Mathematica Eterna
Open Access

Abstract

Steady State Solutions for a Weakly Ionised Plasma in a Sub- and Super-Sonic Axial Flow

Jonathan Blackledge and Andrzej Kawalec

The results presented in this paper relate to an application in aeronautical engineering, in particular, the use of weakly ionised plasma’s to shield an aerospace vehicle from Radar by the absorption of microwave radiation. It is well known that the absorption of an electromagnetic wave with angular frequency ω over a distance x by a conductor with constant conductivity σ is determined by exp(−x p ωµ0σ/2) where µ0 is the permeability of free space. The conductivity of a weakly ionised plasma is determined by its electron number density. Thus in order to evaluate the radar screening effects of a weakly ionised plasma (which is taken to reduce the Radar Cross Section of some aerospace vehicle), it is necessary to compute the steady state electron number density profile of the plasma subject to the axial flow of air over the vehicle. In this paper we consider the case of an axial flow in both the sub-sonic and super-sonic regimes obtained by evaluating the velocity potential for both cases and coupling the result with the rate equation for the plasma. This assumes that, to a good approximation, the plasma flows with the air molecules while at the same time undergoing the processes of ionisation, diffusion and recombination. It is assumed that the plasma is generated by the application of a high energy electron beam, for example, and, in this context, we consider the beam to be generated in front of the aerospace vehicle, e.g. the nose cone