Modeling magneto-plasma dynamic thrusters for space applications

A magnetoplasmadynamic (MPD) thruster (MPDT) is a form of electrically powered spacecraft propulsion which uses the Lorentz force (the force on a charged particle by an electromagnetic field) to generate thrust. Generally, the working principle of such a thruster involves ionization of a gaseous material that is then fed into an acceleration chamber, where the magnetic and electrical fields are created using a power source.

The particles are then propelled by the Lorentz force resulting from the interaction between the current flowing through the plasma and the magnetic field (which is either externally applied, or induced by the current) out through the exhaust chamber. These systems have a unique capability among all other developed electric propulsion systems, of processing megawatt power levels in a simple, small and robust device, producing thrust densities as high as 10⁵ N/m². As such, they provide an attractive option for high energy deep space missions requiring higher thrust levels than other electric thrusters.

In its basic form, the MPD thruster consists of a cylindrical cathode surrounded by a concentric anode. The specific impulse of a self-field MPD thruster is related to the parameter I²/ṁ (square current per propellant mass flux) which is often used to characterize MPD thruster performance. The best way to study such systems has been through computational fluid dynamics (CFD) simulations as the experimental cost is prohibitive. This, however, requires the development of a realistic CFD code. Regardless, development of such a code is quite elusive leaving the only feasible alternative to be numerical research. Still, despite all the important progress realized so far by various researchers in using computational approach, there is much to be done to ensure proper modeling.

Recently, researchers from the Center of Applied Space Technology and Microgravity University of Bremen Dr. Charles Chelem Mayigué and Dr. Rodion Groll presented a study showing the implementation of a density-based scheme including a divergence cleaning method for the simulation of the magnetohydrodynamic equations under a finite volume formulation. Their ultimate goal was to develop a novel algorithm for both ideal and resistive MHD equations and makes use of the central-upwind schemes of Kurganov and Tadmor for flux calculation. Their work is currently published in European Journal of Mechanics/B Fluids.

The authors implemented their code while ensuring that the physical model remained as simple as possible. The robustness and accuracy of their code was then demonstrated using one and two-dimensional numerical tests in ideal-MHD. Ideally, application of the new code for the simulations of the self-field MPD thrusters demonstrated that the method presented was competitive when compared to existing methods. Furthermore, the results of Princeton’s Full-Scale Benchmark Thruster (PFSBT) simulations showed good agreement with the experimental values and numerical simulation results.

In summary, a density-based method for the numerical modelling of the magnetohydrodynamics equations was presented. Excellent performance was obtained through the prediction of thrust and plasma voltage of the Princeton’s Extended Anode Thruster (PEAT). Nonetheless, it was noted that the code remained unstable, evident by the high values of discharge current, and for some geometrics, the predominantly electromagnetic acceleration mode was still unachievable. Altogether, the University of Bremen study sets precedence for future works in the broader field of fluid mechanics and for those aspiring to improve the numerical model.