The resolved layer of a collisionless, high β, supercritical, quasi‐perpendicular shock wave: 1. Rankine‐Hugoniot geometry, currents, and stationarity

Abstract

A comprehensive set of experimental observations of a high β (2.4), supercritical (Mf = 3.8), quasi‐perpendicular (ΘBn1 ∼ 76°) bow shock layer is presented, and its local geometry, spatial scales, and stationarity are assessed in a self‐consistent, Rankine‐Hugoniot‐constrained frame of reference. Included are spatial profiles of the ac and dc magnetic and electric fields, electron and proton fluid velocities, current densities, electron and proton number densities, temperatures, pressures, and partial densities of the reflected protons. The transformation of the apparent time scales to the actual spatial scales is performed with unprecedented accuracy. The observed layer profile is shown to be nearly phase standing and one dimensional in a Rankine‐Hugoniot frame, empirically determined by the magnetofluid parameters outside the layer proper. One or both of these properties appear to collapse at the time resolution of 1.5 s in the specific geometry considered in this study. Several pieces of evidence are used to show this stationarity: (1) the similarity of the average magnetic structures seen on the two ISEE spacecraft; (2) the close agreement between the electric currents directly determined from the plasma data and those inferred from the magnetic data assuming the layer is one dimensional and time stationary; (3) the close agreement of the empirically determined scale lengths of the most prominent substructures with those determined by numerical simulations and previous laboratory studies; and (4) the close agreement between the theoretical Rankine‐Hugoniot‐determined normal plasma pressure jump and that of the observed electron and proton fluids. The resolved cross‐field electrical currents (with empirical error estimates) are observed to peak within the main magnetic ramp at a level well below the first stabilization threshold for ion acoustic turbulence suggested for low β shocks by Galeev (1976); clear evidence is also provided for smaller parallel currents throughout the main ramp and overshoot, with a predominant sense as if the shock electric field has caused the lighter electrons to lead the ions along the local magnetic field direction. The width of the shock depends on what structures are used to define it. The upstream pedestal or “foot” is nearly two upstream ion skin depths wide, but the main magnetic ramp is only 1/5 the upstream ion skin depth and thus considerably smaller than “conventional wisdom” and most simulations. The ramp scale length is directly corroborated by the current densities determined from the plasma instruments.

Cluster magnetic field observations at a quasi-parallel bow shock

“…Moving from right (upstream of the enhancement) to left (through the enhancement): upstream of the leading edge, the magnetic field direction is within 45 • of the model bow shock normal; across the leading edge θ Bn rises, with a slight plateau at the end of the sharp ramp, then rises more quickly to a value near 90 • within the enhancement. The magnetic field magnitude at Cluster 2 has a feature similar to a shock foot, typically observed at quasiperpendicular shocks (e.g Scudder et al, 1986). Cluster 3 sees a similar feature, but it is less pronounced, and Cluster 4 and 1 observe short ramps, lasting for about 0.5 s, on the leading edge.…”

“…Magnetic field observations typically show a short ramp in |B|, possibly with a "foot" ahead of the ramp, an overshoot after the ramp, or a high frequency wave train upstream of the ramp (e.g. Scudder et al, 1986). Quasiperpendicular shocks have been studied in detail over many years and recently Cluster data have been used to examine…”

Microstructure in two- and three-dimensional hybrid simulations of perpendicular collisionless shocks

“…The difficulties are associated with interpreting differences between multipoint spacecraft measurements when only a few spatial scales can be observed and the fact that the conversion from time to space in the data relies on knowledge of the shock speed relative to the observation points. The separation between macrostructure and microstructure was already considered in an influential two-spacecraft study using International Sun-Earth Explorer (ISEE) data, where it was found that, by using inter-correlation with different averaging periods, the correlation between the two spacecrafts decreased strongly when the averaging period was approximately 0.15 times the upstream proton gyroperiod (Scudder et al 1986). The inference is that fluctuations seen at short time scales are associated with non-stationarity, or the breakdown of the usual assumption of one-dimensionality.…”

Efficient electron heating in relativistic shocks and gamma-ray-burst afterglow

“…However, the profiles become steeper with the increase of the Mach number [6] so that the conditions for demagnetization may be achieved more easily. The transition layer of quasi-perpendicular non-relativistic shocks consists of several distinct regions [7], the steepest magnetic field increase is a "ramp" (whose width is less than the ion inertial length l i = c/ω pi , ω 2 pi = 4πn u e 2 /m i ) and a large magnetic overshoot (whose width is of the order of the downstream ion gyroradius). The overshoot height is found experimentally to increase with the increase of the Mach number [8].…”