In order for human kind to expand our reach beyond the Earth, and create a meaningful human presence throughout the solar system, it is almost certain that the current means of propelling spacecraft will be insufficient. With current propulsion systems that derive their energy from chemical reactions, there is an upper limit to how energetic a chemical reaction can be. This fact, together with the fact that a spacecraft must carry all of its fuel with it, means that interplanetary trips with chemical rockets require an impractically large amount of fuel. Other means of propulsion which do not have an upper limit on the energy that can be used to power the spacecraft are available. One such method, referred to as a Helicon Thruster, or a Magnetic Nozzle thruster, works as follows: first, an inert gas is introduced into the thruster. Then, a powerful antenna is used to break electrons off of the atoms of the gas, which generates ions (atoms that have had one or more of their electrons removed). This results in what is know as a plasma, or a gas made up entirely of charged particles. Common examples of plasma are lightning bolts, the gas inside of fluorescent lights, and the sun. Plasmas differ from normal gasses in that they feel the effects of magnetic and electric fields, and can conduct electricity. Once this plasma has been generated inside of the thruster, another antenna may be used to further heat up the plasma. Then, the plasma is directed by a strong magnetic field out the back of the thruster, propelling the spacecraft forward. This propulsion technique requires much less fuel than traditional chemical approaches, making long interplanetary trips more practical. A number of research questions need to be answered before this propulsion method can be put into practice. This thesis contributes to this effort by building the tools necessary to run a computer simulation of the magnetic field that is used to channel the plasma used by this propulsion technique.

A means of space propulsion using the channeling of plasma by a divergent magnetic field, referred to as a magnetic nozzle has been explored by a number of research groups. This research develops the capability to apply the high order accurate Runge-Kutta discontinuous Galerkin numerical method to the simulation of magnetic nozzles. The resistive magnetohydrodynamic model of plasma behavior is developed for these simulations. To facilitate this work, several modeling capabilities are developed, including the implementation of appropriate inflow and far-field boundary conditions, the application of a technique for correcting errors that develop in the divergence of the magnetic field, and a split formulation for the magnetic field between the applied and the perturbed component. This model is then applied to perform a scaling study of the performance of magnetic nozzles over a range of Bk and Rm. In addition, the effect of the choice of simulation domain size is investigated. Finally, recommendations for future work are made.

Master of Science