Modulation of cosmic-ray ground-level enhancements by solar-wind stream interfaces: a case study

Impulsive,3He-rich events originate close to the interface between slow solar wind overlying active regions and a faster solar wind coming from small coronal holes. This causes large-scale magnetic compressions to be an interplanetary environment for solar energetic particle (SEP) transport in impulsive events, which is typically ignored by SEP modelers. We have modeled SEP transport in a simplified corotating solar wind structure to estimate the possible effect of the rising wind speed on particle anisotropy and spectra at 1 AU. Along with traditional modeling of SEP transport in the static magnetic field and the field-aligned solar wind flow of the corotating frame of reference, we have formulated and tested a new model that is the first model of focused transport applicable to a general case of SEP propagation in realistic, dynamic, and structured solar wind. Numerical modeling shows that a fast increase of the wind speed by only 200 km s−1 can strongly affect the SEP flux anisotropy at 1 AU. Accurate analysis of impulsive SEP events can be done with the use of solar wind data, SEP flux anisotropy measurements, and the new approach that accounts for the solar wind structures associated with the sources of impulsive events and uses the general solution of the focused transport problem applicable to SEPs in realistic solar wind.

The transport of solar energetic charged particles along the interplanetary magnetic field in the ecliptic plane of the sun can be described roughly by a one-dimensional diffusion equation. Large-scale spatial variations of the guide magnetic field can be taken into account by adding an additional term to the diffusion equation that includes the effect of adiabatic focusing. We solve this equation analytically by assuming a point-like particle injection in time and space and a spatial power-law dependence for the focusing length and the spatial diffusion coefficient. We infer the intensity- and anisotropy-time profiles of solar energetic particles from this solution. Through these the influence of different assumptions for the diffusion parameters can be seen in a mathematically closed form. The comparison of calculated and measured intensity- and anisotropy-time profiles, which are a powerful diagnostic tool for interplanetary particle transport, gives information about the large-scale spatial dependence of the focusing length and the diffusion coefficient. For an exceptionally large solar energetic particle event, which did occur on 2001 April 15, we fit the 27−512 keV electron intensities and anisotropies observed by the Wind spacecraft using the theoretically derived profiles. We find a linear spatial dependence of the mean free path along the guiding magnetic field. We also find the mean free path to be energy independent, which supports the theory of “velocity-dependent diffusion”. This means that the intensity profiles for the discussed energies exhibit the same shape if they are plotted against the traveled distance and not against the time. In this case the profiles differ only in their maximum values and we can determine the energy spectra of the solar flare electrons out of the scaling factor we need to fit the data. The derived spectra exhibits a power-law dependence ∝E −3 kin in an energy range from ∼50 keV to ∼500 keV.

Wave damping and cascading processes have been found to be important for the heating and acceleration of the solar wind. However, it remains a difficult task to extract details of these processes from observations of the thermal plasma only. The wave power required for efficient heating and acceleration of the solar wind also affects the acceleration and transport of solar energetic particles. Thus, their observation could provide valuable clues for the actual evolution of the wave power close to the coronal base and, in turn, give constraints for solar wind modeling. Pursuing this idea, we have developed a steady‐state two‐fluid model for the wave heating and acceleration of the solar wind. The dissipation frequency determining the heating is obtained from a cyclotron damping rate that depends on the plasma beta and, thus, differs from the usual assumption, a fixed fraction of the ion cyclotron frequency. We present first results obtained with the two‐fluid code and, in particular, discuss the implications of the corresponding mean free path of energetic particles.

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

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.

Our code of solar energetic particle (SEP) acceleration and transport developed in Arizona is combined with the realistic CME simulations of Michigan, using the solar wind and magnetic field data of the Michigan CME‐simulation as input to the SEP code. We suggest that, in addition to the acceleration at the shock significant acceleration may also occur in the sheet behind the shock, where magnetic field lines are compressed as they are bent around the expanding cloud. We consider field aligned motion and cast the proper Fokker‐Planck equation into a non‐inertial comoving frame, that follows field lines as they evolve. Illustrative simulation results are presented.

Implications of improved measurements of the highest energy SEPs by AMS and PAMELA

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

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.

<p>The lower and middle solar corona up to about 30 solar radii is thought to be 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 over 50 separate global coronal shock events between 1 and 30 solar radii. As part of the SPREAdFAST framework project, we analyzed the interaction of off-limb coronal bright fronts (CBF) observed with the SDO/AIA EUV telescope with realistic model coronal plasma based on results from synoptic magnetohydrodynamic (MHD) and differential emission measure (DEM) models. We used realistic quiet-time proton spectra observed near Earth to form seed suprathermal populations accelerated in our diffusive shock acceleration model (Kozarev & Schwadron, 2016). We summarize our findings and present implications for nowcasting SEP acceleration and heliospheric connectivity.</p>

