Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves

Abstract : Whistler wave trains are observed in the foot region of high Mach number quasiperpendicular shocks. The waves are oblique with respect to the ambient magnetic field as well as the shock normal. The Poynting flux of the waves is directed upstream in the shock normal frame starting from the ramp of the shock. This suggests that the waves are an integral part of the shock structure with the dispersive shock as the source of the waves. These observations lead to the conclusion that the shock ramp structure of supercritical high Mach number shocks is formed as a balance of dispersion and nonlinearity. Shock plasma waves are ubiquitous in our Universe. They play an important role in redistributing kinetic energy in supersonic flow into plasma thermal energy and energetic particles. In particular, Earth's bow shock defines the boundary between the supersonic solar wind plasma and the subsonic region of the near-Earth space environment. Despite the absence of collisions, low Mach number collisionless shocks are treated as steady state fast magne-tosonic nonlinear waves or discontinuities in a dissipative MHD approximation. This allows one to determine the asymptotic state of the plasma and magnetic field across a shock, by using the Rankine-Hugoniot conservation laws. Any deviation from MHD such as two-fluid or kinetic descriptions results in the appearance of dispersive effects. When the Mach number of the shock increases past a critical Mach number, M crit , inferred in the frame of a MHD description, neither resistive nor viscous effects can provide sufficient dissipation to sustain a stationary shock transition [1]. For these so-called supercritical shocks the major dissipation mechanism is related to reflected ions [2–4] that require a kinetic description. It is well known that a subcritical shock has a nonlinear whistler wave train upstream of its front [5,6]. The major transition of such a dispersive shock, the ramp, behaves as the largest peak of the whistler precursor wave package [7–10]. The presence of whistler or fast magnetosonic precursor wave trains in supercritical shocks as well was experimentally established in [11–13]. These whistler waves have rather large amplitudes, and their role in energy transformation and redistribution between different particle populations and in the formation of the shock front structure is still an open question. Often the precursor waves are almost phase standing in the shock frame. However, their group velocity can still be greater than zero in the shock reference frame, which would allow energy flow in the form of Poynting flux to be emitted towards the upstream of the shock transition. In this Letter we address this problem and present the first direct measurement of the Poynting flux of the upstream whistler waves. It has been suggested that the shock front structure of quasiperpendicular supercritical shocks is formed similarly to that of subcritical shocks [14]. The observed dynamic features of shocks have also been studied extensively using computer particle-in-cell (PIC) or hybrid simulations, often with focus on the precursor wave activity and reflected ions [15–17]. From a kinetic viewpoint, however, it may be argued that the shock-reflected ions change the physical picture and that the principal scales, temporal and spatial, could be determined by the characteristics of the reflected ion population [18]. Upstream waves can then be generated due to counterstreaming ions and electrons in the shock front region, forming unstable particle distributions with respect to some wave modes [16,17,19]. While this is probably the case for some higher frequency waves, our analysis below leads to the conclusion that the source of the upstream low frequency whistler waves is related to the presence of the nonlinear ramp transition, emitting smaller scale dispersive waves towards the upstream flow. The existence of phase-standing upstream whistler waves depends on the value of the upstream flow speed Mach number relative to the phase velocity. If the Mach number of the shock does not exceed the whistler critical Mach number M w ¼ V w;max =V A ¼ 1=2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffi m i =m e p cos Bn , the highest possible phase velocity, then phase-standing (linear) whistler wave trains can exist upstream of the shock [9,14]. In the above equation V A is the Alfvén speed and Bn is the angle between the upstream magnetic field and the normal to the shock. Below we establish the energy source of the waves by calculating the Poynting flux of the waves in the normal incidence frame (NIF) of the shock, using multisatellite
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David Sundkvist, V Krasnoselskikh, S.D. Bale, S.J. Schwartz, J Soucek, et al.. Dispersive Nature of High Mach Number Collisionless Plasma Shocks: Poynting Flux of Oblique Whistler Waves. Physical Review Letters, American Physical Society, 2012, 108 (2), pp.025002 ⟨10.1103/PhysRevLett.108.025002⟩. ⟨insu-01259308⟩

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