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NASA NTRS2000

Global MHD Simulations of Space Plasma Environments: Heliosphere, Comets, Magnetospheres of Plants and Satellites

Magnetohydrodynamics (MHD) provides an approximate description of a great variety of processes in space physics. Accurate numerical solutions of the MHD equations are still a challenge, but in the past decade a number of robust methods have appeared. Once these techniques made the direct solution of MHD equations feasible, a number of global three-dimensional models were designed and applied to many space physics objects. The range of these objects is truly astonishing, including active galactic nuclei, the heliosphere, the solar corona, and the solar wind interaction with planets, satellites, and comets. Outside the realm of space physics, MHD theory has been applied to such diverse problems as laboratory plasmas and electromagnetic casting of liquid metals. In this paper we present a broad spectrum of models of different phenomena in space science developed in the recent years at the University of Michigan. Although the physical systems addressed by these models are different, they all use the MHD equations as a unifying basis.

Kabin, K.↗

NASA NTRS1983

MHD stability of incompressible coronal loops with radiative energy loss

Previous studies of the magnetohydrodynamic (MHD) stability of solar coronal loops have not taken into account the effects of radiative energy loss in the energy equation. However, since coronal loops continuously lose energy by radiation and heat conduction, it is important to understand how these energy loss mechanisms affect MHD stability. We investigate the problem assuming that a magnetic loop has cylindrical geometry. As a first step, stability is studied for a localized mode, and the result is applied to a specific equilibrium. We find that the radiative energy loss effect not only changes the growth rate of ideally unstable modes, but also alters the stability boundary predicted by ideal MHD theory.

An, C.-H.↗

NASA NTRS1986

Synopsis of Magnetohydrodynamic Power Generation

Concise summary of magnetohydrodynamic (MHD) theory, history, and future trends presented in report. Worldwide research on MHD covered, and selected data from key research projects included. Magnetohydrodynamic generator produces electric current by passing fluid at high speed through strong magnetic field. Fluid ionized gas, plasma, or liquid metal. Magnetohydrodynamic generators offer potential for high efficiency, low power cost, and cleaner emissions.

Smith, J. L.↗

NASA NTRS1998

Determination of Particle Sources for a Geotail Distribution Function Observed on May 23, 1995

On May 23, 1995, the Comprehensive Plasma Instrumentation (CPI) onboard the Geotail spacecraft observed a complex and structured ion distribution function near the magnetotail midplane at x approximately -10 R(sub E). On the same day, the Wind spacecraft observed a very high density (approximately 40/cubic cm) solar wind and an interplanetary magnetic field (IMF) that was predominantly northward but had several southward turnings. We have inferred the sources of the ions in this distribution function by following approximately 90,000 ion trajectories backward in time using time-dependent electric and magnetic fields obtained from a global MHD (magnetohydrodynamic) simulation. Wind data were used as input for the MHD model. We found that three sources contributed to this distribution: the ionosphere, the plasma mantle which had near-Earth and distant tail components, and the low latitude boundary layer (LLBL). Moreover, distinct structures in the low energy part of the distribution function were found to be associated with individual sources. Structures near 0 deg pitch angle were made up of either ionospheric or plasma mantle ions, while structures near 90 deg pitch angle were dominated by ions from the LLBL source. Particles that underwent nonadiabatic acceleration were numerous in the higher energy part of the ion distribution function, whereas ionospheric and LLBL ions were mostly adiabatic. A large proportion of the near-Earth mantle ions underwent adiabatic acceleration, while most of the distant mantle ions experienced nonadiabatic acceleration.

Ashour-Abdalla, M.↗

NASA NTRS1997

An MHD variational principle that admits reconnection

The variational approach of Pfirsch and Sudan's averaged magnetohydrodynamics (MHD) to the stability of a line-tied current layer is summarized. The effect of line-tying on current sheets that might arise in line-tied magnetic flux tubes by estimating the growth rates of a resistive instability using a variational method. The results show that this method provides a potentially new technique to gauge the stability of nearly ideal magnetohydrodynamic systems. The primary implication for the stability of solar coronal structures is that tearing modes are probably constant at work removing magnetic shear from the solar corona.

