Numerical Study of an Electron-Beam-Confined Faraday Accelerator

The numerical solution of a magnetoplasmadynamics accelerator intended for supersonic airbreathing propulsion systems is presented. The numerical method solves the Favre-averaged Navier-Stokes equations closed by the Wilcox kw model, including the nitrogen vibrational energy and a finite rate chemical solver accounting for electron-beam ionization, electron attachment, and dissociative recombination. The fluid-flow equations are solved in conjunction with the electric-field-potential equation. Because of the recombination time of the electrons with the charged particles being in the order of microseconds, the interaction region is more or less confined to the area when e-beam ionization is applied. In this manner, a Faraday-type configuration can be obtained by using only one electrode pair. The impact of the length of the interaction region and the strength of the magnetic field on the efficiency are assessed. It is observed that the efficiency obtained numerically is as much as 40% less than the theoretical predictions for the highest magnetic field considered of 4 T. This is attributed to 1) the current concentration near the electrodes' edges causing a significant voltage drop and 2) unsteady behavior in the center of the channel due to the interaction between finite rate chemistry and electromagnetism. Nonetheless, an efficiency within 25% of the theoretical predictions can be obtained at high magnetic field by decreasing the width of the interaction region to one-tenth of its height.