We investigate multi-spacecraft observations of the 17 January 2010 solar energetic particle event. Energetic electrons and protons have been observed over a remarkable large longitudinal range at ...the two STEREO spacecraft and SOHO, suggesting a longitudinal spread of nearly 360 degrees at 1 AU. The flaring active region, which was on the backside of the Sun as seen from Earth, was separated by more than 100 degrees in longitude from the magnetic footpoints of each of the three spacecraft. The event is characterized by strongly delayed energetic particle onsets with respect to the flare and only small or no anisotropies in the intensity measurements at all three locations. The presence of a coronal shock is evidenced by the observation of a type II radio burst from the Earth and STEREO-B. In order to describe the observations in terms of particle transport in the interplanetary medium, including perpendicular diffusion, a 1D model describing the propagation along a magnetic field line (model 1) (Dröge,
Astrophys. J
.
589
, 1027 – 1039,
2003
) and the 3D propagation model (model 2) by Dröge
et al
. (
Astrophys. J
.
709
, 912 – 919,
2010
) including perpendicular diffusion in the interplanetary medium have been applied. While both models are capable of reproducing the observations, model 1 requires injection functions at the Sun of several hours. Model 2, which includes lateral transport in the solar wind, reveals high values for the ratio of perpendicular to parallel diffusion. Because we do not find evidence for unusual long injection functions at the Sun, we favor a scenario with strong perpendicular transport in the interplanetary medium as an explanation for the observations.
We investigate the combined effects of solar energetic particle propagation, parallel and perpendicular to the large-scale magnetic field in the solar wind. Numerical methods employing stochastic ...differential equations are used incorporating pitch-angle diffusion, focusing, and pitch-angle-dependent diffusion perpendicular to the magnetic field. We compute spatial distributions of approx100 keV electrons and 4 MeV protons in the inner heliosphere, assuming impulsive injection near the Sun over a limited range of solar longitude and latitude. In addition, spatial distributions and intensity-time profiles for various combinations of the parallel and perpendicular mean free path, with different assumptions for the dependence of lambda{sub perpendicular} on the radial distance and pitch angle, are investigated. We find that realistic results can be obtained when we assume that the perpendicular mean free path scales in the inner heliosphere with the gyroradius of the particles. Step-like decreases of particle intensities as frequently observed in impulsive events at 1 AU can be reproduced for a ratio of lambda{sub perpendicular}/lambda{sub ||} a few times 10{sup -5}.
We analyze 65–105 keV electrons in the 7 February 2010 solar electron event observed simultaneously by STEREO‐A, STEREO‐B, and ACE. A method to reconstruct the full‐electron pitch angle distributions ...from the four Solar Electron and Proton Telescope sensors on STEREO‐A/B and the Solar Electron and Proton Telescope instrument on ACE in the energy range of approximately 60–300 keV for periods of incomplete angular coverage is presented. A transport modeling based on numerical solutions of a three‐dimensional particle propagation model which includes pitch angle scattering and focused transport is applied to the intensity and anisotropy profiles measured on all three spacecraft. Based on an analysis of intensity gradients observed between the three spacecraft, we find that the lateral transport of the electrons occurs partially close to the Sun, due to effects of nonradial divergence of magnetic field lines or particle diffusion, and partially in the interplanetary medium. For the mean free paths characterizing the electron diffusion parallel and perpendicular to the interplanetary magnetic field, we derive values of λ∥∼ 0.1 AU and λ⟂∼ 0.01 AU. In comparison with results from other particle events which we had previously analyzed in a similar manner we discuss whether the diffusion mean free paths parallel and perpendicular to the average magnetic field might be related with each other, and whether the particle transport perpendicular to the average magnetic field is more likely due to particles following meandering magnetic field lines, or due to particles being scattered off individual field lines.
