Engineering topics

Low, B. C.

Publications and source records attributed to Low, B. C..

At least 19 records

NASA NTRS2003

The Mass of a Solar Quiescent Prominence

This paper follows up on our recent paper on the role of prominence mass in the storage of magnetic energy for driving a coronal mass ejection (CME). The previous paper erroneously rejected a set of sheet- prominence solutions, the recovery of which allows for a simple theoretical estimate of the mass of a quiescent prominence. For coronal fields of 5-10 G, these hydromagnetic solutions suggest that a prominence mass of (1-26) x 10(exp 6) g is needed to hold detached magnetic fields of intensity comparable to the coronal fields in an unbounded atmosphere such that the global magnetic field is energetically able to spontaneously open up and still have enough energy to account for the kinetic and gravitational potential energies carried away in a CME. This simple result is discussed in relation to observed prominence magnetic field intensities, densities, and masses, pointing to the relevance of such observations to the question of magnetic energy storage in the solar corona.

Low, B. C.↗

NASA NTRS1993

The free energies of partially open coronal magnetic fields

A simple model of the low corona is examined in terms of a static polytropic atmosphere in equilibrium with a global magnetic field. The question posed is whether magnetostatic states with partially open magnetic fields may contain magnetic energies in excess of those in fully open magnetic fields. Based on the analysis presented here, it is concluded that the cross-field electric currents in the pre-eruption corona are a viable source of the bulk of the energies in a mass ejection and its associated flare.

Low, B. C.↗

NASA NTRS1989

Steady hydromagnetic flows in open magnetic fields. II - Global flows with static zones

A theoretical study of an axisymmetric steady stellar wind with a static zone is presented, with emphasis on the situation where the global magnetic field is symmetrical about the stellar equator and is partially open. In this scenario, the wind escapes in open magnetic fluxes originating from a region at the star pole and a region at an equatorial belt of closed magnetic field in static equilibrium. The two-dimensional balance of the pressure gradient and the inertial, gravitational, and Lorentz forces in different parts of the flow are studied, along with the static interplay between external sources of energy (heating and/or cooling) distributed in the flow and the pressure distribution.

Tsinganos, K.↗

NASA NTRS1988

Spontaneous formation of electric current sheets and the origin of solar flares

It is demonstrated that the continuous boundary motion of a sheared magnetic field in a tenuous plasma with an infinite electrical conductivity can induce the formation of multiple electric current sheets in the interior plasma. In response to specific footpoint displacements, the quadrupolar magnetic field considered is shown to require the formation of multiple electric current sheets as it achieves a force-free state. Some of the current sheets are found to be of finite length, running along separatrix lines of force which separate lobes of magnetic flux. It is suggested that current sheets in the form of infinitely thin magnetic shear layers may be unstable to resistive tearing, a process which may have application to solar flares.

Low, B. C.↗

NASA NTRS1987

The velocity field of a coronal mass ejection - The event of September 1, 1980

The velocity field of a mass ejection that was observed by the coronagraph of the SMM satellite over the northwest limb of the sun at about 0600 UT on September 1, 1980 is studied in detail. A descriptive account of the event is given, concentrating on qualitative features of the mass motion and suggesting a possible origin of the unusual two-loop structure. The velocity field is analyzed quantitatively, and the implications of the results for the mass ejection theory are considered. It is concluded that a self-similar description of the velocity field is a gross oversimplification and that although some evidence of wave propagation can be found, the bright features in the mass ejection are plasma structures moving with frozen-in magnetic fields, rather than waves propagating through plasmas and magnetic fields.

Low, B. C.↗

NASA NTRS1986

Static current-sheet models of quiescent prominences

A particular class of theoretical models idealize the prominence to be a discrete flat electric-current sheet suspended vertically in a potential magnetic field. The weight of the prominence is supported by the Lorentz force in the current sheet. These models can be extended to have curved electric-current sheets and to vary three-dimensionally. The equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9 z=zero. Using Cartesian coordinates we take, for simplicity, a uniform gravity with constant acceleration g in the direction -z. If we are interested not in the detailed internal structure of the prominence, but in the global magnetic configuration around the prominence, we may take prominence plasma to be cold. Consideration is given to how such equilibrium states can be constructed. To simplify the mathematical problem, suppose there is no electric current in the atmosphere except for the discrete currents in the cold prominence sheet. Let us take the plane z =0 to be the base of the atmosphere and restrict our attention to the domain z greater than 0. The task we have is to solve for a magnetic field which is everywhere potential except on some free surface S, subject to suit able to boundary conditions. The surface S is determined by requiring that it possesses a discrete electric current density such that the Lorentz force on it is everywhere vertically upward to balance the weight of the material m(S). Since the magnetic field is potential in the external atmosphere, the latter is decoupled from the magnetic field and its plane parallel hydrostatic pressure and density can be prescribed.

