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Register a new userTest particle energization and the anisotropic effects of dynamical MHD turbulence
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In this paper we analyze the effect of dynamical three-dimensional MHD turbulence on test particle acceleration, and compare how this evolving system affects particle energization by current sheets interaction, against frozen-in-time fields. To do this we analize the ensamble particle acceleration for static electromagnetic fields extracted from direct numerical simulations of the MHD equations, and compare with the dynamical fields. We show that a reduction in particle acceleration in the dynamical model results from the particle trapping in the field lines, which forces the particles to remain in a moving current sheet that suppress the longer exposure at the strong electric field gradients located between structures, which is an efficient particle acceleration mechanism. In addition, we analize the effect of anisotropy caused by the mean magnetic field. It is well known that for sufficiently strong external fields, the system suffers a transition towards a two-dimensional flow. This causes an increment in the size of the coherent structures, resulting in a magnetized state of the particles and the reduction of the particle energization.
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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.
The effect of compressibility in charged particle energization by magnetohydrodynamic (MHD) fields is studiedin the context of test particle simulations. This problem is relevant to the solar wind and the solar corona due to the compressible nature of the flow in those astrophysical scenarios. We consider turbulent electromagnetic fields obtained from direct numerical simulations of the MHD equations with a strong background magnetic field. In order to explore the flow compressibilty effect over the particle dynamics we performed different numerical experiments: an incompressible case, and two weak compressible cases with Mach number M = 0.1 and M = 0.25. We analyze the behavior of protons and electrons in those turbulent fields, which are well known to form aligned current sheets in the direction of the guide magnetic field. What we call protons and electrons are test particles with scales comparable to (for protons) and much smaller than (for electrons) the dissipative scale of MHD turbulence, maintaining the correct mass ratio me /mi. For these test particles we show that compressibility enhances the efficiency of proton acceleration, and that the energization is caused by perpendicular electric fields generated between currents sheets. On the other hand, electrons remain magnetized and display an almost adiabatic motion, with no effect of compressibility observed. Another set of numerical experiments takes into account two fluid modifications, namely electric field due to Hall effect and electron pressure gradient. We show that the electron pressure has an important contribution to electron acceleration allowing highly parallel energization. In contrast, no significant effect of these additional terms is observed for the protons.
This review puts the developments of the last few years in the context of the canonical time line (Kolmogorov to Iroshnikov-Kraichnan to Goldreich-Sridhar to Boldyrev). It is argued that Beresnyaks objection that Boldyrevs alignment theory violates the RMHD rescaling symmetry can be reconciled with alignment if the latter is understood as an intermittency effect. Boldyrevs scalings, recovered in this interpretation, are thus an example of a physical theory of intermittency in a turbulent system. Emergence of aligned structures brings in reconnection physics, so the theory of MHD turbulence intertwines with the physics of tearing and current-sheet disruption. Recent work on this by Loureiro, Mallet et al. is reviewed and it is argued that we finally have a reasonably complete picture of MHD cascade all the way to the dissipation scale. This picture appears to reconcile Beresnyaks Kolmogorov scaling of the dissipation cutoff with Boldyrevs aligned cascade. These ideas also enable some progress in understanding saturated MHD dynamo, argued to be controlled by reconnection and to contain, at small scales, a tearing-mediated cascade similar to its strong-mean-field counterpart. On the margins of this core narrative, standard weak-MHD-turbulence theory is argued to require adjustment - and a scheme for it is proposed - to take account of the part that a spontaneously emergent 2D condensate plays in mediating the Alfven-wave cascade. This completes the picture of the MHD cascade at large scales. A number of outstanding issues are surveyed, concerning imbalanced MHD turbulence (for which a new theory is proposed), residual energy, subviscous and decaying regimes of MHD turbulence (where reconnection again features prominently). Finally, it is argued that the natural direction of research is now away from MHD and into kinetic territory.
The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $lambdasim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $lambda$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the sub-inertial, reconnection interval of MHD turbulence, with the Fourier energy spectrum $E(k_perp)propto k_perp^{-5/2}$, where $k_perp$ is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas ($Pm$), where the reconnection scale is found to be $lambda/Lsim S_L^{-4/7}Pm^{-2/7}$.
We present results of statistical analysis of solar wind turbulence using an approach based on the theory of Markov processes. It is shown that the Chapman-Kolmogorov equation is approximately satisfied for the turbulent cascade. We evaluate the first two Kramers-Moyal coefficients from experimental data and show that the solution of the resulting Fokker-Planck equation agrees well with experimental probability distributions. Our results suggest the presence of a local transfer mechanism for magnetic field fluctuations in solar wind turbulence.
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