The nonlinear dynamics of axisymmetric, as well as helical, frozen-in vortex structures is investigated by the Hamiltonian method in the framework of ideal incompressible electron magnetohydrodynamics. For description of current-sheet formation from a smooth initial magnetic field, local and nonlocal nonlinear approximations are introduced and partially analyzed that are generalizations of the previously known exactly solvable local model neglecting electron inertia. Finally, estimations are made that predict finite-time singularity formation for a class of hydrodynamic models intermediate between that local model and the Eulerian hydrodynamics.
Current-sheet Evolution near a Hyperbolic Magnetic Neutral Line in Hall Magnetohydrodynamics: An Exact Solution
研究了双曲磁中性线附近的\large{\bf Abstract-}非定常霍尔磁流体动力学。给出了描述自相似演化的精确解析解。该解显示，在小时候，霍尔效应对双曲磁中性线附近的电流片形成过程的影响可以忽略不计，但随后，理想磁流体力学中表现出的有限时间奇异性的霍尔效应会猝灭，从而防止电流密度在大时间内爆炸。由这个含时解给出的渐近结果与$X$型磁中性线附近的\textit{steady} Hall MHD公式（Shivamoggi [23]）完全定量一致。后一公式表明，这个渐近结果确实对应于\textit{steady}情形中磁场的双曲线构形。
An integrable localized approximation for interaction of two nearly anti-parallel sheets of the generalized vorticity in 2D ideal electron-magnetohydrodynamic flows
We derive the coarse-graining (CG) equations of incompressible Hall Magnetohydrodynamics (HMHD) turbulence to investigate the {\it local (in space)} energy cascade rate as a function of the filtering scale $\ell$. First, the CG equations are space averaged to obtain the analytical expression of the mean cascade rate. Its application to 3 dimensional (3D) simulations of (weakly compressible) HMHD shows a cascade rate consistent with the value of the mean dissipation rate in the simulations and with the classical estimates based on the "third-order" law. Furthermore, we developed an anisotropic …
Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities
Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics I: Lagrangian mechanics on semidirect product of two volume preserving diffeomorphisms and conservation laws
利用拉格朗日力学，在两个保体积同形群的半直积上，建立了无耗散不可压缩霍尔磁流体动力学（HMHD）介质的动力学方程。在$\mathbb{T}^3$或$E^3$的情况下，Galtier（S. Galtier 2006 J. Plasma Phys.72 721-769）给出了诸如李代数的结构常数、运动运动方程和守恒定律的基本公式和方程的非常简单的表达式。四个常数的运动，其中三个是独立的，自然来自广义Elsasser变量表示的运动方程的HMHD系统：总等离子体能量，磁螺旋度，混合螺旋度，和修改后的交叉螺旋度。
Rigorous theories of the tearing instability are mathematically quite involving. Therefore, the present note aims to demonstrate how their main results can be reproduced by a simple qualitative analysis of the respective magnetohydrodynamic (MHD) equations.
The transport of waves and turbulence beyond the photosphere is central to the coronal heating problem. Turbulence in the quiet solar corona has been modeled on the basis of the nearly incompressible magnetohydrodynamic (NI MHD) theory to describe the transport of low-frequency turbulence in open magnetic field regions. It describes the evolution of the coupled majority quasi-2D and minority slab component, driven by the magnetic carpet and advected by a subsonic, sub-Alfvenic flow from the lower corona. In this paper, we couple the NI MHD turbulence transport model with an MHD model of the so…
Hamiltonian extended magnetohydrodynamics (XMHD) is restricted to respect helical symmetry by reducing the Poisson bracket for 3D dynamics to a helically symmetric one, as an extension of the previous study for translationally symmetric XMHD (D.A. Kaltsas et al, Phys. Plasmas 24, 092504 (2017)). Four families of Casimir invariants are obtained directly from the symmetric Poisson bracket and they are used to construct Energy-Casimir variational principles for deriving generalized XMHD equilibrium equations with arbitrary macroscopic flows. The system is then cast into the form of Grad-Shafranov…
The present paper provides comprehensive description of various regimes involved in the two-fluid model of the resistive tearing instability. These include two novel regimes of this instability, which correspond to the long-wave modes that can develop in a highly-elongated current sheet. This issue is relevant to the study of fast magnetic reconnection and magnetic turbulence in magnetohydrodynamic (MHD) objects with a large value of the Lundquist number.