Rilee, M. L.↗

NASA NTRS2008

Gas Core Reactor Numerical Simulation Using a Coupled MHD-MCNP Model

Analysis is provided in this report of using two head-on magnetohydrodynamic (MHD) shocks to achieve supercritical nuclear fission in an axially elongated cylinder filled with UF4 gas as an energy source for deep space missions. The motivation for each aspect of the design is explained and supported by theory and numerical simulations. A subsequent report will provide detail on relevant experimental work to validate the concept. Here the focus is on the theory of and simulations for the proposed gas core reactor conceptual design from the onset of shock generations to the supercritical state achieved when the shocks collide. The MHD model is coupled to a standard nuclear code (MCNP) to observe the neutron flux and fission power attributed to the supercritical state brought about by the shock collisions. Throughout the modeling, realistic parameters are used for the initial ambient gaseous state and currents to ensure a resulting supercritical state upon shock collisions.

Kazeminezhad, F.↗

NASA NTRS1989

Time evolution from linear to nonlinear stages in magnetohydrodynamic parametric instabilities

The nonlinear evolution of the magnetohydrodynamic (MHD) parametric instability of wave fluctuations propagating along an unperturbed magnetic field is investigated. Both a magnetohydrodynamic perturbation-theoretical approach and a nonlinear MHD simulation are used. It is shown that high harmonic waves are rapidly excited by wave-wave coupling, and that the wave spectrum evolves from a state containing a small number of degrees of freedom in k space to one which contains a large number of degrees of freedom. It is found that the spectral evolution prior to nonlinear saturation is well described by the prturbation theory. During this stage, the ratio of the growth rate of the nth harmonic wave to the linear growth rate of the fundamental wave is n. The nonlinear saturation stage is characterized by a frequency shift of the fundamental wave that destroys the wave-wave resonance condition which, in turn, causes the wave amplitude to cease its growth.

Hoshino, M.↗

NASA NTRS2001

Improvement of Scramjet Performance-Experimental Demonstration of MHD Acceleration

One of the critical technologies of MHD (Magnetohydrodynamics) bypass scramjet propulsion for space launch and cruise vehicles is MHD acceleration. An experiment in a shock tunnel is described in which MHD acceleration is investigated experimentally. The objectives, the methods used and the preliminary results are described in this paper.

Bogdanoff, David W.↗

NASA NTRS1994

MHD modeling of magnetotail instability for localized resistivity

We present results of a three-dimensional magnetohydrodynamic (MHD) simulation of magnetotail evolution initiated by a sudden occurrence or increase of spatially localized resistivity as the major expected concequence of some localized microinstability. Because of the absence of a quantitative model, possible variations of resistivity levels with current density, or the reduction thereof, are not incorporated in the present investigation. The emphasis of the study is on an investigation of the changes to the overall evolution brought about by this localization, in particular, on the disruption and diversion of the cross-tail current and the nonlinear evolution of the magnetotail instability. The immediate consequences of the occurrence of the localized resistance and the resulting electric field are a reduction and diversion of the electric current around the region of high resistivity, associated with an increase of B(sub z) ('dipolarization') at the earthward edge and a decrease of B(sub z) at the tailward edge of this region. These effects, however, are localized and do not involve a reduction of the total cross-tail current and hence do not lead to the global development of a 'substorm current wedge,' which includes not only the reduction of the cross-tail current but also the buildup of a global field-aligned current system of 'regional 1' type (toward the Earth on the dawnside and away on the duskside of the tail). Such signatures develop at a later time, as consequences of a three-dimensional tearing instability, which is triggered by the occurrence of the resistivity. These features are found in combination with plasmoid formation and ejection, quite similar to results of earlier simulations with uniform resistivity. Differences are found in the timescale of the evolution, which tends to be shorter for localized resistivity, and in the propagation of the dipolarization effects in the equatorial plane. Whereas for uniform resistivity the temporal increase in B(sub z) tends to propagate tailward, apparently due to a pileup effect in the near-Earth region, an earthward propagation is found for the localized resistivity. This propagation results from an earthward convection of the gradient in B(sub z), which is set up by the reconnection process further tailward.

