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Register a new userElectron Firehose Instabilities in High-$beta$ ICM shocks
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Sunjung Kim
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The preacceleration of electrons through reflection and shock drift acceleration (SDA) is essential for the diffusive shock acceleration (DSA) of nonthermal electrons in collisionless shocks. Previous studies suggested that, in weak quasi-perpendicular ($Q_perp$) shocks in the high-$beta$ ($beta=P_{rm gas}/P_{rm B}$) intracluster medium (ICM), the temperature anisotropy due to SDA-reflected electrons can drive the electron firehose instability, which excites oblique nonpropagating waves in the shock foot. In this paper, we investigate, through a linear analysis and particle-in-cell (PIC) simulations, the firehose instabilities driven by an electron temperature anisotropy (ETAFI) and also by a drifting electron beam (EBFI) in $betasim100$ ICM plasmas. The EBFI should be more relevant in describing the self-excitation of upstream waves in $Q_perp$-shocks, since backstreaming electrons in the shock foot behave more like an electron beam rather than an anisotropic bi-Maxwellian population. We find that the basic properties of the two instabilities, such as the growth rate, $gamma$, and the wavenumber of fast-growing oblique modes are similar in the ICM environment, with one exception; while the waves excited by the ETAFI are nonpropagating ($omega_r=0$), those excited by the EBFI have a non-zero frequency ($omega_r eq0$). However, the frequency is small with $omega_r<gamma$. Thus, we conclude that the interpretation of previous studies for the nature of upstream waves based on the ETAFI remains valid in $Q_perp$-shocks in the ICM.
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The selfgenerated 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 the firehose and the ordinary-mode instabilities can develop under the same conditions, confusing 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 $T_parallel > T_perp$, where $parallel$ and $perp$ denote directions with respect to the local mean magnetic field. In addition to the previous comparative analysis, here the entire 3D wave-vector spectrum of the competing instabilities is investigated, paying particular attention to 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 larger anisotropies, the ordinary mode can grow faster, with maximum growth rates exceeding the ones of the oblique firehose instability. In contrast to previous studies that claimed a possible activity of the ordinary-mode in the small $beta [< 1]$ regimes, here it is rigorously shown that only the large $beta [> 1]$ regimes are susceptible to these instabilities.
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