Electron Magnetohydrodynamics Research Articles

Physical processes in an electron current layer causing intense plasma heating and formation of x-lines

We study the evolution of an electron current layer (ECL) through its several stages by means of three-dimensional particle-in-cell (PIC) simulations with ion to electron mass ratio M/me = 400. An ECL evolves through the following stages: (i) Electrostatic (ES) current-driven instability (CDI) soon after its formation with half width w about 2 electron skin depth (de), (ii) current disruption in the central part of the ECL by trapping of electrons and generation of anomalous resistivity, (iii) electron tearing instability (ETI) with significantly large growth rates in the lower end of the whistler frequency range, (iv) widening of the ECL and modulation of its width by the ETI, (v) gradual heating of electrons by the CDI-driven ES ion modes create the condition that the electrons become hotter than the ions, (vi) despite the reduced electron drift associated with the current disruption by the CDI, the enhanced electron temperature continues to favor a slow growth of the ion waves reaching nonlinear amplitudes, (vii) the nonlinear ion waves undergo modulation and collapse into localized density cavities containing spiky electric fields like in double layers (DLs), (viii) such spiky electric fields are very effective in further rapid heating of both electrons and ions. As predicted by the electron magnetohydrodynamic (EMHD) theories, the ETI growth rate maximizes at wave numbers in the range 0.4 < kxW < 0.8 where kx is the wave number parallel to the ECL magnetic field and w is the evolving half width of the ECL. The developing ETI generates in-plane currents that support out-of-plane magnetic fields around the emerging x-lines. The ETI and the spiky electrostatic structures are accompanied by fluctuations in the magnetic fields near and above the lower-hybrid (ion plasma) frequency, including the whistler frequency range. We compare our results with experimental results and satellite observation.

INVERSE CASCADE IN IMBALANCED ELECTRON MAGNETOHYDRODYNAMIC TURBULENCE

Electron magnetohydrodynamics (EMHD) provides a fluid-like description of small-scale magnetized plasmas. Balanced EMHD turbulence has been studied for a long time. However, driven imbalanced EMHD turbulence, in which waves moving in one direction (dominant waves) have higher amplitudes than waves moving in the other direction (sub-dominant waves), has not been well studied. In this paper, we numerically study driven three-dimensional imbalanced weak EMHD turbulence. We find the following results. First, in driven imbalanced EMHD turbulence, we clearly observe inverse cascade of magnetic helicity, as well as magnetic energy. This is because magnetic helicity is a conserved quantity and non-zero magnetic helicity is injected into the system in driven imbalanced EMHD turbulence. Second, the magnetic energy spectrum of the dominant waves on scales larger than the energy injection scale does not show a single power-law spectrum, which indicates that the inverse cascade is not a self-similar process. The peak of the spectrum roughly follows a k –3/2 spectrum, which can be explained by a Kolmogorov-type argument for weak turbulence. Third, a small amount of sub-dominant waves is induced by the dominant waves on large scales and the ratio of helicity densities of the dominant and the sub-dominant waves on large scales seems to converge to a certain value.

Electron magnetohydrodynamic turbulence: universal features

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 of the EMHD turbulent system are found to be universal which seem to transcend the existence of the characteristic length scale d e (which is the electron skin depth) in the EMHD problem: equipartition spectrum; Reynolds-number scaling of the dissipative microscales; scaling of the probability distribution function (PDF) of the electron-flow velocity (or magnetic field) gradient (even with intermittency corrections); dissipative anomaly; and critical exponent scaling.

Magnetar activity mediated by plastic deformations of neutron star crust

We advance a "Solar flare" model of magnetar activity, whereas a slow evolution of the magnetic field in the upper crust, driven by electron MHD (EMHD) flows, twists the external magnetic flux tubes, producing persistent emission, bursts and flares. At the same time the neutron star crust plastically relieves the imposed magnetic field stress, limiting the strain $ \epsilon_t $ to values well below the critical strain $ \epsilon_{crit}$ of a brittle fracture, $ \epsilon_t \sim 10^{-2}\epsilon_{crit} $. Magnetar-like behavior, occurring near the magnetic equator, takes place in all neutron stars, but to a different extent. The persistent luminosity is proportional to cubic power of the magnetic field (at a given age), and hence is hardly observable in most rotationally powered neutron stars. Giant flares can occur only if the magnetic field exceeds some threshold value, while smaller bursts and flares may take place in relatively small magnetic fields. Bursts and flares are magnetospheric reconnection events that launch Alfven shocks which convert into high frequency whistlers upon hitting the neutron star surface. The resulting whistler pulse induces a strain that increases with depth both due to the increasing electron density (and the resulting slowing of the waves), and due to the increasing coherence of a whistler pulse with depth. The whistler pulse is dissipated on a time scale of approximately a day at shallow depths corresponding to $\rho \sim 10^{10} {\rm g cm}^{-3}$; this energy is detected as enhanced post-flare surface emission.

