Engineering topics

Forbes, T. G.

Publications and source records attributed to Forbes, T. G..

At least 19 records

NASA NTRS1994

On the maximum energy release in flux-rope models of eruptive flares

We determine the photospheric boundary conditions which maximize the magnetic energy released by a loss of ideal-magnetohydrodynamic (MHD) equilibrium in two-dimensional flux-rope models. In these models a loss of equilibrium causes a transition of the flux rope to a lower magnetic energy state at a higher altitude. During the transition a vertical current sheet forms below the flux rope, and reconnection in this current sheet releases additional energy. Here we compute how much energy is released by the loss of equilibrium relative to the total energy release. When the flux-rope radius is small compared to its height, it is possible to obtain general solutions of the Grad-Shafranov equation for a wide range of boundary conditions. Variational principles can then be used to find the particular boundary condition which maximizes the magnetic energy released for a given class of conditions. We apply this procedure to a class of models known as cusp-type catastrophes, and we find that the maximum energy released by the loss of equilibrium is 20.8% of the total energy release for any model in this class. If the additional restriction is imposed that the photospheric magnetic field forms a simple arcade in the absence of coronal currents, then the maximum energy release reduces to 8.6%

Forbes, T. G.↗

NASA NTRS1994

On current sheet approximations in models of eruptive flares

We consider an approximation sometimes used for current sheets in flux-rope models of eruptive flares. This approximation is based on a linear expansion of the background field in the vicinity of the current sheet, and it is valid when the length of the current sheet is small compared to the scale length of the coronal magnetic field. However, we find that flux-rope models which use this approximation predict the occurrence of an eruption due to a loss of ideal-MHD equilibrium even when the corresponding exact solution shows that no such eruption occurs. Determination of whether a loss of equilibrium exists can only be obtained by including higher order terms in the expansion of the field or by using the exact solution.

Bungey, T. N.↗

NASA NTRS1992

Does fast magnetic reconnection exist?

The main features of the Priest-Forbes (1986) and Priest-Lee (1990) models of magnetic reconnection in astrophysical plasmas are discussed, and the Priest-Lee model is generalized to include inflow pressure gradients and thus different regimes of reconnection. It is shown that different scaling results can be obtained depending on the boundary conditions. These results are compared to the ones observed in the numerical experiments of Biskamp (1986) and Lee and Fu (1986). It is concluded that numerical experiments with suitably designed boundary conditions are likely to exhibit fast reconnection, and that such reconnection is a common process in astrophysical and space plasmas.

Priest, E. R.↗

NASA NTRS1992

Weighted current sheets supported in normal and inverse configurations - A model for prominence observations

A technique which incorporates both photospheric and prominence magnetic field observations is used to analyze the magnetic support of solar prominences in two dimensions. The prominence is modeled by a mass-loaded current sheet which is supported against gravity by magnetic fields from a bipolar source in the photosphere and a massless line current in the corona. It is found that prominence support can be achieved in three different kinds of configurations: an arcade topology with a normal polarity; a helical topology with a normal polarity; and a helical topology with an inverse polarity. In all cases the important parameter is the variation of the horizontal component of the prominence field with height. Adding a line current external to the prominence eliminates the nonsupport problem which plagues virtually all previous prominence models with inverse polarity.

Demoulin, P.↗

NASA NTRS1992

Magnetic flipping - Reconnection in three dimensions without null points

In three dimensions, magnetic reconnection may take place in a sheared magnetic field at any singular field line, where the nearby field has X-type topology in planes perpendicular to the field line and where an electric field is present parallel to the field line. In the ideal region around the singular line there will, in general, be singularities in the plasma flow and electric field, both at the singular line and at 'magnetic flipping layers', which are remnants of local magnetic separatrices. In the absence of a three-dimensional magnetic neutral point or null point, reconnection of field lines can still occur by a process of magnetic flipping, in which the plasma crosses the flipping layers but the field lines rapidly flip along them by magnetic diffusion. Depending on the boundary conditions, there may be two or four flipping layers which converge on the singular line. A boundary layer analysis of a flipping layer is given, in which the magnetic field parallel to the layer decreases as one crosses it while the plasma pressure (or magnetic pressure associated with the field along the singular line) increases. The width of the flipping layer decreases with distance from the singular line.

Priest, E. R.↗

NASA NTRS1991

A numerical simulation of magnetic reconnection and radiative cooling in line-tied current sheets

Radiative MHD equations are used for an optically thin plasma to carry out a numerical experiment related to the formation of 'postflare' loops. The numerical experiment starts with a current sheet that is in mechanical and thermal equilibrium but is unstable to both tearing-mode and thermal-condensation instabilities. The current sheet is line-tied at one end to a photospheric-like boundary and evolves asymmetrically. The effects of thermal conduction, resistivity variation, and gravity are ignored. In general, reconnection in the nonlinear stage of the tearing-mode instability can strongly affect the onset of condensations unless the radiative-cooling time scale is much smaller than the tearing-mode time scale. When the ambient plasma is less than 0.2, the reconnection enters a regime where the outflow from the reconnection region is supermagnetosonic with respect to the fast-mode wave speed. In the supermagnetosonic regime the most rapidly condensing regions occur downstream of a fast-mode shock that forms where the outflow impinges on closed loops attached to the photospheric-like boundary. A similar shock-induced condensation might occur during the formation of 'postflare' loops.

