René Chavan, Ambrogio Fasoli, Jonathan Bryan Lister, Jean-Marc Moret, Theodoros Panis, Francisco Sanchez, Duccio Testa, Matthieu Toussaint
Analysis of magnetic fluctuations is important for understanding the magneto-hydrodynamic (MHD) properties of fusion plasmas. These properties affect nearly all aspects of behaviour of magnetic confinement, and thus are of interest in topics ranging from global plasma stability, control, and disruption avoidance, to more subtle areas such as MHD spectroscopy. Mode number analysis is generally accomplished by interpreting signals from a finite number of Mirnov coils, which typically are unevenly spaced in the spatial coordinates. Many aspects of the MHD spectroscopy technique rely specifically on the precise determination of the toroidal (n) and poloidal (m) mode numbers. Moreover, in fusion plasmas it is often of further benefit to be able to perform such analysis in “real–time”, i.e. using a clock-rate of the order of 1ms. The variety of methods in common use to determine the spatial structure of MHD phenomena in fusion plasmas from magnetic measurements is quite small. Traditionally, the linear phase fitting, the Fourier decomposition, the Lomb periodogram and fitting techniques such as the Wigner and Choi-Williams distributions have been proposed. More recently, Singular Value Decomposition and wavelets have also been used regularly. However, all these techniques suffer variously from at least one between these four main limitations: (1) the phase relation between the in-phase and quadrature (I/Q) components of the measured (complex) fluctuations is not always conserved (Wigner, Choi-Williams distributions); (2) multiple degenerate harmonics are not correctly treated (linear phase fitting, Fourier decomposition, Lomb periodogram, Wigner and Choi-Williams distributions); (3) uniform sampling is assumed (Fourier decomposition, Lomb periodogram); (4) a truly blind analysis is very CPU-time consuming, hence it is not suitable for real-time applications (wavelets, SVD). On the other hand, the problem of finding periodic waveforms in unevenly sampled data is ubiquitous in the field of astronomy, where much work has been done. It is easily seen that temporal frequencies in astronomical data correspond to spatial mode numbers in fusion plasmas, and that unevenly sampled data in time domain are the analog of data from unevenly distributed Mirnov sensors in the toroidal and poloidal coordinates. However, in astronomy, the frequencies sought are allowed to take on any value, while periodic boundaries in fusion devices ensure that only modes with integer mode numbers exist. Since all astronomical data is unevenly sampled (due to weather conditions and the earth rotation), considerable effort has gone into the problem of improving upon the limitations of the classic Lomb periodogram. Recently, a new method for fitting sinusoids to irregularly sampled data was proposed, based on the principle of sparse representation of signals: this is implemented in the SparSpec code (available at: http://www.ast.obs-mip.fr/softwares). As the analysis of MHD fluctuations data from the JET tokamak will show, this method has proven to be far superior to other methods in terms of accuracy and computational speed of the calculation, so much so that in fact it has recently been implemented for real-time detection of toroidal mode numbers for the active MHD spectroscopy diagnostic system in JET. Further application of the SparSpec analysis method to the design of the high-frequency magnetic diagnostic system for ITER will be discussed, with a view to develop ideas for future collaborative activities.