Nature of Transonic Sub-Alfvénic Turbulence and Density Fluctuations in the Near-Sun Solar Wind: Insights from Magnetohydrodynamic Simulations and Nearly-Incompressible Models
University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Alabama in Huntsville（阿拉巴马大学亨茨维尔分校）；Center for Space Plasma and Aeronomic Research (CSPAR)（空间等离子体与航空研究发展中心）
We report a numerical investigation of three dimensional, incompressible, Hall magnetohydrodynamic turbulence with a relatively strong mean magnetic field. Using helicity decomposition and cross-bicoherence analysis, we observe that the resonant three--wave coupling is substantial among ion cyclotron and whistler waves. A detailed study of the degree of non-linearity of these two populations shows that the ion cyclotron component experiences a transition from weak to strong wave turbulence going from large to small scales, while the whistler fluctuations display a weak wave turbulence characte…
The incompressibility constraint for fluid flow was imposed by Lagrange in the so-called Lagrangian variable description using his method of multipliers in the Lagrangian (variational) formulation. An alternative is the imposition of incompressibility in the Eulerian variable description by a generalization of Dirac's constraint method using noncanonical Poisson brackets. Here it is shown how to impose the incompressibility constraint using Dirac's method in terms of both the canonical Poisson brackets in the Lagrangian variable description and the noncanonical Poisson brackets in the Eulerian…
A dynamical vectorial equation for homogeneous incompressible Hall-MHD turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibits a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term but the dynamic law derived in the framework of incompressible Hall MHD equations is obtained only in a low plasma beta simulation. …
We present a local approach to the study of scale-to-scale energy transfers in magnetohydrodynamic (MHD) turbulence. This approach is based on performing local averages of the physical fields, which amounts to filtering scales smaller than some parameter $\ell$. A key step in this work is the derivation of a local Kármán-Howarth-Monin relation which provides a local form of Politano and Pouquet's 4/3-law, without any assumption of homogeneity or isotropy. Our approach is exact, non-random, and we show its connection to the usual statistical results of turbulence. Its implementation on data obt…
Sweet-Parker current sheets in high Lundquist number plasmas are unstable to tearing, suggesting they will not form in physical systems. Understanding magnetic reconnection thus requires study of the stability of a current sheet as it forms. Formation can occur due to sheared, sub-Alfvénic incompressible flows which narrow the sheet. Standard tearing theory (Furth et al. 1963; Coppi et al. 1976; Rutherford 1973) is not immediately applicable to such forming sheets for two reasons: first, because the flow introduces terms not present in the standard calculation; second, because the changing equ…
When magnetohydrodynamic turbulence evolves in the presence of a large-scale mean magnetic field, an anisotropy develops relative to that preferred direction. The well-known tendency is to develop stronger gradients perpendicular to the magnetic field, relative to the direction along the field. This anisotropy of the spectrum is deeply connected with anisotropy of estimated timescales for dynamical processes, and requires reconsideration of basic issues such as scale locality and spectral transfer. Here analysis of high-resolution three-dimensional simulations of unforced magnetohydrodynamic t…
We present high resolution 2D and 3D simulations of magnetized decaying turbulence in relativistic resistive magneto-hydrodynamics. The simulations show dynamic formation of large scale intermittent long-lived current sheets being disrupted by the tearing instability into plasmoid chains. These current sheets are locations of enhanced magnetic field dissipation and heating of the plasma. We find magnetic energy spectra $\propto k^{-3/2}$, together with strongly pronounced dynamic alignment of Elsasser fields and of velocity and magnetic fields, for strong guide-field turbulence, whereas we ret…
Negative energy wave phenomena may appear in shear flows in the presence of a wave decay mechanism and external energy supply. We study the appearance of negative energy surface waves in a plasma cylinder in the incompressible limit. The cylinder is surrounded by an axial magnetic field and by a plasma of different density. Considering flow inside and viscosity outside the flux tube, we derive dispersion relations, and obtain analytical solutions for the phase speed and growth rate (increment) of the waves. It is found that the critical speed shear for the occurrence of the dissipative instabi…
PHASE: Multi-Regime Modeling of Incompressible Magnetohydrodynamics
Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；Purdue University（普渡大学）；University of Maryland, College Park（马里兰大学帕克分校）；Flatiron Institute（熨斗研究所）
The plasmoid instability in evolving current sheets has been widely studied due to its effects on the disruption of current sheets, the formation of plasmoids, and the resultant fast magnetic reconnection. In this Letter, we study the role of the plasmoid instability in two-dimensional magnetohydrodynamic (MHD) turbulence by means of high-resolution direct numerical simulations. At sufficiently large magnetic Reynolds number ($R_m=10^6$), the combined effects of dynamic alignment and turbulent intermittency lead to a copious formation of plasmoids in a multitude of intense current sheets. The …
It is well established that the magnetically structured solar atmosphere supports the propagation of MHD waves along various kind of jets including also the solar wind. It is well-known as well that under some conditions, namely high enough jet speeds, the propagating MHD modes can become unstable against to the most common Kelvin--Helmholtz instability (KHI). In this article, we explore how the propagation and instability characteristics of running along a slow solar wind MHD modes are affected when they are investigated in the framework of the ideal Hall-magnetohydrodynamics. Hall-MHD is app…
We construct finite element methods for the incompressible magnetohydrodynamics (MHD) system that precisely preserve magnetic and cross helicity, the energy law and the magnetic Gauss law at the discrete level. The variables are discretized as discrete differential forms in a de Rham complex. We present numerical tests to show the performance of the algorithm.
In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD t…
We study the existence and property of Fast magnetosonic modes in 3D compressible MHD turbulence by carrying out a number of simulations with compressible and incompressible driving conditions. We use two approaches to determine the presence of Fast modes: mode decomposition based on spatial variations only and spatio-temporal 4D-FFT analysis of all fluctuations. The latter method enables us to quantify fluctuations that satisfy the dispersion relation of Fast modes with finite frequency. Overall, we find that the fraction of Fast modes identified via spatio-temporal 4D FFT approach in total f…