Forbes, T. G.↗

NASA NTRS1991

A catastrophe mechanism for coronal mass ejections

The ideal-MHD equations are used to show that a coronal current filament can suddenly lose equilibrium if its magnetic energy exceeds a critical value. The loss of equilibrium in the configuration results from an imbalance between magnetic tension and compression, and this imbalance ejects the filament upwards. Near the critical value, the equilibrium configuration develops a vertical current sheet attached to the photosphere at the point directly below the filament. When equilibrium is lost, field lines anchored to the photosphere are stretched upwards, and the current sheet rapidly grows longer. Without reconnection in the current sheet, the filament travels only a short distance before reaching a new equilibrium, and the net magnetic energy released is less than 1 percent of the stored magnetic energy. However, with reconnection, the filament travels upwards indefinitely, and all of the stored energy is released.

Forbes, T. G.↗

NASA NTRS1991

Magnetic reconnection in solar flares

The magnetic energy stored in the corona is the only plausible source for the energy released during large solar flares. During the last 20 years most theoretical work has concentrated on models which store magnetic energy in the corona in the form of electrical currents, and a major goal of present day research is to understand how these currents are created, and then later dissipated during a flare. Another important goal is to find a flare model which can eject magnetic flux into interplanetary space. Although many flares do not eject magnetic flux, those which do are of special importance for solar-terrestrial relations since the ejected flux can have dramatic effects if it hits the Earth's magnetosphere. Three flare models which have been extensively investigated are the emerging-flux model, the sheared-arcade model, and the magnetic-flux-rope model. All of these models can store and release magnetic energy efficiently provided that rapid magnetic reconnection occurs. However, only the magnetic-flux-rope model appears to provide a plausible mechanism for ejecting magnetic flux into interplanetary space.

Forbes, T. G.↗

NASA NTRS1991

Driven reconnection in the earth's magnetotail

In the standard reconnection model, a low flow speed leads to steady reconnection at a distant-tail x-line, but a high flow speed leads to the formation of a near-earth x-line and the onset of an auroral substorm. This paper discusses recent work which suggests that a pile-up of magnetic flux in the earth's magnetotail will occur whenever reconnection is strongly driven by the solar wind and that the near-earth x-line might result from a flux pile-up at the distant-tail x-line.

Forbes, T. G.↗

NASA NTRS1990

The evolution of coronal magnetic fields

Slow photospheric motions can produce flow speeds in the corona which are fast enough to violate quasi-static evolution. Therefore, high-speed flows observed in the corona are not necessarily due to a loss of equilibrium or stability. This paper presents an example where the flow speed increases indefinitely with height while the coronal magnetic energy increases quadratically with time.

Priest, E. R.↗

NASA NTRS1990

Numerical simulation of a catastrophe model for coronal mass ejections

Van Tend and Kuperus (1978) proposed a simple catastrophe model for magnetically driving coronal mass ejections, prominence eruptions, and two-ribbon flares. Their model, which is based on simple circuit concepts, suggests that a stable configuration containing a current filament will lose equilibrium when the filament current exceeds a critical value. Here, a two-dimensional numerical simulation is used to test how the Van Tend-Kuperus model works in an ideal MHD fluid. The simulation exhibits the expected loss of mechanical equilibrium near the predicted critical value, but the current filament moves only a short distance upward before coming to rest at a new equilibrium. However, this new equilibrium contains a current sheet which is resistively unstable to magnetic reconnection, and if magnetic reconnection occurs rapidly, the filament can continue to move upward at Alfvenic speeds.

Forbes, T. G.↗

NASA NTRS1990

Evaporation in the transition region during the gradual phase of flares

Previous observations have revealed that small, but sustained, H-alpha blueshifts occur in flare ribbons during the gradual, or late, phase of flares. These blueshifts suggest that there is a gentle evaporation of chromospheric material throughout the late phase of flares, but ambiguities in the interpretation of H-alpha leave open the possibility that these blueshifts are caused by downflowing, rather than upflowing, material. Using both C IV and soft (3.5-8 keV) X-ray data from SMM observations, evidence is found which supports the interpretation of the H-alpha blueshifts as upflows in the range from 4-12 km/s. The blueshifts are interpreted in terms of the reconnection model proposed by Carmichael (1964). The model produces a sustained energy release through-out the late phase which accounts for the prolonged soft X-ray emission after a flare. This energy release comes from the reconnecting magnetic field above the flare site, and some of the energy is transported along field lines mapping to the chromosphere where it drives chromospheric evaporation.

