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NASA NTRS1983

The magnetosphere of Uranus - Plasma sources, convection, and field configuration

It is suggested by qualitative considerations based on analogy with earth, Jupiter, and Saturn that the magnetosphere of Uranus may lack a plasma source able to produce significant internal currents, internal convection, and associated effects. A class of approximately self-consistent quantitative magnetohydrostatic equilibrium configurations for the case of a pole-on magnetosphere with variable plasma parameters is presently constructed in order to test this hypothesis by means of forthcoming Voyager measurements. The configurations that can be computed for the geometries of the magnetic field and of the tail current sheet, for a given distribution of plasma pressure, have a single, funnel-shaped polar cusp pointing into the solar wind and a cylindrical tail plasma sheet whose currents close within the tail, rather than on the tail magnetopause. Interconnection of interplanetary and magnetospheric fields yields a highly asymmetric tail-field configuration.

Voigt, G.-H.↗

NASA NTRS1985

Onset of solar flares as predicted by two-dimensional MHD-models of quiescent prominences

The close connection between the sudden disapperance (disparition brusque) of the quiescent prominences and the two-ribbon flares are well known. During this dynamic phase the prominence ascends rapidly (typically with a velocity about 100 Km/sec) and disappears. In another later stage is observed material falling back into the chromosphere. The impact of this downfalling matter on the chromosphere produces the H brightening, which shows the symmetric double pattern. The occurence of the disparition brusque is thought to be a consequence of a plasma instability of magnetohydrostatic (MHD) structures. By means of the MHD-energy principle, the stability properties of four prominence models are analyzed. It is shown that all considered models undergo instabilities for parameters outside of the observed range at quiescent prominences. The possibility that such instabilities in the flare parameter range may indicate just the onset of a flare is considered.

Galindotrejo, J.↗

NASA NTRS1986

Similarity considerations and conservation laws for magneto-static atmospheres

The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, a model magnetostatic atmosphere is constructed in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an 'e-folding' distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J x B force (B, magnetic field induction) and the gas pressure gradient.

Webb, G. M.↗

NASA NTRS1986

Magnetospheric equilibrium configurations and slow adiabatic convection

This review paper demonstrates how the magnetohydrostatic equilibrium (MHE) theory can be used to describe the large-scale magnetic field configuration of the magnetosphere and its time evolution under the influence of magnetospheric convection. The equilibrium problem is reviewed, and levels of B-field modelling are examined for vacuum models, quasi-static equilibrium models, and MHD models. Results from two-dimensional MHE theory as they apply to the Grad-Shafranov equation, linear equilibria, the asymptotic theory, magnetospheric convection and the substorm mechanism, and plasma anisotropies are addressed. Results from three-dimensional MHE theory are considered as they apply to an intermediate analytical magnetospheric model, magnetotail configurations, and magnetopause boundary conditions and the influence of the IMF.

Voigt, Gerd-Hannes↗

NASA NTRS1987

Modeling of the magnetosphere

The derivation of the magnetosphere configuration is discussed, with consideration given to both descriptive models, which represent the observed magnetic field B and perhaps the electric field E, and physical models, which also include plasma effects. Consideration is given to global field models, static physical magnetohydrostatic models, slowly variable E, and MHD tail models, and to the type of data used for their derivation. It is emphasized that the current trend in derivation of magnetospheric models is for incorporating more physics( e.g., V x B) to match regions of observed current flow, plasma pressure obeying equilibrium conditions, E linked to interplanetary sources, and time-dependent convective flows.

Stern, David P.↗

NASA NTRS1987

The effects of magnetic B(y) component on geomagnetic tail equilibria

A two-dimensional linear magnetohydrostatic model of the magnetotail is developed here in order to investigate the effects of a significant B(y) component on the configuration of magnetotail equilibria. It is concluded that the enhanced B(y) values must be an essential part of the quiet magnetotail and do not result from a simple intrusion of the IMF. The B(y) field consists of a constant background component plus a nonuniform field existing only in the plasma sheet, where it is dependent on the plasma paramater beta and the strength of the magnetic B(z) component. B(y) is strongest at the neutral sheet and decreases monotonically in the + or - z direction, reaching a constant tail lobe value at the plasma sheet boundaries. The presence of a significant positive B(y) component produces currents, including field-aligned currents, that flow through the equatorial plane and toward and away from earth in the northern and southern halves of the plasma sheet, respectively.

