Inertial range turbulence in kinetic plasmas

The transfer of turbulent energy through an inertial range from the driving scale to dissipative scales in a kinetic plasma followed by the conversion of this energy into heat is a fundamental plasma physics process. A theoretical foundation for the study of this process is constructed, but the details of the kinetic cascade are not well understood. Several important properties are identified: (a) the conservation of a generalized energy by the cascade; (b) the need for collisions to increase entropy and realize irreversible plasma heating; and (c) the key role played by the entropy cascade--a dual cascade of energy to small scales in both physical and velocity space--to convert ultimately the turbulent energy into heat. A strategy for nonlinear numerical simulations of kinetic turbulence is outlined. Initial numerical results are consistent with the operation of the entropy cascade. Inertial range turbulence arises in a broad range of space and astrophysical plasmas and may play an important role in the thermalization of fusion energy in burning plasmas.Comment: 11 pages, 2 figures, submitted to Physics of Plasmas, DPP Meeting Special Issu

Evidence of Critical Balance in Kinetic Alfven Wave Turbulence Simulations

A numerical simulation of kinetic plasma turbulence is performed to assess the applicability of critical balance to kinetic, dissipation scale turbulence. The analysis is performed in the frequency domain to obviate complications inherent in performing a local analysis of turbulence. A theoretical model of dissipation scale critical balance is constructed and compared to simulation results, and excellent agreement is found. This result constitutes the first evidence of critical balance in a kinetic turbulence simulation and provides evidence of an anisotropic turbulence cascade extending into the dissipation range. We also perform an Eulerian frequency analysis of the simulation data and compare it to the results of a previous study of magnetohydrodynamic turbulence simulations.Comment: 10 pages, 9 figures, accepted for publication in Physics of Plasma

On the two-dimensional state in driven magnetohydrodynamic turbulence

The dynamics of the two-dimensional (2D) state in driven tridimensional (3D) incompressible magnetohydrodynamic turbulence is investigated through high-resolution direct numerical simulations and in the presence of an external magnetic field at various intensities. For such a flow the 2D state (or slow mode) and the 3D modes correspond respectively to spectral fluctuations in the plan $k_\parallel=0$ and in the area $k_\parallel>0$. It is shown that if initially the 2D state is set to zero it becomes non negligible in few turnover times particularly when the external magnetic field is strong. The maintenance of a large scale driving leads to a break for the energy spectra of 3D modes; when the driving is stopped the previous break is removed and a decay phase emerges with alfv\'enic fluctuations. For a strong external magnetic field the energy at large perpendicular scales lies mainly in the 2D state and in all situations a pinning effect is observed at small scales.Comment: 11 pages, 11 figure

Is nonhelical hydromagnetic turbulence peaked at small scales?

Nonhelical hydromagnetic turbulence without an imposed magnetic field is considered in the case where the magnetic Prandtl number is unity. The magnetic field is entirely due to dynamo action. The magnetic energy spectrum peaks at a wavenumber of about 5 times the minimum wavenumber in the domain, and not at the resistive scale, as has previously been argued. Throughout the inertial range the spectral magnetic energy exceeds the kinetic energy by a factor of about 2.5, and both spectra are approximately parallel. At first glance, the total energy spectrum seems to be close to k^{-3/2}, but there is a strong bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}. This is supported by the value of the second order structure function exponent that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure

A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows

We explore some consequences of the ``alpha model,'' also called the ``Lagrangian-averaged'' model, for two-dimensional incompressible magnetohydrodynamic (MHD) turbulence. This model is an extension of the smoothing procedure in fluid dynamics which filters velocity fields locally while leaving their associated vorticities unsmoothed, and has proved useful for high Reynolds number turbulence computations. We consider several known effects (selective decay, dynamic alignment, inverse cascades, and the probability distribution functions of fluctuating turbulent quantities) in magnetofluid turbulence and compare the results of numerical solutions of the primitive MHD equations with their alpha-model counterparts' performance for the same flows, in regimes where available resolution is adequate to explore both. The hope is to justify the use of the alpha model in regimes that lie outside currently available resolution, as will be the case in particular in three-dimensional geometry or for magnetic Prandtl numbers differing significantly from unity. We focus our investigation, using direct numerical simulations with a standard and fully parallelized pseudo-spectral method and periodic boundary conditions in two space dimensions, on the role that such a modeling of the small scales using the Lagrangian-averaged framework plays in the large-scale dynamics of MHD turbulence. Several flows are examined, and for all of them one can conclude that the statistical properties of the large-scale spectra are recovered, whereas small-scale detailed phase information (such as e.g. the location of structures) is lost.Comment: 22 pages, 20 figure

