Non-Homogeneous Charge-Consistent Model for Acceleration of Iron in the Solar Corona

Acceleration of iron ions by a spherical shock wave moving through non-homogeneous solar corona is considered. The energy dependence of the mean charge of iron, _Fe(E), is determined by the characteristic acceleration time, T _a, trapping time, T _tr, and time for charge changes, T _q. The latter varies along with plasma number density during the propagation of the shock wave in the corona. Our calculations have demonstrated that adiabatic energy changes, Coulomb losses and shock broadening do not sufficiently influence the dependence _Fe(E). According to our estimations, the photoionizing processes can scarcely affect the ionic states of accelerated iron, except probably for the most powerful X10 class events.     

Acceleration of multiply charged ions of the anomalous cosmic-ray component at the heliosphere boundary

The formation of the energy spectra of heavy ions at the front of a parallel shock is considered taking into account ionization and recombination during the acceleration. An analytic solution for ions with three possible charge states is obtained and applied to the acceleration of the anomalous cosmic-ray component at the boundary of the heliosphere. In addition, a more general numerical model for such acceleration at a spherical shock front is developed and used to obtain the energy dependence of the mean charges for C, N, O, Ne, Si, S, Ar, and Fe ions. The model implies that highly excited ions begin to dominate over ions with low charges at energies above 1 MeV/nucleon, in agreement with observational data.     

A charge-consistent model for the acceleration of iron in the solar corona: Nonisothermal injection

A charge-consistent numerical model for the joint (regular and stochastic) acceleration of iron by a spherical shock wave propagating in the solar corona is proposed. Large-scale irregularities of the plasma density and the nonisothermal injection of ions are taken into account. For the case of iron, the energy dependence of the mean charge q_Fe(E) is determined by the relationships between the characteristic acceleration time, the charge-variation time for the accelerated ions, and the time for their trapping in regions of high plasma density. Due to the global inhomogeneity of the medium, these relationships depend on the shock speed. Our calculations indicate that photoionization by soft X-rays from flare regions can substantially change the charge states of heavy ions only in the most powerful solar events (both impulsive and gradual).     

Charge state distributions of iron in gradual solar energetic particle events

The energy and charge spectra of Fe ions accelerated in gradual events are calculated numerically. Our results are compared with the available observations. Stripping of Fe ions by thermal electrons and protons during ion acceleration in the solar corona results in the dependence of mean charge barq _Feon energy. We consider the influence of varying plasma parameters (temperature T, number density N, and spectral index of turbulence S) on the charge distribution of iron. Our calculations indicate T10⁶ K and N(0.5–1)×10¹⁰ cm^–3at the accelerating site, provided the characteristic acceleration time is about 1 s. The calculated charge spectra for S>2 and S<2 turn out to be different, but some theoretical and experimental uncertainties do not yet allow this parameter to be extracted from observational data. The theoretically obtained charge distributions of Fe could be important in the light of ACE spacecraft data which are currently available for analysis.     

Heavy Ions From the 6 November 1997 sep Event: a Charge-Consistent Acceleration Model

Based on the observed dependence of the mean charge of several elements (C, O, Ne, Mg, Si and Fe) on energy for the gradual event of 6 November 1997 we deduce plasma parameters in the accelerating site. This is done in the framework of a charge-consistent acceleration model which incorporates ionisation and recombination processes during heavy ion energization by a parallel shock wave. To obtain good fits to observations we have to assume for the product of the characteristic acceleration time and number density T ^q _ac N (3–10) ×10⁹ s cm^–3 and temperature T=10⁶ K of a plasma where all the elements under consideration originated.     

Effect of coulomb losses on the spectra of heavy particles accelerated in prolonged solar events

This paper examines the possibility of using the energy spectra of accelerated solar cosmic-ray ions and features formed by Coulomb losses to study the solar plasma (the power-law index S for the scattering turbulence, particle number density N, and temperature T of the background medium). For an individual solar flare, Coulomb losses can be manifest to different degrees in the spectra of different ions, providing a means to determine S. A comparison of theoretical spectra for H, He, C, O, and Fe ions with observed spectra for the prolonged solar flare of October 20, 1995 yields S≈3, N≈5×10⁹ cm^?3, and T≈10⁶ K, assuming that the characteristic time scale over which these particles gain energy is about a second.