PARTICLE MOTIONS IN A MAGNETIC FIELD
BROWN UNIV PROVIDENCE RI LEFSCHETZ CENTER FOR DYNAMICAL SYSTEMS
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The report is concerned with rigorously establishing the existence of quasi-periodic motions for a charged particle in a magnetic field. The following results are obtained The existence of quasi-periodic motions lying near the equatorial plane for a charged particle moving under the influence of the earths magnetic field considered here as a magnetic dipole. This proves the stability of the periodic equatorial orbits for small values of energy. The existence of quasi-periodic motions which need not lie near the equator, exhibiting thereby the trapping of particles as observed in the Van Allen radiation belt. Moreover, these motions may penetrate arbitrarily close to the dipole, a result which was somewhat unexpected. This existence of quasi-periodic motions in a rotationally symmetrix magnetic minor field.
- Atmospheric Physics
- Nuclear Physics and Elementary Particle Physics