Electrostatic shocks as nonlinear ion acoustic waves

Abstract

We present a one‐dimensional, quasi‐neutral fluid model of the local structure of electrostatic shocks that have been seen in conjunction with ion beams at around one earth radius altitude in the auroral zone. The method is useful when one population of cold ions supports the shock and when one has an idea of how the other particle species behave. The cold ions are described via the ion fluid equations which incorporate a constant magnetic field. The other particle species are described via a plasma model consisting of known expressions, in terms of the electrostatic potential, for the number density of each species. We show how exact time stationary double‐layer solutions may be found when quasi‐neutrality is assumed. We take double‐layer solutions in the wave frame to be possible shock models, with the implications that the cold ions stream into the shocks supersonically, the shock scale length varies with the acoustic Larmor radius, and the shock potential depends only on the incoming parallel cold ion speed, independent of the angle the shock electric field makes with the magnetic field. We examine shock solutions derived from two different plasma models: (1) cold ions and two Boltzmann populations of electrons and (2) cold ions, hot Boltzmann ions, cool Boltzmann electrons, and cold streaming electrons. Assuming reasonable values for the plasma parameters, we find double layers with electric fields of 100–1200 mV/m, widths of 1–4 km, and potential drops of up to 2 kV. This suggests that the electrostatic shocks seen in conjunction with ion beams at one earth radius altitude may be nonlinear ion acoustic waves.