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The effect of hydromagnetic waves upon the motion of charged particles trapped in the geomagnetic field is studied. Application is made to the proton component of the Van Allen radiation belt. It is shown, in agreement with the suggestion of Welch and Whitaker, that hydromagnetic waves of low frequency and amplitude are able to account for the rapid decrease in proton flux that delimits the outer edge of the inner zone of the Van Allen radiation belt. Both the location of the boundary of the inner zone and the ratio between the proton fluxes in the inner and outer zones are obtained. It is found that, near 2 earth radii from the earth's center, the maximum energy of the trapped protons decreases with geocentric distance as r−11.
Alex J. Dragt (Sun,) studied this question.