共查询到20条相似文献，搜索用时 15 毫秒
1.
D. Schmitt 《Astrophysics and Space Science》1995,225(2):315-325
Following the work of Bernsteinet al. (1958), Frieman and Rotenberg (1960) and Unno (1968) a formalism is developed which allows to examine the adiabatic stability of a perfectly conducting, rotating and self-gravitating plasma in non-steady equilibrium. Using this method the stability of a plasma in a dynamical phase of its evolution can be predicted. Global stability investigations are carried out which are based on a variation of the total energy of the system and, in general, lead to sufficient conditions for stability. The formalism is applied to the stability of a horizontal magnetic field in a medium stratified by a gravitational field. 相似文献
2.
The variational principle for stars with a phase transition has been investigated. The term outside the integral in the expression for the second variation of the total energy of a star is shown to be obtained by passage to the limit from the integration over the region of mixed states in the star. The form of the trial functions ensuring this passage has been found. All of the results have been generalized to the case where general relativity is applicable. The known criteria for the dynamical stability of a star when a new phase appears at its center are shown to follow automatically from the variational principle. Numerical calculations of hydrostatically equilibrium models for hybrid stars with a phase transition have been performed. The form of the trial functions for the second variation of the total energy of a star that describes almost exactly the stability boundaries of such stellar models is proposed. 相似文献
3.
G. M. Webb 《Solar physics》1986,106(2):287-313
The equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically. For equilibria with one ignorable spatial coordinate, the equations reduce to a single nonlinear elliptic equation for the magnetic potential A. Similarity solutions of the elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field. The solutions are obtained from a consideration of the invariance group of the elliptic equation. The importance of symmetries of the elliptic equation also appears in the determination of conservation laws. It turns out that the elliptic equation can be written as a variational principle, and the symmetries of the variational functional lead (via Noether's theorem) to conservation laws for the equation. As an example of the application of the similarity solutions, we construct a model magnetostatic atmosphere in which the current density J is proportional to the cube of the magnetic potential, and falls off exponentially with distance vertical to the base, with an e-folding distance equal to the gravitational scale height. The solutions show the interplay between the gravitational force, the J × B force (B, magnetic field induction) and the gas pressure gradient. 相似文献
4.
The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers. 相似文献
5.
Giulio Calamai 《Astrophysics and Space Science》1970,6(2):240-257
The second variation of the mass-energy (by constant baryon number) is analysed to inquire into the stability of the equilibrium for a spherical mass under the action of its own gravitation. The equations of general relativity are used. For zero density at the surface, the sphere is stable if (and only if) a solution of a second order equation (Jacobi equation) has only one zero in the interior (at center) of the sphere. The results obtained in this way coincide of course with those obtained by means of the Chandrasekhar-Misner-Zapolsky variational principle, but the solution of the Jacobi equation is more simple and straightforward. In particular, the stability of the several modes are analysed without making any choice of a trial function for the Lagrangian displacement.The method is applied to the GrattonR-polytropic model of supermassive stars.Work done in the Laboratorio Astrofisico, Frascati-Roma, Italy. 相似文献
6.
In this paper we show how the equations of motion for the smoothed particle hydrodynamics (SPH) method may be derived from a variational principle for both non-relativistic and relativistic motion when there is no dissipation. Because the SPH density is a function of the coordinates the derivation of the equations of motion through variational principles is simpler than in the continuum case where the density is defined through the continuity equation. In particular, the derivation of the general relativistic equations is more direct and simpler than that of Fock. The symmetry properties of the Lagrangian lead immediately to the familiar additive conservation laws of linear and angular momentum and energy. In addition, we show that there is an approximately conserved quantity which, in the continuum limit, is the circulation. 相似文献
7.
The oscillatory modes of a magnetically twisted compressible flux tube embedded in a compressible magnetic environment are investigated in cylindrical geometry. Solutions to the governing equations to linear wave perturbations are derived in terms of Whittaker’s functions. A general dispersion equation is obtained in terms of Kummer’s functions for the approximation of weak and uniform internal twist, which is a good initial working model for flux tubes in solar applications. The sausage, kink and fluting modes are examined by means of the derived exact dispersion equation. The solutions of this general dispersion equation are found numerically under plasma conditions representative of the solar photosphere and corona. Solutions for the phase speed of the allowed eigenmodes are obtained for a range of wavenumbers and varying magnetic twist. Our results generalise previous classical and widely applied studies of MHD waves and oscillations in magnetic loops without a magnetic twist. Potential applications to solar magneto-seismology are discussed. 相似文献
8.
The effect of Hall currents and collision with neutrals on the instability of a horizontal layer of a self-gravitating partially-ionized plasma of varying density have been studied. It is assumed that the plasma is permeated by a variable horizontal magnetic field stratified vertically. A variational principle is shown to characterize the problem. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite plasma in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that the collisions with neutrals have a stabilizing influence while Hall currents have a destabilizing influence. 相似文献
9.
