The statistics of a passive scalar in field-guided magnetohydrodynamic turbulence

A variety of studies of magnetised plasma turbulence invoke theories for the advection of a passive scalar by turbulent fluctuations. Examples include modelling the electron density fluctuations in the interstellar medium, understanding the chemical composition of galaxy clusters and the intergalactic medium, and testing the prevailing phenomenological theories of magnetohydrodynamic turbulence. While passive scalar turbulence has been extensively studied in the hydrodynamic case, its counterpart in MHD turbulence is significantly less well understood. Herein we conduct a series of high-resolution direct numerical simulations of incompressible, field-guided, MHD turbulence in order to establish the fundamental properties of passive scalar evolution. We study the scalar anisotropy, establish the scaling relation analogous to Yaglom’s law, and measure the intermittency of the passive scalar statistics. We also assess to what extent the pseudo Alfvén fluctuations in strong MHD turbulence can be modelled as a passive scalar. The results suggest that the dynamics of a passive scalar in MHD turbulence is considerably more complicated than in the hydrodynamic case.     

Broken ergodicity,magnetic helicity,and the MHD dynamo

We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.     

GPU-accelerated computing of three-dimensional solar wind background

High-performance computational models are required to make the real-time or faster than real-time numerical prediction of adverse space weather events and their influence on the geospace environment. The main objective in this article is to explore the application of programmable graphic processing units (GPUs) to the numerical space weather modeling for the study of solar wind background that is a crucial part in the numerical space weather modeling. GPU programming is realized for our Solar-Interplanetary-CESE MHD model (SIP-CESE MHD model) by numerically studying the solar corona/interplanetary solar wind. The global solar wind structures are obtained by the established GPU model with the magnetic field synoptic data as input. Meanwhile, the time-dependent solar surface boundary conditions derived from the method of characteristics and the mass flux limit are incorporated to couple the observation and the three-dimensional (3D) MHD model. The simulated evolution of the global structures for two Carrington rotations 2058 and 2062 is compared with solar observations and solar wind measurements from spacecraft near the Earth. The MHD model is also validated by comparison with the standard potential field source surface (PFSS) model. Comparisons show that the MHD results are in good overall agreement with coronal and interplanetary structures, including the size and distribution of coronal holes, the position and shape of the streamer belts, and the transition of the solar wind speeds and magnetic field polarities.     

Integral equations in MHD: theory and application

The induction equation of magnetohydrodynamics (MHD) is mathematically equivalent to a system of integral equations for the magnetic field in the bulk of the fluid and for the electric potential at its boundary. We summarize the recent developments concerning the numerical implementation of this scheme and its applications to various forward and inverse problems in dynamo theory and applied MHD.     

Possibility of real time scale MHD simulation above an active region

The MHD simulations of preflare situation in the corona above the real active region (AR) are performed without any assumptions about the solar flare mechanism. All conditions for simulation are taken from observations. Such approach is directed to understand the flare mechanism. The observed SOHO MDI magnetic maps are used. The special numerical methods are developed and realized in the PERESVET code for numerical simulation in the real time scale. The first results of real time scale MHD simulation during several first minutes are presented. Initiation of current sheet (CS) creation in the vicinity of the magnetic field X-line is shown. The possibilities of real time scale MHD simulation of preflare situation on modern computers using the developed mathematical methods are discussed.     

Recent observations of MHD fluctuations in the solar wind

A short review of recent observations of solar wind fluctuations in the magnetohydrodynamic (MHD) range of scales is presented. In recent years, the use of high time-resolution data on an extended interval of heliocentric distance has allowed significant advances in our knowledge of MHD fluctuations. We first focus on the origin and evolution of the Alfvénic-type fluctuations. The role of interplanetary sources and the influence of interactions with structures convected by the solar wind are examined. Then compressive fluctuations are investigated, with special attention being given to their nature and origin. Observations are discussed in the light of recent theories and models. Finally, predictions for MHD turbulence in polar regions of the heliosphere are highlighted.     

MHD nature of the origination,dynamics, geoeffectiveness,and disappearance of the four-sector structure of the solar magnetic field during the cycle 23 decline phase

The MHD nature of the origination, dynamics, geoeffectiveness, and disappearance of the four-sector structure of the solar magnetic field during the cycle 23 decline phase has been established. A prolonged ordered MHD process including the chain of the interrelated phenomena (unknown before this study), which begin and end in one of the main zones of active longitudes and are responsible for the above nature of the four-sector structure, has been detected as a result of the simulation of the large-scale open solar magnetic field and an analysis of the dynamics of this field fluxes. These phenomena are as follows: the extreme concentration of the photospheric field sources of the same sign in the zone of active longitudes; blocking of regular differential rotation by these sources; origination of a nonstationary MHD disturbance in the form of a four-sector structure, traveling in the direction of solar rotation at a nearly Alfvén velocity; upset of blocking, displacement of blocking sources from the zone, and their shearing motion relative to a traveling MHD disturbance; deceleration and dissipation of a four-sector MHD disturbance; and reconstruction of a bisector structure. The interactions during this process, which lasted from May 2004 to December 2005, were accompanied by the generation of an ordered succession of heliospheric and solar-terrestrial disturbances including the series of nine extrastorms that were observed from July 2004 to September 2005 and were the last storms in the finished cycle 23 of solar activity.     