Key Points
We analyze solar electrons observed simultaneously on the STEREO‐A/B and ACEA numerical simulation of the three‐dimensional electron transport is presentedParallel and perpendicular diffusion coefficients are derived
ABSTRACT During 2010 August a series of solar particle events was observed by the two STEREO spacecraft as well as near-Earth spacecraft. The events, occurring on August 7, 14, and 18, originated ...from active regions 11093 and 11099. We combine in situ and remote-sensing observations with predictions from our model of three-dimensional anisotropic particle propagation in order to investigate the physical processes that caused the large angular spreads of energetic electrons during these events. In particular, we address the effects of the lateral transport of the electrons in the solar corona that is due to diffusion perpendicular to the average magnetic field in the interplanetary medium. We also study the influence of two coronal mass ejections and associated shock waves on the electron propagation, and a possible time variation of the transport conditions during the above period. For the August 18 event we also utilize electron observations from the MESSENGER spacecraft at a distance of 0.31 au from the Sun for an attempt to separate between radial and longitudinal dependencies in the transport process. Our modelings show that the parallel and perpendicular diffusion mean free paths of electrons can vary significantly not only as a function of the radial distance, but also of the heliospheric longitude. Normalized to a distance of 1 au, we derive values of λ in the range of 0.15-0.6 au, and values of λ in the range of 0.005-0.01 au. We discuss how our results relate to various theoretical models for perpendicular diffusion, and whether there might be a functional relationship between the perpendicular and the parallel mean free path.
Solar particle events that are rich in 3He typically also exhibit large overabundances of heavy and ultraheavy ions that increase with the mass of the ions. To explain these observations we apply our ...charge-consistent acceleration model, which takes into account the acceleration efficiency as a function of the charge to mass ratio of the ion, as well as the charge-dependent Coulomb energy losses, to consider the acceleration of ions within a wide range of their nuclear charge. Because the considerations of particle acceleration were restricted so far by tabulated values of ionization and recombination coefficients that were available only for a limited set of ions, we make use of our method developed earlier and calculate the rates of ions resembling the three representative mass groups of ultraheavy ions. We demonstrate that smaller Coulomb losses together with higher acceleration efficiency result in the enhancements of heavy and ultraheavy ions, in accordance with recent observations. We also conclude that the existing measurements of ultraheavy ions in impulsive solar energetic particle events provide evidence in favor of a magnetic turbulence in the acceleration region with spectral index S ≥ 2.
We analyze electrons in the energy range 1-180 keV, observed by the Wind spacecraft following an impulsive solar flare on 2002 October 20. The event is characterized by weak, but measurable ...pitch-angle scattering, which allows a characterization of the pitch-angle scattering coefficient , as well as by particle reflection at an outer boundary. Based on numerical solutions of the focused transport equation we present fits to the observed electron fluxes, with emphasis on a detailed modeling of the particles' angular distributions. By means of the wavelet transform method we estimate the slab component of the fluctuation, which is frequently assumed to dominate the particle scattering. We find that the values of obtained from the modeling for several energy ranges disagree strongly with the ones calculated from the estimated slab component for this event and standard quasi-linear theory, in the pitch-angle dependence of the scattering coefficient and also in its magnitude. These results indicate that in this event the scattering of electrons at low energies is much weaker than predicted by the above models, and that at large wavenumbers the slab component makes up only a few per cent of the fluctuations. We discuss whether in weak-scattering events the concept of pitch-angle diffusion due to a resonant interaction of the particles with the turbulence would have to be reconsidered, and whether additional effects such magnetic mirroring of the electrons and intermittency of the fluctuations would have to be taken into account.
By employing our charge-consistent acceleration model we demonstrate a possibility to explain the isotopic ratios observed in a number of 3He-rich events. We investigate the dependence of isotopic ...ratios of heavy ions on the energy of the particles, the acceleration efficiency, the product of acceleration time, and the number density of ambient electrons, of the plasma temperature, and of the spectral index of the magnetic fluctuations by which the ions are energized in the acceleration region. On the basis of the energy spectra of heavy ions and their isotopic ratios observed in the event of 2002 August 20 by the Solar Isotope Spectrometer on board the Advanced Composition Explorer (SIS/ACE) we put constraints on the plasma parameters in the acceleration region. Our investigation gives evidence that the spectral index of the fluctuations with which the ions interact is greater than 2, and that the plasma temperature is about 1 MK.
