Electron–positron planar orbits in a constant magnetic field

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....

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Bibliographic Details
Published inPhysica. D Vol. 404; p. 132349
Main Authors Gonzalez Leon, M.A., Mateos Guilarte, J., de la Torre Mayado, M.
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.03.2020
Subjects
Bifurcation diagram
Elliptic coordinates
Integrable systems
Bifurcation diagram
Elliptic coordinates
Integrable systems
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Summary: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. •The dynamics of a pair electron–positron in a constant magnetic field is described.•The original system is reduced to a Coulomb center plus a harmonic oscillator.•Separability in Euler elliptic coordinates is constructed.•The bifurcation diagram unveils the behavior of the different types of orbits.•A complete classification of the orbits for both problems is performed.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2020.132349