On the Singularity Structure of Alfvénic Turbulence

Abstract The singularity structure of the electromagnetic field fluctuations in strong Alfvénic turbulence is addressed. Owing to the transverse polarization of the fluctuations, the turbulent cascade is essentially perpendicular to the direction of the guiding magnetic field. A scaling analysis of the local energy transfer rates suggests that the most intense singularities are the sites of inertial dissipation of the energy. The lack of smoothness of the electromagnetic fields can give rise to dissipative processes unrelated to collisional transport phenomena in the magnetized plasma. A log-Poisson cascade model is developed. The random multiplicative cascade process is quantized and acts on the Elsässer field increments. In a multifractal interpretation, the log-Poisson cascade is characterized by three parameters: the most probable singularity strength, the strongest singularity, and its fractal codimension. The resulting probability distribution functions are derived from discrete superpositions of dilated integral scale distributions weighted by scale-dependent Poisson distributions. In addition to the three parameters mentioned above, they depend on the standard deviation of the integral scale fluctuations. The four-parameter family of normal log-Poisson mixture distributions is sensitive to the strongest singularities responsible for inertial dissipation of the electromagnetic energy in collisionless space plasma environments.