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NASA NTRS1987

Magnetotail equilibrium theory - The general three-dimensional solution

The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.

Birn, J.↗

NASA NTRS1987

The evolution of a coronal streamer prior to mass ejection

A model describing the quasi-static evolution of a coronal helmet streamer as it is inflated with excess mass was developed. The model produces a sequence of magnetostatic equilibria for a magnetic field configuration that includes a current sheet in the equatorial plane as well as distributed volume currents. The equilibrium solutions are given as Legendre series, and the height at which the current sheet starts is adjusted iteratively to maintain constant flux in the closed-field region. The model was fit to SMM coronagraph/polarimeter observations showing the slow growth of a coronal streamer prior to its disruption in association with an eruptive prominence and mass ejection on August 18, 1980. The results suggest that the early phase of this event is consistent with the quasi-static evolution of the corona in response to the slow addition of mass to the closed-field region of the streamer.

Wolfson, Richard↗

NASA NTRS1989

Nonlinear Parker instability of isolated magnetic flux in a plasma

The nonlinear evolution of the Parker instability in an isolated horizontal magnetic-flux sheet embedded in a two-temperature layer atmosphere is studied by using a two-dimensional MHD code. In the solar case, this two-layer model is regarded as a simplified abstraction of the sun's photosphere/chromosphere and its overlying much hotter (coronal) envelope. The horizontal flux sheet is initially located in the lower temperature atmosphere so as to satisfy magnetostatic equilibrium under a constant gravitational acceleration. Ideal MHD is assumed, and only perturbations with k parallel to the magnetic-field lines are investigated. As the instability develops, the gas slides down the expanding loop, and the evacuated loop rises as a result of enhanced magnetic buoyancy. In the nonlinear regime of the instability, both the rise velocity of a magnetic loop and the local Alfven velocity at the top of the loop increase linearly with height and show self-similar behavior with height as long as the wavelength of the initial perturbation is much smaller than the horizontal size of the computing domain.

Shibata, K.↗

NASA NTRS1989

Three-dimensional simulation of whistler mode excited by the Spacelab 2 electron beam

During the Spacelab 2 mission, while an electron beam was being ejected from the Shuttle, the Plasma Diagnostics Package (PDP) detected a clear funnel-shaped emission that is believed to be caused by whistler-mode emission from the electron beam. In order to understand the mechanism of this emission, simulations with a three-dimensional partially magnetostatic code have been performed. The simulation results show that whistler-mode and lower hybrid waves are excited by the electron beam, which is initially localized in the column in the three-dimensional simulation system, and that they propagate away from the beam. The wave spectra of the electric and magnetic fields diagnosed at some points show several peaks due to the waves excited by the electron beam. The frequency range of these spectra is in qualitative agreement with the PDP data. The intense narrowband electrostatic emission near the electron plasma frequency is observed by the simulations. The simulation results show that the beam instability is responsible for the generation mechanism of these emissions.

Nishikawa, K.-I.↗

NASA NTRS1989

Remote sensing of the ring current using energetic neutral atoms

Energetic neutral atom images of the storm-time ring current obtained from the ISEE-1 spacecraft provide information for a 'zero-order' global model of the energetic ion distribution. With the assumption of isotropic pressure and magnetostatic, nonconvective pressure balance, the global system of electrical currents driven by the ion pressure can be calculated using Euler potentials for the divergenceless current density. Radial pressure gradients drive azimuthal currents, and azimuthal pressure gradients drive radial currents. The radial currents cause current lines in the inner magnetosphere to close in the ionosphere, forming a partial ring current. The intensities and locations of these field-aligned currents driven into and out of the ionosphere resemble those of the observed Region 2 current system, but not all observed properties of the Region 2 system are reproduced by the zero-order model.

Roelof, Edmond C.↗

NASA NTRS1990

Three-dimensional kinematic reconnection in the presence of field nulls and closed field lines

The present investigation of three-dimensional reconnection of magnetic fields with nulls and of fields with closed lines gives attention to the geometry of the former, with a view to their gamma-line and Sigma-surface structures. The geometric structures of configurations with a pair of type A and B nulls permit reconnection across the null-null lines; these are the field lines which join the two nulls. Also noted is the case of magnetostatic reconnection, in which the magnetic field is time-independent and the electrostatic potential is constant along field lines.

