A review is given of recent developments in collisionless-shock-wave research. Theoretical concepts are compared with both numerical simulation results and experimental observations. Particular emphasis is put on the analysis of collisionless dissipation processes, anomalous resistivity and viscosity.

https://iopscience.iop.org/article/10.1088/0029-5515/13/5/010/pdf

Collisionless Shock Waves in Plasmas

It was found that low solar wind parameters M (less than or around 2.5) and beta (much less than 1) and high angles to the local shock normal, theta (greater than or around 65 deg), produced oblique laminar shock profiles as expected from theory, with marginal or vanishing upstream standing whistlers probably damped by acoustic or other plasma wave instabilities. The whistler mode appeared to dominate the electromagnetic spectrum. The laminar shock ramp thickness was several hundred kilometers and equal to (2-4)c/omega-pi. Composition of the shock as an accumulation of near-standing waves and an evidently reproducible varying flux pattern was discernible. Electron thermalization occurred early in, or just before, the magnetic ramp, while proton thermalization appeared to occur later in the ramp. Instantaneous shock velocities derived from the standing whistler wavelength were consistent with average velocities derived from the elapsed time estimates and were as high as 200 km/sec.

Structure of the quasi‐perpendicular laminar bow shock

Structure of the quasi-perpendicular laminar bow shock. [earth-solar wind interaction

A classification of earth's bow shock structures on the basis of upstream MA, β, Δ = ∠ Bn (angle between shock normal and magnetic field direction) has been found. Typical properties for each case are studied. In particular, the downstream turbulence present in has been positively correlated with upstream β. It is suggested that the shock precursor, as far as low-frequency waves are concerned, is always due to waves generated upstream and carried by the solar wind. The use of the shock velocity allows estimation of the shock thickness: if MA > 3, the shock is a few ion gyroradii thick.

Solar wind interaction with the Earth's magnetic field: 3. On the Earth's bow shock structure

Explorer 33 and 35 magnetometers, on the western and eastern flanks of the earth's bow shock, respectively, observed the boundary concurrently between 0130 and 0430 UT, Oct. 30, 1968. Contrasting shock structures were recorded. Explorer 35 saw a quiet abrupt shock, whereas Explorer 33 saw an irregular noisy boundary with much upstream wave activity. The interplanetary field was roughly in the average archimedean spiral angle and was therefore approximately tangent to the shock at Explorer 35 and normal to the shock at Explorer 33. Gross motions and variable tilting of the aberrated shock probably contributed to the peculiar sequence of shock crossings at the two spacecraft. The observations support a model of the shock in which perpendicular and oblique collisionless structures coexist and form a nonuniform magnetosheath outer boundary.

Observation of nonuniform structure of the Earth's bow shock correlated with interplanetary field orientation

In an earlier paper the authors describe a plasma wind tunnel that produces a steady collision‐free flow. A shock wave standing in front of a magnetic obstacle was produced in this flow. The changes in magnitude and direction of the magnetic field across the shock wave were found to be in agreement with values predicted using the magnetohydrodynamic Rankine‐Hugoniot relations. This work has been extended using electric field measurements to determine the over‐all flow patterns. The electron density has been measured with a laser interferometer, and the density ratio across the shock wave has been found to be consistent with the shock wave equations. The power spectra of the magnetic and electric fluctuations have been measured. These fluctuations are consistent with whistler waves standing in the shock front. The power spectrum shows large variations with position in the shock with the highest frequencies appearing near the toe of the shock wave. The amplitude and frequency variation of the power spectrum is quite similar to space data where the latter is available. The electric field fluctuations are found to be proportional to the magnetic fluctuations with a proportionality constant equal to the flow velocity. The absolute magnitude of the magnetic turbulence is too low to absorb all of the dissipation required for the shock wave and a simple model using wave‐particle interactions is suggested.

Richard M. Patrick

Papers

Laboratory study of turbulence in collision-free shocks.