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NASA NTRS2004

Evolutionary Models of Cold, Magnetized, Interstellar Clouds

We modeled the long-term and small-scale evolution of molecular clouds using direct 2D and 3D magnetohydrodynamic (MHD) simulations. This work followed up on previous research by our group under auspices of the ATP in which we studied the energetics of turbulent, magnetized clouds and their internal structure on intermediate scales. Our new work focused on both global and smallscale aspects of the evolution of turbulent, magnetized clouds, and in particular studied the response of turbulent proto-cloud material to passage through the Galactic spiral potential, and the dynamical collapse of turbulent, magnetized (supercritical) clouds into fragments to initiate the formation of a stellar cluster. Technical advances under this program include developing an adaptive-mesh MHD code as a successor to ZEUS (ATHENA) in order to follow cloud fragmentation, developing a shearing-sheet MHD code which includes self-gravity and externally-imposed gravity to follow the evolution of clouds in the Galactic potential, and developing radiative transfer models to evaluate the internal ionization of clumpy clouds exposed to external photoionizing UV and CR radiation. Gammie's work at UIUC focused on the radiative transfer aspects of this program.

Gammie, Charles F.↗

NASA NTRS1994

Core magnetic field enhancement in single X line, multiple X line and patchy reconnection

Magnetic flux transfer events often show a significant increase of the magnetic field strength at the center of the events. Similar magnetic field observations have been reported for structures in or near the plasma sheet of the magnetotail at about 20 R(sub E). We have carried out two-dimensional (2D) and three-dimensional (3D) and simulations of single X line reconnection (SXR), multiple X line reconnection (MXR), and patchy reconnection to determine and compare the amplification of the magnetic field in the center of the developing flux tubes. The various processes are achieved by appropriate choices of 2D or 3D resistivity models. The simulations show that the increase in magnetic field strength depends on both the property of the initial configuration and the particular reconnection geometry. For the chosen initial conditions the MXR process leads to a larger increase in the core magnetic field than the patchy reconnection and SXR caused by larger magnetic tensions in the MXR process. The 3D processes always lead to a larger amplification than the corresponding 2D processes. In the 3D cases, force imbalance in the y direction will accelerate plasma out of the flux tube. This process reduces the thermal pressure and leads to a further compression of the flux rope, which yields an additional increase in the interior magnetic field strength.

Ma, Z. W.↗

NASA NTRS1992

Current collection through the transport of electrons across magnetic field lines

Numerical simulations are used to investigate the collection of electrons by a long conducting cylinder in a flowing plasma. The plasma flow simulates the relative motion between a spacecraft and the plasma. The sheath structures and the levels of electron current collections for the cases with and without an ambient magnetic field are examined. It is found that for the flow perpendicular to the magnetic field, the current is considerably enhanced depending on the relative drift velocity. In the case of a nonzero magnetic field perpendicular to the cylinder axis, the potential structure is a 2D double layer with dimensions L-perpendicular much less than L-parallel. L-perpendicular is found to be the current limiting radius given by the Parker-Murphy model (1967). For the flow along the ambient magnetic field, the electron current is found to be smaller than that for the flow perpendicular to this field. This is explained in terms of the potential structures.

Singh, N.↗

NASA NTRS1999

Coronal Magnetic Field Topology and Source of Fast Solar Wind

We have developed a steady state, 2D semi-empirical MHD model of the solar corona and the solar wind with many surprising results. This model for the first time shows, that the boundary between the fast and the slow solar wind as observed by Ulysses beyond 1 AU, is established in the low corona. The fastest wind observed by Ulysses (680-780 km/s) originates from the polar coronal holes at 70 -90 deg. latitude at the Sun. Rapidly diverging magnetic field geometry accounts for the fast wind reaching down to a latitude of +/- 30 deg. at the orbit of Earth. The gradual increase in the fast wind observed by Ulysses, with latitude, can be explained by an increasing field strength towards the poles, which causes Alfven wave energy flux to increase towards the poles. Empirically, there is a direct relationship between this gradual increase in wind speed and the expansion factor, f, computed at r greater than 20%. This relationship is inverse if f is computed very close to the Sun.

