L. G. Kocharov

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.

Injection of 10 MeV Protons in Association with a Coronal Moreton Wave

We report extreme-UV observations of the coronal Moreton wave and concurrent observations of ~10-100 MeV protons. Observations are carried out with the Extreme-UV Imaging Telescope and the Energetic and Relativistic Nuclei and Electron instrument on board the SOHO spacecraft. We study the proton events associated with coronal mass ejections (CMEs) centered near the central meridian. Observations reveal the initial injection of 10 MeV protons during the period when the coronal Moreton wave was traversing the western hemisphere of the Sun, this being an early signature of the CME launch. Acceleration of the CME-associated protons starts during the CME liftoff, while the main proton production occurs several hours later, when the CME expands in the interplanetary medium. Between the first proton production and the maximum intensity time, a spectral softening is observed. We analyze in detail the 1997 September 24 event. Development of the event indicates that the spectral softening may be due to a change in the acceleration regime, so the proton production starts with the less intensive but hard-spectrum injection and then moves to the more intensive but soft-spectrum injection farther from the Sun.

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.

Analysis of the ground level enhancement on 17 May 2012 using data from the global neutron monitor network

We have analyzed the data of the world neutron monitor network for the first ground level enhancement of solar cycle 24, the ground level enhancement (GLE) on 17 May 2012. A newly computed neutron monitor yield function and an inverse method are applied to estimate the energy spectrum, anisotropy axis direction, and pitch angle distribution of the high-energy solar particles in interplanetary space. The method includes the determination of the asymptotic viewing cones of neutron monitor stations through computations of trajectories of cosmic rays in a model magnetosphere. The cosmic ray particle trajectories are determined with the GEANT-based MAGNETOCOSMICS code using Tsyganenko 1989 and International Geomagnetic Reference Field models. Subsequent calculation of the neutron monitor responses with the model function is carried out, that represents an initial guess of the inverse problem. Derivation of the solar energetic particle characteristics is fulfilled by fitting the data of the global neutron monitor network using the Levenberg-Marquardt method over the nine-dimensional parameter space. The pitch angle distribution and rigidity spectrum of high-energy protons are obtained as function of time in the course of the GLE. The angular distribution appears quite complicated. It comprises a focused beam along the interplanetary magnetic field line from the Sun and a loss-cone feature around the opposite direction, possibly indicative of the particle transport in interplanetary magnetic field structures associated with previous coronal mass ejections.

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.

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.

Charge state distributions of iron in impulsive solar flares: Importance of stripping effects

A model of stochastic acceleration of heavy ions by Alfven wave turbulence has been developed. It takes into account spatial diffusion, Coulomb losses, and the possibility of charge changes for ions during stochastic acceleration. The main processes influencing the ionic charge states are the stripping by thermal electrons and protons as constituents of a surrounding medium and dielectronic and radiative recombination. We have calculated energy spectra and charge distributions of nonthermal Fe ions as a sample species. The dependence of the charge distributions and energy spectra of iron on the parameters of the plasma (temperature and number density) is studied. We compare our results with measurements to date of the mean charge of iron in impulsive solar flare events and conclude that they indicate source plasma ionization temperatures between 6□×106 and 107 K.

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

Recent observations on board the Solar and Heliospheric Observatory (SOHO) indicate that acceleration of solar energetic particles (SEPs) at intermediate scales in the solar corona, between flare acceleration and interplanetary CME-driven shock acceleration, significantly contributes to the production of >10 MeV protons. Coronal shocks seem to be the most plausible candidate for the post-impulsive phase acceleration, which emits ~1-100 MeV protons into the interplanetary medium for about 1 hr after the flare. We have employed a Monte Carlo technique to model the diffusive shock acceleration of protons in a turbulent layer at the base of the solar wind. We find that a power-law spectrum of energetic protons can be emitted from the trailing turbulent layer left behind the shock into the solar wind for a few tens of minutes after the CME liftoff. In contrast to an earlier expectation, the propagation direction of the shock wave is found not to be crucial. Both outward-propagating and refracting shocks can load the corona with energetic protons. Those protons escape into the interplanetary medium well after the passage of the shock. We have studied successive transformations of the particle spectra during shock acceleration, coronal transport, and possible reacceleration, for different populations of seed particles. The simulated production time profiles and energy spectra are found to be consistent with observations of the 1996 July 9 event by the Energetic and Relativistic Nuclei and Electron (ERNE) instrument on board SOHO. The new model can be easily combined with our previous interplanetary transport models, forming a basis on which to interpret SEP observations made at 1 AU.

Energetic (∼10–65 MeV) protons observed by ERNE on August 13–14, 1996: Eruption on the solar back side as a possible source of the event

The onset of the >10-MeV proton event of August 13-14, 1996, revealed a velocity dispersion, which is a signature of its solar origin, but no associated soft X ray flare was observed. The LASCO CME observations, the presence of AR 7981 beyond the west limb, and type II and IV radio burst timing with respect to the proton event onset indicate that the parent solar eruption may be centered on the back side of the Sun, at ∼150°W. In such a case, expanding CME-associated wave can reach the Earth-connected interplanetary magnetic field line in ∼1 hour and so give rise to the >10-MeV proton event observed with the Energetic and Relativistic Nuclei and Electron (ERNE) instrument onboard SOHO. We verify this hypothesis against observational data and conclude that a solar back side eruption is the most plausible explanation of the August 13, 1996, event. We compare the August 13, 1996, event with events associated with Earth directed CMEs and show that the August 13, 1996, event reveals many properties common to >10-MeV proton events originating from solar eruptions centered ∼90° away from the root of the Earth-connected interplanetary magnetic field line. In such events, the first detected protons are released ∼1 hour after the start time of type II and IV radio bursts. The first injection spectrum is essentially harder than the spectrum at the intensity maximum; that is, the hard but less intensive proton production is followed by the major soft-spectrum production when CME expands farther from the Sun.

DYNAMICAL CYCLES IN CHARGE AND ENERGY FOR IRON IONS ACCELERATED IN A HOT PLASMA

We consider a unified model of Fe ion acceleration in the solar corona. The model comprises charge-changing processes, Coulomb energy losses, and both regular and stochastic acceleration. At a given acceleration scenario, the type of acceleration is found to have a minor effect on the mean charge states, but the shapes of the charge-state distributions produced by regular acceleration and by stochastic acceleration are different. During a continual acceleration at coronal temperatures, iron ions typically follow rising trajectories on the charge-energy plane. These trajectories are situated below the mean equilibrium charge curve defined from the balance of ionization and recombination at fixed energy. During stopping, the iron ions cross the equilibrium charge curve and run through a series of charge states above the mean equilibrium charge at current energy, because the Coulomb deceleration rate significantly exceeds the rate of the ion recombination in a hot plasma. As a result, the variety of possible trajectories on the ion charge-energy plane turns out to be much wider than would be expected based on the equilibrium charge-state approximation. In particular, we find dynamical cycles in charge and energy, so that accelerated and highly stripped ions may reappear at low energies. We also find that the equilibrium charge curve cannot be reproduced without strong reduction in the total number of accelerated particles. This implies that the observed iron charge-state distributions essentially depend on the scenario of their acceleration and transport.