J. Demaret 《Astrophysics and Space Science》1976,45(1):31-45
We discuss, in general, the problem of deriving a vibrational stability coefficient of stars in thermal imbalance on the basis of an energy principle.The damped harmonic oscillator with variable spring constant provides a typical illustration of the problem. In fact, for systems with variable parameters (as evolving stars), the vibrational stability coefficients, defined respectively in terms of the behaviour of the small displacement and of the total pulsation energy, are basically different. Davey and Cox's so-called modified energy method, proposed in order to recover the small displacement stability coefficient, is also shown to be unsatisfactory.The use of results obtained in the first two papers by asymptotic methods yields a simple compact general expression for the vibrational stability coefficient relative to the pulsation energy of arbitrary evolving stars. This allows the easy recovery of results obtained by more complicated approaches due to Kato and Unno, Simon and Sastri and Axel and Perkins, valid only in particular cases. 相似文献
10.
The effect of finite conductivity on the Rayleigh-Taylor instability of an incompressible, viscous rotating fluid through a porous medium has been studied in the presence of a two-dimensional horizontal magnetic field. It has been shown that the solution is characterized by a variational principle. By making use of the existence of the variational principle, proper solutions have been obtained for a semi-infinite fluid in which density has a one-dimensional (exponential) vertical stratification. The dispersion relation has been derived and solved numerically. It is found that finite resistivity and porosity have a destabilizing effect on the Rayleigh-Taylor instability while rotation has a stabilizing effect. 相似文献
11.
P. D. Ariel 《Astrophysics and Space Science》1974,29(2):319-329
The hydromagnetic stability of an electrically conducting compressible plasma having variable density in the vertical direction
has been investigated taking into account the effects of Hallcurrents. The solution is shown to be characterized by a variational
principle. Based on the existence of variational principle, the dispersion relation has been obtained for the case of a plasma
having exponentially varying density with special reference to stellar atmosphere. It is found that both compressibility of
the medium and Hall-currents destabilize the configuration for the disturbances, for which it was stable otherwise. The Hall-currents
even suppress the mode of maximum instability for large magnitudes. 相似文献
12.
J. Staude 《Solar physics》1969,8(2):264-270
The discrepancies between theoretical and experimental calibration curves for solar magnetographs (Severny, 1967) may be explained by horizontal inhomogeneities of the observed but not resolved magnetic field region. Using the Unno solution of the equations of transfer simple two-stream models have been constructed. For the more complicated case of a depth dependence of the magnetic field vector it is shown assuming pure absorption and permitting arbitrary variations of the magnetic field vector and the atmosphere model with depth that a solution of the equations of transfer may be found by iteration. 相似文献
13.
P. K. Bhatia 《Astrophysics and Space Science》1974,26(2):319-325
A study has been made of the problem of the Rayleigh-Taylor instability of a hydromagnetic plasma of varying density to investigate the influence of the simultaneous presence of the effects of compressibility and viscosity. The solution is shown to be characterized by a variational principle. Based on the variational principle proper solutions have been obtained for a semi-infinite plasma, in which the density has a one-dimensional gradient along the direction of a uniform vertical magnetic field, confined between two planes. Both the viscosity and magnetic field are found to have a stabilizing influence. The effect of compressibility is found to be destabilizing. 相似文献
14.
We discuss the question whether the way of finding the conservation laws based on variational formalism is applicable to the
multilevel problems of radiative transfer in a homogeneous atmosphere. For expository reasons, the simplest one-dimensional
model case is considered. For the special three-level problem treated in the paper the Lagrangian approach allows one to derive
not only the H- and K-integrals, but also the nonlinear integral which is an analog of the Q-integrals previously obtained
for the classical transfer problems. It is shown that, in general, the constraints imposed by the variational principle on
the symmetry properties of the transfer equations are too stringent to be satisfied.
Translated from Astrofizika, Vol. 42, No. 2, pp. 235–252, April–June, 1999. 相似文献
15.
Twisted magnetic flux tubes are of considerable interest because of their natural occurrence from the Sun’s interior, throughout
the solar atmosphere and interplanetary space up to a wide range of applicabilities to astrophysical plasmas. The aim of the
present work is to obtain analytically a dispersion equation of linear wave propagation in twisted incompressible cylindrical
magnetic waveguides and find appropriate solutions for surface, body and pseudobody sausage modes (i.e. m = 0) of a twisted magnetic flux tube embedded in an incompressible but also magnetically twisted plasma. Asymptotic solutions
are derived in long- and short-wavelength approximations. General solutions of the dispersion equation for intermediate wavelengths
are obtained numerically. We found, that in case of a constant, but non-zero azimuthal component of the equilibrium magnetic
field outside the flux tube the index ν of Bessel functions in the dispersion relation is not integer any more in general.