Guhathakurta, M.↗

NASA NTRS1986

Thermal stability analysis of the fine structure of solar prominences

The linear thermal stability of a 2D periodic structure (alternatively hot and cold) in a uniform magnetic field is analyzed. The energy equation includes wave heating (assumed proportional to density), radiative cooling and both conduction parallel and orthogonal to magnetic lines. The equilibrium is perturbed at constant gas pressure. With parallel conduction only, it is found to be unstable when the length scale 1// is greater than 45 Mn. In that case, orthogonal conduction becomes important and stabilizes the structure when the length scale is smaller than 5 km. On the other hand, when the length scale is greater than 5 km, the thermal equilibrium is unstable, and the corresponding time scale is about 10,000 s: this result may be compared to observations showing that the lifetime of the fine structure of solar prominences is about one hour; consequently, our computations suggest that the size of the unresolved threads could be of the order of 10 km only.

Demoulin, Pascal↗

NASA NTRS1993

Three-dimensional magnetohydrodynamics of the emerging magnetic flux in the solar atmosphere

The nonlinear evolution of an emerging magnetic flux tube or sheet in the solar atmosphere is studied through 3D MHD simulations. In the initial state, a horizontal magnetic flux sheet or tube is assumed to be embedded at the bottom of MHD two isothermal gas layers, which approximate the solar photosphere/chromosphere and the corona. The magnetic flux sheet or tube is unstable against the undular mode of the magnetic buoyancy instability. The magnetic loop rises due to the linear and then later nonlinear instabilities caused by the buoyancy enhanced by precipitating the gas along magnetic field lines. We find by 3D simulation that during the ascendance of loops the bundle of flux tubes or even the flux sheet develops into dense gas filaments pinched between magnetic loops. The interchange modes help produce a fine fiber flux structure perpendicular to the magnetic field direction in the linear stage, while the undular modes determine the overall buoyant loop structure. The expansion of such a bundle of magnetic loops follows the self-similar behavior observed in 2D cases studied earlier. Our study finds the threshold flux for arch filament system (AFS) formation to be about 0.3 x 10 exp 20 Mx.

Matsumoto, R.↗

NASA NTRS2004

Estimation of Length-Scales in Soils by MRI

Soil can be best described as an unconsolidated granular media that forms porous structure. The present macroscopic theory of water transport in porous media rests upon the continuum hypothesis that the physical properties of porous media can be associated with continuous, twice-differentiable field variables whose spatial domain is a set of centroids of Representative Elementary Volume (REV) elements. MRI is an ideal technique to estimate various length-scales in porous media. A 0.267 T permanent magnet at NASA GRC was used for this study. A 2D or 3D spatially-resolved porosity distribution were obtained from the NMR signal strength from each voxel and the spin-lattice relaxation time. A classical spin-warp imaging with Multiple Spin Echos (MSE) was used to evaluate proton density in each voxel. Initial resolution of 256 x 256 was subsequently reduced by averaging neighboring voxels and the porosity convergence was observed. A number of engineered "space candidate" soils such as Isolite(trademark), Zeoponics(trademark), Turface(trademark), and Profile(trademark) were used. Glass beads in the size range between 50 microns to 2 mm were used as well. Initial results with saturated porous samples have shown a good estimate of the average porosity consistent with the gravimetric porosity measurement results. For Profile(trademark) samples with particle sizes ranging between 0.25 to 1 mm and characteristic interparticle pore size of 100 microns the characteristic Darcy scale was estimated to be about delta(sub REV) = 10 mm. Glass beads porosity show clear convergence toward a definite REV which stays constant throughout homogeneous sample. Additional information is included in the original extended abstract.

