Magnetic Field and Ion Density Correlation Analysis of SSX Plasma

Abstract

Chaotic and unpredictable behavior are both hallmarks of turbulence. Turbulence may be understood in a variety of ways, but traditionally is understood statistically. By using a statistical metric, such as the autocorrelation function or power spectrum of a turbulent signal, we may begin find structure or order a signal that is seemingly random. Conversely, we may attempt to reproduce this order by combining a large number of periodic wave signals at various frequencies. The idea that such linear combinations can reproduce some aspects of turbulence is the basis of the quasi-linear premise. If we accept the quasi-linear premise, then we break down a turbulent signal into the waves which compose it. The distribution of these waves could potentially inform us of the fundamental characteristics of the signal itself.\ud It is this lofty goal we have in mind when we consider turbulent signals produced by plasma created at the Swarthmore Spheromak Experiment (SSX). In considering these plasmas, we accept the quasi-linear premise and assert that the turbulent behavior of the plasma can be modeled, in part, by a collection of randomly phased waves of various amplitudes. The waves supported by the plasma are obtained by solving the equations of linearized magnetohydrodynamic (MHD) wave theory. They are identified within the plasma through their characteristic fluctuations in magnetic field magnitude |B| and ion density n. More specifically, the wave modes behave uniquely with respect to the relative phase of |B| and n, so we determine the wave mode composition of SSX plasma through correlation analysis of time series of |B| and n. However, analysis of the time series tells us very little about the higher frequency modes of the plasma, so we also perform correlation analysis spectrally by considering the Fourier transforms of the original |B| and n signals. This allows us to determine the wave mode composition of the plasma at various frequencies, including ones that have relatively little power compared to the rest of the signal. Though our analysis is based on a strong assumption, the quasi-linear premise, it will give us new perspective and insight on the character of SSX plasma that would otherwise not be immediately obvious