This gives rise to a rich mode-structure of degenerated magneto-acoustic waves in solar flux tubes. In a particular case of
a uniform magnetic twist the total pressure is found to be constant across the boundary of the flux tube. Finally, the effect
of magnetic twist on oscillation periods is estimated under solar atmospheric conditions. It was found that a magnetic twist
will increase, in general, the periods of waves approximately by a few percent when compared to their untwisted counterparts. 相似文献
16.
Daniel Atnafu Chekole Gebretsadikan Woldmhret Bahta 《Journal of Astrophysics and Astronomy》2018,39(6):67
Magnetohydrodynamics waves and instabilities in rotating, self-gravitating, anisotropic and collision-less plasma were investigated. The general dispersion relation was obtained using standard mode analysis by constructing the linearized set of equations. The wave mode solutions and stability properties of the dispersion relations are discussed in the propagations transverse and parallel to the magnetic field. These special cases are discussed considering the axis of rotation to be in transverse and along the magnetic field. In the case of propagation transverse to the magnetic field with axis of rotation parallel to the magnetic field, we derived the dispersion relation modified by rotation and self-gravitation. In the case of propagation parallel to the magnetic field with axis of rotation perpendicular to the magnetic field, we obtained two separate modes affected by rotation and self-gravitation. This indicates that the Slow mode and fire hose instability are not affected by rotation. Numerical analysis was performed for oblique propagation to show the effect of rotation and self-gravitation. It is found that rotation has an effect of reducing the value of the phase speeds on the fast and Alfven wave modes, but self-gravitation affect only on the Slow modes, thereby reducing the phase speed compare to the ideal magneto hydrodynamic (MHD) case. 相似文献
17.
Unrestricted second-order tensor virial equations for linear oscillations of magnetic configurations
M. Goossens 《Astrophysics and Space Science》1979,60(2):401-421
This paper deals with the second-order tensor virial equations for the linear oscillations of a gaseous mass in the presence of a magnetic field. It is shown that the commonly used linearized versions of the tensor virial equations are restricted integral equations that incorporate the linearized equation of motion but not the boundary condition. These restricted equations only allow trial functions that fulfil the boundary condition and are of limited practical value.The unrestricted variational principle for the linear oscillations of a magnetic configuration is used to derive a more general formulation of the second-order tensor virial equations so that the linear trial function i =X
ij
x
j can be used to study the oscillations of a configuration with a magnetic field that extends in the exterior vacuum. The unrestricted virial equations have been applied to Ferraro's model and approximate results for the eigenfrequencies and eigenfunctions have been obtained for nine oscillation modes. 相似文献
18.
T. S. Boronenko 《Celestial Mechanics and Dynamical Astronomy》2017,127(2):139-161
In this article, we present the Lie transformation algorithm for autonomous Birkhoff systems. Here, we are referring to Hamiltonian systems that obey a symplectic structure of the general form. The Birkhoff equations are derived from the linear first-order Pfaff–Birkhoff variational principle, which is more general than the Hamilton principle. The use of 1-form in formulating the equations of motion in dynamics makes the Birkhoff method more universal and flexible. Birkhoff’s equations have a tensorial character, so their form is independent of the coordinate system used. Two examples of normalization in the restricted three-body problem are given to illustrate the application of the algorithm in perturbation theory. The efficiency of this algorithm for problems of asymptotic integration in dynamics is discussed for the case where there is a need to use non-canonical variables in phase space. 相似文献
19.
The dynamic stability of a partially ionized, compressible Hall plasma of finite electrical conductivity has been investigated when the plasma is immersed in a uniform, horizontal magnetic field. Based on the variational principle, which is shown to characterize the problem, the solution has been obtained for a semi-infinite plasma confined between two planes and having an exponential density stratification along the vertical. It is found that the effect of neutral gas friction is stabilizing while magnetic resistivity, Hall currents and compressibility all have destabilizing influence.On leave of absence from Department of Mathematics, University of Jodhpur, Jodhpur, India. 相似文献
20.
P. R. Wilson 《Astrophysics and Space Science》1974,26(2):363-369
The stability of a velocity shear in the presence of a parallel but non-uniform magnetic field is considered in general terms. Two special cases are then investigated; (i) the well known case of a plane interface at which a discontinuity in the magnetic field coincides with the velocity shear; (ii) an axially symmetric flow in which discontinuities in the magnetic and velocity fields occur at a cylindrical surface whose axis is parallel to the flow. In the first case the flow is stabilized if the rms Alfvén velocity of the magnetic field exceeds the shear velocity; a result consistent with that obtained by other writers. In the second case it is shown that the discontinuity in the magnetic field increases the stability of the system. The significance of this result for the stability of the flux ropes associated with sunspots in the solar convection zone is considered. 相似文献