Electrostatic waves near the field reversal region in the Earth's magnetotail

The general stability properties of ion distributions with velocity space holes of the type expected in the Earth's central plasma sheet as a consequence of chaotic ion acceleration is investigated. It is shown that such distributions are unstable to electrostatic waves with wave vectors located in a narrow angular region about the Sun-Earth line. These waves can be generated in the magnetotail midplane even if the transition layer in velocity space between the background plasma and an empty hole region is of the order of the ion thermal velocity. Therefore these electrostatic waves would form a robust and persistent component of the electrostatic wave activity in the presence of the background ion hole distributions. The solution of the quasi-linear equation shows that the saturation of the ion hole instability occurs because of velocity space trapping of the low energy background ions and results in a flattening of the reduced distribution function in the region of the original velocity space hole. The energy level of the excited waves in the vicinity of the magnetotail field reversal region is obtained as a function of the ion hole parameters.