共查询到20条相似文献，搜索用时 15 毫秒
1.
A tractable method for investigating the linear stability of line-tied 2-D coronal magnetic fields is introduced. It is based on the Bernstein et al. (1958) energy principle and can be applied to non-isothermal equilibria with gravity, having a translational invariance. The perturbed potential energy integral is manipulated to produce either necessary conditions for stability to localized modes or sufficient conditions for stability to global modes. Each condition only requires the solution of a set of ordinary differential equations, integrated along the magnetic field lines. The tests are employed to two different classes of equilibria. A linear force-free field is shown to be completely stable, regardless of the shear. The role of pressure gradients, footpoint displacements, line-tying and stratification on an isothermal magneto-hydrostatic equilibrium is assessed. 相似文献
2.
The existence of the point of bifurcation of rotating gaseous masses with toroidal magnetic fields is established from the first variations of the integral properties provided by the second-order virial relations. It is shown that the point of bifurcation, where the Jabcobi ellipsoids branch off from the Maclaurin spheroids, is unaffected by the presence of toroidal magnetic fields. 相似文献
3.
B. C. Low 《Solar physics》1988,115(2):269-276
The theoretical force-free magnetic fields in the first paper of this series, modeling magnetic configurations associated with polarity intrusion in active regions, are established to be all stable to linear ideal hydromagnetic perturbations under the boundary condition that anchors the lines of force rigidly to the photosphere. It is shown first that these force-free fields belong to an even larger class found by Chang and Carovillano (1981). A proof by the energy principle is then given to establish that all force-free magnetic fields in the larger class are absolutely stable. The physical implications of this result are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
4.
5.
Methods for investigating the stability of line-tied, cylindrically-symmetric magnetic fields are presented. The energy method is used and the perturbed potential energy integral is manipulated to produce simple tests that predict either stability to general coronal disturbances or instability to localized modes, both satisfying photospheric line-tying. Using these tests the maximum amount of magnetic energy, that can be stored in the coronal magnetic field prior to an instability, can be estimated. The tests are applied to four different classes of equilibria and results are obtained for both arcade and loop geometries. 相似文献
6.
Force-free magnetic fields (f.f.f) are considered as the first approximation of magnetic hydrodynamic equations in the case when the energy of the field exceeds the thermal energy of the medium. Such a relation of energies takes place in the upper atmosphere of the Sun in active regions.The consequence of the virial theorem obtained shows that for any solution of the corresponding non-linear system of equations only two cases are possible: either the total energy of the field is given by a divergent integral, or in some regions the force-free character of field is destroyed. This permits the conclusion that it is impossible to build f.f. current systems everywhere, and therefore boundary problems for this type of fields are of the same importance as for harmonic fields.Integral relations are obtained which are the necessary conditions for the solution of boundary problems. According to the classical principle of Thompson the harmonic fields are always stable, while f.f.f. may be stable or unstable.It is shown that: (1) arbitrary f.f.f. are stable to small changes of boundary conditions; (2) among f.f.f. the hydrodynamically stable configurations exist.The hydrodynamic stability condition restricts the size of force-free currents in such configurations. 相似文献
7.
Using first variations of the integral properties of equilibrium second-order virial relations, the existence of the point of bifurcation of rotating gaseous masses with magnetic fields is substantiated. With the presence of a magnetic field component along the axis of rotation, it is shown that the point of bifurcation, where the Jacobi ellipsoids branch off from the Maclaurin spheroids, is altered, and in fact shifts to higher values of eccentricity compared to the one (namely,e=0.81267) obtained when there is no magnetic field. 相似文献
8.
We focus on quantitative evaluation of several methods for the reconstruction of force-free magnetic fields in the solar corona.
We have studied two topics. The first is to carry out a comparison test of two approaches to implement the optimization method:
(1) using a boundary layer with a weighting function and (2) involving an optimization algorithm for unknown boundary field
vector values. The second approach is shown to provide a better approximation to a desired true solution that is finite in
an unlimited semispace. The approximation obtained by the second approach is reasonably close to the true solution up to the
boundaries of the reconstruction region. Among the applications of the optimization method to real data, we demonstrate its
ability to obtain accurate enough energy estimates and find that the pre- to post-flare energy difference is sufficient in
powering the flare. 相似文献
9.
Solar force-free magnetic fields on and above the photosphere 总被引：1，自引：0，他引：1
If the problem of a magnetic field being force-free with = constant ( 0) is solved by some previously published methods, then the field obtained in the whole exterior of the Sun cannot have a finite energy content and the solution cannot be determined uniquely from only one magnetic field component given at the photosphere. A magnetic field in the volume between two parallel planes has been investigated by us (Chen and Wang, 1986).Based on observational data we present in this paper a suitable physical model for a half-space and adopted an integral transform established by us (Chen, 1980, 1983) to solve this problem. We then obtain a unique analytical solution of the problem from only one magnetic field component (longitudinal field observed) given at the photosphere. Not only the uniqueness of the solution has been proved but also the finiteness of magnetic energy content in the half-space considered has been verified. We have demonstrated that there is no singular point in the solution. It enables us to describe analytically the configurations of magnetic fields on and above the photosphere. 相似文献
10.
