Effects of interplanetary transport on derived energetic particle source strengths

We study the transport of solar energetic particles (SEPs) in the inner heliosphere in order to relate observations made by an observer at 1 AU to the number and total energy content of accelerated particles at the source, assumed to be near the Sun. We use a numerical simulation that integrates the trajectories of a large number of individual particles moving in the interplanetary magnetic field. We model pitch angle scattering and adiabatic cooling of energetic ions with energies from 50 keV nucleon^(−1) to 100 MeV nucleon^(−1). Among other things, we determine the number of times that particles of a given energy cross 1 AU and the average energy loss that they suffer because of adiabatic deceleration in the solar wind. We use a number of different forms of the interplanetary spatial diffusion coefficient and a wide range of scattering mean-free paths and consider a number of different ion species in order to generate a wide range of simulation results that can be applied to individual SEP events. We apply our simulation results to observations made at 1 AU of the 20 February 2002 solar energetic particle event, finding the original energy content of several species. We find that estimates of the source energy based on SEP measurements at 1 AU are relatively insensitive to the mean-free path and scattering scheme if adiabatic cooling and multiple crossings are taken into account

The Effect of Large Scale Magnetic Turbulence on the Acceleration of Electrons by Perpendicular Collisionless Shocks

We study the physics of electron acceleration at collisionless shocks that move through a plasma containing large-scale magnetic fluctuations. We numerically integrate the trajectories of a large number of electrons, which are treated as test particles moving in the time dependent electric and magnetic fields determined from 2-D hybrid simulations (kinetic ions, fluid electron). The large-scale magnetic fluctuations effect the electrons in a number of ways and lead to efficient and rapid energization at the shock front. Since the electrons mainly follow along magnetic lines of force, the large-scale braiding of field lines in space allows the fast-moving electrons to cross the shock front several times, leading to efficient acceleration. Ripples in the shock front occuring at various scales will also contribute to the acceleration by mirroring the electrons. Our calculation shows that this process favors electron acceleration at perpendicular shocks. The current study is also helpful in understanding the injection problem for electron acceleration by collisionless shocks. It is also shown that the spatial distribution of energetic electrons is similar to in-situ observations (e.g., Bale et al. 1999; Simnett et al. 2005). The process may be important to our understanding of energetic electrons in planetary bow shocks and interplanetary shocks, and explaining herringbone structures seen in some type II solar radio bursts.Comment: 23 pages, 6 figures, accepted by Ap

Solar Energetic Particles Produced by a Slow Coronal Mass Ejection at ∼0.25 au

We present an analysis of Parker Solar Probe (PSP) IS⊙IS observations of ~30–300 keV n⁻¹ ions on 2018 November 11 when PSP was about 0.25 au from the Sun. Five hours before the onset of a solar energetic particle (SEP) event, a coronal mass ejection (CME) was observed by STEREO-A/COR2, which crossed PSP about a day later. No shock was observed locally at PSP, but the CME may have driven a weak shock earlier. The SEP event was dispersive, with higher energy ions arriving before the lower energy ones. Timing suggests the particles originated at the CME when it was at ~7.4R_⊙. SEP intensities increased gradually from their onset over a few hours, reaching a peak, and then decreased gradually before the CME arrived at PSP. The event was weak, having a very soft energy spectrum (−4 to −5 spectral index). The earliest arriving particles were anisotropic, moving outward from the Sun, but later, the distribution was observed to be more isotropic. We present numerical solutions of the Parker transport equation for the transport of 30–300 keV n⁻¹ ions assuming a source comoving with the CME. Our model agrees well with the observations. The SEP event is consistent with ion acceleration at a weak shock driven briefly by the CME close to the Sun, which later dissipated before arriving at PSP, followed by the transport of ions in the interplanetary magnetic field

Early-time velocity autocorrelation for charged particles diffusion and drift in static magnetic turbulence

Using test-particle simulations, we investigate the temporal dependence of the two-point velocity correlation function for charged particles scattering in a time-independent spatially fluctuating magnetic field derived from a three-dimensional isotropic turbulence power spectrum. Such a correlation function allowed us to compute the spatial coefficients of diffusion both parallel and perpendicular to the average magnetic field. Our simulations confirm the dependence of the perpendicular diffusion coefficient on turbulence energy density and particle energy predicted previously by a model for early-time charged particle transport. Using the computed diffusion coefficients, we exploit the particle velocity autocorrelation to investigate the time-scale over which the particles "decorrelate" from the solution to the unperturbed equation of motion. Decorrelation time-scales are evaluated for parallel and perpendicular motions, including the drift of the particles from the local magnetic field line. The regimes of strong and weak magnetic turbulence are compared for various values of the ratio of the particle gyroradius to the correlation length of the magnetic turbulence. Our simulation parameters can be applied to energetic particles in the interplanetary space, cosmic rays at the supernova shocks, and cosmic-rays transport in the intergalactic medium.Comment: 10 pages, 11 figures, The Astrophyical Journal in pres

Energetic particle cross-field propagation early in a solar event

Solar energetic particles (SEPs) have been observed to easily spread across heliographic longitudes, and the mechanisms responsible for this behaviour remain unclear. We use full-orbit simulations of a 10 MeV proton beam in a turbulent magnetic field to study to what extent the spread across the mean field can be described as diffusion early in a particle event. We compare the full-orbit code results to solutions of a Fokker-Planck equation including spatial and pitch angle diffusion, and of one including also propagation of the particles along random-walking magnetic field lines. We find that propagation of the particles along meandering field lines is the key process determining their cross-field spread at 1 AU at the beginning of the simulated event. The mean square displacement of the particles an hour after injection is an order of magnitude larger than that given by the diffusion model, indicating that models employing spatial cross-field diffusion cannot be used to describe early evolution of an SEP event. On the other hand, the diffusion of the particles from their initial field lines is negligible during the first 5 hours, which is consistent with the observations of SEP intensity dropouts. We conclude that modelling SEP events must take into account the particle propagation along meandering field lines for the first 20 hours of the event.Comment: 5 pages, 4 figures; Accepted for publication in Astrophysical Journal Letter

Particle acceleration by collisionless shocks containing large-scale magnetic-field variations

Diffusive shock acceleration at collisionless shocks is thought to be the source of many of the energetic particles observed in space. Large-scale spatial variations of the magnetic field has been shown to be important in understanding observations. The effects are complex, so here we consider a simple, illustrative model. Here, we solve numerically the Parker transport equation for a shock in the presence of large-scale sinusoidal magnetic-field variations. We demonstrate that the familiar planar-shock results can be significantly altered as a consequence of large-scale, meandering magnetic lines of force. Because perpendicular diffusion coefficient $\kappa_\perp$ is generally much smaller than parallel diffusion coefficient $\kappa_\parallel$, the energetic charged particles are trapped and preferentially accelerated along the shock front in the regions where the connection points of magnetic field lines intersecting the shock surface converge, and thus create the "hot spots" of the accelerated particles. For the regions where the connection points separate from each other, the acceleration to high energies will be suppressed. Further, the particles diffuse away from the "hot spot" regions and modify the spectra of downstream particle distribution. These features are qualitatively similar to the recent Voyager's observation in the Heliosheath. These results are potentially important for particle acceleration at shocks propagating in turbulent magnetized plasmas as well as those which contain large-scale nonplanar structures. Examples include anomalous cosmic rays accelerated by the solar wind termination shock, energetic particles observed in propagating heliospheric shocks, and galactic cosmic rays accelerated by supernova blast waves, etc.Comment: accepted to Ap