Nonlinear wave collapse, shock, and breather formation in an electron magnetohydrodynamic plasma.

Low-frequency nonlinear wave dynamics is investigated in a two-dimensional inhomogeneous electron magnetohydrodynamic (EMHD) plasma in the presence of electron viscosity. In the long-wavelength limit, the dynamics of the wave is found to be governed by a novel nonlinear equation. The result of the moving-frame nonlinear analysis is noteworthy, which shows that this nonlinear equation does have a breather solution and electron viscosity is responsible for the breather. A breather is a nonlinear wave in which energy accumulates in a localized and oscillatory manner. Analytical solution and time-dependent numerical simulation of this novel equation reveal the collapse of a soliton (localized pulse) into a weak noise shelf and formation of shocklike structures.

Entanglement of helicity and energy in kinetic Alfvén wave/whistler turbulence

The role of magnetic helicity is investigated in kinetic Alfvén wave and oblique whistler turbulence in presence of a relatively intense external magnetic fieldb0e∥. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall magnetohydrodynamics (MHD). We use the asymptotic equations derived by Galtier and Bhattacharjee (2003Phys. Plasmas10, 3065–3076) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation,n + ñ= −6, wherenandñare the power law indices of the perpendicular (tob0) wave number magnetic energy and helicity spectra, respectively. Therefore, the spectra derived in the past from the energy equation only, namelyn= −2.5 andñ= −3.5, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solutionñ= −3 is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that −3 &lt;n&lt; −2.5.

Action principles for extended magnetohydrodynamic models

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended magnetohydrodynamic (MHD), Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.

Whistler interaction with field‐aligned density irregularities in the ionosphere: Refraction, diffraction, and interference

AbstractField‐aligned density irregularities (FAI) with kilometer‐scale sizes transverse to the background magnetic field are a common feature in the ionosphere at all latitudes and local times. In this paper, we investigate the effect of these irregularities on the transionospheric propagation of very low frequency whistler waves and develop a quantitative description of FAI‐related effects on whistler propagation through the lower ionosphere. Using an electron magnetohydrodynamics simulation, we provide two applications of our model. First, we show that the presence of kilometer‐scale FAI in the ionosphere can reduce the power observed in the equatorial magnetosphere by more than 10 dB in some cases. Second, we demonstrate that multiple FAIs can act as a discrete lens for whistlers, providing a possible means for increasing wave power in artificial whistler ducting experiments.

EMHD theory and observations of electron solitary waves in magnetotail plasmas

AbstractA new approach of electron magnetohydrodynamics (EMHD) is developed by including the anisotropy of the electron pressure tensor to take Biermann battery effect into account. Based on the model, the dispersion relation of slow and fast electron magnetosonic modes are derived. A Korteweg‐de Vries equation is then obtained from the wave equation to get a solution of one‐dimensional slow‐mode soliton. Furthermore, according to measurements of Cluster and Time History of Events and Macroscale Interactions during Substorms, we find a good agreement between the theory and observations of magnetic field depression and perpendicular pressure increase.

Density-shear instability in electron magneto-hydrodynamics

We discuss a novel instability in inertia-less electron magneto-hydrodynamics (EMHD), which arises from a combination of electron velocity shear and electron density gradients. The unstable modes have a lengthscale longer than the transverse density scale, and a growth-rate of the order of the inverse Hall timescale. We suggest that this density-shear instability may be of importance in magnetic reconnection regions on scales smaller than the ion skin depth, and in neutron star crusts. We demonstrate that the so-called Hall drift instability, previously argued to be relevant in neutron star crusts, is a resistive tearing instability rather than an instability of the Hall term itself. We argue that the density-shear instability is of greater significance in neutron stars than the tearing instability, because it generally has a faster growth-rate and is less sensitive to geometry and boundary conditions. We prove that, for uniform electron density, EMHD is “at least as stable” as regular, incompressible MHD, in the sense that any field configuration that is stable in MHD is also stable in EMHD. We present a connection between the density-shear instability in EMHD and the magneto-buoyancy instability in anelastic MHD.

