A numerical study of strong kinetic-Alfvén turbulence at scales smaller than the ion gyroscale is presented, and a phenomenological model is proposed that argues that magnetic and density fluctuations are concentrated mostly in two-dimensional structures, which leads to their Fourier energy spectra E(k ⊥ ) ∝ k −8/3 ⊥ , where k ⊥ is the wavevector component normal to the strong background magnetic field. The results may provide an explanation for recent observations of magnetic and density fluctuations in the solar wind at sub-proton scales.

We present an analytical study of subproton electromagnetic fluctuations in a collisionless plasma with a plasma beta of the order of unity. In the linear limit, a rigorous derivation from the kinetic equation is conducted focusing on the role and physical properties of kinetic-Alfvén and whistler waves. Then, nonlinear fluid-like equations for kinetic-Alfvén waves and whistler modes are derived, with special emphasis on the similarities and differences in the corresponding plasma dynamics. The kinetic-Alfvén modes exist in the lower-frequency region of phase space, ω k ⊥ v T i , where they are described by the kinetic-Alfvén system. These modes exist both below and above the ion-cyclotron frequency. The whistler modes, which are qualitatively different from the kinetic-Alfvén modes, occupy a different region of phase space, k ⊥ v T i ω k z v T e , and they are described by the electron magnetohydrodynamics (MHD) system or the reduced electron MHD system if the propagation is oblique. Here, k z and k ⊥ are the wavenumbers along and transverse to the background magnetic field, respectively, and v T i and v T e are the ion and electron thermal velocities, respectively. The models of subproton plasma turbulence are discussed and the results of numerical simulations are presented. We also point out possible implications for solar-wind observations.

We develop a framework for studying the statistical properties of current sheets in numerical simulations of 3D magnetohydrodynamic (MHD) turbulence. We describe an algorithm that identifies current sheets in a simulation snapshot and then determines their geometrical properties (including length, width, and thickness) and intensities (peak current density and total energy dissipation rate). We then apply this procedure to simulations of reduced MHD turbulence and perform a statistical analysis on the obtained population of current sheets. We evaluate the role of reconnection by separately studying the populations of current sheets which contain magnetic X-points and those which do not. We find that the statistical properties of the two populations are different in general. We compare the scaling of these properties to phenomenological predictions obtained for the inertial range of MHD turbulence. Finally, we test whether the reconnecting current sheets are consistent with the Sweet-Parker model.

Strong incompressible three-dimensional magnetohydrodynamic turbulence is investigated by means of high resolution direct numerical simulations. The simulations show that the configuration space is characterized by regions of positive and negative cross-helicity, corresponding to highly aligned or anti-aligned velocity and magnetic field fluctuations, even when the average cross-helicity is zero. To elucidate the role of cross-helicity, the spectra and structure of turbulence are obtained in 'imbalanced' regions where cross-helicity is non-zero. When averaged over regions of positive and negative cross-helicity, the result is consistent with the simulations of balanced turbulence. An analytical explanation for the obtained results is proposed.