N E Daidzic↗

NASA NTRS1992

Numerical simulations of the electrodynamic interactions between the Tethered-Satellite-System and space plasma

The first Tethered-Satellite-System (TSS-1), scheduled for a flight in late 1992, is expected to provide relevant information related to the concept of generating an emf in a 20-km-long (or longer) conducting wire. This paper presents numerical simulations of the electrodynamic interactions between the TSS system and space plasma, using a 2D and 3D models of the system. The 2D case code simulates the motion of a long cylinder past a plasma, which is composed of electrons and H(+) ions. The system is solved by allowing the plasma to flow past the cylinder with an imposed magnetic field. The more complex 3D case is considered to study the dynamics in great detail. Results of 2D simulation show that the interaction of a satellite with plasma flowing perpendicularly to the magnetic field results in an enhancement in the current collection.

Vashi, Bharat I.↗

NASA NTRS2023

Reconnection in a Pinch

A recently published analysis of current sheets has updated the classic Harris 1D static solution by considering multiple classes of charged particle trajectories in a generalized and dynamic current sheet. It uses a 1D PIC simulation to describe dynamic pinching and bifurcation of the current sheet. These 1D results strongly suggest that properties of the inflowing plasma, including the plasma beta, have an important effect on the equilibrium thickness of the pinched current sheet. Since 1D studies cannot describe magnetic reconnection, the time appears right to carry such 1D studies over to 2D or 3D simulations to explore current sheet thickness effects on reconnection. The Magnetospheric Multiscale Mission (MMS), with its well-resolved multipoint measurements of collisionless plasma and fields, has found that collisionless reconnection is accompanied by non-adiabatic motions of electrons that only occur in magnetic structures with a narrow scale comparable to electron inertial lengths (d e ). The recent 1D studies suggest that a plasma pinch to such scales may only occur for inflowing magnetized plasmas with relatively low plasma beta. We conclude that a parametric exploration of simulated and observed reconnection inflow conditions, particularly plasma beta, should shed light on the enablement of reconnection in collisionless plasmas.

reconnection↗

NASA NTRS2011

Interchange Slip-Running Reconnection and Sweeping SEP-Beams

We present a new model to explain how particles, accelerated at a reconnection site that is not magnetically connected to the Earth, could eventually propagate along the well-connected open flux tube. Our model is based on the results of a low-beta resistive magnetohydrodynamics simulation of a three-dimensional line-tied and initially current-free bipole, that is embedded in a non-uniform open potential field. The topology of this configuration is that of an asymmetric coronal null-point, with a closed fan surface and an open outer spine. When driven by slow photospheric shearing motions, field lines, initially fully anchored below the fan dome, reconnect at the null point, and jump to the open magnetic domain. This is the standard interchange mode as sketched and calculated in 2D. The key result in 3D is that, reconnected open field lines located in the vicinity of the outer spine, keep reconnecting continuously, across an open quasi-separatrix layer, as previously identified for non-open-null-point reconnection. The apparent slipping motion of these field lines leads to form an extended narrow magnetic flux tube at high altitude. Because of the slip-running reconnection, we conjecture that if energetic particles would be travelling through, or be accelerated inside, the diffusion region, they would be successively injected along continuously reconnecting field lines that are connected farther and farther from the spine. At the scale of the full Sun, owing to the super-radial expansion of field lines below 3 solar radius, such energetic particles could easily be injected in field lines slipping over significant distances, and could eventually reach the distant flux tube that is well-connected to the Earth.

Masson, S.↗

NASA NTRS2014

MHD Modeling of Coronal Loops: the Transition Region Throat

Context. The expansion of coronal loops in the transition region may considerably influence the diagnostics of the plasma emission measure. The cross-sectional area of the loops is expected to depend on the temperature and pressure, and might be sensitive to the heating rate. Aims. The approach here is to study the area response to slow changes in the coronal heating rate, and check the current interpretation in terms of steady heating models. Methods. We study the area response with a time-dependent 2D magnetohydrodynamic (MHD) loop model, including the description of the expanding magnetic field, coronal heating and losses by thermal conduction, and radiation from optically thin plasma. We run a simulation for a loop 50 Mm long and quasi-statically heated to about 4 millikelvin. Results. We find that the area can change substantially with the quasi-steady heating rate, e.g., by approx. 40% at 0.5 millikelvin as the loop temperature varies between 1 millikelvin and 4 millikelvin, and, therefore, affects the interpretation of the differential emission measure vs. temperature (DEM(T)) curves.

