MHD mode identification of tokamak plasmas from Mirnov signals

Identification of coherent waves from fluctuating tokamak plasmas is important for the understanding of magnetohydrodynamics (MHD) behaviour of the plasma and its control. Toroidicity, plasma shaping, uneven distances between the resonant surfaces and detectors, and non-circular conducting wall geometry have made mode identification difficult and complex, especially in terms of the conventional toroidal and poloidal mode numbers, which we call (m,n)-identification. Singular value decomposition (SVD), without any assumption of the basis vectors, determines its own basis vectors representing the fluctuation data in the directions of maximum coherence. Factorization of a synchronized set of spatially distributed data leads to eigenvectors of time- and spatial-covariance matrices, with the energy content of each eigenvector. SVD minimizes the number of significant basis vectors, reducing noise, and minimizes the data storage required to restore the fluctuation data. For sinusoidal signals, SVD is essentially the same as spectral analysis. When the mode has non-smooth structures the advantage of not having to treat all its spectral components is significant in analysing mode dynamics and in data storage. From time SVD vectors, we can see the evolution of each coherent structure. Therefore, sporadic or intermittent events can be recognized, while such events would be ignored with spectral analysis. We present the use of SVD to analyse tokamak magnetic fluctuation data, time evolution of MHD modes, spatial structure of each time vector, and the energy content of each mode. If desired, the spatial SVD vectors can be least-square fit to specific numerical predictions for the (m,n) identification. A phase-fitting method for (m,n) mode identification is presented for comparison. Applications of these methods to mode locking analysis are presented.