Nonlinear Modeling of Macroscopic Plasma Dynamics Final Scientific Report May 1, 2006 – April 30, 2018
The project entitled, "Nonlinear Modeling of Macroscopic Plasma Dynamics," applied numerical computation to solve mathematical models of plasma behavior in laboratory systems. Plasma is the state of matter with sufficiently large internal energy density such that electrons dissociate from atoms to form gas of electrically charged particles. It occurs naturally in stars, planetary magnetospheres, and interstellar and intergalactic media. It is also used for industrial purposes and in lighting. Fusion energy science seeks to create and sustain plasma conditions where atomic nuclei fuse to create energy that can be captured for power production. Many laboratory experiments for this effort use magnetic field to contain plasma and to thermally insulate it from its surroundings. Possible plasma dynamics in magnetized systems include collective behavior over spatial scales that are comparable to the configuration size, and these dynamics often include evolution of the magnetic field that is used for confinement. Solving the mathematical models that describe these dynamics in specific experiments often requires computer simulations, as done in this project. This project analyzed plasma magnetic relaxation dynamics in the laboratory configurations known as the reversed-field pinch (RFP), the spheromak, and the spherical torus (ST). It also developed capabilities for modeling disruptive plasma dynamics in the tokamak, which has achieved the highest performance for magnetized plasma and is the design of the large international ITER experiment (https://www.iter.org) that is under construction and is expected to be the first to achieve self-heating conditions. Dynamic evolution to states of low energy, the aforementioned magnetic relaxation, is known to be important for generating the RFP and spheromak configurations. Nonlinear computational modeling with the Non-Ideal Magnetohydrodynamics with Rotation, Open Discussion code (NIMROD, https://nimrodteam.org) was applied to understand specific aspects of magnetic relaxation in RFPs, spheromaks, and STs. The RFP study considered how the nonlinear transfer of power among different fluctuation harmonics is altered due to the application of pulses of electric field, as done experimentally in the Madison Symmetric Torus RFP device at the University of Wisconsin-Madison. It also investigated the separation of electron and ion dynamics, known as two-fluid effects, including effects on the evolution of the plasma flow profile. The spheromak study considered the influence of these two-fluid effects in conditions relevant to the Sustained Spheromak Experiment (SSPX), formerly at Lawrence Livermore National Laboratory. Our study found that two-fluid effects enhance stability with respect to interchange in SSPX-relevant conditions, but having a complete model with two-fluid effects in separate electron and ion temperature equations is important. The study for STs focused on plasma startup in the Pegasus Toroidal Experiment at UW-Madison, which uses DC voltage applied through a small plasma gun. The simulations show how the resulting helical current stream relaxes through repetitive merging, forming current rings that accumulate into a tokamak-like configuration. Analytical theory was also developed to help explain behavior that was observed in the RFP and spheromak computations. Although the tokamak configuration has outperformed other magnetic confinement configurations, it has a tendency to undergo discharge-terminating dynamics that release energy onto plasma-facing surfaces and exert electromechanical forces on magnetic coils and structures. Our efforts have improved NIMROD's capabilities to model tokamak disruption by incorporating a resistive wall model that can be applied to axisymmetric, as well as asymmetric, distortions of the magnetic field configuration. Computations addressed whether mathematical conditions applied to plasma flow at the wall influence disruptive dynamics.