# Effects of a quadrupolar magnetic term in a Generalized St\"ormer problem

## TL;DR

This paper introduces a generalized St"ormer problem incorporating quadrupolar magnetic terms to analyze charged particle dynamics around magnetic planets, revealing new stable trajectories and stability behaviors influenced by magnetic field complexity.

## Contribution

It presents a novel generalized model of the St"ormer problem that includes quadrupolar magnetic effects, expanding understanding of particle motion in planetary magnetospheres.

## Key findings

- Existence of specific trajectories due to quadrupolar magnetic terms
- Analysis of equilibrium and stability behaviors for charged dust grains
- Identification of orbital frequencies influenced by magnetic field components

## Abstract

A new generalized St\"ormer problem is proposed. The charged particles motion around a rotating axisymmetric magnetic planet is studied using various conditions mainly in planetary magnetospheres. It is shown that the existence of specific trajectories is due to the quadrupolar and dipolar magnetic terms. Moreover, the equilibrium and stability behaviors and the corresponding orbital frequencies for various kinds of charged dust grains are treated giving rise to a new model describing the dynamical system and leading to more interesting results.