One-point statistics of the induced electric field in quasinormal magnetofluid turbulence

We study one-point statistical properties of the induced turbulent electric field for a magnetohydrodynamic (MHD) plasma under the quasinormal approximation. Assuming exact Gaussianity for both the velocity field and the magnetic field, and different degrees of correlations between their Cartesian components, we derive the probability distribution function (PDF) for the Cartesian components of the electric field e(i). We show that the PDF reduces in some canonical cases to an exponential function of the form exp(-/e(i)/). To study deviations from these results in the more realistic case in which the velocity and magnetic fields are not exactly normal but quasinormal instead, we perform three-dimensional numerical simulations of the MHD equations at moderate Reynolds numbers. For turbulent relaxation from an initial condition, we find that the analytical results give a very good first-order approximation to the computed PDF.