Magnetohydrodynamic Simulation of N₂ Plasma Deflagration Jets for Air-Breathing Electric Propulsion

The current work investigates resistive magnetohydrodynamic (MHD) numerical simulations of a plasma jet in a coaxial pulsed plasma accelerator for air-breathing electric propulsion devices operating in very low Earth orbits (VLEO). The simulated domain features a coaxial electrode configuration with a diameter of 5 cm, a length of 15 cm, and a plume region at the end of the plasma gun. The driver gas in the simulation is molecular nitrogen (N₂). The MHD governing equations are discretized in space using a cell-centered finite volume method on unstructured grids, and in time using a fully implicit backward Euler scheme. The coaxial geometry of the thruster allows for the use of cylindrical polar coordinate system. A 2D plasma-vacuum interface tracking algorithm is implemented to study the physically consistent expansion of a magnetized N₂ plasma jet into a vacuum. Due to the high Reynolds number and rapid plasma transients, the effects of viscous and conductive heat transfer are neglected. The convective flux reconstruction is carried out using a local Lax–Friedrichs method. The diffusive face fluxes are determined using a cell-centered gradient reconstruction technique (i.e., least-squares), followed by averaging adjacent cell gradients to obtain face gradients. The inlet fluid boundary conditions are set to a pressure of 2 Torr, a temperature of 1 eV, and an axial velocity of 1000 m/s, while the background conditions are set to zero density and pressure. The radial current flowing between the coaxial electrodes through the plasma is modelled by applying a purely azimuthal magnetic (B) field as an inlet boundary condition. This implementation consistently ensures zero B-field divergence across the entire domain.