## Adiabatic invariant trapped radiation shells and cosmic ray cutoffs in models of the magnetosphere distorted by the solar wind plasma |

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### Contents

II REVIEW OF PREVIOUS WORK | 7 |

F A New First Integral | 17 |

G Trapped Radiation | 20 |

5 other sections not shown

### Common terms and phrases

actual field adiabatic invariants Alfen motion algebra allowed region azimuth becomes bounce calculated chain rule components computed constant along lines coordinates correction term cos9 Cosmic Ray Cutoffs defined dipole field drift motion drift velocity earth radii earth's field earth's surface energy equations of motion equatorial evaluated expressed field model Finch and Leaton gauss Gaussian coefficients geomagnetic field given gradient guiding center gyrating Hones input point integral invariant Invariant Magnetic Shells invariant of motion invariant shells invariant surfaces Lagrangian Larmour cycle Larmour radius line of force magnetic equator magnetic scalar potential magnetosphere magnetostatic field mirror point obtain partial differential equation Particle mirroring perpendicular plots predicts relativistic mass result right hand side second term solar wind spherical harmonic spherical harmonic expansion St^rmer static magnetic field subroutine tabulated theory trajectory transformation transverse trapped particle trapped radiation vector potential vertical cutoff rigidity zero