Magnetohydrodynamic Field Research Articles

Pulsating electromagnetic casting technique for slab casting

To improve the surface quality of cast slabs in the steelmaking process, the pulsating electromagnetic casting (EMC) technique was developed and assessed using a slab casting bench scale test. Numerical simulation of the magnetohydrodynamic field and numerical simulation of the toughness of the mould were also conducted for the slab casting plant test. Consequently, the mould and coil for slab casting plant tests with pulsating EMC were manufactured and the basic functions were verified. Finally slab casting plant tests with the pulsating EMC technique were conducted.

Numerical simulation of thermal problems coupled with magnetohydrodynamic effects in aluminium cell

A system of partial differential equations describing the thermal behavior of aluminium cell coupled with magnetohydrodynamic effects is numerically solved. The thermal model is considered as a two-phases Stefan problem which consists of a non-linear convection–diffusion heat equation with Joule effect as a source. The magnetohydrodynamic fields are governed by Navier–Stokes and by static Maxwell equations. A pseudo-evolutionary scheme (Chernoff) is used to obtain the stationary solution giving the temperature and the frozen layer profile for the simulation of the ledges in the cell. A numerical approximation using a finite element method is formulated to obtain the fluid velocity, electrical potential, magnetic induction and temperature. An iterative algorithm and 3-D numerical results are presented.

Closure tests for mean field magnetohydrodynamics using a self-consistent reduced model

The mean electromotive force and alpha effect are computed for a forced turbulent flow using a simple nonlinear dynamical model. The results are used to check the applicability of two basic analytic ansatze of mean-field magnetohydrodynamics - the second order correlation approximation (SOCA) and the tau approximation. In the numerical simulations the effective Reynolds number Re is 2-20, while the magnetic Prandtl number varies from 0.1 to $10^{7}$. We present evidence that the $\tau$ approximation may be appropriate in dynamical regimes where there is a small-scale dynamo. Catastrophic quenching of the $\alpha$ effect is found for high $P_{m}$. Our results indicate that for high $P_{m}$ SOCA gives a very large value of the $\alpha$ coefficient compared with the ``exact'' solution. The discrepancy depends on the properties of the random force that drives the flow, with a larger difference occuring for $\delta$-correlated force compared with that for a steady random force.

Mean Field Magnetohydrodynamics of Accretion Disks

We consider the accretion process in a disk with magnetic fields that are dragged in from the interstellar medium by gravitational collapse. Two diffusive processes are at work in the system: (1) viscous torques exerted by turbulent and magnetic stresses, and (2) resistive redistribution of mass with respect to the magnetic flux arising from the imperfect conduction of current. In steady state, self-consistency between the two rates of drift requires that a relationship exists between the coefficients of turbulent viscosity and turbulent resistivity. Ignoring any interactions with a stellar magnetosphere, we solve the steady-state equations for a magnetized disk under the gravitational attraction of a mass point and threaded by an amount of magnetic flux consistent with calculations of magnetized gravitational collapse in star formation. Our model mean field equations have an exact analytical solution that corresponds to magnetically diluted Keplerian rotation about the central mass point. The solution yields the strength of the magnetic field and the surface density as functions of radial position in the disk and their connection with the departure from pure Keplerian rotation in representative cases. We compare the predictions of the theory with the available observations concerning T Tauri stars, FU Orionis stars, and low- and high-mass protostars. Finally, we speculate on the physical causes for high and low states of the accretion disks that surround young stellar objects. One of the more important results of this study is the physical derivation of analytic expressions for the turbulent viscosity and turbulent resistivity.

