The mirror mode is a fundamental process in magnetized plasma environments. It plays many important roles in solar physics, interplanetary, planetary, astrophysical, and laboratory plasma environments, for example, it converts electromagnetic energy and particle kinetic energy (Kivelson & Southwood 1996), excites plasma waves and instabilities (Smith et al. 1969), modulates particle distributions (Yao et al. 2018b), and is suggested as a significant source of turbulent energy (Pokhotelov et al. 2003) and serves as messengers of solar corona (Russell et al. 2008). The most common mirror mode is in space, for example, it is observed to be full of Earth magnetosheath and can exist in the Earth magnetosphere for a long time. These structures are generally suggested to be magnetohydrodynamics (MHD) scale and static in the plasma frame. They display anticorrelation between magnetic and plasma pressures. The spatiotemporal scales and three-dimensional (3D) structures, evolution processes, and other important effects (e.g., drift, finite Larmor radius effect, non-Maxwellian ion distribution, and electron temperature influence) have been extensively studied in the past half century (e.g., Hasegawa 1969; Southwood & Kivelson 1993; Chisham et al. 1998; Pokhotelov et al. 2000, 2013; Gary & Karimabadi 2006; Genot et al. 2009; Hellinger et al. 2009). The studies on the mirror mode were mostly confined to the MHD scale. Numerical simulations and theoretical studies further revealed their kinetic effects, although the fundamental theoretical framework is still at MHD scale and lacks support from observations. If the electron distribution is anisotropic (with perpendicular temperature exceeding the parallel), the electrons become unstable and would excite the electron mirror-mode instability to remove the free energy. This instability was first discovered by Basu & Coppi (1982), and subsequently detailed by Basu & Coppi (1984), Migliuolo (1986), Marchenko et al. (1988), and more recently by Gary & Karimabadi (2006), Pokhotelov et al. (2013), and Hellinger & Štverák (2018). This electron mirror-mode instability condition is similar to the MHD-scale mirror mode and can be expressed as 





, where βe⊥, Te⊥, and Te∥ denote electron perpendicular plasma beta and perpendicular and parallel electron temperature, respectively. This has been theoretically predicted using a linear calculation (Pokhotelov et al. 2000) and also found in more precise numerical simulations (for example, including the effect of off-diagonal terms in dielectric tensor elements for the mirror instability) by Noreen et al. (2017). The contribution of electrons in the mirror instability in the quasilinear regime was then also discussed by Noreen et al. (2017). Historically, the electron mirror mode has been studied in theories and numerical simulations. But so far there have been few unambiguous observations of their existence because the capability to resolve electron-scale structures has been strongly limited by the insufficient measurement resolution of satellite-borne instrumentation. Using magnetic field data obtained from the spacecraft AMPTE-IRM and Equator-S, Treumann & Baumjohann (2018) presented observational evidence for the electron mirror mode in the Earth's magnetosheath. Low-frequency whistler waves were also observed and were used to diagnose the effect of anisotropic electron temperature on the mirror mode. These observations suggest that the whistler waves were probably related to the trapped electrons for which the trapping condition was provided by the magnetic depressions caused by the electron mirror branch. The study also pointed out that high temporal resolution observations are required for the confirmation of the electron mirror mode and its responsibility for electron trapping and wave excitation. In the recent Magnetospheric Multiscale (MMS; Burch et al. 2016) studies, similar low-frequency whistler waves were observed inside mirror-mode structures by Ahmadi et al. (2018) with a detailed in-depth investigation. The electron temperature anisotropy was suggested to provide a favorable environment for the growth of whistler waves. This result indicates the possible existence of localized electrons that were trapped by the electron mirror branch. Similar observations can be found in Breuillard et al. (2018), which observed whistler waves in mirror-mode structures with perpendicular electron temperature anisotropy.
Citation: Chisham et al. 1998
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