E. S. Avdeeva
The Lie group of symmetry of the one-dimensional differential equation of electron magnetohydrodynamics with effect of electron inertia and finite conducting is found. It's indicated that this group is group of shift of independent variables and non single-valuety of a potential. Therefore thee no automodel solution except for running vawes.
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Hall magnetohydrodynamic (MHD) with electron inertia is considered. A much wider class of equilibrium solutions and the concomitant self-organization aspects are discussed. The force-free field state B - J is shown to be a consequence of the triple Beltrami condition.
A version of extended magnetohydrodynamics (MHD) that incorporates electron inertia is obtained by constructing an action principle. Unlike MHD which freezes in magnetic flux, the present theory freezes in an alternative flux related to the electron canonical momentum. The associated Hamiltonian formulation is derived and reduced models that have previously been used to describe collisionless reconnection are obtained.
Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia
本文基于扩展磁流体动力学模型研究等离子体波模式，考虑霍尔漂移和电子惯性效应，推导了不可压缩XMHD的色散关系及其特征向量解，揭示了离子旋磁波和哨波分支的特性，证明XMHD比霍尔MHD更准确描述等离子体动力学。
The extended magnetohydrodynamics (MHD) system, including the Hall effect and the electron inertia effect, has a Hamiltonian structure embodied by a noncanonical Poisson algebra on an infinite-dimensional phase space. A nontrivial part of the formulation is the proof of Jacobi's identity for the Poisson bracket. We unearth a basic Lie algebra that generates the Poisson bracket. A class of similar Poisson algebra may be generated by the same Lie algebra, which encompasses the Hall MHD system and inertial MHD system.
This study investigates the properties of waves in relativistic extended magnetohydrodynamics (RXMHD), which includes Hall and electron thermal inertia effects. We focus on the case when the electron temperature is ultrarelativistic, and thus, the electron thermal inertia becomes finite at near the proton inertial scale. We derive the linear dispersion relation of RXMHD and find that the Hall and electron thermal inertia effects couple with the displacement current, giving rise to three superluminous waves in addition to the slow, fast, and Alfvén waves. We also show that the phase- and group-…
Universal energy cascade and relaxation in three-dimensional inertial electron magnetohydrodynamic turbulence
该研究推导了三维电子磁流体动力学湍流的精确级联关系，通过数值模拟验证了跨电子惯性尺度的普适能量级联，并利用非线性传递消失原理揭示了压力平衡的弛豫态。
Inertial effects in nonlinear magnetic reconnection are studied within the context of 2D electron magnetohydrodynamics (EMHD) with resistive and viscous dissipation. Families of nonlinear solutions for relevant current sheet parameters are predicted and confirmed numerically in all regimes of interest. Electron inertia becomes important for current sheet thicknesses $δ$ below the inertial length $d_{e}$. In this case, in the absence of electron viscosity, the sheet thickness experiences a nonlinear collapse. Viscosity regularizes solutions at small scales. Transition from resistive to viscous …
We have explored the thermodynamics of compressed magnetized plasmas in laboratory experiments and we call these studies "magnetothermodynamics". The experiments are carried out in the Swarthmore Spheromak eXperiment device. In this device, a magnetized plasma source is located at one end and at the other end, a closed conducting can is installed. We generate parcels of magnetized plasma and observe their compression against the end wall of the conducting cylinder. The plasma parameters such as plasma density, temperature, and magnetic field are measured during compression using HeNe laser int…
Charged space debris induced nonlinear magnetosonic waves using inertial magnetohydrodynamics
本文在惯性磁流体动力学框架下建立受迫Kadomtsev-Petviashvili方程，揭示带电空间碎片诱发的慢、快磁声孤波稳定性及精确加速解。
Variational Integrators for Inertial Magnetohydrodynamics
本文提出变分积分器，精确保持惯性磁流体动力学的守恒律，包括总能量和修改的磁能与交叉螺旋度，通过数值示例展示其优秀守恒性质。
A wave turbulence theory is developed for inertial electron magnetohydrodynamics (IEMHD) in the presence of a relatively strong and uniform external magnetic field $\boldsymbol{B_0} = B_0 \hat{\boldsymbol{e}}_\|$. This regime is relevant for scales smaller than the electron inertial length $d_e$. We derive the kinetic equations that describe the three-wave interactions between inertial whistler or kinetic Alfvén waves. We show that for both invariants, energy and momentum, the transfer is anisotropic (axisymmetric) with a direct cascade mainly in the direction perpendicular ($\perp$) to $\bold…
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 bet…
Based on the Langevin equation of Brownian motion, we present a simple model that emulates a typical mode in incompressible magnetohydrodynamic turbulence, providing a demonstration of several key properties. The model equation is consistent with von Kármán decay law and Kolmogorov's symmetries. We primarily focus on the behavior of inertial range modes although we also attempt to include some properties of the large scale modes. Dissipation scales are not considered. Results from the model are compared with results from published Direct Numerical Simulations.