On the possibility of using an electromagnetic ionosphere in global MHD simulations

Global magnetohydrodynamic (MHD) simulations of the Earths magnetosphere must be coupled with a dynamical ionospheric module in order to give realistic results. The usual approach is to compute the Reld-aligned current (FAC) from the magnetospheric MHD variables at the ionospheric boundary. The ionospheric potential is solved from an elliptic equation using the FAC as a source term. The plasma velocity at the boundary is the E × B velocity associated with the ionospheric potential. Contemporary global MHD simulations which include a serious ionospheric model use this method, which we call the electrostatic approach in this paper. We study the possibility of reversing the flow of information through the ionosphere: the magnetosphere gives the electric Reld to the ionosphere. The Reld is not necessarily electrostatic, thus we will call this scheme electromagnetic. The electric Reld determines the horizontal ionospheric current. The divergence of the horizontal current gives the FAC, which is used as a boundary condition for MHD equations. We derive the necessary formulas and discuss the validity of the approximations necessarily involved. It is concluded that the electromagnetic ionosphere-magnetosphere coupling scheme is a serious candidate for future global MHD simulators, although a few problem areas still remain. At minimum, it should be investigated further to discover whether there are any differences in the simulation using the electrostatic or the electromagnetic ionospheric coupling.     

太阳等离子体和磁场输出源表面结构的一种MHD模型

以观测到的光球视向磁场、Ｋ－日冕亮度作为输入,以相应的统计结果为约束条件,利用磁流体力学方程组,给出了等离子体及磁场各参数在源表面上的二维分布．其结果与同期的卫星观测数据和已有的统计结果相比较,显示出相当程度的一致性．     

Generation and evolution of interplanetary slow shocks

It is well known that most MHD shocks observed within 1 AU are MHD fast shocks. Only a very limited number of MHD slow shocks are observed within 1 AU. In order to understand why there are only a few MHD slow shocks observed within 1 AU, we use a one-dimensional, time-dependent MHD code with an adaptive grid to study the generation and evolution of interplanetary slow shocks (ISS) in the solar wind. Results show that a negative, nearly square-wave perturbation will generate a pair of slow shocks (a forward and a reverse slow shock). In addition, the forward and the reverse slow shocks can pass through each other without destroying their characteristics, but the propagating speeds for both shocks are decreased. A positive, square-wave perturbation will generate both slow and fast shocks. When a forward slow shock (FSS) propagates behind a forward fast shock (FFS), the former experiences a decreasing Mach number. In addition, the FSS always disappears within a distance of 150R_⊙ (where R_⊙ is one solar radius) from the Sun when there is a forward fast shock (with Mach number \geq1.7) propagating in front of the FSS. In all tests that we have performed, we have not discovered that the FSS (or reverse slow shock) evolves into a FFS (or reverse fast shock). Thus, we do not confirm the FSS-FFS evolution as suggested by Whang (1987).     

Second generation of a rotational electrochemical seismometer using magnetohydrodynamic technology

Rotational seismometers have many applications. Some require a low self noise with a lower clip specification. Others require many different bandpass specifications, from very low to higher frequencies. The principles of the eentec second-generation R-2 electrochemical triaxial rotational seismometer can achieve many features for various applications. Combining the use of the sophisticated magnetohydrodynamic (MHD) technology increases the current and future features. Principles of the MHD technology used and the many advantages it has in a rotational seismometers are described.     

Broken ergodicity in magnetohydrodynamic turbulence

Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B _o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B _o?=?0 and weakly broken when B _o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B _o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.     

Nonlinear phenomena related to the solar shock motion in the Earth’s magnetosphere

The motion of the MHD nonlinear shock in the Earth’s magnetosphere is considered in the scope of magnetic hydrodynamics. This wave comes from the solar wind and is refracted into the magnetosphere, generating a fast return rarefaction wave. It has been indicated that a wave refracted into the magnetosphere is a weak fast dissipative shock, propagating in magnetospheric plasma at a velocity higher than its propagation velocity in a solar wind stream. The wave motion near the Earth-Sun line with regard to the effect of the geomagnetic field transverse component is described. In this case, shock damping follows the generalized Crussard-Landau law and a wave retains its shock character up to the plasmapause, interacting with this region when an arbitrary MHD discontinuity is disintegrated. It is stated that an MHD shock loses its shock character when moving in a strongly inhomogeneous plasma within the plasmasphere and a weak shock reflected from the plasmapause can combine with a return secondary shock in the magnetosheath, promoting the experimentally observed backward motion of the bow shock front.     

