A Numerical Algorithm for Simulating Two Species Plasma

In our ever-growing technology-dependent society, a great need for cleaner, more lucrative energy sources is being sought out. Nuclear fission power plants have been used to help provide energy for many years now. More recently, fusion test reactors have been built and planned as another means to fill the energy quota. A large part of understanding the fundamental principles in a fusion reactor focuses on the principles of plasma physics. This topic of plasma physics has been studied for many decades and much progress has been made in its understanding. More recently, computers have become larger and faster allowing for more parameters and larger computations to be simulated. With this increase in computer ability and the growing interest in plasma physics, a sway from a previously heavily used simplification, magnetohydrodynamics (MHD), to a two species approach is often being adopted. This study is of the later research type. It focuses on the physical theory that describes a plasma by considering both the ions and electrons as separate species with the ability to have distinct number densities, velocities, and temperatures. In addition the computational results are compared against solutions that have been found by solving for known parameters from a linear analysis of the two fluid equations. Other considerations include the ideas of geometry, linearization, and breaking the problem down into grids, which describe how the plasma behaves in three dimensions, as well as in time. Specific results are presented to agree with previously known parameters such as: electrostatics, plasma oscillations at zero pressure, finite temperature acoustic waves, electromagnetic waves, whistler waves, and magnetohydrodynamics (MHD) waves, as well as an analysis showing fidelity to multiple relationships in a single simulation. Finally a consideration is given to the stability of a two species plasma, noting first the balance of forces in the initial conditions given for a specific MHD benchmark state and a static minimum energy plasma state