Plasma density gradients are known to drive magnetic shocks in electron-magnetohydrodynamics (EMHD). Previous slab modeling has been extended to cylindrical modeling of radially imploding shocks. The main new effect of the cylindrical geometry is found to be a radial dependence in the speed of shock propagation. This is shown here analytically and in numerical simulations. Ion acceleration by the magnetic shock is shown to possibly become substantial, especially in the peaked structures that develop in the shock because of electron inertia.
The concept of magnetic connections is extended to non-ideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic c…
The wave propagation in the partially ionized ionosphere plays an important role in the magnetosphere ionosphere coupling. For example, the ionosphere may supports very low-frequency Alfven wave which can be caused by a balance between the bulk fluid inertia (mostly due to neutrals in the lower and middle E region) and the deformation of the magnetic field. The plasma neutral collisional momentum exchange facilitates the transfer of the magnetic stress (felt directly by the ions) to the neutrals. Therefore, in the low-frequency (with respect to the neutral ion collision frequency) limit, waves…
The evolution of the correlation characteristics in three-dimensional isotropic electron magnetohydrodynamic turbulence is investigated. Universal exact relations between the longitudinal and transverse two-point triple correlations of the components of the fluctuational magnetic fields and the rates of dissipation of the magnetic helicity and energy are obtained in the inertial range.
Magnetic fields can be generated in plasmas by the Biermann battery when the electric field produced by the electron pressure gradient has a curl. The commonly employed magnetohydrodynamic (MHD) model of the Biermann battery breaks down when the electron distribution function is distorted away from Maxwellian. Using both MHD and kinetic simulations of a laser-plasma interaction relevant to inertial confinement fusion we have shown that this distortion can reduce the Biermann-producing electric field by around 50\%. More importantly, the use of a flux limiter in an MHD treatment to deal with th…
Hydrodynamics of plasma in the random magnetic field is considered, which is characterized by the second moment of magnetic induction. Equations of ideal magnetic hydrodynamics in such field are received for an adiabatic process. It is shown that in Euler Equation a new variable is second moment of magnetic induction enters, for which is received time Equation on the basis of Maxwell Equations in the magnetohydrodynamic approximation. The one dimension plane waves in this system are studied and the values of their phase velocities are received.
The energy cascade of electron magnetohydrodynamic (EMHD) turbulence is considered. Fractal and multi-fractal models for the energy dissipation field are used to determine the spatial intermittency corrections to the scaling behavior in the high-wavenumber (electron hydrodynamic limit) and low-wavenumber (magnetization limit) asymptotic regimes of the inertial range. Extrapolation of the multi-fractal scaling down to the dissipative microscales confirms in these asymptotic regimes a dissipative anomaly previously indicated by the numerical simulations of EMHD turbulence. Several basic features…
Effective resistivity for magnetohydrodynamic simulation of collisionless magnetic reconnection
本文将含带电粒子动力学的有效电阻率模型应用于无引导场无碰撞磁重联的2.5维MHD与Hall MHD模拟，显著提升重联率并使结构与PIC及混合模拟吻合。
Large-amplitude Alfvén waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfvén wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfvén waves by an e…
The zeroth law is one of the oldest conjecture in turbulence that is still unproven. Here, we consider weak solutions of one-dimensional compressible magnetohydrodynamics and demonstrate that the lack of smoothness of the fields introduces a new dissipative term, named inertial dissipation, into the expression of energy conservation that is neither viscous nor resistive in nature. We propose exact solutions assuming that the kinematic viscosity and the magnetic diffusivity are equal, and we demonstrate that the associated inertial dissipation is positive and equal on average to the mean viscou…
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 magneto-Rayleigh-Taylor (MRT) instability has been investigated in great detail in previous work using magnetohydrodynamic and kinetic models for low-beta plasmas. The work presented here extends previous studies of this instability to regimes where finite-Larmor-Radius (FLR) effects may be important. Comparisons of the MRT instability are made using a 5-moment and a 10-moment two-fluid model, the two fluids being ions and electrons. The 5-moment model includes Hall stabilization whereas the 10-moment model includes Hall and FLR stabilization. Results are presented for these two models usi…
Employing a simple ideal magnetohydrodynamic model in spherical geometry,we show that the presence of either rotation or finite magnetic helicity is sufficient to induce dynamical reversals of the magnetic dipole moment. The statistical character of the model is similar to that of terrestrial magnetic field reversals, with the similarity being stronger when rotation is present.The connection between long time correlations, $1/f$ noise, and statistics of reversals is supported, consistent with earlier suggestions.
