties of SEPs at 1 au and at locations nearer the Sun. We derive intensity profiles, anisotropies and longitudinal and latitudinal distribution of SEPs, with the aim of supporting observations from Solar Orbiter and Parker Solar Probe.

Context. On 2020 November 29, the first widespread solar energetic particle (SEP) event of solar cycle 25 was observed at four widely separated locations in the inner (. 1 AU) heliosphere. Relativistic electrons as well as protons with energies > 50 MeV were observed by Solar Orbiter (SolO), Parker Solar Probe (PSP), the Solar Terrestrial Relations Observatory (STEREO)-A and multiple near-Earth spacecraft. The SEP event was associated with an M4.4 class X-ray flare and accompanied by a coronal mass ejection (CME) and an extreme ultraviolet (EUV) wave as well as a type II radio burst and multiple type III radio bursts. Aims. We present multi-spacecraft particle observations and place them in context with source observations from remote sensing instruments and discuss how such observations may further our understanding of particle acceleration and transport in this widespread event. Methods. Velocity dispersion analysis (VDA) and time shift analysis (TSA) were used to infer the particle release times at the Sun. Solar wind plasma and magnetic field measurements were examined to identify structures that influence the properties of the energetic particles such as their intensity. Pitch angle distributions and first-order anisotropies were analyzed in order to characterize the particle propagation in the interplanetary medium. Results. We find that during the 2020 November 29 SEP event, particles spread over more than 230° in longitude close to 1 AU. The particle onset delays observed at the different spacecraft are larger as the flare–footpoint angle increases and are consistent with those from previous STEREO observations. Comparing the timing when the EUV wave intersects the estimated magnetic footpoints of each spacecraft with particle release times from TSA and VDA, we conclude that a simple scenario where the particle release is only determined by the EUV wave propagation is unlikely for this event. Observations of anisotropic particle distributions at SolO, Wind

Interplanetary coronal mass ejections (ICMEs) cause decreases, so-called Forbush decreases, in the cosmic ray (CR) intensities. FDs are seen as up to 25% decreases in neutron monitor counts at Earth, lasting up to over a week. An ICME is thought to cause a FD through two mechanisms: by enhancing diffusion in the ICME shock wave sheath; and by preventing the CRs from penetrating the magnetic fluxrope embedded in the ICME. CR propagation during a FD is usually modelled as enhanced diffusion either within the whole ICME or within the embedded fluxrope. However, a question that is so far unanswered is how the CRs can reach the isolated fluxrope fieldlines from the open, external interplanetary fieldlines. We study the propagation of CRs from external field into a fluxrope by employing full-orbit particle simulations with scattering. The interface between the internal and external field lines is modelled analytically. We find that the CRs can access the fluxrope rapidly through x-point region, where the external magnetic field partially cancels the magnetic field of the fluxrope. The access is rapid compared to diffusive radial propagation of CRs within the rope. We find that CR propagation within the fluxrope can be modelled using diffusion models, without need to separately model the access to the isolated field lines, provided that the bounds of the diffusion area are taken as that of the isolated fieldlines instead of the region with smoothly rotating magnetic field. Thus, to evaluate the role of a fluxrope in FDs, the extent of the region where the rope magnetic fields are not connected to the external field must be analysed.

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.

Cosmic ray (CR) fluxes in the heliosphere are affected by the transient interplanetary coronal mass ejections (ICMEs), causing so-called Forbush decreases (FDs), characterised by a decline of up to 25% in the neutron monitor counts at the Earth’s surface, lasting up to over a week. FDs are thought to be caused by the ICME shock wave or the magnetic flux rope embedded in the ICME inhibiting CR propagation through the ICME structure. FDs are typically modelled as enhanced diffusion within the ICME structure. However, so far modelling has not considered the access of the CRs from the interplanetary fieldlines into the isolated magnetic fiedlines of the ICME flux rope. We study the effect of an ICME flux rope on particle propagation by using fullorbit particle simulations, with the interface between the external interplanetary magnetic field and the isolated flux rope fieldlines modelled analytically. We find that the particles can access the flux rope through x-point region, where the external magnetic fields cancel the azimuthal component of the rope field. The transport through this region is fast compared to diffusive radial propagation within the rope. As a result, the propagation of CRs into the flux rope can be modelled as diffusion into a cylinder. The density cavity within the rope is asymmetric, and limited to the magnetic field lines isolated from the external field. Thus, in order to evaluate the role of the flux rope in FDs, one must analyse the extent of the region where the flux rope magnetic field lines are separated from the interplanetary magnetic fields

Context. Solar Energetic Particles (SEPs) with energy in the GeV range can propagate to Earth from their acceleration region near the Sun and produce Ground Level Enhancements (GLEs). The traditional approach to interpreting and modelling GLE observations assumes particle propagation only parallel to the magnetic field lines of interplanetary space, i.e. it is spatially 1D. Recent measurements by PAMELA have characterised SEP properties at 1 AU for the ~100 MeV-1 GeV range at high spectral resolution. Aims. We model the transport of GLE-energy solar protons through the Interplanetary Magnetic Field (IMF) using a 3D approach, to assess the effect of the Heliospheric Current Sheet (HCS) and drifts associated to the gradient and curvature of the Parker spiral. The latter are influenced by the IMF polarity. We derive 1 AU observables and compare the simulation results with data from PAMELA. Methods. We use a 3D test particle model including a HCS. Monoenergetic populations are studied first to obtain a qualitative picture of propagation patterns and numbers of crossings of the 1 AU sphere. Simulations for power law injection are used to derive intensity profiles and fluence spectra at 1 AU. A simulation for a specific event, GLE 71, is used to compare with PAMELA data. Results. Spatial patterns of 1 AU crossings and the average number of crossings are strongly influenced by 3D effects, with significant differences between periods of A+ and A- polarities. The decay time constant of 1 AU intensity profiles varies depending on the polarity and position of the observer, and it is not a simple function of the mean free path as in 1D models. Energy dependent leakage from the injection flux tube is particularly important for GLE energy particles, in many cases resulting in a roll-over in the fluence spectrum.