Ion/ion and electron/ion cross‐field instabilities near the lower hybrid frequency

Abstract

Instabilities near the lower hybrid frequency are investigated by numerically solving the linear Vlasov electromagnetic dispersion equation. The configuration is that of two unmagnetized ion components, a less dense beam and a more dense core, streaming across a uniform magnetic field with magnetized electrons in the zero momentum frame. All three components are considered to have similar temperatures. This paper studies the parametric dependences of maximum growth rate for three distinct modes: the electron/ion beam modified two-stream instability, the electron/ion core modified two-stream instability, and the ion/ion lower hybrid instability. In the electrostatic limit the electron/beam instability has a lower threshold and larger growth rate than its electron/core counterpart. Except near equal beam and core densities, our results also suggest that the electron/beam instability has a maximum growth rate that is equal to or greater than that of the ion/ion instability for all plasma beta values. Thus the electron/beam modified two-stream instability is a likely candidate to account for the presence of lower hybrid fluctuations in the foot of the earth's bow shock at low beta. INTRODUCTION bow shock [Wu et al., 1984' Winske et al., 1985]. We consider Collisionless shocks of sufficiently high Mach number re-the following homogeneous plasma configuration' two unflect a significant fraction of the incident ions as a means of magnetized ion components, a more dense core and a less dissipation [e.g., Tidman and Krall, 1971, chapter 3]. There-dense beam, streaming across a uniform magnetic field B o, in the presence of a magnetized electron component at rest in the fore Auer et al. [1971] and Papadopoulos et al. [1971a] proposed that instabilities driven by the counterstreaming of the zero momentum frame. In this configuration there are at least incident ions and the reflected ions would develop upstream of six distinct instabilities. The high-frequency trio consisting of the shock. Both observations [Paschmann et al., 1982; Sckopke the ion/ion acoustic, the electron/ion acoustic, and the elecet al., 1983] and computer simulations [Papadopoulos et al., 1971b' Leroy et al., 1981, 1982] demonstrated the correlation between reflected ions which gyrate in front of the shock and a "foot" signature in the magnetic field magnitude at supercritical shocks. Furthermore, it has now been shown that there is a correlation between enhanced electrostatic fluctuations in both the lower hybrid and the ion acoustic frequency regimes and the presence of a foot at the earth's bow shock [Vaisber•I et al., 1982, 1983; Gurnett, 1985' Greenstadt and Mellott, 1987' Mellott and Greenstadt, 1986]. The recent work of Mellott and Greenstadt [1986] demonstrates not only that enhanced lower hybrid fluctuations at the earth's bow shock are correlated with the upstream turnaround distance of specularly reflected ions but also that the fluctuating field energy density typically increases through the foot region and peaks in the shock ramp. In this pa...

Non-stationarity of the quasi-perpendicular bow shock: comparison between Cluster observations and simulations

“…almost perpendicular to the magnetic field. The occurrence of the MTSI-2 can change the picture obtained from 1-D simulations; however, the linear stability analysis by Gary et al (1987) has shown that the MTSI-2 is only dominant in the low electron beta case (β e < 0.5), while the present β e ∼ 1.7. We thus expect the MTSI-2 to be of minor importance.…”

“…The waves with maximum growth of the MTSI-1 have wave vectors almost perpendicular to the magnetic field and can thus be observed in 1-D shock simulations. However, the waves with maximum growth of the MTSI-2 propagate oblique to the magnetic field (e.g., Gary et al, 1987) and will thus not be seen in 1-D simulations, which allow only for k vectors in the shock normal direction, i.e. almost perpendicular to the magnetic field.…”

Pickup protons at quasi-perpendicular shocks: full particle electrodynamic simulations

“…The same holds in the ramp region: instabilities with k vectors less oblique to the magnetic field may have larger growth rates and can modify the reformation process. In particular the modified two-stream instability between solar wind electrons and reflected ions with k vector components parallel to the magnetic field can occur in a multi-dimensional spatial system (Gary et al, 1987) and plays an important role in the foot region (Matsukiyo and Scholer, 2006).…”

Lower hybrid waves in the ion diffusion and magnetospheric inflow regions

“…In this region the cold magnetospheric ions and the crescent distribution of magnetosheath ions are distinct from each other. The relative drift between the two ion populations in the M direction perpendicular to B can excite the ion‐ion cross‐field instability, which produces lower hybrid‐like waves [ Papadopoulos et al , ; Gary et al , ]. The observed waves have phase velocities approximately between the two ion populations, consistent with an instability developing between the two ion populations producing the waves.…”