We propose a phenomenological theory of strong incompressible magnetohydrodynamic turbulence in the presence of a strong large-scale external magnetic field. We argue that in the inertial range of scales, magnetic-field and velocity-field fluctuations tend to align the directions of their polarizations. However, the perfect alignment cannot be reached; it is precluded by the presence of a constant energy flux over scales. As a consequence, the directions of shear-Alfvén fluid and magnetic-field fluctuations at each scale lambda become effectively aligned within the angle phi(lambda) proportional to lambda (1/4), which leads to scale-dependent depletion of the nonlinear interaction and to the field-perpendicular energy spectrum E(k(perpendicular)) proportional to k(perpendicular)(-3/2). Our results may be universal, i.e., independent of the external magnetic field, since small-scale fluctuations locally experience a strong field produced by large-scale eddies.

We propose a phenomenological model for incompressible magnetohydrodynamic turbulence. We argue that nonlinear-wave interaction weakens as the energy cascade proceeds to small scales, however, the anisotropy of fluctuations along the large-scale magnetic field increases, which makes turbulence strong at all scales. To explain the weakening of the interaction, we propose that small-scale fluctuations of the velocity and magnetic fields become increasingly dynamically aligned as their scale decreases, so that turbulent eddies become locally anisotropic in the plane perpendicular to the large-scale magnetic field. In the limit of weak anisotropy, that is, weak large-scale magnetic field, our model reproduces the Goldreich-Sridhar spectrum, while the limit of strong anisotropy, that is, strong large-scale magnetic field, corresponds to the Iroshnikov-Kraichnan scaling of the spectrum. This is in good agreement with recent numerical results.Comment: 10 pages, 1 figure; minor changes to match published versio

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.