Engineering topics

Parker, E. N.

Publications and source records attributed to Parker, E. N..

At least 55 records · Page 3

NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. I - Discontinuities in the torsion

Consideration is given to the static force-free equilibrium of a magnetic field in which all of the lines of force connect without knotting between parallel planes. The field is formed by continuous deformation from an initial uniform field, and is conventiently described in terms of the scalar function psi, which is the stream function for the incompressible wrapping and interweaving of the lines of force. Local compression and expansion of the lines of force is described in terms of the scalar function Phi. Equilibrium in the field requires satisfaction of two independent equations which cannot be accomplished without the full freedom of both psi and Phi. It is shown that discontinuities in the torsional characteristics of the lines occur when psi is predetermined by an arbitrary pattern. Discontinuities in the winding pattern of the lines can lead to discontinuities in the associated current sheets.

Parker, E. N.↗

NASA NTRS1986

Equilibrium of magnetic fields with arbitrary interweaving of the lines of force. II - Discontinuities in the field

The surfaces of discontinuity (SDs) identified by Parker (1986) in the torsion of a force-free magnetic field in an infinitely conducting fluid contained betweeen two fixed boundary planes are characterized analytically. It is shown that field discontinuities (current sheets) occur whenever an SD terminates within the fluid or intersects with another SD, that intersections occur in most cases, and that the resulting current sheets are responsible for most field dissipation in highly conducting fluids. The astrophysical implications of these findings and a number of unresolved problems are discussed.

Parker, E. N.↗

NASA NTRS1986

The heliospheric energy source

The solar wind and the heliosphere exist as a consequence of the heat input to the corona, particularly the coronal holes. The necessary energy input to coronal holes has been estimated to be 10 to the 6th erg/sq cm sec, requiring Alfven waves with rms fluid velocities of 100 km/sec. Observational upper limits on coronal fluid velocities are of the order of 25 km/sec, which may not apply to the transparent coronal hole. Alternatively it has been suggested that coronal holes may be heated by agitation from neighboring active regions, suggesting that the vigor of a coronal hole depends upon its location. The Ulysses Mission will provide a direct comparison of the strength of the high speed wind from coronal holes at low latitude and coronal holes at high latitude, from which the nature of the presently unknown energy sources of the coronal holes and the resulting structure of the heliosphere may be better judged. The question is fundamental to the dynamics of the windspheres of all stars.

Parker, E. N.↗

NASA NTRS1985

The future of solar physics

Outstanding problems for the future of solar physics and stellar physics are examined. The physics of stellar interiors has been called into serious question by the very low measured neutrino flux from the sun. The Ga-71 neutrino detection experiment is the next step in unravelling this mystery. The new methods of helioseismology, for probing the interior of the sun, have already found the primordial rapid rotation of the central core. The forthcoming worldwide helioseismology observing network will permit fuller exploitation of the method, promising to provide the first direct sounding of the interior of a star, hitherto known to us only through theoretical inference and the discrepant neutrino emission. An essential step in developing the physics of stellar activity will be the Solar Optical Telescope (presently planned by NASA to be launched early in the next decade) to permit a 'microscopic' examination of the surface of the sun to study the source of the action. The activity and X-ray emission of other stars depend on much the same effects, so that the study of the sun is essential to determining the significance of the X-ray emission from other stars.

Parker, E. N.↗

NASA NTRS1985

Stellar fibril magnetic systems. II - Two-dimensional magnetohydrodynamic equations. III - Convective counterflow

The dynamics of magnetic fibrils in the convective zone of a star is investigated analytically, deriving mean-field equations for the two-dimensional transverse motion of an incompressible fluid containing numerous small widely spaced circular cylinders. The equations of Parker (1982) are extended to account for the inertial effects of local flow around the cylinders. The linear field equation for the stream function at the onset of convection is then rewritten, neglecting large-scale heat transport, and used to construct a model of convective counterflow. The Kelvin impulse and fluid momentum, convective motion initiated by a horizontal impulse, and the effects of a viscous boundary layer are considered in appendices.

