Diagnosis of Magnetic Structures and Intermittency in Space Plasma Turbulence Using the Method of Surrogate Data

Several observations in space plasmas have reported the presence of coherent structures at different plasma scales. Structure formation is believed to be a direct consequence of nonlinear interactions between plasma modes that depend strongly on the phase synchronization of those modes. Despite this important role of phases in turbulence, very limited work has been devoted to study the phases as potential tracers of nonlinearities in comparison with the wealth of literature on power spectra of turbulence, where phases are generally ignored. The reason why the phases are seldom used is probably because they usually appear to be completely mixed (due to their dependence on an arbitrary time origin and to their 2π periodicity). We present a method based on surrogate data allowing one to systematically detect coherent structures in turbulent signals. After validating the method on synthetic data, we present recent results based on Cluster observations. We show in particular a direct relationship between the identified phase coherence and intermittency (classically identified as non Gaussian tails of the probability distribution functions) as well as the turbulent energy cascade. We show also how one can: (i) prove the presence of a cascade of turbulent energy when power law spectra are observed; and (ii) test the validity of the Random Phase Approximation usually used in theoretical modeling of turbulence, particularly in quasilinear and weak turbulence theories.