G. A. Kovaltsov

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.

An Analytic Description of Coronal Proton Trapping

Analytic steady state solutions of the focused diffusion equation are used to deduce proton trapping time, τtrap, an average residence time for all particles injected into the magnetic loop. We take into account the effect of magnetohydrodynamic (MHD) turbulence and the divergence of magnetic field lines in both the corona and chromosphere of the Sun. Numerical simulations of pitch-angle scattering have then been used to check the analytic solutions and to ascertain boundary conditions for the focused diffusion equation. Results are obtained for several different functional forms of B(ζ), the magnetic field as a function of distance along a particular coronal field line. Five cases have been studied, from B constant along the coronal portion of the loop to B(ζ) corresponding to a force-free magnetic structure. The results indicate that a divergence of the magnetic field in the coronal portion of the loop can significantly increase the trapping time, no matter how small the mean free path may be. Derived analytic expressions for τtrap can be used to calculate the intensity of secondary emissions from the loop-top sources. Analytic time-dependent solutions of the focused diffusion equation are considered in the case of constant coronal B to find the basic decay time of the trapped proton number, τdecay, an asymptotic value of the exponential decay time when the time tends to infinity. In the case of variable B in the coronal portion of the loop, Monte Carlo simulations of pitch-angle scattering have been employed to calculate τdecay in a wide range of parameters. However, we have also obtained analytic expressions for how the characteristic time scales with parameters of the magnetic loop. Deduced analytic expressions for τdecay can be used to calculate ion acceleration in the escape-time approximation and to interpret the decay phase of solar gamma-ray flares. Magnetic focusing in the coronal portion of the loop makes acceleration more efficient than would be expected in the approximation without coronal focusing.

TRAPPING AND PRECIPITATION OF PROTONS DURING STOCHASTIC ACCELERATION IN MAGNETIC LOOPS

We study confinement of particles during the stochastic acceleration in coronal magnetic loops. Analytic solutions and Monte Carlo simulations of the coordinate-dependent focused-diffusion transport and acceleration are employed to deduce the effective leaky-box escape time, τesc. The rigorously correct expression of the escape time yields the leaky-box-model spectrum of accelerated particles, which exactly coincides with the high-energy asymptote of a spectrum deduced by including all spatial dependencies into the diffusion equation. Besides the application to the acceleration studies, the deduced escape time allows one to relate the spectra of protons generating neutrons and γ-rays in the coronal portion of the loop to the spectra in and below the chromosphere. As an illustration, we discuss the model implications for γ-ray and neutron observations of the behind-the-limb flares.

The 1990 May 24 solar flare and cosmic ray event

We have analyzed data on solar protons, neutrons, electrons, gamma‐ray, optical and microwave emissions for the 1990 May 24 solar flare. Taking into account high energy neutron and gamma‐ray observations, we have suggested two neutron injections occurred during the flare. These two injections are called f‐ (first) and s‐ (second). Two components of interacting protons correspondingly existed to produce these neutrons at the Sun. The flare gave also a rise to solar cosmic ray event, which was detected by the neutron monitor network and GOES satellites. Two components of protons were observed in the interplanetary medium (p‐ (prompt) and d‐ (delayed) components). A possible spectrum of the s‐component of interacting protons coincided with injection spectrum of p‐component of interplanetary protons. For this reason, s‐ and p‐ components of protons may be considered as different portions of a single population of accelerated particles in the solar corona. The net result is that three proton components (f‐, p/...