Parker, E. N.↗

NASA NTRS1985

The vector structure of active magnetic fields

Observations are needed to show the form of the strains introduced into the fields above the surface of the Sun. The longitudinal component alone does not provide the basic information, so that it has been necessary in the past to use the filamentary structure observed in H sub alpha to supplement the longitudinal information. Vector measurements provide the additional essential information to determine the strains, with the filamentary structure available as a check for consistency. It is to be expected, then, that vector measurements will permit a direct mapping of the strains imposed on the magnetic fields of active regions. It will be interesting to study the relation of those strains to the emergence of magnetic flux, flares, eruptive prominences, etc. In particular we may hope to study the relaxation of the strains via the dynamical nonequilibrium.

Parker, E. N.↗

NASA NTRS1984

Magnetic fields in the radiative interior of stars. I Thermal shadows and forced convection. II - Forced convection and the Li-7 abundance

A theoretical model is developed for thermal shadows of magnetic inhomogeneities and their effects in the radiative cores of stars such as the sun. It is shown that the shadows cause a slight decrease of gas pressure, thereby lowering the opacity and raising the effective heat transport. The shadows produced by the inhomogeneities induce thermal gradients and therefore forced convection. If the field strength is at least 400,000 gauss partial Li-7 depletion will occur due to destruction in convection-dominated thermonuclear reactions. The scale of the field would need to be 30,000 km.

Parker, E. N.↗

NASA NTRS1984

Stellar fibril magnetic systems. I - Reduced energy state

The remarkable fibril structure of the magnetic fields at the surface of the sun (with fibrils compressed to 1,000-2,000 gauss) lies outside existing statistical theories of magnetohydrodynamic turbulence. The total energy of the fibril field is enhanced by a factor of more than 100 above the energy for the mean field in a continuum state. The magnetic energy density within a fibril is of the order of 100 times the local kinetic energy density, so that no simple application of equipartition principles is possible. It is pointed out that the total energy of the atmosphere (thermal + gravitational + magnetic) is reduced by the fibril state of the field by avoiding the magnetic inhibition of the convective overturning, suggesting that the formation of the observed intense fibril state may be in response to the associated energy reduction. Calculation of the minimum total energy of a polytropic atmosphere permeated by magnetic fibrils yields theoretical fibril fields of the order of 1-5 kilogauss when characteristics appropriate to the solar convective zone are introduced, in rough agreement with the actual fields of 1-2 kilogauss. The polytrope model, although crude, establishes that a large reduction in total energy is made possible by the fibril state.

Parker, E. N.↗

NASA NTRS1984

Magnetic buoyancy and the escape of magnetic fields from stars

A loss of magnetic flux through the free surface of a star into the surrounding space has important implications for the generation of the field within the star. The present investigation is concerned with the physics of the escape of net azimuthal flux from a star. The obtained results are used as a basis for the interpretation of some recent observations of the detailed behavior of magnetic fields emerging through the surface of the sun. The buoyancy of an isolated horizontal magnetic flux tube beneath the surface of a star causes the tube to rise at a rate comparable to the Alfven speed. The necessary conditions for escape of the flux are considered along with aspects of magnetic buoyancy, and the conditions on the sun. It appears that the observed retraction of bipolar magnetic fields at the end of their life at the surface is the one phenomenon which requires dynamical intervention. Attention is given to known dynamical effects which suppress the buoyant rise of an azimuthal magnetic field.

Parker, E. N.↗

NASA NTRS1984

Depth of origin of solar active regions

Observations show that the individual bipolar magnetic regions on the sun remain confined during their decay phase, with much of the magnetic field pulling back under the surface, in reverse of the earlier emergence. This suggests that the magnetic field is held on a short rein by subsurface forces, for otherwise the region would decay entirely by dispersing across the face of the sun. With the simple assumption that the fields at the surface are controlled from well-defined anchor points at a depth h, it is possible to relate the length l of the bipolar region at the surface to the depth h, with h about equal to l. The observed dimensions l about equal to 100,000 km for normal active regions, and l about equal to 10,000 km for the ephemeral active regions, indicate comparable depths of origin. More detailed observational studies of the active regions may be expected to shed further light on the problem.

