Electrostatic turbulence in the Earth's central plasma sheet produced by multiple‐ring ion distributions

A mechanism to generate a broad spectrum of electrostatic turbulence in the quiet time central plasma sheet (CPS) plasma is discussed. We show theoretically that multiple‐ring ion distributions can generate short‐wavelength ( kλ de ≲ 1), electrostatic turbulence with frequencies ω ≲ kV j , where V j is the velocity of the j th ring. Using a set of parameters from measurements made in the CPS, we find that electrostatic turbulence can be generated with wavenumbers 10 −2 ≲ kλ de ≲ 1.0, and with real frequencies in the range 0 < ω r /ω pi < 10, and linear growth rates γ/ω pi > 0.01 over a broad range of angles relative to the magnetic field (5° < θ ≤ 90°). The fastest growing modes are caused by an ion ring drift instability and occur for nearly parallel propagating modes (5° < θ < 10°) with ω r ≲ ω pi at wavelengths comparable to the electron Debye length. We also find that lower hybrid waves and electron cyclotron waves can be excited for nearly perpendicular propagating modes (θ ≃ 90°). We compare these theoretical results with wave data from ISEE 1 using an ion distribution function exhibiting multiple‐ring structures observed at the same time. The theoretical results in the linear regime are found to be consistent with the wave data. Finally, we discuss these results in relation to nonlinear particle dynamics in the CPS which can generate the multiple‐ring ion distributions.