magnetohydrodynamics (MHD)↗

NASA NTRS1993

Formation, levitation, and stability of prominences in the magnetized solar atmosphere

The dynamic formation of prominences in the initial magnetothermal equilibrium and their stability to sideward displacements are investigated focusing on the structure of the 2D solar atmosphere in the presence of coronal arcades or loops. A model based on 2D magnetohydrodynamic equations takes into account gravity, compressible flows, heating, radiation, anisotropic thermal conduction, and coupling to a deep chromosphere. It is found that prominences in simple arcades characterized by magnetic field with significant curvature at the apex are unstable to a lateral displacement.

Drake, J. F.↗

NASA NTRS1992

Extra high speed modified Lundell alternator parameters and open/short-circuit characteristics from global 3D-FE magnetic field solutions

The combined magnetic vector potential - magnetic scalar potential method of computation of 3D magnetic fields by finite elements, introduced in a companion paper, is used for global 3D field analysis and machine performance computations under open-circuit and short-circuit conditions for an example 14.3 kVA modified Lundell alternator, whose magnetic field is of intrinsic 3D nature. The computed voltages and currents under these machine test conditions were verified and found to be in very good agreement with corresponding test data. Results of use of this modelling and computation method in the study of a design alteration example, in which the stator stack length of the example alternator is stretched in order to increase voltage and volt-ampere rating, are given here. These results demonstrate the inadequacy of conventional 2D-based design concepts and the imperative of use of this type of 3D magnetic field modelling in the design and investigation of such machines.

Wang, R.↗

NASA NTRS1983

Magnetohydrodynamic simulation of the coronal transient associated with the solar limb flare of 1980, June 29, 18:21 UT

The spatial and temporal behavior of excess and depleted density regions of the coronal transient accompanying the west limb solar flare of 18:21 UT on June 29, 1980, is modeled mathematically on the basis of SMM-X-ray-polychrometer data, and the results are compared to observations made with the radio spectrograph at Harvard Radio Astronomy Station at Fort Davis and with the NCAR/HAO Mark III K-coronameter at Mauna Loa. Input data for the model include T(max) = about 20 x 10 to the 6th K, n(max) = about 4 x 10 to the 11th/cu cm, and an assumed ejection velocity of 200 km/sec. Computations using an improved 2D nonplane MHD model are carried out for locally open and closed magnetic topologies. The spatially wide, large-amplitude, temporarily steepened MHD wave predicted by the model for both magnetic topologies is shown to agree well with the observations, except that the predicted density enhancement exceeded observed values by at least 50 percent for the closed field and by a factor of 3 for the open field. This discrepancy is seen as an indication that the mass emitting soft X-rays was confined in closed-field regions near the sun during the obervation period.

Wu, S. T.↗

NASA NTRS1993

Analysis and design of an ultrahigh temperature hydrogen-fueled MHD generator

A coupled gas dynamics/radiative heat transfer analysis of partially ionized hydrogen, in local thermodynamic equilibrium, flowing through an ultrahigh temperature (10,000-20,000 K) magnetohydrodynamic (MHD) generator is performed. Gas dynamics are modeled by a set of quasi-one-dimensional, nonlinear differential equations which account for friction, convective and radiative heat transfer, and the interaction between the ionized gas and applied magnetic field. Radiative heat transfer is modeled using nongray, absorbing-emitting 2D and 3D P-1 approximations which permit an arbitrary variation of the spectral absorption coefficient with frequency. Gas dynamics and radiative heat transfer are coupled through the energy equation and through the temperature- and density-dependent absorption coefficient. The resulting nonlinear elliptic problem is solved by iterative methods. Design of such MHD generators as onboard, open-cycle, electric power supplies for a particular advanced airbreathing propulsion concept produced an efficient and compact 128-MWe generator characterized by an extraction ratio of 35.5 percent, a power density of 10,500 MWe/cu m, and a specific (extracted) energy of 324 MJe/kg of hydrogen. The maximum wall heat flux and total wall heat load were 453 MW/sq m and 62 MW, respectively.

