Steady-State Interactions in Plasma Accelerators

Abstract

Theme A N analytical study of the steady-state interactions between a gas and a force field is presented. The several different types of interactions that occur for different magnitudes of the body force and heat addition are described. The effect of maintaining an initial pressure difference across the force field is also discussed. Although the analysis is applicable for any type of body force and heat input, reference is made to plasma accelerators where the Lorentz force and Ohmic heating are the appropriate quantities. A stationary, nondiffusive, one-dimensional force field is assumed to have been created in an infinitely long channel initially containing a perfect gas at rest. A single-fluid model is used to investigate the effect of the force field on the gas. The difficulties of such an investigation are reduced considerably by only studying the steady state, which is defined as the state in which the shock and expansion waves have constant strengths and steady-state conditions exist inside the force field. With these approximations the equations that govern the flow of the gas through the force field are derived and are solved along with the equations for shock and expansion waves to determine the resulting interaction. A related problem, that of the interaction of a shock tube flow with an electromagnet ic field, has been treated analytically by Johnson, 1 who used the method of characteristics and by Rosciszewski and Gallaher,2 who used the Lax-Wendroff finite difference method. Experimental results have been reported by Zauderer and Tate.3 Two different types of force field are considered. For the first type the force field is independent of the gas velocity through it and for the other it is altered by the gas velocity. Each of these types is related to a particular class of plasma accelerators. For the case of a force field independent of the gas velocity the possibility of placing a diaphragm at the forward edge of the force field that is burst at the same instant the force field is created is also considered. The parameter formed by this initial pressure difference is represented by P and is equal to the initial pressure ahead of the diaphragm divided by the initial pressure behind it (on the force field side). The gas temperature and the type of gas are assumed to initially be the same on each side of the diaphragm. The seven possible interactions between the gas and the force field in the steady state are indicated schematically in Fig. 1. The force and initial pressure difference accelerate the gas to the right in the figure. The regions in which the flow variables have constant values for each interaction are indicated by the circled