In this work elements of existing eigenmode identification analysis techniques are combined to yield an improved technique for the extraction of mode numbers in toroidal plasmas. The technique, which involves fitting Fourier-time and Fourier-spatial basis functions to magnetic perturbation data, uses singular value decomposition (SVD) to provide an optimal fit across a realistic subset of the full Fourier transform basis and selects the spatial basis with the least solution residue. The method yields best-fit mode numbers, mode amplitudes and phase. A stochastic analysis provides a null-test, yielding the probability that Gaussian noise would produce the same residue of the fit or mode amplitude. The technique quantifies eigenmode mode fits in toroidally confined magnetic systems. Our approach improves upon earlier techniques in that the frequency or mode number of degenerate modes are resolved, all magnetic coil information is used synchronously, wave-train averaging is performed, and a quantitative measure of fit is generated. In turn, weak magnetic signals with long coherence time, and eigenmodes which are degenerate in mode number or frequency are resolved, and the mode fit statistically quantified by comparison with noise. The latter measure enables automated rejection or acceptance of the mode fit, obtained by comparing the probability of the null hypothesis to the 1% confidence level. Convolution of the frequency-resolved mode amplitudes and residues with a Gaussian is used to improve the confidence of identification, reducing scatter at the expense of frequency resolution. Finally, the method is applied to magnetic fluctuation data from the mega Ampere spherical tokamak outboard Mirnov array for high frequency acquisition (OMAHA) in order to analyse strong low-frequency activity and weaker high frequency Alfvénic activity.
The structure of magnetic fluctuations in the HBTX-1A reversed field pinch