Statistical analysis technique for estimation of causal relationship in plasma turbulence

A new method of analyzing the causal relationship of the interaction between various fluctuating quantities and the mean gradient in turbulent plasmas is proposed. This method involves (1) calculating the correlation coefficient R and the directional area A for the pair of turbulent quantities of interest, and (2) creating a time ensemble consisting of (R; A) during many fluctuation periods. The statistical features of each ensemble can be used to determine the order of occurrence, and hence, the causal relationship between the two fluctuating quantities. We apply this analytical method to the analysis of a plasma in which the drift wave and interchange mode interact with and are modulated by the density gradient. The causal relationship between the drift wave and the density gradient is discussed.