Sparsity-Promoting Dynamic Mode Decomposition of Plasma Turbulence

Time-varying structures are frequently observed in non-equilibrium systems. Magnetically confined plasma is a typical non-equilibrium system. The spatial inhomogeneity of plasma, which is produced and sustained by external sources, excites instabilities in the plasma. In turn, transport driven by the instabilities tries to mitigate the plasma’s inhomogeneity. As a result, spatial gradients, waves, flows and eddies coexist in the plasma and interact with each other causing the plasma to become turbulent [1, 2]. Due to the various nonlinearities in plasma, multi-scale spatiotemporal structures can form in the plasma turbulence [3]. The identification of the spatiotemporal structures in plasma turbulence is essential for visualizing their coarse-grained nature, where many decomposition techniques have been applied to time-series data of plasma turbulence [4, 5]. Fourier analysis is frequently used as a decomposition technique, however, ensemble averaging is required when it is applied to random signals. Usually, ensemble averaging is replaced by time averaging [6], which can mask the non-stationarity of the signals. Actually, structure in plasma turbulence varies in time [7], and thus new analysis tools, which can extract the non-stationary spatiotemporal structure of the turbulence, are required. Here we apply a dynamic mode decomposition (DMD) analysis to signals of turbulence in a magnetized laboratory plasma. Laboratory plasma is very useful as it allows us to verify the capability of our method, and because it has excellent reproducibility and controllability and allows for multi-point simultaneous measurements to be made. Since it was introduced in 2008 [8], DMD has been applied to fluid flow studies especially in analyses of nonlinear dynamics [9, 10]. From the spatiotemporal data obtained from an experiment or a numerical simulation,