Differential Equations, Chaos and Variational Problems

Volume 75 of the series Progress in Nonlinear Differential Equations and Their Applications pp 175-194

Chaos in the Störmer Problem

  • Rui DilãoAffiliated withNonlinear Dynamics Group, Instituto Superior Técnico
  • , Rui Alves-PiresAffiliated withFaculdade de Engenharia, Universidade Católica Portuguesa

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We survey the few exact results on the Störmer problem describing the dynamics of charged particles in the Earth magnetosphere. The analysis of this system leads to the the conclusion that charged particles are trapped in the Earth magnetosphere or escape to infinity, and the trapping region is bounded by a torus-like surface, the Van Allen inner radiation belt. In the trapping region, the motion of the charged particles can be periodic, quasi-period or chaotic. The three main effects observed in the Earth magnetosphere, radiation belts, radiation aurorae and South Atlantic anomaly, are described in the framework described here. We discuss some new mathematical problems suggested by the analysis of the Störmer problem.


Störmer problem chaos Van Allen inner radiation belt quasi-periodic motion