Magnetic diagnosis of ion-beam instabilities in the Mercury shock-upstream region

The Mercury shock-upstream region is the ideal, natural laboratory for studying the beam instabilities in-situ in collisionless space plasma, since (1) a smaller Parker spiral angle of about 20 degree (the mean magnetic field is nearly parallel or anti-parallel to the flow direction) is conveniently suited to testing for the beam instabilities against one-dimensional instability study using the analytic and numerical methods, and (2) the magnetic field data are accessible not only by the earlier MESSENGER mission but also by the upcoming BepiColombo MPO-MAG and MGF instruments. Here we develop the polynomial dispersion solver to theoretically and systematically derive the wave and instability properties for the ion-beam plasmas. It is found that the beam instability undergoes a smooth transition from the right-hand resonant instability into the non-resonant firehose-type instability at higher beam velocities. The right-hand resonant instability represents the coupling between the beam-resonant mode and the whistler mode, and is commonly found in the Earth shock-upstream region. The non-resonant instability, in contrast to the right-hand resonant case, represents primarily the coupling between the whistler and ion-cyclotron modes in backward direction to the bam and is mediated by the high-speed beam. The non-resonant instability may be regarded as a kinetic extension of the magnetohydrodynamic firehose instability for a higher pressure in the mean magnetic field direction. Our picture of the beam instabilities serves as a useful diagnostic tool of the beam plasma using the magnetic field data, e.g., reading the beam density from the frequency-broadening in the wave spectrum, and giving a constraint between the flow speed and the beam velocity from the spacecraft-frame of wave frequency. Moreover, the Mercury shock-upstream region exhibits the double beam instability driven by the shock-reflected ions and the pick-up ions hit by the solar wind, which is unique in the solar system plasmas. The double beam scenario raises the fundamental question as to the nonlinear wave evolution in the plasma such as the evolution through the double parametric decay or that through the forced wave-wave coupling.