Force-free magnetic fields can be computed by making use of a new numerical technique, in which the fields are represented
by a boundary integral equation based on a specific Green's function. Vector magnetic fields observed on the photospheric
surface can be taken as the boundary conditions of this equation. In this numerical computation, the following two points
are emphasized: (1) A new method for data reduction is proposed, for removing uncertainties in boundary data and determining
the parameter in this Green's function, which is important for solving the boundary integral equation. In this method, the
transverse components of the observed boundary field are calibrated with a linear force-free field model without changing
their azimuth. (2) The computed 3-D fields satisfy the divergence-free and force-free conditions with high precision. The
alignment of these field lines is mostly in agreement with structures in Hα and Yohkoh soft X-ray images. Since the boundary data are calibrated with a linear force-free field model, the computed 3-D magnetic
field can be regarded as a quasi-linear force-free field approximation. The reconstruction of 3-D magnetic field in active
region NOAA 7321 was taken as an example to quantitatively exhibit the capability of our new numerical technique. 相似文献
11.
On the basis of observations (Zirin and Tanaka, 1973) inferring the presence of shear in magnetic fields, the amount of extractable energy stored in a class of force-free magnetic fields is evaluated for the flares of August 1972, using the formulations developed by Nakagawa and Raadu (1972). It is shown that the evaluated energy storage could be built up by the proper motions of sunspots in the active region McMath 11976 during July 31 and August 7. Then for the flare of August 7, a detailed analysis is made of the manner of energy release in the post maximum phases deduced from the configuration of flare loops. It is shown that the observed flare loops could be represented closely by the force-free magnetic fields and that the evaluated rate of energy release is consistent with observed rate given by the soft X-ray emission. The results of analysis suggest that the flare of August 1972 could be identified with the relaxation of an energetic force-free magnetic field towards lower energy states. The limitations and possible future extension of this type of analysis are discussed.Visiting scientist from the Tokyo Astronomical Observatory, Mitaka, Tokyo, Japan.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献
12.
Global magnetic fields of flare stars evolve very fast—at times of tens–hundreds of days. In our opinion, this is due to mutual addition of local magnetic fields generated by the differential rotation of these objects.With the example of two flare stars,OT Ser and YZCMi, we consider possiblemechanisms of generation and disspation of local and global magnetic fields and the mechanism of “magnetic deceleration” of these stars according to the scheme “differential rotation–generation of local magnetic fields–fluorescence of energy accumulated by local magnetic fields during flares.” We also estimated the rotation energy and global magnetic field for OT Ser and YZCMi. It is shown that even strong dissipation of the accumulated local magnetic energy in the flare on February 9, 2008 (UT 20:22:00) in YZCMi has not had any impact on the global magnetic field. 相似文献
13.
Jiangtao Su Yu Liu Jihong Liu Xinjie Mao Hongqi Zhang Hui Li Xiaofan Wang Wenbin Xie 《Solar physics》2008,252(1):55-71
Zhao and Kosovichev (Astrophys. J.
591, 446, 2003) found two opposite sub-photospheric vortical flows in the depth range of 0 – 12 Mm around a fast rotating sunspot. So far
there is no theoretical model explaining such flow motions. In this paper, we try to explain this phenomenon from the point
of view of magnetic flux tubes interacting with large-scale vortical motions of plasma. In the deeper zone under the photosphere,
the magnetic force may be less than the nonmagnetic force of plasma. The vortical flow located there twists the flux tube
and magnetic free energy is built up in the tube. In the shallower zone under the photosphere, the magnetic force may be greater
than the nonmagnetic force. Thus, part of the stored magnetic free energy is released to drive the plasma to rotate in two
opposite directions, e.g., in the depth ranges of 0 – 3(5) and 9 – 12 Mm. In addition, we also define a vector of nonpotential magnetic stress τ, which can be related to flare occurrence. It is calculated for the active region NOAA 10930 on 11 December 2006. We find
that: i) the integral of its line-of-sight (LOS) stress successively increases around the magnetic neutral line (MNL) prior to and
during the flare and decreases to a minimum after the flare; ii) the integral of its transverse stress exceeds the integral of its LOS component by one order of magnitude over the whole
field of view; iii) the transverse stress first points toward the MNL, then along it, and finally it points away from it. We need other data
to verify whether or not the magnetic energy is transported in the horizontal direction to the neutral line, and then partly
changes into the energy in LOS direction before and during the flare. 相似文献
14.