Lau, Yun-Tung↗

NASA NTRS1990

Intrinsic magnetic discontinuities and solar X-ray emission

The fundamental theorem of magnetostatic equilibrium predicts that the bipolar magnetic fields of active regions on the sun contain tangential discontinuities as an intrinsic part of their equilibrium. It appears that rapid reconnection at these many tangential discontinuities (nanoflares) is the primary source of heat that produces the X-ray emitting corona. The X-ray corona is then a cloud of nanoflares.

Parker, E. N.↗

NASA NTRS1990

Electromagnetic axisymmetric finite elements based on a gauged four-potential variational principle

Electromagnetic finite elements are derived based on a variational principle that uses the electromagnetic four-potential as a primary variable. The Lorentz gage normalization is incorporated as a constraint condition through a Lagrange multiplier field to construct elements suitable for downstream coupling with mechanical and thermal finite elements for the analysis of high-temperature superconductor devices with aerospace applications. The main advantages are: jump discontinuities on interfaces are naturally handled; no a priori approximations are invoked; and the number of degrees of freedom per node remains modest as the problem dimensionality increases. The new elements are tested on two magnetostatic axisymmetric problems. The results are in excellent agreement with analytical solutions and previous solutions for the 1D problem of a conducting infinite wire, in which case the multiplier field has no effect. For materials of widely different permeability, jump conditions are naturally accommodated by the present formulation.

Schuler, J.↗

NASA NTRS1991

Inverse photoelectron spectrometer with magnetically focused electron gun

An inverse photoelectron spectrometer is described which is based on the design of a magnetically focused low energy electron gun. The magnetic lens extends its field over a relatively large segment of the electron trajectory, which could provide a better focusing effect on a high-current-density low-velocity electron beam, providing the magnetic field in the vicinity of the target is reduced sufficiently to preserve the collinearity of the beam. In order to prove the concept, ray tracing is conducted using the Herrmannsfeldt program for solving electron trajectories in electrostatic and magnetostatic focusing systems. The program allows the calculation of the angles of the electron trajectories with the z axis, at the target location. The results of the ray-tracing procedure conducted for this gun are discussed. Some of the advantages of the magnetic focusing are also discussed.

Krainsky, Isay L.↗

NASA NTRS1991

The optical analogy for vector fields

This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.

Parker, E. N.↗

NASA NTRS1991

Generation of field-aligned current in the auroral zone

Generation of a magnetic field-aligned current in the auroral zone connecting the magnetospheric and ionospheric plasmas has been studied by means of a three dimensional particle simulation model. The model is of a magnetostatic variety appropriate for a low beta plasma in which the high frequency transverse displacement current has been eliminated. The simulation model is highly elongated along the magnetic field lines in order to model a highly elongated flux tube in the auroral zone. An enhanced field-aligned current was generated by injection of a magnetospheric plasma across the auroral zone magnetic field at the center of the model. Such a plasma injection may correspond to a plasmoid injection at the geomagnetic tail associated with magnetic reconnection during a substorm or a transverse plasma flow along the low latitude magnetopause boundary layer. The results of the simulations show that the field-aligned current can be enhanced over the thermal current by a factor of 5 - 10 via such injection. Associated with the enhanced current are the electrostatic ion cyclotron waves and shear Alfven waves excited in the auroral zone.

Okuda, Hideo↗

NASA NTRS1992

Manipulation and identification of objects by magnetic forces

An overview is presented of the results of research and engineering design activities over the past 20 years in the area of identification and manipulation of objects by magnetic forces. The relationship is discussed between the properties of objects and the parameters of magnetic fields, with the view toward being able to create forces for efficient manipulation and identification of different kinds of parts. Some of this information, particularly regarding nonferromagnetic materials, is relatively new and can be used to solve a variety of engineering problems by creating new types of automation systems. Topics covered include identification and orientation of bodies by magnetostatic and electrodynamic forces, electromagnetic recognition and orientation of nonsymmetric parts, and assembly and position control of parts by electromagnetic forces.

