This paper presents a review of the current understanding of magnetic nozzle physics. The crucial steps necessary for thrust generation in magnetic nozzles are energy conversion, plasma detachment, and momentum transfer. The currently considered mechanisms by which to extract kinetic energy from the plasma include the conservation of the magnetic moment adiabatic invariant, electric field forces, thermal energy directionalization, and Joule heating. Plasma detachment mechanisms discussed include resistive diffusion, recombination, magnetic reconnection, loss of adiabaticity, inertial forces, and self-field detachment. Momentum transfer from the plasma to the spacecraft occurs due to the interaction between the applied field currents and induced currents which are formed due to the magnetic pressure. These three physical phenomena are crucial to thrust generation and must be understood to optimize magnetic nozzle design. The operating dimensionless parameter ranges of six prominent experiments are considered and the corresponding mechanisms are discussed.

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The formulation and validation of a novel quasi-one-dimensional particle-in-cell code for the simulation of magnetic nozzles is presented. Quasi-one-dimensional effects are included through virtual displacements of magnetized particles from the axis of symmetry and cross-sectional area variation according to preservation of magnetic flux. A modified, semi-implicit Boris algorithm is developed for capturing the Lorentz force effects in quasi-1D. Validation problems are selected to test the components of the code required to model the important physics of magnetic nozzles. Simulations are performed of two stream instabilities, Landau damping, source and collector sheaths, and magnetic mirrors. Results from the validation simulations show that the code produces physically accurate results when compared with both theory and other simulations.

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In this work, the gas-kinetic method (GKM) is enhanced with resistive and Hall magnetohydrodynamics (MHD) effects. Known as MGKM (for MHD-GKM), this approach incorporates additional source terms to the momentum and energy conservation equations and solves the magnetic field induction equation. We establish a verification protocol involving numerical solutions to the one-dimensional (1D) shock tube problem and twodimensional (2D) channel flows. The contributions of ideal, resistive, and Hall effects are examined in isolation and in combination against available analytical and computational results. We also simulate the evolution of a laminar MHD jet subject to an externally applied magnetic field. This configuration is of much importance in the field of plasma propulsion. Results support previous theoretical predictions of jet stretching due to magnetic field influence and azimuthal rotation due to the Hall effect. In summary, MGKM is established as a promising tool for investigating complex plasma flow phenomena.

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