Hilmer, Robert V.↗

NASA NTRS1989

Magnetohydrodynamic instabilities in coronal arcades

The MHD stability of coronal arcades is studied with and without a detached flux using a two-dimensional linear MHD stability numerical model. Two-dimensional magnetohydrostatic equilibria with and without gravity are computed. A coronal arcade without a detached flux tube is found to be stable for any magnetic shear and for any longitudinal mode. On the other hand, an arcade with a detached flux tube is unstable for perturbations with nonzero longitudinal wave number n and the instability mode structure and growth rate vary depending on the field twist and n. All the equilibria studied are stable to n = 0 perturbations. Gravity has a stabilizing effect on the equilibria. As the ratio lambda of the standard arcade width to the gravitational scale height increases from zero to 0.2, the m = 0 transverse mode growth rate decreases, but high m modes are stabilized. The equilibria studied here are completely stabilized for lambda larger than 0.33.

An, Chang-Hyuk↗

NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

The tensor virial theorem is used to analyze the structure and stability of self-gravitating, magnetized spheroids surrounded by a low-density medium with pressure and magnetic field. Analytical expressions are developed for the effect of a weak field and calculate critical states when the effect of the field is arbitrarily strong, comparing the results with full magnetohydrostatic calculations. This analysis suggests that a magnetic field may prevent gravitational collapse but may also be destabilizing, depending on its degree of concentration within the cloud.

Zweibel, Ellen G.↗

NASA NTRS1990

Virial theorem analysis of the structure and stability of magnetized clouds

Zweibel, Ellen G.↗

NASA NTRS1990

Electric current in a unipolar sunspot with an untwisted field

The return flux (RF) sunspot model is applied to a round, unipolar sunspot observed by H. Kawakami (1983). Solving the magnetohydrostatic problem using the gas pressure deficit between the umbral and quiet-sun atmospheres as a source function, a distribution of electric current density in an untwisted, unipolar sunspot as a function of height and radial distance from the sunspot center is observed. Maximum electric current density is about 32 mA/sq m at the bottom of the sunspot.

Osherovich, V. A.↗

NASA NTRS1991

The equilibria and evolutions of magnetized, rotating, isothermal clouds. V - The effect of the toroidal field

The structures of magnetized clouds are studied from a standpoint of magnetohydrostatic equilibrium between the self-gravity and magnetic and thermal pressure forces. Toroidal as well as poloidal magnetic field is taken into account. Poloidal current flowing along the poloidal magnetic field forms a toroidal field which causes the cloud to be pinched toward the symmetric axis. In contrast to the poloidal field, which plays a role in supporting the cloud, the toroidal field has the effect of shrinking the cloud. A cloud that is pinched by the toroidal field but has a low central density often shows a prolate spheroidal shape. With increasing central density the cloud becomes a concaved oblate spheroid. The maximum mass of the cloud supported by magnetic field and thermal pressure decreases with increasing toroidal field strength. Assuming that a cloud encounters a torsional Alfven wave, and the magnetic field begins to be wound up, the cloud begins dynamical collapse if the cloud mass exceeds the marginally supported maximum mass. This indicates a new mode triggering star formation: toroidal field-induced collapse.

Tomisaka, Kohji↗

NASA NTRS1992

A relation between magnetic field strength and temperature in sunspots

We present Stokes I Zeeman splitting measurements of sunspots using the highly sensitive (g = 3) Fe I line at a wavelength of 1.5649 micron. The splittings are compared with simultaneous intensity measurements in the adjacent continuum. The relation between magnetic field strength and temperature has a characteristic, nonlinear shape in all the spots studied. In the umbra, there is an approximately linear relation between B super 2 and T sub b, consistent with magnetohydrostatic equilibrium in a nearly vertical field. A distinct flattening of the B super 2 vs T sub b relationship in the inner penumbra may be due to changes in the lateral pressure balance as the magnetic field becomes more horizontal; spatially unresolved intensity inhomogeneities may also influence the observed relation.