Hesse, Michael↗

NASA NTRS2012

Dipole Alignment in Rotating MHD Turbulence

We present numerical results from long-term CPU and GPU simulations of rotating, homogeneous, magnetohydrodynamic (MHD) turbulence, and discuss their connection to the spherically bounded case. We compare our numerical results with a statistical theory of geodynamo action that has evolved from the absolute equilibrium ensemble theory of ideal MHD turbulence, which is based on the ideal MHD invariants are energy, cross helicity and magnetic helicity. However, for rotating MHD turbulence, the cross helicity is no longer an exact invariant, although rms cross helicity becomes quasistationary during an ideal MHD simulation. This and the anisotropy imposed by rotation suggests an ansatz in which an effective, nonzero value of cross helicity is assigned to axisymmetric modes and zero cross helicity to non-axisymmetric modes. This hybrid statistics predicts a large-scale quasistationary magnetic field due to broken ergodicity , as well as dipole vector alignment with the rotation axis, both of which are observed numerically. We find that only a relatively small value of effective cross helicity leads to the prediction of a dipole moment vector that is closely aligned (less than 10 degrees) with the rotation axis. We also discuss the effect of initial conditions, dissipation and grid size on the numerical simulations and statistical theory.

Shebalin, John V.↗

NASA NTRS1992

Solar-wind/magnetospheric dynamos: MHD-scale collective entry of the solar wind energy, momentum and mass into the magnetosphere

A quasi open MHD (Magnetohydrodynamic) scale anomalous transport controlled boundary layer model is proposed, where the MHD collective behavior of magnetofluids (direct dynamo effect, anomalous viscous interaction and anomalous diffusion of the mass and the magnetic field) plays the main role in the conversion of the Solar Wind (SW) kinetic and magnetic energy into electromagnetic energy in the Magnetosphere (MSp). The so called direct and indirect dynamo effects are based on inductive and purely dissipative energy conversion, respectively. The self organization ability of vector fields in turbulent magnetofluids implies an inductive response of the plasma, which leads to the direct dynamo effect. The direct dynamo effect describes the direct formation of localized field aligned currents and the transverse Alfven waves and provides a source for MHD scale anomalous diffusivity and viscosity. The SW/MSp coupling depends on the dynamo efficiency.

Song, Yan↗

NASA NTRS1973

Flare-induced MHD disturbances in the corona - Moreton waves and type 2 shocks

The propagation in the corona of the magnetohydrodynamic (MHD) disturbance possibly emitted at the explosive stage in the initial phase of a flare is considered. The behavior of the MHD fast-mode wavefront, whose source is located at the flare, is calculated by using eiconal-characteristic method in the High Altitude Observatory (HAO) realistic models of coronal magnetic field and density for the days of some particular flare events. It is shown as the result that the peculiar behavior of Moreton's surface wave and the peculiar appearance in the shape and position of the type 2 burst sources can be consistently understood by considering the refraction, focussing, and formation of shocks of MHD fast-mode disturbance in the actual distribution of Alfven velocity in the corona. Moreton waves seem to appear only when the flare explosion happens to occur at the edge of an active region and faces a low-Alfven-velocity region lying on the surface. The wave, which is initially emitted isotropically is refracted into a direction in which the condition for down-refraction holds to allow chromospheric reentrance of disturbance.

