On double-structured, perpendicular, magneto-plasma shock waves

This paper presents a theory of double-structured shock waves, which possess a precursor `foot' due to the reflection of ions from a resistive shock front. It is an extension of an earlier study by the author. Above a critical Alfvén-Mach number M A the reflected ions generate a streaming instability with the electrons that results in the flow of a transverse electric current and a change in the magnetic field well ahead of the resistive front. The electrons in the foot are preheated by mixing with some hot downstream electrons that are assumed to be drawn forwards by the reflected ions. This model enables M A to be calculated as a function of β 1 , the upstream plasma beta. When a foot does develop, the theory enables its profile in magnetic field to be determined. The critical Alfvén-Mach number M A at which the foot fully sumberges the resistive rise is also estimated, so that the upstream Alfvén-Mach number M A 1 of double-structured shocks satisfies doublehat-M. It is found that this range for M A 1 narrows considerably with increasing β 1 ; below doublehat-M is infinite. With doublehat-M, the shocks are fully developed ion reflecting shocks, with a thickness of order ( c/ω pi ), which is about the same as the length of the foot of the double-structured shocks. There is good agreement with the few available experimental results.