First Correction to the Second Adiabatic Invariant of Charged-Particle Motion

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  • T. G. Northrop
    Lawrence Radiation Laboratory, University of California, Berkeley, California
  • C. S. Liu
    Lawrence Radiation Laboratory, University of California, Berkeley, California
  • M. D. Kruskal
    Plasma Physics Laboratory, Princeton University, Princeton, New Jersey

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<jats:p>The second term has been obtained in the asymptotic series for the second (longitudinal) adiabatic invariant of charged-particle motion in a static magnetic field. This correction to the lowest-order invariant has two sources: the correction to the lowest-order magnetic moment and the integrated effect of the guiding-center drift across the field lines. The second term is found to vanish at the mirror points; therefore, during its motion between mirror reflections, the guiding center deviates from the surface on which the lowest-order invariant is constant and intersects this surface at reflection.</jats:p>

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