# Electron-positron planar orbits in a constant magnetic field

## TL;DR

This paper classifies and analyzes the various planar orbits of two equal-mass, opposite-charge particles in a constant magnetic field, reducing the problem to a Coulomb center plus harmonic oscillator and explaining the bifurcation diagram.

## Contribution

It provides a complete classification of orbits and a detailed bifurcation analysis for the classical two-particle system in a magnetic field.

## Key findings

- Orbits are classified based on system parameters.
- The bifurcation diagram of the system is fully explained.
- Dynamics of the two particles are described in detail.

## Abstract

The different types of orbits in the classical problem of two particles with equal masses and opposite charges on a plane under the influence of a constant orthogonal magnetic field are classified. The equations of the system are reduced to the problem of a Coulomb center plus a harmonic oscillator. The associated bifurcation diagram is fully explained. Using this information the dynamics of the two particles is described.