Dirichlet sigma models and mean curvature flow

The mean curvature flow describes the parabolic deformation of embedded branes in Riemannian geometry driven by their extrinsic mean curvature vector, which is typically associated to surface tension forces. It is the gradient flow of the area functional, and, as such, it is naturally identified with the boundary renormalization group equation of Dirichlet sigma models away from conformality, to lowest order in perturbation theory. D-branes appear as fixed points of this flow having conformally invariant boundary conditions. Simple running solutions include the paper-clip and the hair-pin (or grim-reaper) models on the plane, as well as scaling solutions associated to rational (p, q) closed curves and the decay of two intersecting lines. Stability analysis is performed in several cases while searching for transitions among different brane configurations. The combination of Ricci with the mean curvature flow is examined in detail together with several explicit examples of deforming curves on curved backgrounds. Some general aspects of the mean curvature flow in higher dimensional ambient spaces are also discussed and obtain consistent truncations to lower dimensional systems. Selected physical applications are mentioned in the text, including tachyon condensation in open string theory and the resistive diffusion of force-free fields in magneto-hydrodynamics.

Storm‐time configuration of the inner magnetosphere: Lyon‐Fedder‐Mobarry MHD code, Tsyganenko model, and GOES observations

We compare global magnetohydrodynamic (MHD) simulation results with an empirical model and observations to understand the magnetic field configuration and plasma distribution in the inner magnetosphere, especially during geomagnetic storms. The physics‐based Lyon‐Fedder‐Mobarry (LFM) code simulates Earth's magnetospheric topology and dynamics by solving the equations of ideal MHD. Quantitative comparisons of simulated events with observations reveal strengths and possible limitations and suggest ways to improve the LFM code. Here we present a case study that compares the LFM code to both a semiempirical magnetic field model and to geosynchronous measurements from GOES satellites. During a magnetic cloud event, the simulation and model predictions compare well qualitatively with observations, except during storm main phase. Quantitative statistical studies of the MHD simulation shows that MHD field lines are consistently under‐stretched, especially during storm time (Dst < −20 nT) on the nightside, a likely consequence of an insufficient representation of the inner magnetosphere current systems in ideal MHD. We discuss two approaches for improving the LFM result: increasing the simulation spatial resolution and coupling LFM with a ring current model based on drift physics (i.e., the Rice Convection Model (RCM)). We show that a higher spatial resolution LFM code better predicts geosynchronous magnetic fields (not only the average Bz component but also higher‐frequency fluctuations driven by the solar wind). An early version of the LFM/RCM coupled code, which runs so far only for idealized events, yields a much‐improved ring current, quantifiable by decreased field strengths at all local times compared to the LFM‐only code.

Compression of magnetohydrodynamic simulation data using singular value decomposition

Numerical calculations of magnetic and flow fields in magnetohydrodynamic (MHD) simulations can result in extensive data sets. Particle-based calculations in these MHD fields, needed to provide closure relations for the MHD equations, will require communication of this data to multiple processors and rapid interpolation at numerous particle orbit positions. To facilitate this analysis it is advantageous to compress the data using singular value decomposition (SVD, or principal orthogonal decomposition, POD) methods. As an example of the compression technique, SVD is applied to magnetic field data arising from a dynamic nonlinear MHD code. The performance of the SVD compression algorithm is analyzed by calculating Poincaré plots for electron orbits in a three-dimensional magnetic field and comparing the results with uncompressed data.

Test Particle Energization by Current Sheets and Nonuniform Fields in Magnetohydrodynamic Turbulence

We perform numerical experiments of test particle energization in turbulent magnetic and electric fields obtained from pseudospectral direct numerical solutions of compressible three-dimensional magnetohydrodynamic (MHD) equations with a strong background magnetic field. The natural tendency of turbulent MHD fields is to form current sheets along the magnetic field direction, as well as strong nonuniform fields in the transverse directions. By associating the MHD dissipation length scale with the ion inertial scale, we found differential energization in parallel and perpendicular directions according to the type of particles considered. Electrons develop large parallel velocities, especially in current sheets. Protons instead show higher perpendicular energization due to the nonuniform perpendicular induced electric field produced by the plasma MHD velocity, which varies on proton length scales. Implications for dissipation mechanisms in a coronal heating model are discussed.

