T. Laitinen

Monte Carlo Simulations of Coronal Diffusive Shock Acceleration in Self-generated Turbulence

We report on Monte Carlo simulations of solar energetic particle (SEP) acceleration at quasi-parallel coronal shocks under the influence of self-generated Alfven waves. The results indicate that the accelerated particles amplify ambient Alfven waves efficiently and that the solution close to the shock can be qualitatively described with the results from quasi-steady theories of diffusive shock acceleration, provided that the acceleration and injection parameters do not change rapidly. The escape of the first particles to the interplanetary medium occurs before the waves have grown appreciably to trap the particles in the vicinity of the shock wave. The escape process is well described by the analytical model developed by Vainio, at least for the promptly escaping component. In addition to the compression ratio and speed of the shock wave, the rate of injection of low-energy particles to the acceleration process is a key factor for the acceleration efficiency of shocks that are driven by coronal mass ejection. Quasi-parallel coronal shocks seem to be capable of accelerating suprathermal protons up to 100 MeV and beyond after some number of minutes. Extrapolations of our simulation results indicate, however, that the wave intensities may reach nonlinear values before acceleration to GeV energies occurs in the corona. This may mean that the quasi-linear approach has to be replaced by a more general theory to describe particle acceleration at quasi-parallel coronal shocks in the largest SEP events.

Drift-induced Perpendicular Transport of Solar Energetic Particles

Drifts are known to play a role in galactic cosmic ray transport within the heliosphere and are a standard component of cosmic ray propagation models. However, the current paradigm of solar energetic particle (SEP) propagation holds the effects of drifts to be negligible, and they are not accounted for in most current SEP modeling efforts. We present full-orbit test particle simulations of SEP propagation in a Parker spiral interplanetary magnetic field (IMF), which demonstrate that high-energy particle drifts cause significant asymmetric propagation perpendicular to the IMF. Thus in many cases the assumption of field-aligned propagation of SEPs may not be valid. We show that SEP drifts have dependencies on energy, heliographic latitude, and charge-to-mass ratio that are capable of transporting energetic particles perpendicular to the field over significant distances within interplanetary space, e.g., protons of initial energy 100 MeV propagate distances across the field on the order of 1 AU, over timescales typical of a gradual SEP event. Our results demonstrate the need for current models of SEP events to include the effects of particle drift. We show that the drift is considerably stronger for heavy ion SEPs due to their larger mass-to-charge ratio. This paradigm shift has important consequences for the modeling of SEP events and is crucial to the understanding and interpretation of in situ observations.

Interplanetary and Interacting Protons Accelerated in a Parallel Shock Wave

We present a test-particle model of diffusive shock acceleration on open coronal field lines based on one-dimensional diffusion-convection equation with finite upstream and downstream diffusion regions. We calculate the energy spectrum of protons escaping into the interplanetary space and that of protons interacting with the subcoronal material producing observable secondary emissions. Our model can account for the observed power-law and broken power-law energy spectra as well as the values of the order of unity for the ratio of the interplanetary to interacting protons. We compare our model to Monte Carlo simulations of parallel shock acceleration including the effects of the diverging magnetic field. A good agreement between the models is found if (i) the upstream diffusion length is much smaller than the scale length LB of the large-scale magnetic field, κ1/U1 LB, where U1 is the upstream scattering center speed and κ1(p) is the momentum dependent upstream diffusion coefficent; (ii) the downstream diffusion length is much smaller than the length of the downstream diffusive region L2, for which L2 LB has to be satisfied; and (iii) most of the particles are injected to the acceleration process within a couple of LBs above the solar surface. We emphasize that concurrently produced interplanetary and interacting protons can be used as probes of turbulence in the vicinity of the shock; our model has two turbulence parameters, the scattering-center compression ratio at the shock and the number of diffusion lengths in the upstream region, that may be experimentally determined if the interplanetary and interacting proton spectra are measured.

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 behavior 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 hr, which is consistent with the observations of SEP intensity dropouts. We conclude that modeling SEP events must take into account the particle propagation along meandering field lines for the first 20 hr of the event.

