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Structure and Dynamics of the Solar Corona

Advanced computational techniques were used to study solar coronal heating and coronal mass ejections. A three dimensional, time dependent resistive magnetohydrodynamic code was used to study the dynamic response of a model corona to continuous, slow, random magnetic footpoint displacements in the photosphere. Three dimensional numerical simulations of the response of the corona to simple smooth braiding flows in the photosphere were calculated to illustrate and understand the spontaneous formation of current filaments. Two dimensional steady state helmet streamer configurations were obtained by determining the time asymptotic state of the interaction of an initially one dimensinal transponic solar wind with a spherical potential dipole field. The disruption of the steady state helmet streamer configuration was studied as a response to shearing of the magnetic footpoints of the closed field lines under the helmet.

Schnack, D. D.↗

Magnetohydrodynamic Augmented Propulsion Experiment

A fundamental obstacle to routine space access is the specific energy limitations associated with chemical fuels. In the case of vertical take-off, the high thrust needed for vertical liftoff and acceleration to orbit translates into power levels in the 10 GW range. Furthermore, useful payload mass fractions are possible only if the exhaust particle energy (i.e., exhaust velocity) is much greater than that available with traditional chemical propulsion. The electronic binding energy released by the best chemical reactions (e.g., LOX/LH2 for example, is less than 2 eV per product molecule (approx. 1.8 eV per H2O molecule), which translates into particle velocities less than 5 km/s. Useful payload fractions, however, will require exhaust velocities exceeding 15 km/s (i.e., particle energies greater than 20 eV). As an added challenge, the envisioned hypothetical RLV (reusable launch vehicle) should accomplish these amazing performance feats while providing relatively low acceleration levels to orbit (2-3g maximum). From such fundamental considerations, it is painfully obvious that planned and current RLV solutions based on chemical fuels alone represent only a temporary solution and can only result in minor gains, at best. What is truly needed is a revolutionary approach that will dramatically reduce the amount of fuel and size of the launch vehicle. This implies the need for new compact high-power energy sources as well as advanced accelerator technologies for increasing engine exhaust velocity. Electromagnetic acceleration techniques are of immense interest since they can be used to circumvent the thermal limits associated with conventional propulsion systems. This paper describes the Magnetohydrodynamic Augmented Propulsion Experiment (MAPX) being undertaken at NASA Marshall Space Flight Center (MSFC). In this experiment, a 1-MW arc heater is being used as a feeder for a 1-MW magnetohydrodynamic (MHD) accelerator. The purpose of the experiment is to demonstrate that an MHD accelerator can be an effective augmentation system for increasing engine exhaust velocity. More specifically, the experiment is intended to show that electromagnetic effects are effective at producing flow acceleration whereas electrothermal effects do not cause unacceptable heating of the working fluid. The MHD accelerator was designed as an externally diagonalized segmented Faraday channel, which will be inserted into an existing 2-tesla electromagnet. This allows the external power to be connected through two terminals thereby minimizing the complexity and cost associated with powering each segment independently. The design of the accelerator and other components in the flow path has been completed and fabrication activities are underway. This paper provides a full description of MAPX including performance analysis, design, and test plans, and current status.

Litchford, Ron J.↗

Large-scale computations in fluid mechanics; Proceedings of the Fifteenth Summer Seminar on Applied Mathematics, University of California, La Jolla, CA, June 27-July 8, 1983. Parts 1 & 2

Papers are presented on such topics as the use of semi-Lagrangian advective schemes in meteorological modeling; computation with high-resolution upwind schemes for hyperbolic equations; dynamics of flame propagation in a turbulent field; a modified finite element method for solving the incompressible Navier-Stokes equations; computational fusion magnetohydrodynamics; and a nonoscillatory shock capturing scheme using flux-limited dissipation. Consideration is also given to the use of spectral techniques in numerical weather prediction; numerical methods for the incorporation of mountains in atmospheric models; techniques for the numerical simulation of large-scale eddies in geophysical fluid dynamics; high-resolution TVD schemes using flux limiters; upwind-difference methods for aerodynamic problems governed by the Euler equations; and an MHD model of the earth's magnetosphere.

Engquist, B. E.↗

The Analysis of a Vortex Type Magnetohydrodynamic Induction Generator

Consideration it is given to the performance to the characteristics of an AC magnetohydrodynamic power generator, A rotating magnetic field is imposed on the vortex flow of an electrically conducting fluid, which is injected tangentially into an annulus formed by two nonconducting concentric cylinders and two nonconducting end plates. A perturbation technique is used to determine the two dimensional velocity and three dimensional electromagnetic field and current distributions. Finally, the generated power, the ohmic losses, the effective power and the electrical efficiency of the converter system are calculated.

