Test-particle acceleration in a hierarchical three-dimensional turbulence model

The acceleration of charged particles is relevant to the solar corona over a broad range of scales and energies. High-energy particles are usually detected in concomitance with large energy release events like solar eruptions and flares, nevertheless acceleration can occur at smaller scales, characterized by dynamical activity near current sheets. To gain insight into the complex scenario of coronal charged particle acceleration, we investigate the properties of acceleration with a test-particle approach using three-dimensional magnetohydrodynamic (MHD) models. These are obtained from direct solutions of the reduced MHD equations, well suited for a plasma embedded in a strong axial magnetic field, relevant to the inner heliosphere. A multi-box, multi-scale technique is used to solve the equations of motion for protons. This method allows us to resolve an extended range of scales present in the system, namely from the ion inertial scale of the order of a meter up to macroscopic scales of the order of $10,$km ($1/100$th of the outer scale of the system). This new technique is useful to identify the mechanisms that, acting at different scales, are responsible for acceleration to high energies of a small fraction of the particles in the coronal plasma. We report results that describe acceleration at different stages over a broad range of time, length and energy scales.

Intermittency in Hall-magnetohydrodynamics with a strong guide field

We present a detailed study of intermittency in the velocity and magnetic field fluctuations of compressible Hall-magnetohydrodynamic turbulence with an external guide field. To solve the equations numerically, a reduced model valid when a strong guide field is present is used. Different values for the ion skin depth are considered in the simulations. The resulting data is analyzed computing field increments in several directions perpendicular to the guide field, and building structure functions and probability density functions. In the magnetohydrodynamic limit we recover the usual results with the magnetic field being more intermittent than the velocity field. In the presence of the Hall effect, field fluctuations at scales smaller than the ion skin depth show a substantial decrease in the level of intermittency, with close to monofractal scaling.

Local Anisotropy, Higher Order Statistics, and Turbulence Spectra

Correlation anisotropy emerges dynamically in magnetohydrodynamics (MHD), producing stronger gradients across the large-scale mean magnetic field than along it. This occurs both globally and locally, and has significant implications in space and astrophysical plasmas, including particle scattering and transport, and theories of turbulence. Properties of local correlation anisotropy are further documented here by showing through numerical experiments that the effect is intensified in more localized estimates of the mean field. The mathematical formulation of this property shows that local anisotropy mixes second-order with higher order correlations. Sensitivity of local statistical estimates to higher order correlations can be understood in connection with the stochastic coordinate system inherent in such formulations. We demonstrate this in specific cases, illustrate the connection to higher order statistics by showing the sensitivity of local anisotropy to phase randomization, and thus establish that the local structure function is not a measure of the energy spectrum. Evidently the local enhancement of correlation anisotropy is of substantial fundamental interest, and this phenomenon must be understood in terms of higher order correlations, fourth-order and above.

Large scale behavior and statistical equilibria in rotating flows

We examine long-time properties of the ideal dynamics of three--dimensional flows, in the presence or not of an imposed solid-body rotation and with or without helicity (velocity-vorticity correlation). In all cases the results agree with the isotropic predictions stemming from statistical mechanics. No accumulation of excitation occurs in the large scales, even though in the dissipative rotating case anisotropy and accumulation, in the form of an inverse cascade of energy, are known to occur. We attribute this latter discrepancy to the linearity of the term responsible for the emergence of inertial waves. At intermediate times, inertial energy spectra emerge that differ somewhat from classical wave-turbulence expectations, and with a trace of large-scale excitation that goes away for long times. These results are discussed in the context of partial two-dimensionalization of the flow undergoing strong rotation as advocated by several authors.