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Low, B. C.

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

30 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

The heating of a thermally conducting stratified medium. II - A simple plane model of an atmosphere

Exact solutions of the following theoretical problem are presented: A plane atmosphere is in hydrostatic equilibrium with a uniform gravity. The ideal gas law is assumed. Heat is generated everywhere at a rate proportional to the local density. The atmosphere is maintained in a steady state through cooling by thermal conduction and radiation. This problem is reducible to quadratures for a thermal conductivity which is an arbitrary, but prescribed, function of the temperature, and for a radiative loss which is expressible as the product of the density and an arbitrary, but prescribed, function of the pressure. The analysis is carried out for the case of power law thermal conductivity, and a radiative loss proportional to the square of the density and to the first power of the temperature. The radiative cooling function adopted here has the basic mathematical form for an optically thin medium. The solutions reproduce the macroscopic ordering of a hot 'corona' separated from a 'photosphere' by a layer of temperature minimum. The analytic solutions allow direct illustration of the interplay between steady energy transport and the requirements of hydrostatic equilibrium.

Lerche, I.↗
NASA NTRS1980

On the equilibrium of a cylindrical plasma supported horizontally by magnetic fields in uniform gravity

The mechanical equilibrium of a cylinder of plasma suspended horizontally by magnetic fields in uniform gravity is examined. A set of exact solutions describing the equilibrium is derived assuming the plasma distribution to be cylindrically symmetric to obtain an exact force balance between plasma pressure, the Lorentz pressure, and gravity in space. The set of solutions considers a case of uniform temperature and cases where the temperature rises from zero at the center of the plasma cylinder to reach a constant asymptotic value outside the cylinder.

Lerche, I.↗
NASA NTRS1980

On the equilibrium structures of self-gravitating masses of gas containing axisymmetric magnetic fields

The general equations describing the equilibrium shapes of self-gravitating gas clouds containing axisymmetric magnetic fields are presented. The general equations admit of a large class of solutions. It is shown that if one additional (ad hoc) asumption is made that the mass be spherically symmetrically distributed, then the gas pressure and the boundary conditions are sufficiently constraining that the general topological structure of the solution is effectively determined. The further assumption of isothermal conditions for this case demands that all solutions possess force-free axisymmetric magnetic fields. It is also shown how the construction of aspherical (but axisymmetric) configurations can be achieved in some special cases, and it is demonstrated that the detailed form of the possible equilibrium shapes depends upon the arbitrary choice of the functional form of the variation of the gas pressure along the field lines.

Lerche, I.↗
NASA NTRS1980

On the resistive diffusion of force-free magnetic fields

Reid and Laing (1979) conjectured on the general behavior of resistive force-free magnetic fields in a slab model following a numerical study. However, the basic properties of resistive force-free magnetic fields had been established previously. Some results from the previous work are extended to show that the conjecture of Reid and Laing is incorrect. A general analytic treatment of the problem provides the correct physical properties that Reid and Laing were unable to deduce from their numerical solutions. A criticism is also given of the results presented in another numerical study treating cylindrical resistive force-free magnetic fields, by the same authors.

Low, B. C.↗
NASA NTRS1980

The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields

Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas.

Lerche, I.↗
NASA NTRS1980

Evolving force-free magnetic fields. III - States of nonequilibrium and the preflare stage

The paper considers whether a neighboring magnetostatic equilibrium exists to allow a magnetic field initially in a force-free configuration to accommodate any imposed weak pressure. The following problem is treated. The foot points of the field are fixed and the plasma is frozen into the field lines under the approximation of infinite electrical conductivity. A weak pressure is introduced. It is determined infinitesimal plasma displacements exist to adjust the field lines to a new equilibrium without changing the field line connectivity. The analysis is carried out for the bipolar force-free fields forming one of two evolutionary sequences modeling the development of the preflare stage. It was found that for the force-free field corresponding to the quasi-static stage of evolution, the neighboring magnetostatic equilibrium always exists and the imposed gas pressure can be accommodated with a slight departure of the field from being exactly force free.

Low, B. C.↗
NASA NTRS1980

Analytic solutions for single and multiple cylinders of gravitating polytropes in magnetostatic equilibrium

Exact analytic solutions for the static equilibrium of a gravitating plasma polytrope in the presence of magnetic fields are presented. The means of generating various equilibrium configurations to illustrate directly the complex physical relationships between pressure, magnetic fields, and gravity in self-gravitating systems is demonstrated. One of the solutions is used to model interstellar clouds suspended by magnetic fields against the galactic gravity such as may be formed by the Parker (1966) instability. It is concluded that the pinching effect of closed loops of magnetic fields in the clouds may be a dominant agent in further collapsing the clouds following their formation.

Lerche, I.↗
NASA NTRS1980

Cylindrical prominences and the magnetic influence of the photospheric boundary

The paper constructs exact, nonlinear solutions for a horizontal, cylindrical, current-carrying prominence supported against solar gravity by the Lorentz force. The solutions incorporate the photosphere boundary condition, proposed by van Tend and Kuperus (1978), who analyzed it for line filaments. The solutions have a finite radius for the prominence material and satisfy the equations of magnetostatic equilibrium, and allow for the continuity of gas pressure and of the normal and tangential components of magnetic field across the circular prominence boundary. It is shown that an infinity of solutions is possible; a method is presented for constructing equilibrium fields for any horizontal prominence with arbitrary cross-section and with an arbitrary external magnetic field.

Lerche, I.↗
NASA NTRS1973

Resistive diffusion of force-free magnetic fields in a passive medium.

We consider the resistive diffusion of a force-free magnetic field in a tenuous compressible medium, which is free to move to accommodate the changing magnetic-field configuration. This process is nonlinear, contrary to the usual magnetic field diffusion in a fixed medium. We show that the force-free magnetic field may evolve slowly for an extended period of time, whereupon it abruptly develops steep gradients and passes into an explosive phase. We suggest that it is this process that sets the stage for the onset of solar flares.

Low, B. C.↗