Wu, F.↗

NASA NTRS1986

Three-dimensional magnetostatic models of the large-scale corona

A special class of magnetostatic equilibria is described, which are mathematically simple and yet sufficiently versatile so as to fit any arbitrary normal magnetic flux prescribed at the photosphere. With these solutions, the corona can be modeled with precisely the same mathematically simple procedure as has previously been done with potential fields. The magnetostatic model predicts, in addition to the coronal magnetic field, the three dimensional coronal density which can be compared with coronagraph observations.

Bogdan, T. J.↗

NASA NTRS1986

Steady hydromagnetic flows in open magnetic fields. I - A class of analytic solutions

In the case of an establishment of theoretical models of the hydromagnetic solar wind, the inclusion of the effects of the magnetic field in the solar wind makes it extremely dificult to solve the mathematical problem. This paper has the objective to present a set of particular analytic solutions. The general formulation of Tsinganos (1982) is used to identify a class of analytic solutions to the equations of steady hydromagnetic flows in spherical coordinates. Flow in an open magnetic field are studied, taking into account the problem in dimensionless form, the special case of radial flows with alpha = 0, general radial flows, illustrative examples for flows in which alpha is not equal to 0, a parametric study of nonradial flows in which alpha is not equal to zero, variations in the parameter nu, and variations in the initial speed eta.

Low, B. C.↗

NASA NTRS1985

Modeling solar magnetic structures

Some ideas in the theoretical study of force-free magnetic fields and magnetostatic fields, which are relevant to the effort of using magnetograph data as inputs to model the quasi-static, large-scale magnetic structures in the solar atmosphere are discussed. Basic physical principles will be emphasized. An attempt will be made to assess what we may learn, physically, from the models based on these ideas. There is prospect for learning useful physics and this ought to be an incentive for intensifying the efforts to improve vector magnetograph technology and to solve the basic radiative-transfer problems encountered in the interpretation of magnetograph raw data.

Low, B. C.↗

NASA NTRS1982

Nonlinear force-free magnetic fields

The nonlinear properties of force-free magnetic fields are reviewed with particular reference to the mechanisms for the sudden release of stored energy in flares during the quasi-steady evolution of solar fields. It is shown that in the solar atmosphere, force-free fields with a nonconstant scalar function in the field equations are more likely to occur than those with a constant scalar function, and the nonlinear properties of these fields may give rise to many interesting physical effects. Consideration is then given to two possible mechanisms of field evolution: a model in which a force-free field in a medium of infinite electrical conductivity evolves in response to slowly changing boundary conditions brought about by photospheric motions in the solar active region, and a model in which a field in a medium of small finite electrical conductivity evolves in response to the slow Ohmic dissipation of the electric current.

Low, B. C.↗

NASA NTRS1982

The vertical filamentary structures of quiescent prominences

The thin vertical filaments making up the quiescent prominence plasma, as revealed by fine spatial resolution H-alpha photographs, are characterized by a magnetostatic theory in which a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines is described by a class of exact equilibrium solutions. The Kippenhahn-Schlueter (1957) solution for a long sheet without filamentary structures is a member of this class of solutions. In illustrating the role of the magnetic field in supporting and thermally shielding the filament plasma, it is found that the filament can have a sharp transition perpendicular to the local field, while the transition in the direction of the local field is diffuse. A consequence of the filamentary structure is that its support by the Lorentz force requires the electric current to have a component along the magnetic field.

Low, B. C.↗

NASA NTRS1981

Eruptive solar magnetic fields

The quasi-steady evolution of solar magnetic fields in response to gradual photospheric changes is considered, with particular attention given to the threshold of a sudden eruption in the solar atmosphere. The formal model of an evolving, force-free field dependent on two Cartesian coordinates is extended to a field which is not force free but in static equilibrium with plasma pressure and gravity. The basic physics is illustrated through the evolution of a loop-shaped electric current sheet enclosing a potential bipolar field with footpoints rooted in the photosphere. A free-boundary problem is posed and then solved for the equilibrium configuration of the current sheet in a hydrostatically supported isothermal atmosphere. As the footpoints move apart to spread a constant photospheric magnetic flux over a larger region, the equilibria available extend the field to increasing heights.

Low, B. C.↗

NASA NTRS1981

On the presence of electric currents in the solar atmosphere. I - A theoretical framework

The general magnetic field above the solar photosphere is divided by an elementary analysis based on Ampere's law into two parts: a potential field due to electric currents below the photosphere and a field produced by electric currents above the photosphere combined with the induced mirror currents. The latter, by symmetry, has a set of field lines lying in the plane taken to be the photosphere which may be constructed from given vector magnetograph measurements. These field lines also represent all the information on the electric currents above the photosphere that a magnetograph can provide. Theoretical illustrations are given, and implications for data analysis are discussed.