Partially transverse and partially longitudinal wave in non-uniform electron plasmas

It is pointed out that in the slow time scale perturbations the displacement current is ignored but it does not imply that the electron density fluctuations vanish. The dispersion relation of the low-frequency electromagnetic wave described within the framework of electron magnetohydrodynamics (EMHD) is modified by taking into account the longitudinal effects. This wave can couple with plasma lower hybrid oscillations if ion dynamics is also considered. The low-frequency wave discussed here can have many applications in plasma transport and plasma opening switches.

Purely helical absolute equilibria and chirality of (magneto)fluid turbulence

AbstractPurely helical absolute equilibria of incompressible neutral fluids and plasmas (electron, single-fluid and two-fluid magnetohydrodynamics) are systematically studied with the help of helical (wave) representation and truncation, for genericities and specificities about helicity. A unique chirality selection and amplification mechanism and relevant insights, such as the one-chiral-sector-dominated states, among others, about (magneto)fluid turbulence follow.

Electron magnetohydrodynamics: Dynamics and turbulence

We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron magnetohydrodynamics (EMHD). We argue that there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. On the other hand, the relaxation principle, the long term evolution of a weakly dissipative system towards Taylor-Beltrami state, remains valid in EMHD. We consider the turbulent cascade of whistler modes. We show that (i) harmonic whistlers are exact nonlinear solutions; (ii) collinear whistlers do not interact (including counterpropagating); (iii) waves with the same value of the wave vector k(1)=k(2) do not interact; (iv) whistler modes have a dispersion that allows a three-wave decay, including into a zero frequency mode; (v) the three-wave interaction effectively couples modes with highly different wave numbers and propagation angles. In addition, linear interaction of a whistler with a single zero mode can lead to spatially divergent structures via parametric instability. All these properties are drastically different from MHD, so that the qualitative properties of the Alfvén turbulence can not be transferred to the EMHD turbulence. We derive the Hamiltonian formulation of EMHD, and using Bogoliubov transformation reduce it to the canonical form; we calculate the matrix elements for the three-wave interaction of whistlers. We solve numerically the kinetic equation and show that, generally, the EMHD cascade develops within a broad range of angles, while transiently it may show anisotropic, nearly two-dimensional structures. Development of a cascade depends on the forcing (nonuniversal) and often fails to reach a steady state. Analytical estimates predict the spectrum of magnetic fluctuations for the quasi-isotropic cascade [proportionality]k(-2). The cascade remains weak (not critically balanced). The cascade is UV local, while the infrared locality is weakly (logarithmically) violated.

Current disruption and its spreading in collisionless magnetic reconnection

Recent magnetic reconnection experiments (MRX) [Dorfman et al., Geophys. Res. Lett. 40, 233 (2013)] have disclosed current disruption in the absence of an externally imposed guide field. During current disruption in MRX, both the current density and the total observed out-of-reconnection-plane current drop simultaneous with a rise in out-of-reconnection-plane electric field. Here, we show that current disruption is an intrinsic property of the dynamic formation of an X-point configuration of magnetic field in magnetic reconnection, independent of the model used for plasma description and of the dimensionality (2D or 3D) of reconnection. An analytic expression for the current drop is derived from Ampere's Law. Its predictions are verified by 2D and 3D electron-magnetohydrodynamic (EMHD) simulations. Three dimensional EMHD simulations show that the current disruption due to localized magnetic reconnection spreads along the direction of the electron drift velocity with a speed which depends on the wave number of the perturbation. The implications of these results for MRX are discussed.

Whistler propagation in ionospheric density ducts: Simulations and DEMETER observations

On 16 October 2009, the Detection of Electromagnetic Emissions Transmitted from Earthquake Regions (DEMETER) satellite observed VLF whistler wave activity coincident with an ionospheric heating experiment conducted at HAARP. At the same time, density measurements by DEMETER indicate the presence of multiple field‐aligned enhancements. Using an electron MHD model, we show that the distribution of VLF power observed by DEMETER is consistent with the propagation of whistlers from the heating region inside the observed density enhancements. We also discuss other interesting features of this event, including coupling of the lower hybrid and whistler modes, whistler trapping in artificial density ducts, and the interference of whistlers waves from two adjacent ducts.