Moder, Jeffrey P.↗

NASA NTRS1993

A renormalization group analysis of two-dimensional magnetohydrodynamic turbulence

The renormalization group (RNG) method is used to study the physics of two-dimensional (2D) magnetohydrodynamic (MHD) turbulence. It is shown that, for a turbulent magnetofluid in two dimensions, no RNG transformation fixed point exists on account of the coexistence of energy transfer to small scales and mean-square magnetic flux transfer to large scales. The absence of a fixed point renders the RNG method incapable of describing the 2D MHD system. A similar conclusion is reached for 2D hydrodynamics, where enstrophy flows to small scales and energy to large scales. These analyses suggest that the applicability of the RNG method to turbulent systems is intrinsically limited, especially in the case of systems with dual-direction transfer.

Liang, Wenli Z.↗

NASA NTRS2010

Formation and Reconnection of Three-Dimensional Current Sheets in the Solar Corona

Current-sheet formation and magnetic reconnection are believed to be the basic physical processes responsible for much of the activity observed in astrophysical plasmas, such as the Sun s corona. We investigate these processes for a magnetic configuration consisting of a uniform background field and an embedded line dipole, a topology that is expected to be ubiquitous in the corona. This magnetic system is driven by a uniform horizontal flow applied at the line-tied photosphere. Although both the initial field and the driver are translationally symmetric, the resulting evolution is calculated using a fully three-dimensional magnetohydrodynamic (3D MHD) simulation with adaptive mesh refinement that resolves the current sheet and reconnection dynamics in detail. The advantage of our approach is that it allows us to apply directly the vast body of knowledge gained from the many studies of 2D reconnection to the fully 3D case. We find that a current sheet forms in close analogy to the classic Syrovatskii 2D mechanism, but the resulting evolution is different than expected. The current sheet is globally stable, showing no evidence for a disruption or a secondary instability even for aspect ratios as high as 80:1. The global evolution generally follows the standard Sweet- Parker 2D reconnection model except for an accelerated reconnection rate at a very thin current sheet, due to the tearing instability and the formation of magnetic islands. An interesting conclusion is that despite the formation of fully 3D structures at small scales, the system remains close to 2D at global scales. We discuss the implications of our results for observations of the solar corona. Subject Headings: Sun: corona Sun: magnetic fields Sun: reconnection

Edmondson, J. K.↗

NASA NTRS2008

Development of Solar Wind Model Driven by Empirical Heat Flux and Pressure Terms

We are developing a time stationary self-consistent 2D MHD model of the solar corona and solar wind as suggested by Sittler et al. (2003). Sittler & Guhathakurta (1999) developed a semiempirical steady state model (SG model) of the solar wind in a multipole 3-streamer structure, with the model constrained by Skylab observations. Guhathakurta et al. (2006) presented a more recent version of their initial work. Sittler et al. (2003) modified the SG model by investigating time dependent MHD, ad hoc heating term with heat conduction and empirical heating solutions. Next step of development of 2D MHD models was performed by Sittler & Ofman (2006). They derived effective temperature and effective heat flux from the data-driven SG model and fit smooth analytical functions to be used in MHD calculations. Improvements of the Sittler & Ofman (2006) results now show a convergence of the 3-streamer topology into a single equatorial streamer at altitudes > 2 R(sub S). This is a new result and shows we are now able to reproduce observations of an equatorially confined streamer belt. In order to allow our solutions to be applied to more general applications, we extend that model by using magnetogram data and PFSS model as a boundary condition. Initial results were presented by Selwa et al. (2008). We choose solar minimum magnetogram data since during solar maximum the boundary conditions are more complex and the coronal magnetic field may not be described correctly by PFSS model. As the first step we studied the simplest 2D MHD case with variable heat conduction, and with empirical heat input combined with empirical momentum addition for the fast solar wind. We use realistic magnetic field data based on NSO/GONG data, and plan to extend the study to 3D. This study represents the first attempt of fully self-consistent realistic model based on real data and including semi-empirical heat flux and semi-empirical effective pressure terms.

Sittler, Edward C., Jr.↗