R. Vainio

Supermagnetosonic Jets behind a Collisionless Quasiparallel Shock

The downstream region of a collisionless quasiparallel shock is structured containing bulk flows with high kinetic energy density from a previously unidentified source. We present Cluster multispacecraft measurements of this type of supermagnetosonic jet as well as of a weak secondary shock front within the sheath, that allow us to propose the following generation mechanism for the jets: The local curvature variations inherent to quasiparallel shocks can create fast, deflected jets accompanied by density variations in the downstream region. If the speed of the jet is super(magneto)sonic in the reference frame of the obstacle, a second shock front forms in the sheath closer to the obstacle. Our results can be applied to collisionless quasiparallel shocks in many plasma environments.

Adiabatic Deceleration of Solar Energetic Particles as Deduced from Monte Carlo Simulations of Interplanetary Transport

Monte Carlo simulations of interplanetary transport are employed to study adiabatic energy losses of solar protons during propagation in the interplanetary medium. We consider four models. The first model is based on the diffusion-convection equation. Three other models employ the focused transport approach. In the focused transport models, we simulate elastic scattering in the local solar wind frame and magnetic focusing. We adopt three methods to treat scattering. In two models, we simulate a pitch-angle diffusion as successive isotropic or anisotropic small-angle scatterings. The third model treats large-angle scatterings as numerous small-chance isotropizations. The deduced intensity–time profiles are compared with each other, with Monte Carlo solutions to the diffusion-convection equation, and with results of the finite-difference scheme by Ruffolo (1995). A numerical agreement of our Monte Carlo simulations with results of the finite-difference scheme is good. For the period shortly after the maximum intensity time, including deceleration can increase the decay rate of the near-Earth intensity essentially more than would be expected based on advection from higher momenta. We, however, find that the excess in the exponential-decay rate is time dependent. Being averaged over a reasonably long period, the decay rate of the near-Earth intensity turns out to be close to that expected based on diffusion, convection, and advection from higher momenta. We highlight a variance of the near-Earth energy which is not small in comparison with the energy lost. It leads to blurring of any fine details in the accelerated particle spectra. We study the impact of realistic spatial dependencies of the mean free path on adiabatic deceleration and on the near-Earth intensity magnitude. We find that this impact is essential whenever adiabatic deceleration itself is important. It is also found that the initial angular distribution of particles near the Sun can markedly affect MeV-proton energy losses and intensities observed at 1 AU. Computations invoked during the study are described in detail.

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.

STOCHASTIC ACCELERATION IN RELATIVISTIC PARALLEL SHOCKS

We present results of test-particle simulations of both the first- and the second-order Fermi acceleration (i.e., stochastic acceleration) at relativistic parallel shock waves. We consider two scenarios for particle injection: (1) particles injected at the shock front, then accelerated at the shock by the first-order mechanism and subsequently by the stochastic process in the downstream region; and (2) particles injected uniformly throughout the downstream region into the stochastic process, mimicking injection from the thermal pool by cascading turbulence. We show that regardless of the injection scenario, depending on the magnetic field strength, plasma composition, and the turbulence model employed, the stochastic mechanism can have considerable effects on the particle spectrum on temporal and spatial scales too short to be resolved in extragalactic jets. Stochastic acceleration is shown to be able to produce spectra that are significantly flatter than the limiting case of N(E) ∝ E-1 of the first-order mechanism. Our study also reveals a possibility of reacceleration of the stochastically accelerated spectrum at the shock, as particles at high energies become more and more mobile as their mean free path increases with energy. Our findings suggest that the role of the second-order mechanism in the turbulent downstream of a relativistic shock with respect to the first-order mechanism at the shock front has been underestimated in the past, and that the second-order mechanism may have significant effects on the form of the particle spectra and its evolution.

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.

