The Electron Firehose and Ordinary-Mode Instabilities in Space Plasmas

Self-generated wave fluctuations are particularly interesting in the solar wind and magnetospheric plasmas, where Coulomb collisions are rare and cannot explain the observed states of quasi-equilibrium. Linear theory predicts that firehose and ordinary-mode instabilities can develop under the same conditions, which makes it challenging to separate the role of these instabilities in conditioning the space-plasma properties. The hierarchy of these two instabilities is reconsidered here for nonstreaming plasmas with an electron-temperature anisotropy T (ayen)> T (aSyen), where ayen and aSyen denote directions with respect to the local mean magnetic field. In addition to the previously reported comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, with a focus on the oblique firehose instability and the relatively poorly known ordinary-mode instability. Results show a dominance of the oblique firehose instability with a threshold lower than the parallel firehose instability and lower than the ordinary-mode instability. For stronger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding those of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the low beta [< 1] regimes, here it is rigorously shown that only the high beta [> 1] regimes are susceptible to these instabilities.