Engineering topics

Wolfson, Richard

Publications and source records attributed to Wolfson, Richard.

8 records

NASA NTRS1995

Shear-induced opening of the coronal magnetic field

This work describes the evolution of a model solar corona in response to motions of the footpoints of its magnetic field. The mathematics involved is semianalytic, with the only numerical solution being that of an ordinary differential equation. This approach, while lacking the flexibility and physical details of full MHD simulations, allows for very rapid computation along with complete and rigorous exploration of the model's implications. We find that the model coronal field bulges upward, at first slowly and then more dramatically, in response to footpoint displacements. The energy in the field rises monotonically from that of the initial potential state, and the field configuration and energy appraoch asymptotically that of a fully open field. Concurrently, electric currents develop and concentrate into a current sheet as the limiting case of the open field is approached. Examination of the equations shows rigorously that in the asymptotic limit of the fully open field, the current layer becomes a true ideal MHD singularity.

Wolfson, Richard↗

NASA NTRS1992

Energy buildup in sheared force-free magnetic fields

Photospheric displacement of the footpoints of solar magnetic field lines results in shearing and twisting of the field, and consequently in the buildup of electric currents and magnetic free energy in the corona. The sudden release of this free energy may be the origin of eruptive events like coronal mass ejections, prominence eruptions, and flares. An important question is whether such an energy release may be accompanied by the opening of magnetic field lines that were previously closed, for such open field lines can provide a route for matter frozen into the field to escape the sun altogether. This paper presents the results of numerical calculations showing that opening of the magnetic field is permitted energetically, in that it is possible to build up more free energy in a sheared, closed, force-free magnetic field than is in a related magnetic configuration having both closed and open field lines. Whether or not the closed force-free field attains enough energy to become partially open depends on the form of the shear profile; the results presented compare the energy buildup for different shear profiles. Implications for solar activity are discussed briefly.

Wolfson, Richard↗

NASA NTRS1991

Force-free magnetic fields - Generating functions and footpoint displacements

This paper presents analytic and numerical calculations that explore equilibrium sequences of bipolar force-free magnetic fields in relation to displacments of their magnetic footpoints. It is shown that the appearance of magnetic islands - sometimes interpreted as marking the loss of equilibrium in models of the solar atmosphere - is likely associated only with physically unrealistic footpoint displacements such as infinite separation or 'tearing' of the model photosphere. The work suggests that the loss of equilibrium in bipolar configurations, sometimes proposed as a mechanism for eruptive solar events, probably requires either fully three-dimensional field configurations or nonzero plasma pressure. The results apply only to fields that are strictly bipolar, and do not rule out equilibrium loss in more complex structures such as quadrupolar fields.

Wolfson, Richard↗

NASA NTRS1990

Linear evolution of current sheets in sheared force-free magnetic fields with discontinuous connectivity

Thin current sheets arising in tenuous, magnetized solar coronal plasmas may constitute an important mechanism for energy buildups and subsequent energy releases; they could arise from the continuous-and-random motion of magnetic footprints associated with photospheric velocity fields. A model is presented for study of the quasi-static evolution of current sheets due to shearing of the footpoints, in a highly idealized geometry that incorporates an abrupt jump in field-line connectivity. The model highlights that formation of thin current layers and allows large shearing motions prior to violation of the linear approximation. Excess energy comparable to that released by solar flares can be stored in a sheared field.

Wolfson, Richard↗

NASA NTRS1989

Current sheet formation in a sheared force-free-magnetic field

This paper presents the results of a study showing how continuous shearing motion of magnetic footpoints in a tenuous, infinitely conducting plasma can lead to the development of current sheets, despite the absence of such sheets or even of neutral points in the initial state. The calculations discussed here verify the earlier suggestion by Low and Wolfson (1988) that extended current sheets should form due to the shearing of a force-free quadrupolar magnetic field. More generally, this work augments earlier studies suggesting that the appearance of discontinuities - current sheets - may be a necessary consequence of the topological invariance imposed on the magnetic field geometry of an ideal MHD system by virtue of its infinite conductivity. In the context of solar physics, the work shows how the gradual and continuous motion of magnetic footpoints at the solar photosphere may lead to the buildup of magnetic energy that can then be released explosively when finite conductivity effects become important and lead to the rapid dissipation of current sheets. Such energy release may be important in solar flares, coronal mass ejections, and other eruptive events.

Wolfson, Richard↗

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 NTRS1987

The configuration of slow-mode shocks

A simple method for computing blunt-body flows containing slow shocks is presented. The method is based on the solution of a free-boundary problem for the shock configuration that matches a postshock potential flow to a uniform preshock flow. The method is applied to shocks arising from flow about spherical and paraboloidal obstacles. The results of a parametric study of shock formation as a function of sonic and Alfven Mach numbers showed that when either Mach number decreased, the standoff distance increased. The results should give estimates of the location and the configuration of slow shocks, provided that two as yet unverified assumptions are correct: (1) that the standoff distance and the slow-shock configuration along the stagnation streamline are not affected significantly by portions of the shock still forming far upstream of the shock nose, and (2) that fast-mode waves propagating at small angles to the magnetic field do not significantly affect the formation of the slow shock.

Wolfson, Richard↗

NASA NTRS1986

Quasistatic evolution of magnetostatic coronal structures

Four separate but related studies of coronal magnetostatic equilibria under a variety of boundary conditions and distributions of coronal current are reviewed. Physically, all four studies assume an axisymmetric corona whose radial magnetic field at the coronal base is dipolar. Electric currents in the model coronas are assumed to flow in the azimuthal direction, giving rise to Lorentz forces that must be balanced by pressure gradients and gravity. Mathematically, such coronas are described by the equation of magnetostatic force balance and Ampere's law. Although highly idealized, the axisymmetric magnetostatic models described provide insights into the behavior of a variety of coronal structures. The models show how more realistic current sheet boundary conditions and coronal density variations may be modeled.

Wolfson, Richard↗