Physical models of the geospace radiation environment

A goal of predictive models of the space radiation environment is to provide advanced knowledge of significant variations in the highly energetic particle populations that form the Earth's radiation belts. The global geomagnetic field models that result from the Center for Integrated Space-weather Modeling (CISM) effort will provide a necessary input, a real-time description of the dynamic variation of the electromagnetic fields in the magnetosphere, for conducting detailed simulations of the radiation belts. In this work, we describe the issues and techniques that CISM will use to provide a physical space radiation model. An analysis of the global field configurations typical of the magneto hydrodynamic (MHD) models used in CISM suggest that much of the radiation belt modeling can proceed under a guiding center particle approximation, whereby individual, non-interacting test particles are used to track the aggregate dynamics of the radiation belts. This technique provides a relatively simple means of both conducting the necessary simulations, and coupling the relevant codes with other elements of the CISM project. The guiding center equations used to track the particles are based on a phase-space conserving approximation that conserves energy in regions of high curvature. Examples of test particle simulations with the MHD fields are given, both in the initial trapped particle population, and among the energetic particles that form the plasma sheet in the tail. These simulations suggest that multiple radiation belt models running simultaneously in the framework provided by CISM can be combined to provide an overall picture of the energetic particle environment. Finally, analysis of the spectral properties of the fields suggests how an alternate approach to modeling the global radiation belts, solution of the appropriate transport equations, might be advanced through the CISM effort.

The long-time evolution of mean field magnetohydrodynamics

The equations of mean field magnetohydrodynamics with constantmean velocity are proved to posses solutions bounded in the$H^{1}$-norm for all time, and a compact attractor whose dimensionis estimated. It is shown that depending on the functional form ofthe so-called alpha term the attractor may reduce to zero or be alarger set. If, as usual in physical situations, there exists aset of solutions with a minimum size $N$, the dimension of thisset decreases rapidly with increasing $N$. Finally, the dependenceof the dimension on the magnetic diffusivity is analyzed,suggesting that the evolution of a magnetic field under the meanfield equation is much more restricted than the one deduced fromthe full magnetohydrodynamic system.

The mean electromotive force for MHD turbulence: The case of a weak mean magnetic field and slow rotation

The mean electromotive force in the framework of mean--field magnetohydrodynamics is found with a particular attention to the effect of a mean rotation of the fluid on the mean electromotive force. Anisotropy of the turbulence due to gradients of its intensity or its helicity are admitted. The mean magnetic field is considered to be weak enough to exclude quenching effects. Magnetic fluctuations with a zero mean magnetic field are taken into account. The Omega x J -effect works in the same way with velocity fluctuations and magnetic fluctuations. A contribution to the electromotive force connected with the symmetric parts of the gradient tensor of the mean magnetic field was found in the case of rotation, resulting from velocity or magnetic fluctuations. The implications of the results for the mean electromotive force for mean--field dynamo models are discussed with special emphasis to dynamos working without alpha-effect.

3-D magnetohydrodynamic field computation of supersonic duct flow of weakly ionized plasma

Supersonic magnetohydrodynamic field analysis is carried out for energy conversion using a weakly ionized plasma. The magnetic field induced by a generated electric current is taken into account. A three-dimensional simulation shows that the Lorentz force induces a shock wave and boundary-layer separation in the plasma duct flow.

Excitation of field line resonances by MHD waves originating in the solar wind

Recent observations suggest that in some circumstances a field line resonance may be driven by discrete oscillations in the solar wind. A theoretical model of excitation of magnetohydrodynamic (MHD) field line resonances by waves originating in the solar wind is presented. Such waves occur in the solar wind although their source is not understood. The propagation of an MHD wave in the solar wind is followed through the bow shock and magnetosheath. It is shown how the properties of the magnetospheric cavity are functions of longitude. The incident wave is captured at a longitude where its azimuthal wave number has a value allowing matching to the cavity oscillation. There is significant amplification at the bow shock and at the magnetopause. It is found that the signal penetrates the cavity and excites a field line resonance on the flanks of the magnetosphere in the morning and afternoon sectors. Rather than behaving as a waveguide, the cavity behaves more like an optical filter.