Parker, E. N.↗

NASA NTRS1984

The role of flux ejection in stellar dynamos

Magnetic buoyancy causes the magnetic field in the convective zone of a star to escape through the surface in times short compared to the period of the magnetic cycle. The sun serves as a prototype, where fields of 100-1000 gauss or stronger are present in the convective zone, as part of the 22 year magnetic cycle. The theoretical alpha-omega dynamo effect cannot cope with the rapid escape (in a year or so) because increasing the rate of generation of field serves also to shortern the period, to a value comparable to the escape time. It is suggested that the flux ejection dynamo effect may be operating in the deep convective zone, where the cyclonic rotation of the convective cells may be as large as 180 deg. If so, then the flux ejection effectively opposes the buoyant rise. It is shown that the net effect of flux ejection in the lower convective zone, and unopposed buoyancy in the upper convective zone, permits the alpha-omega-dynamo effect to carry on the cyclic regeneration of the magnetic field much as in the absence of either buoyancy or flux ejection, except that the magnetic field is strongly concentrated against the bottom of the convective zone. It is suggested that the lower and upper regions of the dynamo may be related to the normal and ephermeral active regions, as has already been suggested by others on the basis of the observed distinctions in distribution.

Parker, E. N.↗

NASA NTRS1984

Alfven waves in a thermally stratified fluid

The properties of Alfven waves propagating along a uniform horizontal field in a highly conducting incompressible medium in the presence of strong convective instability are examined in the Boussinesq approximation. In particular, it is sought to determine whether there are exact solutions to the dynamical equations in the presence of convective forces. It is shown that a class of exact solutions of arbitrary amplitude, but of limited form, which may be of some physical interest, does exist. For large amplitudes, any mixtures of polarization states are shown to cause scattering into new modes.

Parker, E. N.↗

NASA NTRS1984

Magnetic reconnection and magnetic activity

A large-scale magnetic field extending through a highly conducting tenuous fluid may become distorted on a small scale as a consequence of slow small-scale shuffling of the magnetic lines of force at the boundaries of the tenuous fluid. Any slow wrapping and winding introduced at the boundaries is distributed along the field (at the Alfven speed). It is a curious and little-known fact that such wrapping and winding possesses no static equilibrium (except for a set of solutions of extreme symmetry). The result is neutral-point reconnection of the strains in the field, rapidly dissipating the wrapping and winding. It is suggested that this is the principal cause of the extreme heating that produces the active corona of the sun and other stars. The shuffling of the footpoints of the magnetic field in the photospheric turbulence introduces small-scale wrapping and twisting into the coronal loops. The work done by the turbulence in twisting the fields is dissipated within a matter 10-20 hours by neutral-point reconnection, introducing heat into the corona at a rate of about 10 Mergs/sq cm sec for photospheric turbulence of 0.5 km/sec. It is suggested that this is the basic cause of the X-ray corona.

Parker, E. N.↗

NASA NTRS1983

Direct coronal heating from dissipation of magnetic field

The visible corona of the Sun appears to be heated by direct dissipation of magnetic fields. The magnetic fields in the visible corona are tied at both ends to the photosphere where the active convection continually rotates and shuffles the footpoints in a random pattern. The twisting and wrapping of flux tubes about each other produce magnetic neutral sheets in a state of dynamical nonequilibrium such that the current sheets become increasingly concentrated with the passage of time. Dissipation of the high current densities takes place regardless of the high electrical conductivity of the fluid. The convection on the feet of the lines of force at the surface of the Sun goes directly (within a matter of 10 to 20 hours) into heat in the corona. The rate of doing work seems adequate to supply the necessary 10 to the 7th power ergs/square cm. sec for the active corona.

