Enhancement of wave growth for warm plasmas with a high‐energy tail distribution

Abstract

We consider the classical linear theory of electromagnetic wave growth in a warm plasma for waves propagating parallel to a uniform ambient magnetic field. Wave growth rates γ are calculated for ion‐driven right‐hand mode waves for Kappa (bi‐Lorentzian) and Maxwellian particle distribution functions. Systematic calculations of γ are carried out for various values of the spectral index κ, the temperature anisotropy A+ = 1 ‐ (T⊥+ / T∥+), and the ratio β+ of plasma pressure to magnetic pressure, appropriate to the solar wind. When the anisotropy is low (A+ ≪ 1), the wave growth is limited to frequencies below the proton gyrofrequency, and the growth rate increases dramatically as the spectral index κ is reduced (i.e., as the high‐energy tail becomes more pronounced). The growth rate for any Kappa distribution greatly exceeds (often by several orders of magnitude) that for a Maxwellian with the same bulk properties. For large thermal anisotropy (T∥+, ≫ T⊥+) the growth rate from either distribution is greatly enhanced. In comparison to a Maxwellian distribution the growth rates from a Kappa distribution are generally larger, and significant wave growth occurs over a broader range of frequencies. Evidently, the theory is important in the study of microinstabilities in space plasmas in which a high‐energy tail distribution is generally present.