The allowed regions in the problem concerning dynamics of a charged particle in a superposition of dipole and uniform magnetic fields

Abstract

The motion of charged particles in the Earth’s magnetic field has been of interest to mathematicians and physicists in connection with the study of the polar aurora and cosmic rays. In 1907 norwegian mathematician Stormer gave the mathematical formulation of this problem. It became the problem of great importance with the discovery of the Van Allen radiation. As is known that the magnetic field of the Earth can be considered approximately as a superposition of dipole and uniform magnetic fields, and the dipole’s magnetic moment is either parallel or antiparallel to the induction of the uniform field. Thus, the problem concerning the dynamics of the charged particle in the magnetic field of the Earth is reduced to that of the dynamics of the charged particle in the composed field. The paper is devoted to the construction and investigation of the allowed regions in the problem of dynamics of charged particles in a superposition of dipole and uniform magnetic fields for positive values of Stormer’s constant γ and the same orientation of magnetic moment and uniform field. Refs 4. Figs 1.