Linear analysis and PIC simulations of electron cyclotron harmonic instability driven by a subtracted-kappa velocity distribution

A recent study proposed a subtracted-kappa (SK) distribution that incorporates a loss cone and an extended high-energy tail. While the application of the SK distribution in the earlier work was limited to the instabilities at propagation parallel to the background magnetic field, B0, such a loss-cone distribution function is well suited for analyzing the instabilities whose free energy is drawn from the positive slope of the distribution, ∂f/∂v⊥>0, in directions perpendicular to B0. The present study explores the influence of the SK distribution on the electron cyclotron harmonic (ECH) instability with parameters suitable for ECH emissions found in Earth's magnetosphere. Linear theory analysis is carried out with a range of spectral indices (κ) and the parameters controlling the loss-cone depth and width. The analysis is complemented by one-dimensional particle-in-cell simulations for a subset of cases. It is shown that the maximum growth rates are found to increase monotonically with κ; for fixed κ, a wider loss-cone width generally yields a stronger instability growth; and a larger concentration of hot electrons leads to transition of unstable modes to lower harmonics. The simulations further reveal that the energetic electron scattering and wave saturation process as a result of wave–particle interactions depend on the wave propagation direction. This study represents the first systematic investigation of ECH instability driven by a loss-cone distribution with suprathermal tails modeled by the SK distribution and demonstrates the robust capability of SK distribution as a tool for analyzing kinetic waves and instabilities in space plasmas.