On the Dynamics of Charged Particle Close to Equatorial Plane of Earth in the Störmer Problem: Cylindrical Case of Dipole Magnetic Field

Document Type : Research Paper

Author
Sergey V. Ershkov 1 , 2 , 3
1 Sternberg Astronomical Institute, M.V. Lomonosov's Moscow State University, 13 Universitetskij prospect, Moscow 119992, Russia
2 Plekhanov Russian University of Economics, Scopus number 60030998, Stremyanny lane, 36, Moscow, 115054, Russian Federation
3 MIREA - Russian Technological University, 78 Vernadsky Avenue, Moscow 119454, Russia
10.22055/jacm.2025.48054.4946
Abstract
The classical Störmer problem (dynamics of charged particle in Earth’s magnetic field) has been fully considered hereby since the first part of such problem has been successfully solved recently for the case of dipole magnetic field associated with the spherical case (of a magnetized sphere). New semi-analytical solution along with illuminating approach have been presented for the second part of Störmer problem (associated with the cylindrical case of classical dipole magnetic field of a magnetized infinite cylinder) for the partial class of charged particle’s motions close to the equatorial plane of Earth. Aforementioned motions, determined by Lorentz force in non-relativistic case, thereby are explored semi-analytically with presenting by graphical plots. Revisited Störmer problem are reduced to 3 nonlinear ODEs of 1st order. Analytical part of solution is presented in polar coordinates which can be transformed then to cartesian ones. Resulting Earth’s global magnetic field can be approximated by a linear combination of the expressions provided for the spherical and cylindrical cases (with appropriate constant factors which indicate the contribution of each magnetic field to the real magnetic field of Earth). The application is vital for protecting Earth’s atmosphere from solar wind.
Keywords
s equatorial plane
s magnetic field
Earth&rsquo
s radiation belts
Dipole magnetic field of cylinder
Dynamics of charged particle
Stö
rmer problem
Subjects

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Journal of Applied and Computational Mechanics
Volume 12, Issue 1
Winter 2026
Pages 31-39