Stably trapped proton limits for Jupiter

A general introduction to pitch-angle diffusion for Earth and Jupiter magnetospheres is given. The instabilities which might limit the trapped fluxes in the earth magnetosphere are identified as the interchange or ballooning mode, electrostatic loss cone modes, and electromagnetic ion cyclotron wave. The instability theory of the ion cyclotron wave is discussed. This wave can be unstable only if protons can be in cyclotron resonance with the wave. The instability growth rate is proportional to the cyclotron frequency, the fractional number density of fast particles, and the anisotropy of the fast particle distribution. The critical proton energy is the lowest energy for which the stably trapped limit applies, and is calculated to be 150 MeV at L = 2 and for 10 ion pairs/cu cm. Particles above the critical threshold energy are considered and their stability limit is approximately 3 x 10 to the 10th power/sq cm/sec divided by L to the 4th power.