J. H. Piddington 《Astrophysics and Space Science》1975,35(2):269-283
The traditional model of solar magnetic fields is based on convection which dominates generally weak, diffuse fields and so tends to create increasingly tangled fields. Surplus fields must be eliminated by merging of opposite polarities; for example a solar dynamo of period≈10 yr requires fields to be reduced to a scale of<100 km or diffusivity to be increased by a factor of≈107 over molecular diffusivity. It is now shown that the true requirements of any diffuse-field theory are far more stringent, and that surplus fields must be eliminated within a single eddy period of 1 day (10 min) for the supergranules (granules). The reason is that during that period fresh fields are created with flux and energy comparable with those of the old fields. The numerical models of Weiss and Moss are used to confirm this result which is fatal to all diffuse-field theories. The basic error in these theories is found in the assumption that because heat and other passive properties of a fluid diffuse much faster in the presence of turbulence, passive magnetic fields should do likewise. The error is that the heat content of an eddy is not increased by the motion while the magnetic flux and energy are increased rapidly. It is shown that the observed concentrations of surface fields into strengths of?100 G cannot be accounted for by observed surface motions. Nor are they accounted for by the numerical models of turbulence of Weiss or Moss whatever values of the magnetic Reynolds number are assumed. A detailed comparison is made between both small-scale and large-scale surface magnetic features and the predictions of the diffuse-field theory. The differences appear irreconcilable and the features only explicable in terms of the twisted flux-rope model. 相似文献
15.
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
16.
The energetical aspect of solar phenomena of different spatial and time scales has been studied with special attention to global magnetic fields. Cyclic regularities in the heliosphere are determined by energetics of global magnetic fields. The energy variation of global fields consists of a number of maxima and minima coinciding with reference points of the sunspot cycle. The correlations of a number of well-known indices in the heliosphere with Wolf numbers and with indices of energetics of the global magnetic field have been investigated. The results can be used to identify more exactly the reference points of the cycle. 相似文献
17.
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
18.
The stability of force-free magnetic fields with cylindrical symmetry in the context of solar flares
Ulrich Anzer 《Solar physics》1968,3(2):298-315
The problem of the accumulation and storage of the energy released in solar flares is discussed; it is proposed that convective energy of the photosphere is transformed into magnetic energy of the chromosphere and corona. The consequences of a large ratio of magnetic pressure to gas pressure are investigated. In this case the field must be approximately force-free. The only suitable force-free fields which allow an analytical treatment are those of cylindrical symmetry. The stability of these fields is studied with the energy principle. It is shown that they are always unstable due to kink type instabilities. The shape of the unstable perturbations is described in detail and an upper limit for their amplitude is estimated. The consequences for the proposed mechanism of energy storage are briefly discussed. 相似文献
19.
J. Büchner 《Astronomische Nachrichten》1986,307(3):191-199
Charged particle motion is studied in magnetic fields with an inversion of field direction and a strong curvature in the reversal region, that means field structures which are expected to play a crucial role in energetics and dynamics of space plasma. Investigations are performed in a typical field model. Due to its symmetry and stationarity two of the integrals of motion of the resulting Hamiltonian immediately arise. The question is analyzed whether the system is integrable (this means regular solutions exist) and of what kind the third integral is. Two different third integrals are found, which are valid in different parts of the phase space. Their validity is estimated analytically for particles, crossing the neutral plane (z = 0) -- in addition the action integral Iz previously unusual in plasma applications is verified numerically. Further numerical research establishes that there are no more third integrals -- all remaining parts of the phase space are filled with chaotic solutions. Because in strongly curved field reversals the conservation of the magnetic moment as an integral of motion is shown to be restricted to very small energies or very large pitch angles, the unusual Iz-integral will be an important tool for solution of plasma problems of cosmical current sheets and plasma boundaries. 相似文献
20.
G. N. Duboshin 《Celestial Mechanics and Dynamical Astronomy》1972,6(1):27-39
The existence of ten first integrals for the classical problem of the motion of a system of material points, mutually attracting according to Newtonian law, is well known.The existence of the analogous ten first integrals for the more complicated problem of the motion of a system of absolutely rigid bodies, whose elementary particles mutually attract according to the Newtonian law, was established by the author (Duboshin, 1958, 1963, 1968).In his later papers (Duboshin, 1969, 1970), the problem of the motion of a system of material points, attracting each other according to a more general law, was considered and, in particular, it was shown under what conditions the ten first integrals, analogous to the classical integrals, may exist for this problem.In the present paper, the generalized problem of translatory-rotatory motion of rigid bodies, whose elementary particles acting upon each other according to arbitrary laws of forces along the straight line joining them, is discussed.The author has shown that the first integrals for this general problem, analogous to the integrals of the problem of the translatory-rotatory motion of rigid bodies, whose elementary particles acting according to the Newtonian law, exist under certain well known conditions.That is, it has been established that if the third axiom of dynamics (action = reaction) is satisfied, then the integrals of the motion of centre of inertia and the integrals of the moment of momentum exist for this generalized problem.If the third axiom is not satisfied, then the above mentioned integrals do not exist.The third axiom is a necessary but not a sufficient condition for the existence of the tenth integral-the energy integral. The tenth integral always exists if the elementary particles of the bodies acting with a force, depend only on the mutual distances between them. In this case the force function exists for the problem and the energy integral can be expressed in a well known form.The tenth integral may exist for some more general case, without expressing the principle of conservation of energy, but permitting calculation of the kinetic energy, if the configuration of a system is given.The problem, in which the elementary particles acting according to the generalized Veber's law (Tisserand, 1896) has been cited as an example of this more general case. 相似文献