Context.
Solar Orbiter, launched in February 2020, started its cruise phase in June 2020, in coincidence with its first perihelion at 0.51 au from the Sun. The in situ instruments onboard, including ...the Energetic Particle Detector (EPD), operate continuously during the cruise phase enabling the observation of solar energetic particles.
Aims.
In situ measurements of the first near-relativistic solar electron events observed in July 2020 by EPD are analyzed and the solar origins and the conditions for the interplanetary transport of these particles investigated.
Methods.
Electron observations from keV energies to the near-relativistic range were combined with the detection of type III radio bursts and extreme ultraviolet (EUV) observations from multiple spacecraft in order to identify the solar origin of the electron events. Electron anisotropies and timing as well as the plasma and magnetic field environment were evaluated to characterize the interplanetary transport conditions.
Results.
All electron events were clearly associated with type III radio bursts. EUV jets were also found in association with all of them except one. A diversity of time profiles and pitch-angle distributions was observed. Different source locations and different magnetic connectivity and transport conditions were likely involved. The July 11 event was also detected by Wind, separated 107 degrees in longitude from Solar Orbiter. For the July 22 event, the Suprathermal Electron and Proton sensor of EPD allowed for us to not only resolve multiple electron injections at low energies, but it also provided an exceptionally high pitch-angle resolution of a very anisotropic beam. This, together with radio observations of local Langmuir waves suggest a very good magnetic connection during the July 22 event. This scenario is challenged by a high-frequency occultation of the type III radio burst and a nominally non-direct connection to the source; therefore, magnetic connectivity requires further investigation.
Diffusive shock acceleration (DSA) of ions occurs due to pitch-angle diffusion in the upstream and downstream regions of the shock and multiple crossing of the shock by these ions. The classical DSA ...theory implies continuity of the distribution at the shock transition and predicts a universal spectrum of accelerated particles, depending only on the ratio of the upstream and downstream fluid speeds. However, the ion dynamics at the shock front occurs within a collision-free region and is gyrophase dependent. The ions fluxes have to be continuous at the shock front. The matching conditions for the gyrophase-averaged distribution functions at the shock transition are formulated in terms of the transition and reflection probabilities. These probabilities depend on the shock angle and the magnetic compression as does the power spectrum of accelerated ions. Their spectral index is expressed in terms of the reflectivity. The spectrum is typically harder than the spectrum predicted by the classical DSA theory.
ABSTRACT We use numerical solutions of the focused transport equation obtained by an implicit stochastic differential equation scheme to study the evolution of the pitch-angle dependent distribution ...function of protons in the vicinity of shock waves. For a planar stationary parallel shock, the effects of anisotropic distribution functions, pitch-angle dependent spatial diffusion, and first-order Fermi acceleration at the shock are examined, including the timescales on which the energy spectrum approaches the predictions of diffusive shock acceleration theory. We then consider the case that a flare-accelerated population of ions is released close to the Sun simultaneously with a traveling interplanetary shock for which we assume a simplified geometry. We investigate the consequences of adiabatic focusing in the diverging magnetic field on the particle transport at the shock, and of the competing effects of acceleration at the shock and adiabatic energy losses in the expanding solar wind. We analyze the resulting intensities, anisotropies, and energy spectra as a function of time and find that our simulations can naturally reproduce the morphologies of so-called mixed particle events in which sometimes the prompt and sometimes the shock component is more prominent, by assuming parameter values which are typically observed for scattering mean free paths of ions in the inner heliosphere and energy spectra of the flare particles which are injected simultaneously with the release of the shock.
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