Hydromagnetic waves and the trapped radiation: Part 3. Effects on protons above the proton belt

In parts 1 and 2 [Wentzel, 1961] it was shown that hydromagnetic waves in the magnetosphere cause a systematic drift of the mirror points of energetic protons. Above the proton belt these waves do not travel parallel to the dipole field. The systematic changes of the magnetic moment due to such waves are computed numerically for a variety of particle orbits and waves. The results are qualitatively similar to those for transverse waves unless the Larmor gyration carries the particle across a major part of a wave, in which case systematic changes are small. The hm waves above the proton belt are estimated to be nearly sinusoidal and are estimated to travel at a typical angle of 45° relative to the dipole field. It is found that such waves systematically raise the mirror points of proton orbits above the proton belt, especially if the mirror points are near the atmosphere. The numerical estimates indicate that this process is about as efficient as the lowering of the mirror points by random walk [Dragt, 1961], but the uncertain nature of the hm waves permits only the conclusion that the time needed to remove a proton into the atmosphere is longer than that estimated from random walk alone. The only mirror points that appear to be systematically lowered are near the upper boundary of the proton belt, which is determined jointly by systematic and random-walk effects.