Injection and Interplanetary Transport of Near-Relativistic Electrons: Modeling the Impulsive Event on 2000 May 1

We present a Monte Carlo method to model the transport of solar near-relativistic electrons in the interplanetary medium, including adiabatic focusing, pitch-angle dependent scattering, and solar wind effects. By taking into account the angular response of the LEFS60 telescope of the EPAM instrument on board the ACE spacecraft, we transform the simulated pitch-angle distributions into the sectored intensities measured by the telescope. The goal is to deconvolve the effects of the interplanetary transport in order to infer the underlying injection profile and the radial mean free path of the electrons. We apply the model to the near-relativistic electron event observed on 2000 May 1, associated with an impulsive X-ray flare, type III radio bursts, and a narrow fast CME. The deconvolved interplanetary transport conditions reveal a long radial mean free path of 0.9 AU and pitch-angle dependent scattering. The eight observed sectored intensities are fitted in detail for more than 90 minutes, except for a short period (~12 minutes) right after the time of peak intensities. This discrepancy may suggest that the assumed scattering model performs more efficiently than the actual scattering processes at work. The resulting injection profile consists of two main components, an initial component lasting 2-3 minutes and probably related to a type III radio burst observed by WIND WAVES at ~10:21 UT, and a delayed component starting at the Sun around 10:35 UT with a typical injection decay timescale of ~0.5 hr. The delayed component may be related to the CME-driven shock.

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.

Diffusive shock acceleration to relativistic energies in the solar corona

Aims. We study the effect of magnetic geometry on the efficiency of diffusive shock acceleration (DSA) of protons in the solar corona with emphasis on conditions that may lead to the formation of so-called ground level enhancements (GLEs) where the protons are accelerated into energies ≳ 1 GeV. Methods. We use Monte Carlo simulations of DSA in a semirealistic large scale coronal magnetic field near a bipolar active region. This active region is assumed to be the source region of a coronal mass ejection (CME) driving a shock wave in the corona. The shock geometry evolves in time, and the obliquity angle goes through a wide range of values from perpendicular to quasi-parallel. We consider the effect of the evolving magnetic geometry on the acceleration efficiency in five selected field lines. Results. In most of the considered field lines the maximum proton energies are of the order of 100 MeV, which is rather typical for gradual solar energetic particle (SEP) events. We find that the DSA can be more effective on field lines where the shock starts out by being oblique and gradually turns quasi-perpendicular than on field lines where the shock starts perpendicularly.

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.

The 1990 May 24 solar cosmic-ray event

This paper presents an integrated analysis of GOES 6, 7 and neutron monitor observations of solar cosmic-ray event following the 1990 May 24 solar flare. We have used a model which includes particle injection at the Sun and at the interplanetary shock front and particle propagation through the interplanetary medium. The model does not attempt to simulate the physical processes of coronal transport and shock acceleration, therefore the injections at the Sun and at the shock are represented by source functions in the particle transport equation. By fitting anisotropy and angle-average intensity profiles of high-energy (>30 MeV) protons as derived from the model to the ones observed by neutron monitors and at GOES 6 and 7, we have determined the parameters of particle transport, the injection rate and spectrum at the source. We have made a direct fit of uncorrected GOES data with both primary and secondary proton channels taken into account.The 1990 May 24–26 energetic proton event had a double-peaked temporal structure at energies ∼ 100 MeV. The Moreton (shock) wave nearby the ‘flare core’ was seen clearly before the first injection of accelerated particles into the interplanetary medium. Some (correlated with this shock) acceleration mechanism which operates in the solar corona at a height up to one solar radius is regarded as a source of the first (prompt) increase in GOES and neutron monitor counting rates. The proton injection spectrum during this increase is found to be hard (spectral index γ ≈ 1.6) at lower energies (∼ 30 MeV) with a rapid steepening above 300 MeV. Large values of the mean free path (λ ≈ 1.8 AU for 1 GV protons in the vicinity of the Earth) led to a high anisotropy of arriving protons. The second (delayed) proton increase was presumably produced by acceleration/injection of particles by an interplanetary shock wave at height of ≈ 10 solar radii. Our analysis of the 1990 May 24–26 event is in favour of the general idea that a number of components of energetic particles may be produced while the flare process develops towards larger spatial/temporal scales.