Parker, E. N.↗

NASA NTRS1983

Magnetic neutral sheets in evolving fields. I - General theory. II - Formation of the solar corona

The problem of the hydrostatic equilibrium of a large-scale magnetic field embedded in a fluid with infinite electrical conductivity is considered. It is pointed out that a necessary condition for static equilibrium is the invariance of the small-scale pattern in the field along the large-scale direction. A varying topological pattern implies that no fluid pressure distribution exists for which the field is everywhere static. Magnetic neutral sheets form, and dynamical reconnection of the field takes place. It is shown here that the invariance is also a sufficient condition for the existence of a fluid pressure distribution producing static equilibrium. Even in the simplest cases, however, the requirements on the fluid pressure are extreme and, a priori, are unlikely. It is concluded that almost all twisted flux tubes packed together produce dynamical nonequilibrium and dissipation of their twisting. This is the basic effect underlying the long-standing conjecture that the shuffling of the footpoints of the bipolar magnetic fields in the sun is responsible for heating the active corona. Attention is then given to the consequences of this general dynamical dissipation in the magnetic fields that produce the active corona of the sun. The footpoints of the field are continually manipulated by the subphotospheric convection in such a way that the lines of force are continually wrapped and rotated about one another.

Parker, E. N.↗

NASA NTRS1983

Absence of equilibrium among close-packed twisted flux tubes

The lack of equilibrium in twisted, close-packed flux tubes is demonstrated in terms of a topology of the transverse field and the necessity of defining restricted solutions for an arbitrary function in the equilibrium equation. It is shown that nearly all combinations of flux connections and functional forms have no mutual equilibrium and that the flux connections in nature are formed by footprint convection at an origin. The most close-packed twisted flux tubes are subject to dynamical nonequilibrium, with the transverse flux connections being reduced through neutral point rapid reconnection. The precise solutions which can be obtained through functional forms in the equilibrium equation do not have an analog in the real world.

Parker, E. N.↗

NASA NTRS1983

The hydrodynamics of magnetic nonequilibrium

Because the dynamical nonequilibrium of closely packed twisted flux tubes is essentially the problem of two-dimensional MHD turbulence, the extensive literature on two-dimensional turbulence represents the hydrodynamics of magnetic nonequilibrium. Many features of the turbulence can conversely be understood as a consequence of the dynamical nonequilibrium. Attention is presently given to the dynamics of the strong fluid jets, issuing from reconnection points, that are exhibited by numerical simulations of two-dimensional turbulence. Simple examples are given which show that the uniformity of jet width observed is a consequence of the form of the pressure of the magnetic fields between which the jets are confined. The general hydrodynamics of a layer of fluid confined by steady pressures is reducible to a quadrature, so that a variety of effects may be considered, including gravitation. The dissipation of the solar corona is discussed.

Parker, E. N.↗

NASA NTRS1983

The propagation of torsion along flux tubes subject to dynamical nonequilibrium

It is noted that the dynamical nonequilibrium of close-packed flux tubes is driven by the torsion in the individual tubes. Because of this, whenever tubes with the same sense of twisting come into contact, there is reconnection of their azimuthal field components. The reconnection consumes the local torsion, and this causes the propagation of torsional Alfven waves into the region from elsewhere along the tubes. The formal problem of the propagation of the torsion along twisted flux tubes is presented, along with some of the basic physical properties worked out in the limit of small torsion. It is noted that in tubes with finite twisting the propagation of torsional Alfven waves can be a more complicated phenomenon. Application to the sun suggests that the propagation of torsion from below the visible surface up into the corona is an important energy supply to the corona for a period of perhaps 10-20 hours after the emergence of the flux tubes through the surface of the sun, bringing up torsion from depths of 10,000 km or more. Torsion is of course continually furnished by the manipulation and shuffling of the field by the convection.

Parker, E. N.↗