A sparsity-based method for the analysis of magnetic fluctuations in unevenly-spaced Mirnov coils

Abstract

A new method for identifying toroidal mode numbers in Mirnov data from toroidal plasmas has been found, and benchmarked with simulated and real data from the JET tokamak. Embodied in the SparSpec code, and originally developed for the analysis of unevenly time-sampled astronomical data, this new method fits signals which are unevenly sampled in the toroidal coordinate to a sum of an arbitrarily large number of toroidal modes with integer mode numbers. The method has proven to be extremely robust, and is especially useful for resolving the amplitudes and phases of multiple Alfvén eigenmodes (AEs) which are ringing with the same or nearly the same frequency. The great efficiency with which the SparSpec method detects multiple modes in large datasets suggests that it may be used in real-time applications such as resistive wall mode or tearing mode control, among others. Examples involving unstable AEs as well as stable AEs, (excited by an array of external antennas) in the JET tokamak are used to illustrate the efficacy of the method. Some additional general considerations regarding optimized spatial sampling strategies are also briefly addressed.(Some figures in this article are in colour only in the electronic version) BackgroundAnalysis of magnetic fluctuations external to toroidal plasmas is important for understanding the magneto-hydrodynamic (MHD) properties of the plasma, among other things. These properties affect nearly all aspects of behavior of magnetic confinement, and thus are of interest in topics ranging from gross global plasma stability, control and disruption avoidance to the 5

The JET Alfvén Eigenmode Local Manager for the real-time detection and tracking of a frequency-degenerate spectrum of MHD instabilities

“…As   W  may take values greater than 1/3 (as shown in figA1), the previous condition guarantees exact detection only if the signal consists of a single mode number. Nevertheless, it has been shown from many simulations and analysis of measurements using comparison between different numerical methods that such a solution generally gives very satisfactory results in terms of detection, even in the case of multiple modes (see for instance [12,25] and [31, part-2]. Moreover, for irregular sampling, uniqueness of the global minimizer is almost surely guaranteed if it has less than P/2 non-zero components, where P is the data size [12].…”

“…This has prompted the developments and the applications of various methods 4 to the analysis of MHD data in thermonuclear fusion plasmas, such as the Singular Value (SVD) [18,19] decomposition of unevenly sampled data using a very small number of measurement points. As some of the mathematical background of this method has been presented elsewhere [11,12,25,26], here we only briefly review its theoretical foundations, with a more compete overview given in Appendix-A to facilitate the reading of this contribution.In the standard tokamak coordinate system (toroidal angle , poloidal angle θ), and taking explicitly into account the usual 2D boundary conditions along the longitudinal (toroidal) axis and on the plane perpendicular to it (the poloidal direction), magnetic perturbations can be represented by functions involving toroidal (n) and poloidal (m) harmonics. Considering now the usual case of a perturbation with a specific toroidal mode number n, this can be written as ( , ) i t in im mn m n e e A e…”

“…This has prompted the developments and the applications of various methods 4 to the analysis of MHD data in thermonuclear fusion plasmas, such as the Singular Value (SVD) [18,19] decomposition of unevenly sampled data using a very small number of measurement points. As some of the mathematical background of this method has been presented elsewhere [11,12,25,26], here we only briefly review its theoretical foundations, with a more compete overview given in Appendix-A to facilitate the reading of this contribution.…”

“…Conversely, a method based on the Sparse Representation of Signals, as implemented in the SparSpec code (freeware available at: http://www.ast.obs-mip.fr/Softwares) has been demonstrated to perform efficiently and correctly the task of a post-pulse [25] and real-time [26] blind and unsupervised signal decomposition of unevenly sampled data using a very small number of measurement points. As some of the mathematical background of this method has been presented elsewhere [11,12,25,26], here we only briefly review its theoretical foundations, with a more compete overview given in Appendix-A to facilitate the reading of this contribution.…”

“…As some of the mathematical background of this method has been presented elsewhere [11,12,25,26], here we only briefly review its theoretical foundations, with a more compete overview given in Appendix-A to facilitate the reading of this contribution.…”