Schmieder, B.↗

NASA NTRS1990

Magnetic field evolution during prominence eruptions and two-ribbon flares

Simple models for the MHD eruption of a solar prominence are presented in which the prominence is treated as a twisted magnetic flux tube that is being repelled from the solar surface by magnetic pressure forces. Including a background magnetic field allows the prominence to be in equilibrium initially with an inverse polarity and then to erupt due to magnetic nonequilibrium when the background magnetic field is too small or the prominence twist is too great. The electric field at the neutral point below the prominence rapidly increases to a maximum value and then declines. Including the effect of gravity also allows an equilibrium with normal polarity to exist. Finally, an ideal MHD solution is found which incorporates self-consistently a current sheet below the prominence and which implies that a prominence will still erupt and form a current sheet even if no reconnection occurs. When reconnection is allowed it is, therefore, driven by the eruption.

Priest, E. R.↗

NASA NTRS1990

The role of Magnetic Reconnection in flares and prominence eruptions

Magnetic Reconnection is often invoked as the primary mechanism for driving a flare or a prominence eruption. This paper argues that a catastrophic loss of mechanical equilibrium, rather than reconnection, is probably the primary mechanism for driving these phenomena. However, reconnection is still essential in order for any significant amount of energy to be released. To illustrate this idea, some recent results are presented from an MHD simulation based on a catastrophe mechanism first proposed by Van Tend and Kuperus. In order for this mechanism to be effective, a substantial amount of reconnection must occur within a few Alfven-scale times. Such rapid reconnection is plausible since the loss of mechanical equilibrium can generate flows which drive the reconnection at a rapid rate.

Forbes, T. G.↗

NASA NTRS1990

Basic properties and models of solar prominences

Prominences are relatively cool (10,000 K) and dense plasma clouds which may persist for 100 days or more in the midst of the much hotter (1 million K) and more tenuous (10 exp 9/cu cm) corona. Many observations imply that the magnetic field in and around prominences is responsible both for isolating prominences from the corona and for supporting them against gravity. It is not at all obvious how the magnetic field can do both these tasks, but the limited theoretical models that are available suggest that a magnetic-flux rope is involved. Using a new analytical model, it is argued that the flux rope could also play a key role in the eruption of a prominence by supplying the magnetic energy necessary to drive the prominence outwards.

Forbes, T. G.↗

NASA NTRS1989

Steady magnetic reconnection in three dimensions

The concept of magnetic reconnection, defined to occur when there is an electric field parallel to field lines which are potential reconnection locations and near which the field has an X-type topology in a plane normal to the field line, has been generalized to three-dimensional configurations. A continuum of neighboring potential singular lines is found to exist, one of which supports reconnection, depending upon the imposed flow or electric field. For the case of steady reconnection, the nearby flow and electric field are shown to be severely constrained in the ideal region by the condition that the electric field = 0 there. It is noted that reconnection may occur at singularities of the electric field where this constraint fails and there is singular plasma jetting.

Priest, E. R.↗

NASA NTRS1989

The formation flare loops by magnetic reconnection and chromospheric ablation

Noncoplanar compressible reconnection theory is combined here with simple scaling arguments for ablation and radiative cooling to predict average properties of hot and cool flare loops as a function of the coronal vector magnetic field. For a coronal field strength of 100 G, the temperature of the hot flare loops decreases from 1.2 x 10 to the 7th K to 4.0 x 10 to the 6th K as the component of the coronal magnetic field perpendicular to the plane of the loops increases from 0 percent to 86 percent of the total field. When the perpendicular component exceeds 86 percent of the total field or when the altitude of the reconnection site exceeds 10 to the 6th km, flare loops no longer occur. Shock-enhanced radiative cooling triggers the formation of cool H-alpha flare loops with predicted densities of roughly 10 to the 13th/cu cm, and a small gap of roughly 1000 km is predicted to exist between the footpoints of the cool flare loops and the inner edges of the flare ribbons.

Forbes, T. G.↗

NASA NTRS1988

Magnetohydrodynamic boundary conditions for global models

Boundary conditions in the ionosphere and the upstream solar wind are important in determining the dynamics of global magnetohydrodynamic models of the magnetosphere. It is generally recognized that the orientation of the magnetic field in the upstream solar wind strongly modulates the rate of energy input into the magnetosphere by magnetic reconnection. However, other aspects of the upstream boundary conditions may determine whether the reconnection occurs in a patchy manner, as in flux transfer events, or in a global manner, as in the Paschmann et al. (1979) events. Ionospheric boundary conditions should also affect the reconnection process. For example, ionospheric line-tying can cause x-line motion in the outer magnetosphere. If it is assumed that auroras occur on field lines mapping to x-lines, then auroral motions are different than the local convective motion of the plasma in which they occur. Global magnetohydrodynamic models which incorporate both magnetospheric reconnection and ionospheric convection could be used to investigate the effect of reconnection and convection upon dayside and nightside auroral motions during the course of a magnetic substorm.

Forbes, T. G.↗