Modeling and Analyzing MHD Waves in a Sheared-Flow Z-Pinch Plasma

Abstract

The ZaP-HD Z-Pinch device is a modification of the Z-Pinch nuclear fusion device usinga sheared plasma flow to promote stability and reduce the traditional downfalls of the highly unstable Z-Pinch design. Z-Pinches are confined by generating their own magnetic field that manifests tangentially around an axial “Z”-facing current. The plasma is then compressed to high densities and temperatures where it would ultimately lead to fusion in a commercial device. Inherent to plasma are waveforms that are created from the microscopic perturbations of particles and electromagnetic fields within its medium. Unlike simpler electrostatic environments both theoretical or in real-world cases like grid-acceleration ion thrusters, however, magnetic fields create vast anisotropies that cause a “zoo” of waves to appear within the plasma. These waves can cause nonlinear/higher order effects when coupled with particle energy exchanges that can lead to significant instabilities. Despite this, wave phenomena and their resonant interactions with the plasma are helpful for applications like heating to fusion temperature or understanding radiation transmission. To best take advantage of these useful properties, it is best to get an accurate picture of the wave behavior within ZaP-HD that is tailored to its specific geometry, plasma energy, and field strength. The problem is that when analyzing the wide spectrum of possible wave modes, the “zoo” is vast. Even with just oscillatory modes this is an issue and it gets even more complicated to accurately predict and experimentally analyze when the above mentioned instabilities are introduced. Therefore, a baseline model that starts from and approximates a subsection of the whole plasma wave spectrum without these instabilities is useful. It can serve as a spring-board for further spectral sub-regions and higher-order effects while ensuring accuracy for the many interwoven components of the whole spectrum. This baseline model uses observable data (like magnetic field, density, and flow velocity) within ZaP-HD’s cylindrical fusion plasma environment and predicts the low frequency magnetohydrodynamic (MHD) range. The iteration process then begins with with frequency analysis methods such as cross-correlation and Fourier analysis to compare with the model and check for differences in results. All experimental data is retrieved using probes positioned within the main assembly region of ZaP-HD where the fusion process occurs.