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1.
B. C. Low 《Solar physics》1980,65(1):147-165
This is a study of the relationship between a magnetic field and its embedding plasma in static equilibrium in a uniform gravity. The ideal gas law is assumed. A system invariant in a given direction is treated first. We show that an exact integral of the equation for force balance across field lines can be derived in a closed form. Using this integral, exact solutions can be generated freely by integrating directly for the distributions of pressure, density and temperature necessary to keep a given magnetic field in equilibrium. Particular solutions are presented for illustration with the solar atmosphere in mind. Extending the treatment to the general system depending on all three spatial coordinates, we arrive at the general form of a theorem of Parker that a magnetic field in static equilibrium must possess certain symmetries. We derive an equation involving the Euler potentials of the magnetic field stipulating these necessary symmetries. Only those magnetic fields satisfying this equation can be in static equilibrium and for these fields, the endowed symmetries make the construction of exact solutions an essentially two dimensional problem as exemplified by the special case of invariance in a given direction. 相似文献
2.
3.
B. C. Low 《Solar physics》1980,67(1):57-77
A method is prescribed for generating exact solutions of magnetostatic equilibrium describing a cylindrically symmetric magnetic flux tube oriented vertically in a stratified medium. Given the geometric shape of the field lines, compact formulae are presented for the direct calculation of all the possible distributions of pressure, density, temperature and magnetic field strength compatible with these field lines under the condition of static equlibrium. The plasma satisfies the ideal gas law and gravity is uniform in space. A particular solution is obtained by this method for a medium sized sunspot whose magnetic field obeys the similarity law of Schlüter and Temesváry (1958). With this solution, it is possible for the first time to illustrate explicitly the confinement of the magnetic field of the cool sunspot by the hotter external plasma in an exact relationship involving both magnetic pressure and field tension as well as the support of the weight of the plasma by pressure gradients. It is found that the cool region of the sunspot is not likely to extend much more than a few density scale heights below the photosphere. The sunspot field approaches being potential in the neighbourhood of the photosphere so that the Lorentz force exerting on the photosphere is less than what the magnetic pressure would suggest. This accounts for how the sunspot field can be confined in the photosphere where its magnetic pressure is often observed to even exceed the normal photospheric pressure. The energy mechanism operating in the sunspot and the question of mechanical stability are not treated in this paper.Normally at Lau Kuei Huat (Singapore) Private Limited, 55 Shipyard Road, Singapore 22, Singapore. 相似文献
4.
We present a theoretical model of quiescent prominences in the form of an infinite vertical sheet. Self-consistent solutions are obtained by integrating simultaneously the set of nonlinear equations of magnetostatic equilibrium and thermal balance. The basic features of the models are: (1) The prominence matter is confined to a sheet and supported against gravity by a bowed magnetic field. (2) The thermal flux is channelled along magnetic field lines. (3) The thermal flux is everywhere balanced by Low's (1975b) hypothetical heat sink which is proportional to the local density. (4) A constant component of the magnetic field along the length of the prominence shields the cool plasma from the hot surrounding. We assume that the prominence plasma emits more radiation than it absorbs from the radiation fields of the photosphere, chromosphere and corona, and we interpret the above hypothetical heat sink to represent the amount of radiative loss that must be balanced by a nonradiative energy input. Using a central density and temperature of 1011 particles cm–3 and 5000 K respectively, a magnetic field strength between 2 to 10 gauss and a thermal conductivity that varies linearly with temperature, we discuss the physical properties implied by the model. The analytic treatment can also be carried out for a class of more complex thermal conductivities. These models provide a useful starting point for investigating the combined requirements of magnetostatic equilibrium and thermal balance in the quiescent prominence. 相似文献
5.
B. C. Low 《Solar physics》1982,75(1-2):119-131
We present a simple magnetostatic theory of the thin vertical filaments that make up the quiescent prominence plasma as revealed by fine spatial resolution H photographs. A class of exact equilibrium solutions is obtained describing a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines. A free function is available to generate different assortments of filament sizes and spacings, as well as different density and temperature variations. The classic Kippenhahn-Schlüter solution for a long sheet without filamentary structures is a particular member of this class of solutions. The role of the magnetic field in supporting and thermally shielding the filament plasma is illustrated. It is found that the filament can have a sharp transition perpendicular to the local field, whereas the transition in the direction of the local field is necessarily 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. This electric current flowing into the rarefied region around the prominence can contain substantial energy stored in the form of force-free magnetic fields. This novel feature has implications for the heating and the disruption of prominences. 相似文献
6.
A normal-polarity prominence is modelled as a series of cool fibrils set in the hotter corona. Equations of magnetostatic equilibrium are solved and each fibril corresponds to a dip in the mgnetic field. The ratio of fibril width to interfibril spacing is dependent on the prominence-coronal temperature ratio and the ratio of plasma to magnetic pressure. The prominence mass is found to depend on the square of the magnetic field strength. When variations along the prominence are allowed in addition to those across the prominence, an apparently random pattern of fibrils results. 相似文献
7.
