Enrichment of solar cosmic rays by heavy and ultraheavy elements: mathematical model and calculation results

This article is devoted to the development of a mathematical model of the phenomenon of enrichment of solar cosmic rays (SCR) with heavy elements with simultaneous processes of particle injection and SCR formation. It is believed that SCR are enriched in the solar atmosphere at the injection stage, after which SCR enriched in heavy elements propagate in interplanetary space without a significant change in composition. The developed model is based on the numerical solution of the Fokker — Planck equation describing the process of injection of particles into SCR during their collisionless interaction with Plasmon’s of ion-acoustic turbulence of the solar flare plasma. A modified particle-in-cell method is used for modeling. It has been established in the work that the main factor determining the shape and form of the graph of the dependence of the enrichment coefficient on the atomic number of elements is the ionization temperature of the flare plasma; variation of other parameters of the model (energy density of ion-acoustic turbulence, magnetic field strength) leads only to a «rotation» of the graph relative to the base element (oxygen) without a significant change in the shape of the graph. Thus, the shape of the graph of the dependence of the enrichment factor of elements on their mass numbers can be used in the procedure for estimating the ionization temperature of the flare solar plasma. It is shown that the enrichment of SCR with ultraheavy elements and neutron-rich isotopes of heavy elements can be explained by the interaction of plasma particles with ion-acoustic waves.