Energetic (∼ 1 to 50 MeV) protons associated with Earth‐directed coronal mass ejections

During the period from January through mid-May, 1997, four large Earth-directed CMEs were observed by the Large Angle Spectroscopic Coronograph (LASCO). These CMEs were associated with long-lasting fluxes of >1.6 MeV protons detected by the Energetic and Relativistic Nuclei and Electron instrument (ERNE). However, the magnitudes of energetic proton events differed dramatically on different occasions. In strong proton events, production of 10-50 MeV protons started during expansion of the coronal Moreton wave in the western hemisphere of the Sun. The new SOHO observations suggest that potentialities of CMEs to produce energetic particles in the interplanetary medium crucially depend on the previous evolution of the explosion below ∼2R⊙. Forecasting of the near-Earth >10 MeV proton intensity requires multiwavelength observations of the early phase of an event particularly the Extreme-ultraviolet Imaging Telescope (EIT) observations.

A simple analytical expression for the power spectrum of cascading Alfvén waves in the solar wind

Alfven wave transport in the solar wind, including non-linear spectral energy transfer, is studied. We present numeri- cal solutions of wave transport using a diusive flux function previously introduced for spectral energy transfer, and compare it with the analytical solution obtained for a convective flux function. The two models of cascading produce very similar behavior of a power spectrum initially of 1= f -form at the solar surface, provided that the cascading constants are tuned to produce the same spectral flux in the inertial range. We present an analytical expression for the power spectrum of the diusively-cascading Alfven waves in the solar wind derived from a solution of the wave transport equation and show that it compares well with the exact solutions. Our expression enables (semi) analytical evaluation of the cyclotron heating rate, the wave pressure gradient, and the energetic-particle mean free path related to the Alfven waves in the corona and solar wind.

Solar energetic particle drifts in the Parker spiral

Drifts in the Parker spiral interplanetary magnetic field are known to be an important component in the propagation of galactic cosmic rays, while they are thought to be negligible for Solar Energetic Particles (SEPs). As a result they have so far been ignored in SEP propagation modelling and data analysis. We examine drift velocities in the Parker spiral within single particle first-order adiabatic theory, in a local coordinate system with an axis parallel to the magnetic field. We show that, in the presence of scattering in interplanetary space, protons at the high end of the SEP energy range experience significant gradient and curvature drift. In the scatter-free case, drift due to magnetic field curvature is present. The magnitude of drift velocity increases by more than an order of magnitude at high heliographic latitudes compared to near the ecliptic; it has a strong dependence on radial distance r from the Sun, reaching a maximum at r~1 AU at low heliolatitudes and r~10 AU at high heliolatitudes. Due to the mass over charge dependence of drift velocities, the effect of drift for partially ionised SEP heavy ions is stronger than for protons. Drift is therefore likely to be a considerable source of cross field transport for high energy SEPs.

Solar energetic particle access to distant longitudes through turbulent field-line meandering

Context. Current solar energetic particle (SEP) propagation models describe the effects of interplanetary plasma turbulence on SEPs as diffusion, using a Fokker-Planck (FP) equation. However, FP models cannot explain the observed fast access of SEPs across the average magnetic field to regions that are widely separated in longitude within the heliosphere without using unrealistically strong cross-field diffusion. Aims. We study whether the recently suggested early non-diffusive phase of SEP propagation can explain the wide SEP events with realistic particle transport parameters. Methods. We used a novel model that accounts for the SEP propagation along field lines that meander as a result of plasma turbulence. Such a non-diffusive propagation mode has been shown to dominate the SEP cross-field propagation early in the SEP event history. We compare the new model to the traditional approach, and to SEP observations. Results. Using the new model, we reproduce the observed longitudinal extent of SEP peak fluxes that are characterised by a Gaussian profile with

SPARX: A modeling system for Solar Energetic Particle Radiation Space Weather forecasting

\sigma=30-50^\circ

Modeling the Shock Aftermath Source of Energetic Particles in the Solar Corona

, while current diffusion theory can only explain extents of 11