Confronting spin flavor solutions of the solar neutrino problem with current and future solar neutrino data

A global analysis of spin flavor precession (SFP) solutions to the solar neutrino problem is given, taking into account the impact of the full set of latest solar neutrino data, including the recent SNO data and the 1496-day Super-Kamiokande data. These are characterized by three effective parameters: $\ensuremath{\Delta}{m}_{\mathrm{SOL}}^{2}\ensuremath{\equiv}\ensuremath{\Delta}{m}^{2},$ the neutrino mixing angle ${\ensuremath{\theta}}_{\mathrm{SOL}}\ensuremath{\equiv}\ensuremath{\theta},$ and the magnetic field parameter $\ensuremath{\mu}{B}_{\ensuremath{\perp}}.$ For the last we adopt a self-consistent magnetohydrodynamics field profile in the convective zone and identify an optimum ${B}_{\ensuremath{\perp}}\ensuremath{\sim}80\mathrm{kG}$ strength for $\ensuremath{\mu}{=10}^{\ensuremath{-}11}{\ensuremath{\mu}}_{B}.$ We find that no low mass (LOW) quasivacuum or vacuum solutions are present at $3\ensuremath{\sigma}.$ In addition to the standard large mixing angle (LMA) oscillation solution, there are two SFP solutions, in the resonant (RSFP) and nonresonant (NRSFP) regimes. These two SFP solutions have a goodness of fit of 84% (RSFP) and 83% (NRSFP), slightly better than the LMA oscillation solution (78%). We discuss the role of solar antineutrino searches in the fit and present a table of best-fit parameters and ${\ensuremath{\chi}}_{\mathrm{min}}^{2}$ values. Should the KamLAND experiment confirm the LMA solution, the SFP solutions may at best be present at a subleading level, leading to a constraint on $\ensuremath{\mu}{B}_{\ensuremath{\perp}}.$ In the event the LMA is not the solution realized in nature, then experiments such as Borexino can help in distinguishing the LMA solution from the NRSFP solution and the simplest RSFP solution with no mixing.

Second-order structure function scaling derivation from the Euler and magnetohydrodynamic equations.

An anomalous scaling paradigm that has recently come to be canonical has two features limiting its range of applicability: The driving and driven fields are separated dyamically and the driving field statistics is prescribed, in terms of the (inertial subrange) scaling of its second-order structure functions and of white-noise statistics in time. Then the spectrum of scaling exponents for the driven field, scalar or vector, depends parametrically on the driving. Here, the coupling of turbulent vorticity to the driving velocity field is considered. Using simple approximations and no white-noise statistics assumption, equations are derived for the evolution of two-point second-order correlations. The turbulent magnetohydrodynamic (MHD) case is treated in an analogous fashion. In the neutral case, the kinematic coupling between vorticity and velocity leads to a unique prediction for the scaling exponent of the second-order structure functions of the two turbulent fields. The velocity scaling exponent estimate is zeta(2)=3(1/2)-1 approximately equal to 0.732, i.e., close to experimental data. Unlike Kolmogorov scaling, this result is systematically derived from the Euler equations. The analogous scaling of MHD fields is now treated beyond the dynamo theory approximation. In contrast to the uniqueness found in the neutral case, predicted MHD scalings depend on one parameter, similar to the "plasma beta" parameter beta(T) relating kinetic to magnetic energy. The nature of predicted dependence of inertial-range scaling exponents on beta(T) agrees with an observed dichotomy between high-beta(T) and low-beta(T) turbulence regimes.

The nonlinear properties of a large-scale dynamo driven by helical forcing

By considering an idealized model of helically forced flow in an extended domain that allows scale separation, we have investigated the interaction between dynamo action on different spatial scales. The evolution of the magnetic field is studied numerically, from an initial state of weak magnetization, through the kinematic and into the dynamic regime. We show how the choice of initial conditions is a crucial factor in determining the structure of the magnetic field at subsequent times. For a simulation with initial conditions chosen to favour the growth of the small-scale field, the evolution of the large-scale magnetic field can be described in terms of the α-effect of mean field magnetohydrodynamics. We have investigated this feature further by a series of related numerical simulations in smaller domains. Of particular significance is that the results are consistent with the existence of a nonlinearly driven α-effect that becomes saturated at very small amplitudes of the mean magnetic field.

