Plasma expansion guided by strong external magnetic fields are a common occurrence both in nature and in the laboratory. Space plasmas are riddled with examples of magnetized plasmas with one example being the plasma generated in the Earth's magnetoshere due to interactions of the solar wind or by ionization which occurs in the ionosphere. In the laboratory, magnetized plasma jet expansions are an integral part of plasma sources used for spacecraft propulsion and plasma processing. In spacecraft propulsion, the strong magnetic field guiding the plasma flow is known as a magnetic nozzle. The prevalence of these magnetized plasma expansions makes them an important phenomenon to understand to better describe both space plasmas and device plasmas. The Self-consistent Quasi-1D (SQu1D) Particle-In-Cell (PIC) code has been developed to kinetically study these magnetized plasma expansions.
Figure 1. Particle oscillations in a magnetic mirror forming loss cone.
SQu1D contains a novel Q1D technique which models two-dimensional magnetic field effects in a one-dimensional electrostatic particle-in-cell code. The Q1D model is enabling by significantly reducing the computational cost compared to fully 2D simulations while still reproducing important 2D results. This quasi-one-dimensional formulation incorporates two-dimensional effects through the inclusion of cross-sectional area variation and magnetic field forces. The new method is verified with a newly formulated set of test cases of a two-particle system, magnetic mirrors, and fully two dimensional simulations.
Magnetic nozzle physics and ion acceleration in low temperature plasmas were investigated with a simple test problem using these kinetic simulations. The effects of the density variation due to plasma expansion and the magnetic field forces on ion acceleration were investigated. The density variation only weakly affected ion acceleration. Magnetic field forces acting on the electrons were found to be responsible for the formation of potential structures which accelerate ions. The formation of a high energy ion beam is seen due to ion acceleration. Strongly diverging magnetic fields drive more rapid potential drops and the length of the radio frequency heating region was found to significantly affect the electron temperature profiles. Simulations were performed with both argon and xenon. For the same driving current, argon simulations demonstrated higher ion velocities while xenon simulations showed higher plasma densities.
The ion acceleration physics was investigated verifying that ion acceleration occurs due to potential structures established by the magnetic field forces on the electrons. The effects of anisotropic electron pressure tensors were also found to be important for determining a simple Ohm's law used to solve for the induced electric field which accelerates the ions. Bi-Maxwellian and non-Maxwellian velocity distributions were seen for the electrons in the simulations along with the anisotropic temperatures, verifying the need for kinetic simulations. Electron thermodynamic relations (isothermal, adiabatic, polytropic, double adiabatic) were evaluated for a number of simulation results.
Results from quasi-one-dimensional simulations of magnetic nozzles were used to estimate thruster performance parameters such as specific impulse and thrust. The performance parameters were consistent with those expected in similar devices.
Figure 2. Example of current driven radio frequency discharge simulation.
Selected Relevant Publications
Ebersohn, F.H., "Kinetic Method for Quasi-One-Dimensional Simulation of Magnetic Nozzle Plasmadynamics,"
Ph.D. Dissertation, University of Michigan, 2016.
Ebersohn, F.H., Sheehan, J.P., Gallimore, A.D., and Shebalin, J.V., "Quasi-One-Dimensional Particle-In-Cell Simulation of Magnetic Nozzles", IEPC 2015-357 , 34th International Electric Propulsion Conference, Kobe, Japan, July 6-10, 2015.
Ebersohn, F.H., Sheehan, J.P., Longmier, B.W., and Shebalin, J.V., "Quasi-one-dimensional code for particle-in-cell simulation of magnetic nozzle expansion", AIAA 2014-4027 , 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, Cleveland, OH, July 28-30, 2014.