TY - JOUR

T1 - Allowed regions in the problem concerning dynamics of a charged particle in a superposition of dipole and uniform magnetic fields

AU - Kolesnikov, E. K.

AU - Klyushnikov, G. N.

PY - 2016/4/1

Y1 - 2016/4/1

N2 - 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 Stromer 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, the Earth’s magnetic field 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 charged particle dynamics in the composed field. The paper is devoted to the construction and investigation of the allowed regions 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.

AB - 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 Stromer 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, the Earth’s magnetic field 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 charged particle dynamics in the composed field. The paper is devoted to the construction and investigation of the allowed regions 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.

KW - allowed regions

KW - charged particles

KW - Hamiltonian

KW - integral of the motion

KW - magnetic field

UR - http://www.scopus.com/inward/record.url?scp=84976402800&partnerID=8YFLogxK

U2 - 10.3103/S1063454116020072

DO - 10.3103/S1063454116020072

M3 - Article

AN - SCOPUS:84976402800

VL - 49

SP - 191

EP - 195

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 2

ER -