Circulation-strain sum rule in stochastic magnetohydrodynamics

We study probability density functions (PDFs) of the circulation of velocity and magnetic fields in magnetohydrodynamics, computed for a circular contour within inertial range scales. The analysis is based on the instanton method as adapted to the Martin-Siggia-Rose field theory formalism. While in the viscous limit the expected Gaussian behavior of fluctuations is indeed verified, the case of vanishing viscosity is not suitable of a direct saddle-point treatment. To study the latter limit, we take into account fluctuations around quasistatic background fields, which allows us to derive a sum rule relating PDFs of the circulation observables and the rate of the strain tensor. A simple inspection of the sum rule definition leads straightforwardly to the algebraic decay rho(Gamma)-1/Gamma(2) at the circulation PDF tails.

A global MHD and empirical magnetic field model investigation of the magnetospheric cusp

Magnetic field configurations, cusp locations, merging, and interconnection regions for the Lyon‐Fedder global magnetohydrodynamic (MHD) simulation model and the Tsyganenko 96 (T96_01) empirical model are presented and compared for three different interplanetary magnetic field (IMF) directions (north, south, and dusk directed). Field line configurations indicate a significantly larger magnetosphere in the T96_01 model compared to the MHD model for all IMF directions. In each of the models the polar cusp is identified by depressions in the magnetic field residual and by the boundary between dayside closed and open field lines. It is found that the MHD model exhibits a much stronger residual magnetic field depression in the cusp region than does the T96_01 model. The MHD field depression is associated with the presence of diamagnetic magnetosheath plasma that enters the cusp via the MHD merging process. In the northward IMF case, MHD merging above both poles results in an MHD open‐closed field line boundary located at 89° invariant latitude with MHD cusp plasma and field depressions centered on closed field lines near 81°. The T96_01 model is very different from this with its north IMF open‐closed boundary located at 79° invariant latitude. For the southward IMF case the T96_01 open‐closed boundary at 74° invariant latitude lies slightly poleward of the MHD open‐closed boundary at 73°. In this case the MHD cusp plasma is centered near 75° invariant latitude. In the dusk‐directed IMF case the MHD cusp plasma shifts ∼2 hours in magnetic local time (MLT) toward dusk and remains poleward of the MHD open‐closed boundary. In this case the MHD dayside open‐closed boundary extends from dawn to dusk, while the T96_01 dayside open‐closed boundary extends only from dawn to ∼13 MLT and near local noon is coincident with the MHD boundary at ∼74° invariant latitude. Differences between the two models are due in large part to differences in the form of their interconnectivity with the interplanetary magnetic field lines. For each IMF direction the MHD merging locations and T96_01 strongest interconnection regions are identified and are found to be very different. On the basis of comparisons with numerous case and statistical studies of the cusp it is concluded that the MHD model provides a fairly realistic representation of the cusp and dayside magnetic field configuration, while the T96_01 model is limited in its ability to model the cusp region.

THE FORMATION OF SHOCK WAVES OF THE EQUATIONS OF MAGNETOHYDRODYNAMICS

The property of fluid field of one-dimensional magnetohydrodynamics (MHD) transverse flow after the appearance of singularity is discussed. By the method of iteration, the strong discontinuity (shock wave) and entropy solution are constructed and the estimations on the singularity of the solution near the point of blow-up are obtained.

Laboratory studies of magnetic vortices. I. Directional radiation of whistler waves based on helicity injection

A novel principle for the directional excitation of whistler waves is demonstrated in a laboratory experiment. It is based on helicity conservation of electron magnetohydrodynamic fields in plasmas. Whistler wave packets propagating in opposite directions to a static magnetic field have opposite signs of helicity. Injection of helicity of one sign produces radiation in one direction. This is accomplished with an antenna consisting of a loop linked through a torus. Directionality of 20 dB is readily achieved. The direction of radiation is electronically reversible. Transmission between two antennas is unidirectional, hence nonreciprocal. Possible applications include secure communication, direction finding, and efficient power deposition in radio frequency (rf) heating.