Joffe, Benjamin↗

NASA NTRS1991

Combined magnetic vector-scalar potential finite element computation of 3D magnetic field and performance of modified Lundell alternators in Space Station applications

A method of combined use of magnetic vector potential (MVP) based finite element (FE) formulations and magnetic scalar potential (MSP) based FE formulations for computation of three-dimensional (3D) magnetostatic fields is developed. This combined MVP-MSP 3D-FE method leads to considerable reduction by nearly a factor of 3 in the number of unknowns in comparison to the number of unknowns which must be computed in global MVP based FE solutions. This method allows one to incorporate portions of iron cores sandwiched in between coils (conductors) in current-carrying regions. Thus, it greatly simplifies the geometries of current carrying regions (in comparison with the exclusive MSP based methods) in electric machinery applications. A unique feature of this approach is that the global MSP solution is single valued in nature, that is, no branch cut is needed. This is again a superiority over the exclusive MSP based methods. A Newton-Raphson procedure with a concept of an adaptive relaxation factor was developed and successfully used in solving the 3D-FE problem with magnetic material anisotropy and nonlinearity. Accordingly, this combined MVP-MSP 3D-FE method is most suited for solution of large scale global type magnetic field computations in rotating electric machinery with very complex magnetic circuit geometries, as well as nonlinear and anisotropic material properties.

Wang, Ren H.↗

NASA NTRS1992

Magnetic field decay in isolated neutron stars

Three mechanisms that promote the loss of magnetic flux from an isolated neutron star - Ohmic decay, ambipolar diffusion, and Hall drift - are investigated. Equations of motions are solved for charged particles in the presence of a magnetic field and a fixed background of neutrons, while allowing for the creation and destruction of particles by weak interactions. Although these equations apply to normal neutrons and protons, the present interpretations of their solutions are extended to cover cases of neutron superfluidity and proton superconductivity. The equations are manipulated to prove that, in the presence of a magnetic force, the charged particles cannot be simultaneously in magnetostatic equilibrium and chemical equilibrium with the neutrons. The application of the results to real neutron stars is discussed.

Goldreich, Peter↗

NASA NTRS1993

On the magnetic and velocity field geometry of simple sunspots

It is presently shown that a simple sunspot model with azimuthal variations in inclination, but lacking azimuthal field-strength variations, is free from azimuthal Lorentz forces. The meridional currents arising from the inclination variations are parallel to the field lines, suggesting that a cylindrically symmetric magnetostatic sunspot model can be perturbed into one with azimuthal variations in inclination with adjustment of the meridional force balance.

Title, Alan M.↗

NASA NTRS1993

Three-dimensional magnetotail equilibria by numerical relaxation techniques

Consideration is given to a numerical method to iteratively approach 3D magnetostatic force equilibria, with modeling emphasis on the development of a suitable model of the earth's magnetotail, including a portion of the inner magnetosphere, i.e., on models which violate the 'tail approximation' commonly employed in analytical models. The numerical approach is compared to methods developed for laboratory plasma physics. The method is applied to the magnetotail outside of 10 R(E), using Tsyganenko's (1987) model for the quiet magnetosphere as an initial condition. The changes of the magnetic field necessary to yield an equilibrium configuration and the resulting distribution of the self-consistently derived pressure are discussed. It is shown that a self-consistent magnetotail equilibrium based on a close approximation to Tsyganenko's requires a region 1 type current system, which is not present in the initial configuration.

Hesse, Michael↗

NASA NTRS1993

Resistive dissipation and magnetic field topology in the stellar corona

Tangential discontinuities, or current sheets, in a magnetic field embedded in a fluid with vanishing resistivity are created by discontinuous fluid motion. Tangential discontinuities are also created when a magnetic field is allowed to relax to magnetostatic equilibrium after mixing by fluid motions (either continuous or discontinuous) into any but the simplest topologies. This paper shows by formal examples that the current sheets arising solely from discontinuous fluid motions do not contribute significantly to the dissipation of magnetic free energy when a small resistivity is introduced. Dissipation that is significant under coronal conditions occurs only by rapid reconnection, which arises when, and only when, the current sheets are required by the field topology. Hence it is topological dissipation that is primarily responsible for heating tenuous coronal gases in astronomical settings, whether the fluid displacements of the field are continuous or discontinuous.

Parker, E. N.↗

NASA NTRS1993

Solar magnetic field studies using the 12 micron emission lines. II - Stokes profiles and vector field samples in sunspots

Polarimetric observations at 12 microns of two sunpots are reported. The horizontal distribution of parameters such as magnetic field strength, inclination, azimuth, and magnetic field filling factors are presented along with information about the height dependence of the magnetic field strength. Comparisons with contemporary magnetostatic sunspot models are made. The magnetic data are used to estimate the height of 12 micron line formation. From the data, it is concluded that within a stable sunspot there are no regions that are magnetically filamentary, in the sense of containing both strong-field and field-free regions.

Hewagama, Tilak↗