Aims: This paper presents a H2020 project aimed at developing an advanced space weather forecasting tool, combining the MagnetoHydroDynamic (MHD) solar wind and coronal mass ejection (CME) evolution modelling with solar energetic particle (SEP) transport and acceleration model(s). The EUHFORIA 2.0 project will address the geoeffectiveness of impacts and mitigation to avoid (part of the) damage, including that of extreme events, related to solar eruptions, solar wind streams, and SEPs, with particular emphasis on its application to forecast geomagnetically induced currents (GICs) and radiation on geospace.Methods: We will apply innovative methods and state-of-the-art numerical techniques to extend the recent heliospheric solar wind and CME propagation model EUHFORIA with two integrated key facilities that are crucial for improving its predictive power and reliability, namely (1) data-driven flux-rope CME models, and (2) physics-based, self-consistent SEP models for the acceleration and transport of particles along and across the magnetic field lines. This involves the novel coupling of advanced space weather models. In addition, after validating the upgraded EUHFORIA/SEP model, it will be coupled to existing models for GICs and atmospheric radiation transport models. This will result in a reliable prediction tool for radiation hazards from SEP events, affecting astronauts, passengers and crew in high-flying aircraft, and the impact of space weather events on power grid infrastructure, telecommunication, and navigation satellites. Finally, this innovative tool will be integrated into both the Virtual Space Weather Modeling Centre (VSWMC, ESA) and the space weather forecasting procedures at the ESA SSCC in Ukkel (Belgium), so that it will be available to the space weather community and effectively used for improved predictions and forecasts of the evolution of CME magnetic structures and their impact on Earth.Results: The results of the first six months of the EU H2020 project are presented here. These concern alternative coronal models, the application of adaptive mesh refinement techniques in the heliospheric part of EUHFORIA, alternative flux-rope CME models, evaluation of data-assimilation based on Karman filtering for the solar wind modelling, and a feasibility study of the integration of SEP models.

We continue the systematical empirical search for small size ground level enhancements (GLEs) (also called “hidden” or sub-GLEs) using data from ground-based instruments for Solar Cycle 24. The starting point of this research is the hypothesis that small size GLEs may be indicative of the acceleration of solar energetic particles (SEPs) by shocks driven by coronal mass ejections (CMEs). A crucial parameter for solving the problem seems to be the SEP energy spectrum at the Earth’s orbit measured by spacecraft detectors and ground-based neutron monitors (NMs). We try to recover the SEP spectrum in a wide range of energies – from GOES non-relativistic energy channels to the relativistic range from NM data, as well as from relevant measurements of some ground-based non-standard (mainly muon) cosmic ray detectors. The main factors that determine the SEP intensity and spectrum shape near the Earth are the source power, location, and/or shock strength. Every “suspected” small GLE is analyzed separately. Finally, we compile the list of statistically confirmed small GLEs and give our interpretation within the frame of the above hypothesis. The three considered models of shock wave acceleration are not suitable to physically and unambiguously explain some features of the observed solar cosmic ray (SCR) spectra. The results emphasize the importance of studying the GLEs of low intensity (hidden GLEs) for better understanding the SEP spectrum formation, especially in the range of relativistic energies. The GLE events from behind-the-limb sources are of special interest.

Solar energetic particle (SEP) fluxes, after their propagation from the particles' source to the Earth's orbit, depend on the state of solar wind, which is known to be highly variable in both time and space. Commonly used SEP transport models are based on the assumption of the standard interplanetary magnetic field, which would be the case for a uniform, steady state expansion of solar wind. Modeling of SEP transport in the standard solar wind can be facilitated by the use of a corotating reference frame, wherein the solar wind speed is parallel to interplanetary magnetic field at each point and the magnetic field is static. However, this approach is not possible in the realistic solar wind. This necessitates development of a more general SEP model applicable to particle transport in arbitrarily structured solar wind and in interplanetary coronal mass ejections, magnetic clouds, and shocks. In the framework of focused transport theory, we formulate a practical model of SEP transport in an evolving, structured solar wind. This unified model accommodates the results of three‐dimensional MHD modeling of solar wind based on observations of the sun, solar wind, and SEPs in a particular event. A relation between the generalized focused transport model and the diffusion‐convection equation of cosmic ray transport is discussed.

We model the transport of solar energetic particles (SEPs) in the solar wind. We propagated relativistic test particles in the field of a steady three-dimensional magnetohydrodynamic simulation of the solar wind. We used the code MPI-AMRVAC for the wind simulations and integrated the relativistic guiding center equations using a new third-order-accurate predictor-corrector time-integration scheme. Turbulence-induced scattering of the particle trajectories in velocity space was taken into account through the inclusion of a constant field-aligned scattering mean free path λ∥. We considered mid-range SEP electrons of 81 keV injected into the solar wind at a heliocentric distance of 0.28 AU and a magnetic latitude of 24°. For λ∥ = 0.5 AU, the simulated velocity pitch angle distributions agree qualitatively well with in situ measurements at 1 AU. More generally, for λ∥ in the range 0.1–1 AU, an energy-loss rate associated with the velocity drift of about 10% per day is observed. The energy loss is attributable to the magnetic curvature and gradient-induced poleward drifts of the electrons against the dominant component of the electric field. In our case study, which is representative of the average solar wind conditions, the observed drift-induced energy-loss rate is fastest near a heliocentric distance of 1.2 AU. We emphasize that adiabatic cooling is the dominant mechanism during the first 1.5 hours of propagation. Only at later times does the drift-associated loss rate become dominant.