MHD/Shocks: Specularly Reflected Ions

The foot in the magnetic profile of quasi-perpendicular, supercritical shocks develops upstream of the main ramp when the magnetic field makes its main and irreversible jump to its downstream value. This foot is caused by gyrating ions which are nearly specularly reflected at the shock boundary, i.e., the incident ions’ components of velocity parallel to the shock normal are reversed at the shock while components along the shock surface remain unchanged. These reflected ions are turned around by the upstream magnetic field and returned to the shock.

This module is based on the expression developed by J.T. Gosling and M.F. Thomsen (Specularly reflected ions, shock foot thicknesses, and shock velocity determinations in space, J. Geophys. Res., 90, 9893–9896, 1985) for the turnaround distance of specularly reflected ions at arbitrary orientations of incident velocity and upstream magnetic field. Given this characteristic distance and the time taken for the shock foot to pass by the observing spacecraft, the shock velocity can also be determined (assuming that the velocity is constant throughout the foot observation).

These parameters are calculated from the following inputs:

Upstream velocity
The component of the incident velocity along the shock normal, in km/s.
Magnetic field strength
Measure in nT upstream of the shock.
The angle between the magnetic field and shock normal directions. This parameter ranges from 0° (parallel orientation) to 90° (perpendicular orientation). When θBn is 90° the magnetic field is in the shock plane. When θBn is 0° the magnetic field is along the shock normal.

After entering the input parameters, click Calculate to display the foot length, the theoretical maximum distance from the shock reached by the ion if ions are perfectly specularly reflected at the shock boundary.

Note: A shock foot will form only for quasi-perpendicular shocks, because the reflected particles will escape upstream along the magnetic field for quasi-parallel shocks, and so results when θBn is less than 39.9° when escape first occurs (for decreasing θBn) are not calculated.