Strong Imbalanced Turbulence

We consider stationary, forced, imbalanced, or cross-helical MHD Alfvenic turbulence where the waves traveling in one direction have higher amplitudes than the opposite waves. This paper is dedicated to so-called strong turbulence, which cannot be treated perturbatively. Our main result is that the anisotropy of the weak waves is stronger than the anisotropy of a strong waves. We propose that critical balance, which was originally conceived as a causality argument, has to be amended by what we call a propagation argument. This revised formulation of critical balance is able to handle the imbalanced case and reduces to old formulation in the balanced case. We also provide phenomenological model of energy cascading and discuss possibility of self-similar solutions in a realistic setup of driven turbulence.Comment: this is shorter, 5 page version of what is to appear in ApJ 682, Aug. 1, 200

Numerical simulations of strong incompressible magnetohydrodynamic turbulence

Magnetised plasma turbulence pervades the universe and is likely to play an important role in a variety of astrophysical settings. Magnetohydrodynamics (MHD) provides the simplest theoretical framework in which phenomenological models for the turbulent dynamics can be built. Numerical simulations of MHD turbulence are widely used to guide and test the theoretical predictions; however, simulating MHD turbulence and accurately measuring its scaling properties is far from straightforward. Computational power limits the calculations to moderate Reynolds numbers and often simplifying assumptions are made in order that a wider range of scales can be accessed. After describing the theoretical predictions and the numerical approaches that are often employed in studying strong incompressible MHD turbulence, we present the findings of a series of high-resolution direct numerical simulations. We discuss the effects that insufficiencies in the computational approach can have on the solution and its physical interpretation

Suppression of small scale dynamo action by an imposed magnetic field

Non-helical hydromagnetic turbulence with an externally imposed magnetic field is investigated using direct numerical simulations. It is shown that the imposed magnetic field lowers the spectral magnetic energy in the inertial range. This is explained by a suppression of the small scale dynamo. At large scales, however, the spectral magnetic energy increases with increasing imposed field strength for moderately strong fields, and decreases only slightly for even stronger fields. The presence of Alfven waves is explicitly confirmed by monitoring the evolution of magnetic field and velocity at one point. The frequency omega agrees with vA k1, where vA is the Alfven speed and k1 is the smallest wavenumber in the box.Comment: Final version (7 pages

On the Nature of Incompressible Magnetohydrodynamic Turbulence

A novel model of incompressible magnetohydrodynamic turbulence in the presence of a strong external magnetic field is proposed for explanation of recent numerical results. According to the proposed model, in the presence of the strong external magnetic field, incompressible magnetohydrodynamic turbulence becomes nonlocal in the sense that low frequency modes cause decorrelation of interacting high frequency modes from the inertial interval. It is shown that the obtained nonlocal spectrum of the inertial range of incompressible magnetohydrodynamic turbulence represents an anisotropic analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on the analysis performed in the framework of the weak coupling approximation, which represents one of the equivalent formulations of the direct interaction approximation, it is shown that incompressible magnetohydrodynamic turbulence could be both local and nonlocal and therefore anisotropic analogues of both the Kolmogorov and Kraichnan spectra are realizable in incompressible magnetohydrodynamic turbulence.Comment: Physics of Plasmas (Accepted). A small chapter added about 2D MHD turbulenc

Spectral energy dynamics in magnetohydrodynamic turbulence

Spectral direct numerical simulations of incompressible MHD turbulence at a resolution of up to $1024^3$ collocation points are presented for a statistically isotropic system as well as for a setup with an imposed strong mean magnetic field. The spectra of residual energy, $E_k^\mathrm{R}=|E_k^\mathrm{M}-E_k^\mathrm{K}|$, and total energy, $E_k=E^\mathrm{K}_k+E^\mathrm{M}_k$, are observed to scale self-similarly in the inertial range as $E_k^\mathrm{R}\sim k^{-7/3}$, $E_k\sim k^{-5/3}$ (isotropic case) and $E^\mathrm{R}_{k_\perp}\sim k_\perp^{-2}$, $E_{k_\perp}\sim k_\perp^{-3/2}$ (anisotropic case, perpendicular to the mean field direction). A model of dynamic equilibrium between kinetic and magnetic energy, based on the corresponding evolution equations of the eddy-damped quasi-normal Markovian (EDQNM) closure approximation, explains the findings. The assumed interplay of turbulent dynamo and Alfv\'en effect yields $E_k^\mathrm{R}\sim k E^2_k$ which is confirmed by the simulations.Comment: accepted for publication by PR