Kopp, Greg↗

NASA NTRS1992

Limits on plasma anisotropy in a tail-like magnetic field

The condition of magnetohydrostatic equilibrium implies tight constraints on the degree of anisotropy that is supportable in a magnetotail field geometry. If the plasma pressure tensor is assumed to be gyrotropic at the tail midplane (z = 0), then equilibrium requires that it also be nearly isotropic there, with P-perpendicular sub 0/P-parallel sub 0 in the range 1 +/- delta square, where delta of about 0.1 is the ratio of the normal field component at the symmetry plane to the field strength in the tail lobe. The upper and the lower limits are essentially equivalent, respectively, to the marginal mirror and firehose stability conditions evaluated at z = 0, which have been invoked previously to limit the degree of anisotropy in the plasma sheet.

Hill, T. W.↗

NASA NTRS1992

The Yohkoh mission for high-energy solar physics

Data on solar flare mechanisms and the sun's corona will be generated by Japan's Yohkoh satellite's X-ray imaging sensors and X-ray and gamma-ray spectrometers. It is noted that the X-ray corona above active regions expands, in some cases almost continually, in contradiction of the widely accepted model of magnetohydrostatic equilibrium in such regions. Flaring X-ray bright points have been discovered to often involve ejecta into an adjacent, much larger and fainter magnetic loop, which brightens along its length at speeds up to 1000 km/sec.

Acton, L.↗

NASA NTRS1994

Equilibrium structure of solar magnetic flux tubes: Energy transport with multistream radiative transfer

We examine the equilibrium structure of vertical intense magnetic flux tubes on the Sun. Assuming cylindrical geometry, we solve the magnetohydrostatic equations in the thin flux-tube approximation, allowing for energy transport by radiation and convection. The radiative transfer equation is solved in the six-stream approximation, assuming gray opacity and local thermodynamic equilibrium. This constitutes a significant improvement over a previous study, in which the transfer was solved using the multidimensional generalization of the Eddington approximation. Convection in the flux tube is treated using mixing-length theory, with an additional parameter alpha, characterizing the suppression of convective energy transport in the tube by the strong magnetic field. The equations are solved using the method of partial linearization. We present results for tubes with different values of the magnetic field strength and radius at a fixed depth in the atmosphere. In general, we find that, at equal geometric heights, the temperature on the tube axis, compared to the ambient medium, is higher in the photosphere and lower in the convection zone, with the difference becoming larger for thicker tubes. At equal optical depths the tubes are generally hotter than their surroundings. The results are comparatively insensitive to alpha but depend upon whether radiative and convective energy transport operate simultaneously or in separate layers. A comparison of our results with semiempirical models shows that the temperature and intensity contrast are in broad agreement. However, the field strengths of the flux-tube models are somewhat lower than the values inferred from observations.

Hasan, S. S.↗

NASA NTRS1996

Magnetopause Transects

A novel method is described for reconstruction of two-dimensional current-layer structures from measurements taken by a single spacecraft traversing the layer. In its present form, the method is applicable only to 2D magnetohydrostatic structures that are passively convected past the observing spacecraft. It is tested on a magnetopause crossing of the tangential-discontinuity type by the spacecraft AMPTE/IRM. The magnetic structures recovered include a magnetic island located between two X-type nulls as well as a magnetic 'worm hole' through which a bundle of weak magnetic flux appears to connect the magnetosphere and the magnetosheath.

Sonnerup, B. U. O↗

NASA NTRS1965

On the magneto-hydrostatic theory of sunspots.

Sunspot models used to derive relations between coolness of spot and its magnetic field strength and between magnetic field strength and ratio of mixing length to pressure scale height

SUNSPOT↗

NASA NTRS1966

Fluidmagnetic buoyancy.

Fluidmagnetic buoyancy effects in ferrohydrodynamic /FHD/ flows and implications of Ernshaw levitation theorem

FLUID MECHANICS↗