TOWARD A THEORY OF ASTROPHYSICAL PLASMA TURBULENCE AT SUBPROTON SCALES

We present an analytical study of subproton electromagnetic fluctuations in a collisionless plasma with a plasma beta of the order of unity. In the linear limit, a rigorous derivation from the kinetic equation is conducted focusing on the role and physical properties of kinetic-Alfvand whistler waves. Then, nonlinear fluid-like equations for kinetic-Alfvwaves and whistler modes are derived, with special emphasis on the similarities and differences in the corresponding plasma dynamics. The kinetic-Alfvmodes exist in the lower-frequency region of phase space, ω � k⊥v Ti , where they are described by the kinetic-Alfvsystem. These modes exist both below and above the ion-cyclotron frequency. The whistler modes, which are qualitatively different from the kinetic-Alfv´ modes, occupy a different region of phase space, k⊥v Ti � ω � kzv Te , and they are described by the electron magnetohydrodynamics (MHD) system or the reduced electron MHD system if the propagation is oblique. Here, kz and k⊥ are the wavenumbers along and transverse to the background magnetic field, respectively, and v Ti and v Te are the ion and electron thermal velocities, respectively. The models of subproton plasma turbulence are discussed and the results of numerical simulations are presented. We also point out possible implications for solar-wind observations.

电子磁流体模型及Biermann电池效应和位移电流效应

Electron magnetohydrodynamics (EMHD) theory is extensively applied in astrophysical and space plasma studies, particularly in important physical processes such as magnetic field generation and/or reconnection. In recent laboratory simulation of certain space and astrophysical phenomena, and related laser plasma and high energy density physics researches, effects of displacement current and/or Biermann battery on conventional EMHD model are found significant. Based on analysis of EMHD approximations, in this paper, we study those effects on EMHD model and related important plasma physical processes.

Theory and simulations of electron vortices generated by magnetic pushing

Vortex formation and propagation are observed in kinetic particle-in-cell (PIC) simulations of magnetic pushing in the plasma opening switch. These vortices are studied here within the electron-magnetohydrodynamic (EMHD) approximation using detailed analytical modeling. PIC simulations of these vortices have also been performed. Strong v×B forces in the vortices give rise to significant charge separation, which necessitates the use of the EMHD approximation in which ions are fixed and the electrons are treated as a fluid. A semi-analytic model of the vortex structure is derived, and then used as an initial condition for PIC simulations. Density-gradient-dependent vortex propagation is then examined using a series of PIC simulations. It is found that the vortex propagation speed is proportional to the Hall speed vHall≡cB0/4πneeLn. When ions are allowed to move, PIC simulations show that the electric field in the vortex can accelerate plasma ions, which leads to dissipation of the vortex. This electric field contributes to the separation of ion species that has been observed to occur in pulsed-power experiments with a plasma-opening switch.

Kinetic effects on robustness of electron magnetohydrodynamic structures

Following recent remarkable progress in the development of high-power short-pulse lasers, exploration is ongoing into hitherto unknown phenomena at fast time scales of electrons, the understanding of which is becoming crucial. For a simplified description of such phenomena, the Electron Magnetohydrodynamics (EMHDs) fluid description is often adopted. For the possibility of electron transport in high-density plasma, exact solutions of the EMHD model in the form of electron vortex currents, together with their associated magnetic fields, have been considered. However, the fluid EMHD model does not incorporate kinetic effects. Here, the finite Larmor radius effects owing to a finite electron temperature on the robustness of the exact EMHD structures are investigated using two-dimensional particle-in-cell simulations. It is found that larger EMHD vortex structures can sustain themselves for long periods, even in high temperature plasma; however, sustaining structures at higher temperatures tends to be difficult. With increasing temperature, electrons with finite Larmor radii become disengaged from the localized region. It is also shown that structures localized in smaller regions are more difficult to sustain. A quantitative criterion in terms of the structure size and Larmor radius has been established by simulations over a wide range of parameters. Finally, we conclude that a structure, larger than about eight times the typical Larmor radius at r=R, could form and exist even under the effects of finite electron temperature.

Spontaneous Chiral Symmetry Breaking of Hall Magnetohydrodynamic Turbulence

Hall magnetohydrodynamics (MHD) is investigated through three-dimensional direct numerical simulations. We show that the Hall effect induces a spontaneous chiral symmetry breaking of the turbulent dynamics. The normalized magnetic polarization is introduced to separate the right- (R) and left-handed (L) fluctuations. A classical k(-7/3) spectrum is found at small scales for R magnetic fluctuations which corresponds to the electron MHD prediction. A spectrum compatible with k(-11/3) is obtained at large-scales for the L magnetic fluctuations; we call this regime the ion MHD. These results are explained heuristically by rewriting the Hall MHD equations in a succinct vortex dynamical form. Applications to solar wind turbulence are discussed.