Relaxation Processes in Solar Wind Turbulence

Based on global conservation principles, magnetohydrodynamic (MHD) relaxation theory predicts the existence of several equilibria, such as the Taylor state or global dynamic alignment. These states are generally viewed as very long-time and large-scale equilibria, which emerge only after the termination of the turbulent cascade. As suggested by hydrodynamics and by recent MHD numerical simulations, relaxation processes can occur during the turbulent cascade that will manifest themselves as local patches of equilibrium-like configurations. Using multi-spacecraft analysis techniques in conjunction with Cluster data, we compute the current density and flow vorticity and for the first time demonstrate that these localized relaxation events are observed in the solar wind. Such events have important consequences for the statistics of plasma turbulence.

Yaglom law in the expanding solar wind

We study the Yaglom law, which relates the mixed third order structure function to the average dissipation rate of turbulence, in a uniformly expanding solar wind by using the two scales expansion model of magnetohydrodynamic (MHD) turbulence. We show that due to the expansion of the solar wind two new terms appear in the Yaglom law. The first term is related to the decay of the turbulent energy by nonlinear interactions, whereas the second term is related to the non-zero cross-correlation of the Elsasser fields. Using magnetic field and plasma data from WIND and Helios 2 spacecrafts, we show that at lower frequencies in the inertial range of MHD turbulence the new terms become comparable to Yagloms third order mixed moment, and therefore they cannot be neglected in the evaluation of the energy cascade rate in the solar wind.

Small Scale Energy Cascade of the Solar Wind Turbulence

Magnetic fluctuations in the solar wind are distributed according to Kolmogorovs power law $f^{-5/3}$ below the ion cyclotron frequency $f_{ci}$. Above this frequency, the observed steeper power law is usually interpreted in two different ways: a dissipative range of the solar wind turbulence or another turbulent cascade, the nature of which is still an open question. Using the Cluster magnetic data we show that after the spectral break the intermittency increases toward higher frequencies, indicating the presence of non-linear interactions inherent to a new inertial range and not to the dissipative range. At the same time the level of compressible fluctuations raises. We show that the energy transfer rate and intermittency are sensitive to the level of compressibility of the magnetic fluctuations within the small scale inertial range. We conjecture that the time needed to establish this inertial range is shorter than the eddy-turnover time, and is related to dispersive effects. A simple phenomenological model, based on the compressible Hall MHD, predicts the magnetic spectrum $sim k^{-7/3+2alpha}$, which depends on the degree of plasma compression $alpha$.