The St{\o}rmer problem for an aligned rotator

TL;DR

This paper analyzes the effective potential energy of charged particles around a rotating magnetized celestial body with combined magnetic and electric fields, revealing complex trapping regions influenced by rotation and field strength.

Contribution

It extends the classical Størmer problem by considering combined magnetic and electric fields and the effects of rotation, identifying new trapping region topologies.

Findings

Identification of multiple trapping regions influenced by rotation and field parameters

Demonstration of the division of the classical toroidal trapping region

Analysis of potential energy topology variations with magnetic field and rotation speed

Abstract

The effective potential energy of the particles in the field of rotating uniformly magnetized celestial body is investigated. The axis of rotation coincides with the axis of the magnetic field. Electromagnetic field of the body is composed of a dipole magnetic and quadrupole electric fields. The geometry of the trapping regions is studied as a function of the magnetic field magnitude and the rotation speed of the body. Examples of the potential energy topology for different values of these parameters are given. The main difference from the classical St{\o}rmer problem is that the single toroidal trapping region predicted by St{\o}rmer is divided into equatorial and off-equatorial trapping regions. Applicability of the idealized model of a rotating uniformly magnetized sphere with a vacuum magnetosphere to real celestial bodies is discussed.