The biorthogonal decomposition as a tool for investigating fluctuations in plasmas

Abstract

The investigation of fluctuation phenomena in plasmas often necessitates the analysis of spatiotemporal signals. It is shown how such signals can be analyzed using the biorthogonal decomposition, which splits them into orthogonal spatial and temporal modes. The method, also referred to as the singular value decomposition, allows complex spatiotemporal patterns to be decomposed into a few coherent modes that are often easier to interpret. This is illustrated with two applications to fluctuating soft x-ray and magnetic signals, as measured in a tokamak. Emphasis is given to the physical interpretation of the biorthogonal components and their link with known physical models is discussed. It is shown how new insight can be gained in the interpretation of spatiotemporal plasma dynamics.