Hagyard, M.↗

NASA NTRS1981

A class of analytic solutions for the thermally balanced magnetostatic prominence sheet

A theoretical study is presented for the nonlinear interplay between magnetostatic equilibrium and energy balance in a Kippenhahn-Schlueter type solar prominence sheet. A class of theoretical models is presented, expressed in closed analytic forms, thus facilitating the direct illustration of the nonlinear physical properties. The model couples the equilibrium between magnetic field, plasma pressure, and weight on the one hand, with the balance between a rho-squared T radiative loss, a rho wave heating (where rho equals plasma density, and T equals plasma temperature), and thermal conduction channeled along magnetic field lines on the other. The steady solutions are divided into three classes, and are characterized by the total wave heating in the prominence sheet which is greater than, equal to, or less than the total radiative loss. The compaction of the plasma along the field lines, under its own weight, and the energy transport effects determine which of the three basic behaviors obtains in a particular situation. A discussion is presented of the implications of the steady solutions for the formation of prominences.

Low, B. C.↗

NASA NTRS1981

The field and plasma configuration of a filament overlying a solar bipolar magnetic region

This paper presents an analytic model for a finite-size straight filament suspended horizontally in a steady state over a bipolar magnetic region. The equations of magnetostatic equilibrium are integrated exactly. The solution obtained illustrates the roles played by the electric current, magnetic field, pressure, and plasma weight in the balance of force everywhere in space. A specific example of a filament of diameter 50,000 km, with a density two orders of magnitude over the corona and supported by a magnetic field of about 4 gauss is included. The filament temperature can take values ranging from a small fraction to a few times the coronal temperature, depending on the internal electric current of the filament. To produce a cool filament, such as the quiescent prominence, the solution is required to have an internal field with a strong component along the filament, giving rise to helical structures. A hot filament such as the X-ray coronal loop can be produced as a twisted magnetic flux tube embedded in a strong background field aligned parallel to the filament and having lower density and temperature. The basic steps of construction can be used to develop models more realistic than the ones presented for their analytic simplicity.

Low, B. C.↗

NASA NTRS1981

A variational approach to the question of temporal stability of equilibrium models of solar prominences. I - The formal theory

A Lagrangian approach to the equations describing small amplitude departures from equilibrium of solar prominences is presented. Seven quantities are derived which, by analogy to the concepts of energy, momentum, and angular momentum, are conserved under conditions corresponding to ignorable coordinates of classical mechanics. It is expected that these conservation laws will be useful as criteria of accuracy in obtaining eigenfrequencies for the perturbation equations when numerical techniques are used. The method is capable of handling complicated spatial dependences and has internal criteria for assessing the accuracy of any given numerical convergence scheme.

Lerche, I.↗

NASA NTRS1980

On the equilibrium of heated self-gravitating masses - Cooling by conduction

An investigation is given of the equilibrium states available to a self-gravitating mass of gas, cooling by conduction, and being heated at a rate proportional to the local gas density. The plane geometry situation is shown to be reducible to quadratures for the pressure, density, temperature, and gravitational potential. For a constant thermal conductivity it is shown that the gas density has either a central maximum or a central minimum, depending on the ratio of the thermal conductivity to a parameter taken to be a measure of the rate of heating. For a thermal conductivity which is a positive power of the temperature, it is shown that the gas density always has a central minimum and a maximum at the outer boundary of the configuration. For cylindrical and spherical geometrical configurations the same general properties are obtained. The physical origin of this behavior is discussed, and it is suggested that these exploratory calculations provide an effect which may not only aid in understanding thin filamentary structure observed in supernova remnants, but also help to assuage the difficulties of producing maser activity in the interior regions of 'cocoon' protostars.

Lerche, I.↗

NASA NTRS1980

On equilibrium states of heated self-gravitating gas clouds cooling by conduction in an external gravitational field

Exact analytic solutions are presented for equilibrium states of a self-gravitating one-dimensional cloud of gas, embedded in an external gravitational field due to a plane of 'stars' being heated at a rate proportional to the local gas density, and cooling by thermal conduction. It is found that the general topology of the solutions is such that the gas density has a minimum on the plane of 'stars', rising to an infinite but integrable peak away from the plane so that the total mass of gas in the cloud is finite. The results may be of interest in investigations of interstellar molecular clouds and of filamentary structures in supernova remnants as well as in the modeling of gas distributions around 'cocoon' protostars.

Lerche, I.↗