MAGNETOHYDRODYNAMIC GENERATOR↗

Theoretical Investigation of the High-Altitude Cusp Region using Observations from Interball and ISTP Spacecraft

A fundamental goal of magnetospheric physics is to understand the transport of plasma through the solar wind-magnetosphere-ionosphere system. To attain such an understanding, we must determine the sources of the plasma, the trajectories of the particles through the magnetospheric electric and magnetic fields to the point of observation, and the acceleration processes they undergo enroute. This study employed plasma distributions observed in the near-Earth plasma sheet by Interball and Geotail spacecraft together with theoretical techniques to investigate the ion sources and the transport of plasma. We used ion trajectory calculations in magnetic and electric fields from a global Magnetohydrodynamics (MHD) simulation to investigate the transport and to identify common ion sources for ions observed in the near-Earth magnetotail by the Interball and Geotail spacecraft. Our first step was to examine a number of distribution functions and identify distinct boundaries in both configuration and phase space that are indicative of different plasma sources and transport mechanisms. We examined events from October 26, 1995, November 29-30, 1996, and December 22, 1996. During the first event Interball and Geotail were separated by approximately 10 R(sub E) in z, and during the second event the spacecraft were separated by approximately 4(sub RE). Both of these events had a strong IMF By component pointing toward the dawnside. On October 26, 1995, the IMF B(sub Z) component was northward, and on November 1-9-30, 1996, the IMF B sub Z) component was near 0. During the first event, Geotail was located near the equator on the dawn flank, while Interball was for the most part in the lobe region. The distribution function from the Coral instrument on Interball showed less structure and resembled a drifting Maxwellian. The observed distribution on Geotail, on the other hand, included a great number of structures at both low and high energies. During the third event (December 22, 1996) both spacecraft were in the plasma sheet and were separated bY approximately 20 R(sub E) in the y direction. During this event the IMF was southward.

Ashour-Abdalla, Maha↗

Computational techniques for solar wind flows past terrestrial planets: Theory and computer programs

The interaction of the solar wind with terrestrial planets can be predicted using a computer program based on a single fluid, steady, dissipationless, magnetohydrodynamic model to calculate the axisymmetric, supersonic, super-Alfvenic solar wind flow past both magnetic and nonmagnetic planets. The actual calculations are implemented by an assemblage of computer codes organized into one program. These include finite difference codes which determine the gas-dynamic solution, together with a variety of special purpose output codes for determining and automatically plotting both flow field and magnetic field results. Comparisons are made with previous results, and results are presented for a number of solar wind flows. The computational programs developed are documented and are presented in a general user's manual which is included.

Stahara, S. S.↗

Interplanetary Fast Shocks and Associated Drivers Observed through the Twenty-Third Solar Minimum by WIND Over its First 2.5 Years

A list of the interplanetary (IP) shocks observed by WIND from its launch (in November 1994) to May 1997 is presented. Forty two shocks were identified. The magnetohydrodynamic nature of the shocks is investigated, and the associated shock parameters and their uncertainties are accurately computed using a practical scheme which combines two techniques. These techniques are a combination of the "pre-averaged" magnetic-coplanarity, velocity-coplanarity, and the Abraham-Schrauner-mixed methods, on the one hand, and the Vinas and Scudder [1986] technique for solving the non-linear least-squares Rankine-Hugoniot shock equations, on the other. Within acceptable limits these two techniques generally gave the same results, with some exceptions. The reasons for the exceptions are discussed. It is found that the mean strength and rate of occurrence of the shocks appears to correlated with the solar cycle. Both showed a decrease in 1996 coincident with the time of the lowest ultraviolet solar radiance, indicative of solar minimum and start of solar cycle 23, which began around June 1996. Eighteen shocks appeared to be associated with corotating interaction regions (CIRs). The distribution of their shock normals showed a mean direction peaking in the ecliptic plane and with a longitude (phi(sub n)) in that plane between perpendicular to the Parker spiral and radial from the Sun. When grouped according to the sense of the direction of propagation of the shocks the mean azimuthal (longitude) angle in GSE coordinates was approximately 194 deg for the fast-forward and approximately 20 deg for the fast-reverse shocks. Another 16 shocks were determined to be driven by solar transients, including magnetic clouds. These shocks had a broader distribution of normal directions than those of the CIR cases with a mean direction close to the Sun-Earth line. Eight shocks of unknown origin had normal orientation well off the ecliptic plane. No shock propagated with longitude phi(sub n) >= 220 +/- 10 deg, this would suggest strong hindrance to the propagation of shocks contra a rather tightly winding Parker spiral. Examination of the obliquity angle theta(sub Bn) (that between the shock normal and the upstream interplanetary magnetic field) for the full set of shocks revealed that about 58% was quasi-perpendicular, and some were very nearly perpendicular. About 32% of the shocks were oblique, and the rest (only 10%) were quasi-parallel, with one on Dec. 9, 1996 that showed field pulsations. Small uncertainty in the estimated angle theta(sub Bn) was obtained for about 10 shocks with magnetosonic Mach numbers between 1 and 2, hopefully significantly contributing to studies researching particle acceleration mechanisms at IP shocks, and to investigations where accurate values of theta(sub Bn) are crucial.