A conserved local cross helicity for non-barotropic MHD

Cross helicity is not conserved in non-barotropic magnetohydro-dynamics (MHD) (as opposed to barotropic or incompressible MHD). Here we show that variational analysis suggests a new kind of local cross helicity which is conserved in the non-barotropic case. This local cross helicity can be integrated to a global non-barotropic cross helicity which was suggested in the work of Webb et al. (2014a,b). The non-barotropic cross helicity reduces to the standard cross helicity under barotropic assumptions. The new local cross helicity is conserved even for topologies for which the variational principle does not apply.     

Weakly nonlinear analysis of the α effect

We address mathematical issues raised by the so-called α?effect of dynamo theory, which is a dynamo mechanism arising in conducting flows with small scale fluctuations. Analytical results on the α?effect concern the linear induction equation, and are usually claimed to hold for the whole magnetohydrodynamics (MHD) system, as long as the amplitude of the perturbations is small. We discuss the justification of that claim, in the case of periodic fluctuations of the fields. We show a nonlinear instability result on the MHD system, that predicts dynamo action for a large class of high frequency periodic flows, up to the fully nonlinear regime.     

A mode filter for plasma waves in the Hall-MHD approximation

A filter method is presented which allows a qualitative and quantitative identification of wave modes observed with plasma experiments on satellites. Hitherto existing mode filters are based on the MHD theory and thus they are restricted to low frequencies well below the ion cyclotron frequency. The present method is generalized to cover wave modes up to the characteristic ion frequencies. The spectral density matrix determined by the observations is decomposed using the eigenvectors of the linearized Hall-MHD equations. As the wave modes are dispersive in this formalism, a precise determination of the κ-vectors requires the use of multi-point measurements. Therefore the method is particularly relevant to multi-satellite missions. The method is tested using simulated plasma data. The Hall-MHD filter is able to identify the modes excited in the model plasma and to assign the correct energetic contributions. By comparison with the former method it is shown that the simple MHD filter leads to large errors if the frequency is not well below the ion cyclotron frequency. Further the range of validity of the linear theory is examined rising the simulated wave amplitudes.     

MHD evolutionary processes in the Earth’s model magnetic resonator

Specific features of the spatial-temporal dynamics of LF disturbances of the Earth’s magnetosphere have been analyzed by the method of numerical simulation of magnetic hydrodynamic equations taking into account plasma temperature variations. The effects related to the appearance of long-living magnetospheric jumps of density and temperature, MHD wave scattering on such inhomogeneities, Alfvén wave reflection from the near-Earth region, and magnetospheric plasma heating as a result of dissipative processes at a repeated propagation of MHD waves between magnetically conjugate regions have been considered. The problems of conformity of the discrete mathematical model with continuous equations of magnetic hydrodynamics are discussed.     

Impact of solar wind tangential discontinuities on the Earth’s magnetosphere

The collision of a solar wind tangential discontinuity with the bow shock and magnetopause is considered in the scope of an MHD approximation. Using MHD methods of trial calculations and generalized shock polars, it has been indicated that a fast shock refracted into the magnetosheath originates when density increases across a tangential discontinuity and a fast rarefaction wave is generated when density decreases at this discontinuity. It has been indicated that a shock front shift under the action of collisions with a tangential discontinuity is experimentally observed and a fast bow shock can be transformed into a slow shock. Using a specific event as an example, it has been demonstrated that solar wind tangential discontinuity affects the geomagnetic field behavior.     

Magnetohydrodynamic Simulation of Preflare Situations in the Solar Corona with the Use of Parallel Computing

Geomagnetism and Aeronomy - The use of parallel computations on Nvidia Tesla GPUs allows the magnetohydrodynamic (MHD) simulation of preflare situations in the solar corona above an active region...     

Dissipative structures in a nonlinear dynamo

This article considers magnetic field generation by a fluid flow in a system referred to as the Archontis dynamo: a steady nonlinear MHD state is driven by a prescribed body force. The field and flow become almost equal and dissipation is concentrated in cigar-like structures centred on straight-line separatrices. Numerical scaling laws for energy and dissipation are given that extend previous calculations to smaller diffusivities. The symmetries of the dynamo are set out, together with their implications for the structure of field and flow along the separatrices. The scaling of the cigar-like dissipative regions, as the square root of the diffusivities, is explained by approximations near the separatrices. Rigorous results on the existence and smoothness of solutions to the steady, forced MHD equations are given.