We analyse the magnetic support of solar prominences in two-dimensional linear force-free fields. A line current is added to model a helical configuration, well suited to trap dense plasma in its bottom part. The prominence is modeled as a vertical mass-loaded current sheet in equilibrium between gravity and magnetic forces.We use a finite difference numerical technique which incorporates both vertical photospheric and horizontal prominence magnetic field measurements. The solution of this mixed boundary problem generally presents singularities at both the bottom and top of the model prominence. The removal of the singularities is achieved by superposition of solutions. Together with the line current equilibrium, these three conditions determine the amplitude of the magnetic field in the prominence, the flux below the prominence and the current intensity, for a given height of the line current. A numerical check of accuracy in the removal of singularities, is done by using known analytical solutions in the potential limit.We have investigated both bipolar and quadrupolar photospheric regions. In this mixed boundary problem the polarity of the field component orthogonal to the prominence is mainly fixed by the imposed height of the line current. For bipolar regions above (respectively below) a critical height the configuration is inverse (respectively normal). For quadrupolar regions the polarity is reversed if we refer the prominence polarity to the closest photospheric polarities. We introduce the polarity of the component parallel to the prominence axis with reference to a sheared arcade. Increasing the shear with fixed boundary conditions can increase or decrease the mass supported depending on the configuration. 相似文献
8.
A dynamical model of prominence loops is constructed on the basis of the theory of hydromagnetic buoyancy force. A prominence loop is regarded as a flux rope immersed in the solar atmosphere above a bipolar region of the photospheric magnetic field. The motion of a loop is partitioned into a translational motion, which accounts for the displacement of the centroidal axis of the loop, and an expansional motion, which accounts for the displacement of the periphery of the loop relative to the axis. The translational motion is driven by the hydromagnetic buoyancy force exerted by the surrounding medium of the solar atmosphere and the gravitational force exerted by the Sun. The expansional motion is driven by the pressure gradient that sustains the pressure difference between internal and external gas pressures and the self-induced Lorentz force that results from interactions among internal currents. The main constituent of the hydromagnetic buoyancy force on a prominence loop is the diamagnetic force exerted on the internal currents by the external currents that sustain the pre-existing magnetic field. By spatial transformation between magnetic and mechanical stresses, the diamagnetic force is manifested through a mechanical force acting at various mass elements of the prominence. For a prominence loop in equilibrium, the gravitational force is balanced by the hydromagnetic buoyancy force and the Lorentz force of helical magnetic field is balanced by a gradient force of gas pressure. 相似文献
9.
A numerical simulation is performed to investigate the prominence formation in a magnetic arcade by photospheric shearing motions. A two-and-a-half-dimensional magnetohydrodynamic (MHD) code is used, in which the gravitational force, radiative cooling, thermal conduction and a simplified form of coronal heating are included. It is found that a footpoint shear induces an expansion of the magnetic arcade and cooling of the plasma in it. Simultaneously the denser material from the lower part of the arcade is pulled up by the expanding field lines. A local enhancement of radiative cooling is thus effected, which leads to the onset of thermal instability and the condensation of coronal plasma. The condensed material grows vertically to form a sheet-like structure making dips on field lines, leading to the formation of the Kippenhahn- Schlüter type prominence. The mass of the prominence is found to be supplied not only by the condensation of the material in the vicinity but also by the siphon-type upflows. The upward growth of the vertical sheet-structure of the prominence is saturated at a certain stage and the newly condensed material is found to slide down from above the prominence along magnetic field lines. This drainage of material leads to the formation of an arc-shaped cavity of low density and low pressure around the prominence. The problem of force and heat balance is addressed and the prominence is found to be not in a static equilibrium but in a dynamic interaction with its environment. 相似文献
10.
The temperature and density are obtained for coronal plasma in thermal and hydrostatic equilibrium and located in a force-free magnetic arcade. The isotherms are found to be inclined to the magnetic field lines and so care should be taken in inferring the magnetic structure from observed emission.When the coronal pressure becomes too great, the equilibrium ceases to exist and the material cools to form a quiescent prominence. The same process can be initiated at low heating rates when the width or shear of the arcade exceeds a critical value.We suggest that the prominence should be modelled as a dynamic structure with plasma always draining downwards. Material is continually sucked up along field lines of the ambient arcade and into the region lacking a hot equilibrium, where it cools to form new prominence material. 相似文献
11.
