Kinetic instability of a gyrating ring distribution with application to satellite pickup in planetary magnetospheres

Abstract

We assume that pickup ions released by a satellite in a rapidly rotating planetary magnetosphere can be modeled by a gyrating ring distribution with a finite isotropic thermal velocity spread. This distribution can provide a source of free plasma energy for the excitation of plasma waves, and we explore the kinetic instability of the distribution. Specifically, we obtain general analytical solutions for the (linear) growth rate of oblique plasma waves due to resonant particle-wave interactions. Advantages of the analytical approach are that in the limits of either quasi-longitudinal or quasi-transverse propagation the solutions reduce to simple algebraic expressions that may be readily used to compare contributions from any specific harmonic resonance. Further, the analytical solutions are especially powerful for treating the case of oblique wave propagation, the standard procedure for which has hitherto been tedious and potentially inaccurate numerical integration. We obtain a marginal stability criterion appropriate to the ring distribution, and we use the analytical solutions to calculate the marginal stability frequency as a function of propagation angle for first-order cyclotron resonance with whistler-mode waves. Ramifications of the results for pickup ions and electrons released by satellites in the rapidly rotating magnetospheres of the giant planets are briefly discussed.