Uchida, Y.↗

NASA NTRS1991

MHD shocks in coronal mass ejections

The primary objective of this research program is the study of the magnetohydrodynamic (MHD) shocks and nonlinear simple waves produced as a result of the interaction of ejected lower coronal plasma with the ambient corona. The types of shocks and nonlinear simple waves produced for representative coronal conditions and disturbance velocities were determined. The wave system and the interactions between the ejecta and ambient corona were studied using both analytic theory and numerical solutions of the time-dependent, nonlinear MHD equations. Observations from the SMM coronagraph/polarimeter provided both guidance and motivation and are used extensively in evaluating the results. As a natural consequence of the comparisons with the data, the simulations assisted in better understanding the physical interactions in coronal mass ejections (CME's).

Steinolfson, R. S.↗

NASA NTRS1994

MHD simulations of boundary layer formation along the dayside Venus ionopause due to mass loading

A two-dimensional magnetohydrodynamic (MHD) simulation of mass-loaded solar wind flow around the dayside of Venus is presented. For conditions appropriate to a low-altitude ionopause the simulations show that mass loading from the pickup of oxygen ions produces a boundary layer of finite thickness along the ionopause. Within this layer the temperatures exhibit strong gradients normal to and away from the ionopause. Furthermore, there is a shear in the bulk flow velocity across the boundary layer, such that the (predominantly tangential) flow decreases in speed as the ionopause is approached and remains small along the ionopause, consistent with Pioneer Venus observations. The total mass density increases significantly as the flow approaches the ionopause, where the contribution of O(+) to the total number density is a few percent. Numerical simulations are carried out for various mass addition rates and demonstrate that the boundary layer develops when oxygen ion production exceeds approximately 2 x 10(exp 5)/cu m/s. For the upstream solar wind parameters and mass loading rates chosen for these simulations, the results are consistent with observations made on the dayside of Venus for average ionopause conditions near 300 km.

Mcgary, J. E.↗

NASA NTRS2011

Broken Ergodicity in MHD Turbulence in a Spherical Domain

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

Shebalin, John V.↗

NASA NTRS1983

Viscous, resistive MHD stability computed by spectral techniques

Expansions in Chebyshev polynomials are used to study the linear stability of one dimensional magnetohydrodynamic (MHD) quasi-equilibria, in the presence of finite resistivity and viscosity. The method is modeled on the one used by Orszag in accurate computation of solutions of the Orr-Sommerfeld equation. Two Reynolds like numbers involving Alfven speeds, length scales, kinematic viscosity, and magnetic diffusivity govern the stability boundaries, which are determined by the geometric mean of the two Reynolds like numbers. Marginal stability curves, growth rates versus Reynolds like numbers, and growth rates versus parallel wave numbers are exhibited. A numerical result which appears general is that instability was found to be associated with inflection points in the current profile, though no general analytical proof has emerged. It is possible that nonlinear subcritical three dimensional instabilities may exist, similar to those in Poiseuille and Couette flow.

Dahlburg, R. B.↗

NASA NTRS2003

Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm

A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magnetohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS algorithm. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous complete Navier-Stokes calculations.

Kato, Hiromasa↗

NASA NTRS2000

Power Requirement for Nonequilibrium MHD-Bypass Scramjet

It has been suggested previously that the performance of scramjet propulsion system may be improved by the use of magnetohydrodynamic (MHD) energy bypass: an MHD generator could be made to decelerate the flow entering the combustor, thereby improving combustion efficiency, and the electrical power generated could be made to accelerate the flow exiting from the combustor prior to expanding through the nozzle. In one of such proposed schemes, the MHD generator is proposed to be operated at a low temperature and ionization is to be achieved under nonequilibrium by the application of an external power. In the present work, the required power of such an external source is calculated assuming a 100%-efficient nonequilibrium ionization scheme. The power required is that needed to prevent the degree of ionization from reaching equilibrium with the low gas temperature. The flow is seeded with potassium or cesium. Specific impulse is calculated with and without turbulent friction. The results show that, for typical intended flight conditions, the specific impulse obtained is substantially higher than that of a typical scramjet, but the required external-power is several times that of the power generated in the MHD generator.

Park, Chul↗