Two possible limiting scenarios are proposed for the production of a coronal mass ejection. In the first the magnetic field around a prominence evolves until it loses equilibrium and erupts, which drives reconnection below the prominence and an eruption of the overlying magnetic arcade. In the second a large-scale magnetic arcade evolves until it loses equilibrium and erupts, thereby causing a prominence to erupt. In general it is likely to be the non-equilibrium of the coupled system which creates the eruption. Furthermore, large quiescent prominences are expected to be centred within the magnetic bubble of a coronal mass ejection whereas when active-region prominences erupt they are likely to be located initially to one side of the bubble.A model is set up for the eruption of a magnetically coupled prominence and coronal mass ejection. This represents a development of the Anzer and Pneuman (1982) model by overcoming two limitations of it, namely that: it is not globally stable initially and so one wonders how it can be set up in a stable way before the eruption; it has reconnection driving the CME whereas recent observations suggest that the reverse may be happening. In our model we assume that magnetic reconnection below the prominence is driven by the eruption and the driver is magnetic non-equilibrium in the coupled prominence-mass ejection system. The prominence is modelled as a twisted flux tube and the mass ejection as an overlying void and magnetic bubble. Two different models of the prominence are considered. In one a globally stable equilibrium becomes unstable when a threshold magnetic flux below the prominence is exceeded and, in the other, equilibrium ceases to exist. In both cases, the prominence and mass-ejection accelerate upwards before reaching constant velocities in a manner that is consistent with observations. It is found that the greater the reconnection that is driven by the eruption, the higher is the final speed. 相似文献
12.
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. The effects of different physical assumptions to deal with this magneto-hydrodynamically complex phenomenon are evaluated, such as holding constant the prominence current, radius, flux or twist or modelling the prominence as a current sheet. Including a background magnetic field allows the prominence to be in equilibrium initially with an Inverse Polarity and then to erupt due to magnetic non-equilibrium 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. 相似文献
13.
A two-dimensional model of prominence formation in a region containing a magnetic neutral sheet is constructed for a variety of initial conditions, assuming the coronal plasma to be described by the usual hydromagnetic approximation, with infinite electric conductivity. In each case the magnetic field is initially vertical, varying antisymmetrically with respect to the neutral sheet, to a maximum value at a distance of 70 000 km from the neutral sheet. In the first case, the plasma is initially in hydrostatic equilibrium, whereas in successive cases, the pressure is assumed to be of such a value that the plasma is in lateral equilibrium of total pressure (gas plus magnetic). In a variation of this case, the value of the solar gravitational field was artificially reduced, and the effects considered. Large lateral motions are produced in each case, thus apparently inhibiting the condensation of prominences, with the exception of the unrealistic case of artificially reduced gravity. The results suggest that consideration either of a third component of the magnetic field (horizontal and parallel to the neutral sheet), or a finite conductivity, allowing magnetic recombination across the neutral sheet, or both, would more realistically represent the problem and might thus show the development of prominences. 相似文献
14.
G. W. Pneuman 《Solar physics》1980,65(2):369-385
The observed interrelationship between coronal transients and eruptive prominences is used as the basis for a theoretical MHD model of these events. The model begins with an equilibrium configuration consisting of a coronal loop or arcade with a filament lying underneath with its axis oriented perpendicular to the overlying field. The lifting of the filament from the solar surface produces an increase in magnetic pressure under the helmet which drives it outward. This increased pressure is associated with the internal field of the filament as well as the field beneath it. The underlying field could be that which produced the filament eruption or, alternatively, reconnected field lines formed by the inward collapse of the legs of the transient towards the neutral line beneath the rising prominence. We do not attempt to explain the filament eruption which may be due to internal forces in the prominence or, alternatively, from forces imposed from beneath as would be produced by emerging flux. In the latter case, the filament is passive and merely acts as a tracer for the more fundamental underlying process.It is shown that the outward force per unit mass produced by the driving magnetic field and the inward restoring forces in the overlying field due to magnetic tension and gravity all decrease with distance at the same rate - namely, as the inverse square of the distance from the solar center. Hence, the ratio of net outward to inward force is independent of radial distance from the Sun. A stability analysis shows that this situation is one of neutral stability.A mathematical model of this physical process is described in which the MHD equations in simplified form, neglecting gas pressure forces, are solved in time for the velocity, width, density, and magnetic field strength of the transient. The solutions show that the velocity increases sharply close to the Sun but quickly approaches a constant value. The width increases linearly with radial distance. Both of these results are in agreement with observations. An examination of the forces exerted on the legs of the transient shows that their motion should be horizontally inward.On leave from the High Altitude Observatory, National Center for Atmospheric Research, Boulder, Colo., U.S.A. 相似文献
15.
Realistic models of solar prominence flux ropes are numerically constructed. The models are in 2.5 dimensions, including the effects of non-isothermal temperature, density and gravity, and pressure. Stability of the equilibria to pressure- and gravity-driven instabilities is numerically investigated, using the ballooning formalism of fusion plasma theory. The equilibrium models can become unstable to pressure- and gravity-driven modes at plasma parameters characteristic of prominences. 相似文献
16.