Mariani, F.↗

Ion Sources and Acceleration Mechanisms Inferred from Local Distribution Functions

This study investigates the sources of the ions up the complex and nonisotropic H(+) velocity distribution functions observed by the Geotail spacecraft on May 23, 1995, in the near-Earth magnetotail region and recently reported by Frank et al. [1996]. A distribution function observed by Geotail at -10 R(sub E) downtail is used as input for the large scale kinetic (LSK) technique to follow the trajectories of approximately 90,000 H(+) ions backward in time. Time-dependent magnetic and electric fields are taken from a global magnetohydrodynamic (MHD) simulation of the magnetosphere and its interactions with appropriate solar wind and IMF conditions. The ion population described by the Geotail distribution function was found to consist of a mixture of particles originating from three distinct sources: the ionosphere, the low latitude boundary layer (LLBL), and the high latitude plasma mantle. Ionospheric particles had direct access along field lines to Geotail, and LLBL ions convected adiabatically to the Geotail location. Plasma mantle ions, on the other hand, exhibited two distinct types of behavior. Most near-Earth mantle ions reached Geotail on adiabatic orbits, while distant mantle ions interacted with the current sheet tailward of Geotail and had mostly nonadiabatic orbits. Ions from the ionosphere, the LLBL, and the near-Earth mantle were directly responsible for the well-separated, low energy structures easily discernible in the observed and modeled distribution functions. Distant mantle ions formed the higher energy portion of the Geotail distribution. Thus, we have been successful in extracting useful information about particle sources, their relative contribution to the measured distribution and the acceleration processes that affected particle transport during this time.

Ashour-Abdalla, M.↗

Scientific Visualization to Study Flux Transfer Events at the Community Coordinated Modeling Center

In this paper we present results of modeling of reconnection at the dayside magnetopause with subsequent development of flux transfer event signatures. The tools used include new methods that have been added to the suite of visualization methods that are used at the Community Coordinated Modeling Center (CCMC). Flux transfer events result from localized reconnection that connect magnetosheath magnetic field and plasma with magnetospheric fields and plasma and results in flux rope structures that span the dayside magnetopause. The onset of flux rope formation and the three-dimensional structure of flux ropes are studied as they have been modeled by high-resolution magnetohydrodynamic simulations of the dayside magnetosphere of the Earth. We show that flux transfer events are complex three-dimensional structures that require modern visualization and analysis techniques. Two suites of visualization methods are presented and we demonstrate the usefulness of those methods through the CCMC web site to the general science user.

Rastatter, Lutz↗

Modeling the Formation and Eruption of Coronal Structures by Linking Data-Driven Magnetofrictional and MHD Simulations for AR 12673

Context .The data-driven and time-dependent modeling of coronal magnetic fields is crucial for understanding solar eruptions. These efforts are complicated by the challenges of finding a balance between physical realism and computing efficiency. One possible technique is to couple two modeling approaches. Aims . Our aim here is to showcase our progress in using time-dependent magnetofrictional model (TMFM) results as input to dynamical magnetohydrodynamic (MHD) simulations. However, due to the different evolution processes in these two models, using TMFM snapshots in an MHD simulation is nontrivial. We address these issues, both physically and numerically, discuss the incompatibility of the TMFM output to serve as the initial condition in MHD simulations, and show our methods of mitigating this. The evolution of the flux systems and the cause of the eruption are investigated. Methods . TMFM is a prevalent approach that has proven to be a very useful tool in the study of the formation of unstable structures in the solar corona. In particular, it is capable of incorporating observational data as initial and boundary conditions and requires shorter computational time compared to MHD simulations. To leverage the efficiency of data-driven TMFM and also to simulate eruptive events in the MHD framework, one can apply TMFM up to a certain time before the expected eruption(s) and then proceed with the simulation in the full or ideal MHD regime in order to more accurately capture the eruption process. Results . We show the results of a benchmark test case with a linked TMFM and MHD simulation to study the evolution of NOAA active region 12673. A rise of a twisted flux bundle through the MHD simulation domain is observed, but we find that the rate of the rise and the altitude reached depends on the time of the TMFM snapshot that was used to initialize the MHD simulation and the helicity injected into the system. The analysis suggested that torus instability and slip-running reconnection could play an important role in the eruption. Conclusions . The results show that the linkage of TMFM and zero-β MHD models can be successfully used to model the eruptive coronal magnetic fields.