Two types of Eulerian action principles for relativistic extended magnetohydrodynamics (MHD) are formulated. With the first, the action is extremized under the constraints of density, entropy, and Lagrangian label conservation, which leads to a Clebsch representation for a generalized momentum and a generalized vector potential. The second action arises upon transformation to physical field variables, giving rise to a covariant bracket action principle, i.e., a variational principle in which constrained variations are generated by a degenerate Poisson bracket. Upon taking appropriate limits, t…
Generalized Expanding-Box Formulations of Reduced Magnetohydrodynamics in the Solar Wind
本文推导了一组用于研究径向膨胀太阳风小区域内约化磁流体动力学湍流的简化方程，支持盒子静止或沿磁场线以任意速度运动，特别关注与向外传播的 Alfvén 波同速的情况，并采用标量势和 Clebsch 坐标表示，以辅助未来高分辨率数值模拟的设计与优化。
Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the…
We use the framework of generalised global symmetries to study various hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The latter of these describes a one-form superfluid, which is characterised by a vector Goldstone mode and a two-form superfluid velocity. Two special limits of this theory have been studied in detail: the string fluid limit where the U(1) one-form symmetry is partly restored, and the electric limit in which the symmetry is completely broken. The transport properties of thes…
Hall effect on the joint cascades of magnetic energy and helicity in helical magnetohydrodynamic turbulence
本文通过直接数值模拟和Ulysses观测数据，揭示了螺旋磁流体湍流中霍尔效应通过诱导交叉螺旋度抑制逆级联，从而促进大尺度磁能与螺旋度积累的新机制。
The equilibrium of a cylindrical plasma with purely poloidal mass flow and cross section of arbitrary shape is investigated within the framework of the ideal MHD theory. For the system under consideration it is shown that only incompressible flows are possible and, conscequently, the general two dimensional flow equilibrium equations reduce to a single second-order quasilinear partial differential equation for the poloidal magnetic flux function $ψ$, in which four profile functionals of $ψ$ appear. Apart from a singularity occuring when the modulus of Mach number associated with the Alfvén vel…
The nonlinear dynamics of magnetic helicity, $H^M$, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of $H^M$ is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. \textbf{77} 321 (1976)]. By revisiting this theory a universal dynamical balance relation is …
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 stu…
A generalized fluid-particle hybrid model for collisionless plasmas under the assumption of quasi-neutrality is presented. The system consists of fluid ions and electrons as well as arbitrary numbers of species whose dynamics is governed by the Vlasov equation. The proposed model is thus a generalized version of the well-known standard hybrid plasma simulation model, in which the ions are fully kinetic whereas the electrons are assumed to be a fluid. Since the proposed model employs the exact form of the generalized Ohm's law, the mass and energy densities, as well as the charge-to-mass ratio …
We present a full two-fluid magnetohydrodynamic (MHD) description for a completely ionized hydrogen plasma, retaining the effects of the Hall current, electron pressure and electron inertia. According to this description, each plasma species introduces a new spatial scale: the ion inertial length $λ_{i}$ and the electron inertial length $λ_{e}$, which are not present in the traditional MHD description. In the present paper, we seek for possible changes in the energy power spectrum in fully developed turbulent regimes, using numerical simulations of the two-fluid equations in two-and-a-half dim…
We present a reduced magnetohydrodynamic (MHD) mathematical model describing the dynamical behavior of highly conducting plasmas with frozen-in magnetic fields, constrained by the assumption that, there exists a frame of reference, where the magnetic field vector, $\mathbf{B}$, is aligned with the plasma velocity vector, $\mathbf{u}$, at each point. We call this solution "stream-aligned MHD" (SA-MHD). Within the framework of this model, the electric field, $\mathbf{E} = -\mathbf{u} \times \mathbf{B} \equiv 0$, in the induction equation vanishes identically and so does the electromagnetic energ…
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. …
The three-dimensional (3D) Hall magnetohydrodynamics (HMHD) equations are often used to study turbulence in the solar wind. Some earlier studies have investigated the statistical properties of 3D HMHD turbulence by using simple shell models or pseudospectral direct numerical simulations (DNSs) of the 3D HMHD equations; these DNSs have been restricted to modest spatial resolutions and have covered a limited parameter range. To explore the dependence of 3D HMHD turbulence on the Reynolds number $Re$ and the ion-inertial scale $d_{i}$, we have carried out detailed pseudospectral DNSs of the 3D HM…
A constrained-transport embedded boundary method for compressible resistive magnetohydrodynamics
本文提出了一种用于可压缩电阻磁流体动力学的受限传输嵌入边界方法，通过有限体积法和鬼体方法实现任意形状边界，并验证了其在不同条件下的收敛性。
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