Limit of temperature anisotropy relaxation by ion cyclotron waves: A statistical theory

The ion velocity distribution resulting from ion anisotropy reduction by th e growth of ion cyclotron waves has been investigated by the use of a Maxim um Entropy Principle. The anisotropy is reduced due to waves induced by an electromagnetic instability, but the system saturates before a completely i sotropic Maxwellian distribution is realized, and a nonzero level of anisot ropy remains in the final state. This is because the scattering process has a restriction; waves do not alter particle energy in the wave rest frame. Taking this restriction into account as an additional constraint, the final state is calculated by maximizing the entropy. The results show that the u pper bound of the plasma beta and anisotropy are inversely collelated, whic h is quantitatively in agreement with recent studies on satellite observati ons, numerical simulations, and laboratory experiments. (C) 2000 American I nstitute of Physics. [S1070-663X(00)03412-1].