Abstract
The change of the mirror points of trapped particles under displacements of the guiding centers across the lines of force is studied in a dipole field with small-amplitude perturbations whose periods are of the order of the particles' drift period. It is demonstrated that there is no general principle that would cause the constancy of the second adiabatic invariant to an order higher than that of the third invariant. The diffusion of particles, owing to many random disturbances, is anisotropic, but only in the equatorial plane clearly one-dimensional. For higher-latitude mirror points, the diffusion along the lines of force cannot be neglected, though the direction of maximum diffusion coefficient is essentially across field lines, being somewhat inclined with respect to lines of constant latitude. The degree of anisotropy depends on the relative importance of the two main components into which the perturbation is resolved. It is argued that the observed proton distribution in the outer belt can be explained only by a superposition of a diffusion across the lines of force, which occurs with constant μ,the magnetic moment invariant, and a process that mixes particles along the lines of force at about constant energy and thus violates μ.
Published Version
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