Orbital Characteristics Of Charged Particles In Dipole Magnetic Field

Since the discovery of cosmic rays in the 20 th century,the orbits of charged particles trapped in a dipole magnetic field(the St?rmer problem)plays fundamental roles in plasma physics,space science,and astrophysics.Since the earth’s magnetic field is similar to a dipole magnetic field,the St?rmer problem provides inspiration for related research directions such as the behavior of cosmic rays,the dynamics of particles in the upper atmosphere,the structure of radiation belts,and aurora.Therefore,it is extremely important to study the orbital properties of charged particles in the magnetic dipole field.Previous research mainly focused on particles with relatively low energy,so the guidance center theory can be applied.For example,in order to explain the dynamic system related to aurora and magnetic mirrors,an adiabatic approximation is used and it is assumed that the movement of charged particles in the magnetosphere is similar to the movement in a cyclotron with a constant magnetic field.In addition,the cycle track of the equatorial plane has been widely studied,and there are some cycle of cycle tracks,which have relatively low energy,with different track shapes.In addition,the periodic orbits of the equatorial plane have been extensively studied,and the meridian plane also has some branches of periodic orbits,all of which have relatively low energy and have different orbital shapes.But high energy particles usually have chaotic orbits except those on a periodic orbit or near stable periodic orbits.This article still follows the Dragt(1965)method,simplifying the St?rmer problem into a two-dimensional mamidian system,calculating of the maximal Lyapunov exponent of orbits of particles launched from the equatorial plane with an axial velocity(the angular velocity sets the length and energy scales of the system),and using Poincaré regressio,Poincaré maps and other methods to analyze the orbital characteristics of charged particles in the dipole magnetic field.It can be found that a significant set of quasi-periodic orbits around stable periodic orbits in the equatorial plane at high-energies.Particles in these orbits oscillate around the equatorial plane and their radial distance from the dipole can vary by a factor of ～ 2.They oscillate near the equatorial plane and have a larger radial range.These results may have significant implications on studies of charged particle motions in a nonuniform magnetic field and particles on these orbits may be detected in space and/or experiments on the Earth.