F. Daei↗

An adaptive grid, unsteady model for two-dimensional magnetohydrodynamic (MHD) flow

An adaptive grid finite difference method for solving multi-dimensional, time-dependent, magnetohydrodynamic (MHD) equations is developed. The method is capable of solving problems that include high gradients due to geometry, propagation of shock waves and unsteady boundary conditions. The grid generation technique is based on variational principles with direct control over grid concentration, smoothness and skewness. An example for a two-dimensional MHD simulation of the propagation of a solar-flare-generated shock wave in solar wind flow in the heliographic equatorial plane is selected for illustration of this method.

Panitchob, Supat↗

Interplanetary shock normals

A scheme has been developed to improve the estimate of an interplanetary shock normal by using both magnetic field and plasma data from a single spacecraft. Calculation of the basic shock model employs a subset of the eight magnetohydrodynamic conservation relations for a shock in an isotropic medium. This subset consists of six equations that are devoid of pressure and temperature terms. A sigma-weighted least squares loss function technique is used to best fit the overdetermination equations with respect to the eleven parameters of the system. This procedure usually yields a normal much more accurate than the one obtained using magnetic field values alone. An example is given of the use of the technique on the data for the Pioneer 7 shock of 29 August 1966.

Lepping, R. P.↗

Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind

Measurements of the total energy, cross helicity, and magnetic helicity of the solar wind at 1, 2.8, and 5 AU are presented. These quantities are the three rugged invariants of three-dimensional ideal incompressible MHD turbulence theory. The theoretical technique for measuring the magnetic helicity from the matrix of two-point correlations is shown. The length scales characterizing the magnetic helicity are found to be equal to or greater than those which characterize the magnetic energy. The magnetic helicity typically lies at scales larger than the magnetic correlation length, consistent with the expectations of the inverse cascade and selective decay hypotheses of three-dimensional MHD turbulence. At smaller scales, the magnetic helicity oscillates in sign. Measurements of the cross helicity are not fully consistent with the usual interpretation in terms of outward propagating Alfvenic functions. Especially during the interval at 5 AU the cross helicity is found to oscillate in sign indicating fluctuations propagating both outward and inward.

Matthaeus, W. H.↗

The evolution of cosmic-ray-mediated magnetohydrodynamic shocks: A two-fluid approach

We study the shock structure and acceleration efficiency of cosmic-ray mediated Magnetohydrodynamic (MHD) shocks both analytically and numerically by using a two-fluid model. Our model includes the dynamical effect of magnetic fields and cosmic rays on a background thermal fluid. The steady state solution is derived by following the technique of Drury & Voelk (1981) and compared to numerical results. We explore the time evolution of plane-perpendicular, piston-driven shocks. From the results of analytical and numerical studies, we conclude that the mean magnetic field plays an important role in the structure and acceleration efficiency of cosmic-ray mediated MHD shocks. The acceleration of cosmic-ray particles becomes less efficient in the presence of strong magnetic pressure since the field makes the shock less compressive. This feature is more prominent at low Mach numbers than at high Mach numbers.

Jun, Byung-Il↗

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.↗

Physics of the inner heliosphere 1-10R sub O plasma diagnostics and models

The physics of solar wind flow in the acceleration region and impulsive phenomena in the solar corona is studied. The study of magnetohydrodynamic wave propagation in the corona and the solutions for steady state and time dependent solar wind equations gives insights concerning the physics of the solar wind acceleration region, plasma heating and plasma acceleration processes and the formation of shocks. Also studied is the development of techniques for placing constraints on the mechanisms responsible for coronal heating.

Withbroe, G. L.↗

Radial variations of large-scale magnetohydrodynamic fluctuations in the solar wind

Two time periods are studied for which comprehensive data coverage is available at both 1 AU using IMP-8 and ISEE-3 and beyond using Voyager 1. One of these periods is characterized by the predominance of corotating stream interactions. Relatively small scale transient flows characterize the second period. The evolution of these flows with heliocentric distance is studied using power spectral techniques. The evolution of the transient dominated period is consistent with the hypothesis of turbulent evolution including an inverse cascade of large scales. The evolution of the corotating period is consistent with the entrainment of slow streams by faster streams in a deterministic model.

Burlaga, L. F.↗