Ulrich Anzer 《Solar physics》1972,24(2):324-335
A 2-dimensional model of the magnetic field associated with quiescent prominences is presented. The coronal field is assumed to be current-free, currents are only allowed in the photosphere and inside the prominence. The prominence is taken to be infinitely thin. For this model a method is given to calculate the field configuration from the observed normal component of the field both in the photosphere and the prominence. The normal field components are inferred from disc observations and H limb observations. The sheet currents inside the prominence are calculated and the resulting Lorentz force is compared with the gravitational force. Within the range of uncertainty in the total hydrogen density of quiescent prominences it is possible to give models where the gravity is balanced by the Lorentz force. 相似文献
17.
Model calculations are presented for the rising motion of the top section of a prominence loop, which is represented by a straight flux rope immersed in a coronal medium permeated with a bipolar magnetic field. Initially the prominence is at rest, in equilibrium with the surrounding coronal medium. When the magnetic monopoles that account for the source current for the bipolar field strengthen, the upward hydromagnetic buoyancy force overcomes the downward gravitational force so that the prominence is initiated into rising motion. The illustrative examples show that prominences can move away from the solar surface by the action of the hydromagnetic buoyancy force, which is preponderant with the diamagnetic force due to the current carried by the prominence interacting with the coronal magnetic field produced by the photospheric currents, if the changes in the photospheric magnetic field are sufficiently large. 相似文献
18.
Charles W. Querfeld Raymond N. Smartt Veronique Bommier Egidio Landi Degl'innocenti Lewis L. House 《Solar physics》1985,96(2):277-292
The Stokes components of He i D3 emission in two quiescent prominences, using full spectral profile measurements, are analyzed to derive vector magnetic fields. Two independently developed schemes, based on the Hanle effect, are used for interpretation. They involve solutions of the statistical equilibrium equations for the He i D3 multiplet, including the effect of coherency and full level crossing, which predict the magnetic field dependence of the observed polarization. Derived magnetic field vector solutions for each pair of linear polarization Stokes profiles corresponding to an observational point in the prominence are, intrinsically, not uniquely determined, and a set of possible solutions is usually obtained. However, mutual consistency of these solutions with those independently predicted by the form of the circular polarized component, allow, in almost all cases, rejection of all solutions of a set except one symmetrical pair. Of such a pair, a unique solution can be determined with a high confidence level by reference to independent potential field information. Field vectors are found usually to be close to horizontal and normal to the prominence surface, but extreme exceptions are found. Field values range from 6 G to 60 G. The derived vectorfield configurations and their magnitudes are briefly discussed relative to these prominences and to different quiescent prominence models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation. 相似文献
19.
This paper considers the structural properties of a sunspot-like magnetic flux tube which lacks perfect axisymmetry. The flux tube is taken to be in static equilibrium with an atmosphere in a uniform gravity. Assuming the departure from axisymmetry to be slight, the equations for the first order non-axisymmetric part of the equilibrium are derived in cylindrical coordinates. These first order equations reduce to a linear second order hyperbolic partial differential equation in the r-z plane. Whereas Cauchy type boundary conditions are appropriate for hyperbolic equations, physical considerations dictate the specification of boundary conditions on a closed surve for our problem of interest. The construction of solutions to this boundary value problem is illustrated with three analytically soluble cases, where the zero-order axisymmetric equilibria are chosen to have magnetic field geometry of different complexity. A physical discussion of the results is given. 相似文献
20.
This paper is an exploration of the possibility that the large-scale equilibrium of plasma and magnetic fields in the solar corona is a minimum energy state. Support for this conjecture is sought by considering the simplest form of that equilibrium in a dipole solar field, as suggested by the observed structure of the corona at times of minimum solar activity. Approximate, axisymmetric solutions to the MHD equations are constructed to include both a magnetically closed, hydrostatic region and a magnetically open region where plasma flows along field lines in the form of a transonic, thermally-driven wind. Sequences of such solutions are obtained for various degrees of magnetic field opening, and the total energy of each solution is computed, including contributions from both the plasma and magnetic field. It is shown that along a sequence of increasingly closed coronal magnetic field, the total energy curve is a non-monotonic function of the parameter measuring the degree of magnetic field opening, with a minimum occurring at moderate field opening.For reasonable choices of model parameters (coronal temperature, base density, base magnetic field strength, etc.), the morphology of the minimum energy solution resembles the observed quiet, solar minimum corona. The exact location energy minimum along a given sequence depends rather sensitively on some of the adopted parameter values. It is nevertheless argued that the existence of an energy minimum along the sequences of solutions should remain a robust property of more realistic coronal wind models that incorporate the basic characteristics of the equilibrium corona- the presence of both open and closed magnetic regions.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献