Ion diffusion coefficients from resonant interactions with broadband turbulence in the magnetotail

Abstract

A potentially important source of hot ions within the central plasma sheet (CPS) is warm plasma sheet boundary layer (PSBL) ions which interact with broadband electrostatic waves and electric field drift toward the CPS. In the PSBL, the local interaction between the waves and particles can be assumed to be unmagnetized. The effect of the magnetic field is to organize wave and particle distributions in velocity space. Under these conditions, particle diffusion is, in general, two‐dimensional and is similar to magnetized diffusion. The general quasi‐linear equations describing such diffusion are presented assuming that a spectrum of waves is excited similar to the waves observed in the boundary layer. In order to apply the general quasi‐linear diffusion coefficients, two particle distribution models are assumed based on PSBL observations. One is for the outer edge and one is for the inner edge of the boundary. An expression for the unmagnetized dielectric function is given and evaluated for wave frequency and growth rate for the assumed particle distribution models. It is found that slow and fast mode ion‐sound waves can be unstable for the range of plasma parameters considered. The diffusion coefficients are then evaluated for resonant warm PSBL ion interactions with ion‐sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k space. For the model of the outer edge of the PSBL, pitch angle diffusion is found to dominate energy diffusion, whereas both types of diffusion can be important for the model of the inner edge of the PSBL. It is found that the characteristic time for resonant warm boundary layer ions to diffuse in velocity space is ∼10 min (for a wave electric field of 1 mV/m), which is approximately an ion bounce period. In addition, significant pitch angle and energy diffusion should occur resulting in isotropization of the warm PSBL ion beams to form the hot isotropic ion component in the CPS.