Equations of Electrogasdynamics and Applications

Abstract

This report presents in summary work done in the period from 1959 to 1963 at the Hypersonic Research Project, Graduate Aeronautical Laboratories California Institute of Technology, on some theoretical aspects of the dynamics of ionized gases. The objective of this work was to set up a system of conservation equations when no magnetic field or complicated chemical effects are present. Emphasis is placed on the gross exchange processes among species at a point, rather than the gradient transport mechanisms (e. g. , viscosity and heat conduction); in the past this point of view was often called "Gaseous Electronics". In subordinatipg the magnetic field and the chemistry to the dynamics it has been possible to explain a gratifying number of commonplace physical phenomena from first principles and to demonstrate the intimate connection between gaseous electronics and aerodynamics. The conservation equations needed for a neutral-ion-electron mixture were derived with the aid of the elementary integral transport (Maxwell-Chapman) theory exactly as used for any ternary mixture. Departures made necessary because of the ionization include (a) the collisionless ("Vlasov") approximation, (b) a reformulation of the Chapman-Enskog prosedure to include electric forces and (c) a convenient recourse to the inverse-fifth-power interparticle force law. Even so the resulting equations are merely a re-statement of the formidable problem of plasma physics. "Inviscid" equations are therefore written as counterparts of the inviscid (ideal) equations of aerodynamics. To illustrate where mathematical difficulties first appear, practical problems are solved with the aid of further approximations. These problems, as well as the physical departures mentioned above, are relegated to Appendices.