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1.
We analyse the behaviour of linear magnetohydrodynamic perturbations of a coronal arcade modelled by a half-cylinder with an azimuthal magnetic field and non-uniform radial profiles of the plasma pressure, temperature, and the field. Attention is paid to the perturbations with short longitudinal (in the direction along the arcade) wavelengths. The radial structure of the perturbations, either oscillatory or evanescent, is prescribed by the radial profiles of the equilibrium quantities. Conditions for the corrugation instability of the arcade are determined. It is established that the instability growth rate increases with decreases in the longitudinal wavelength and the radial wave number. In the unstable mode, the radial perturbations of the magnetic field are stronger than the longitudinal perturbations, creating an almost circularly corrugated rippling of the arcade in the longitudinal direction. For coronal conditions, the growth time of the instability is shorter than one minute, decreasing with an increase in the temperature. Implications of the developed theory for the dynamics of coronal active regions are discussed.  相似文献   

2.
A semianalytic method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. The assumptions made are that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law with uniform albedo. By using expressions for the components of the radiation-pressure force due to Lochry, the expressions for the perturbations of the elements were developed into series in the true anomalyv. The perturbations within a given revolution can be obtained analytically by integrating with respect tov while holding all slowly varying quantities constant. The long-range perturbations are then obtained by accumulating the net perturbations at the end of each revolution.  相似文献   

3.
We examine the spectrum of perturbations for a scalar field with an arbitrary curvature coupling parameter in the de Sitter stage of cosmological expansion when a cosmic string is present. These perturbations are caused by vacuum fluctuations in the field and serve as seed perturbations for the formation of galaxies in the postinflationary stage. A cosmic string disrupts the homogeneity of a de Sitter space, so that the spectrum of the perturbations depends on the distance from the string. This dependence is oscillatory in character with a period on the order of the perturbation wavelength.  相似文献   

4.
There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.  相似文献   

5.
The solution to the motion of a satellite in an eccentric orbit and in resonance with the second-degree sectorial harmonic of the potential field is developed. The method of solution used parallels the well known von Zeipel method of general perturbations. The solution consists of expressions for the variations of the Delaunay variables. These expressions are composed of the perturbations developed by Brouwer in 1959 for the motion of an artificial satellite plus first-order perturbations due to the second-degree sectorial harmonic (in terms of the Legendre normal elliptic integrals of the first and second kind).This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.  相似文献   

6.
A semi-analytical solution to the problem of the motion of a satellite of the moon is presented. Perturbative effects which are considered include those due to the attraction of the moon, earth, and sun, the non-sphericity of the moon's gravitational field, coupling of lower-order terms, solar radiation pressure, and physical libration. Short-period terms and intermediate-period terms, terms with the period of the moon's longitude, are produced by means of von Zeipel's method; it is proposed to obtain the secular perturbations, and those depending only on the argument of perilune, by numerical integration of the equations of motions. The short-period terms and intermediate-period terms are developed up to second order, where first order is 10–2. The secular perturbations and perturbations dependent on the argument of perilune are obtained to third order.  相似文献   

7.
A semianalytical method has been developed to calculate the radiation-pressure perturbations of a close-Earth satellite due to sunlight reflected from the Earth. It is assumed that the satellite is spherically symmetric and that the solar radiation is reflected from the Earth according to Lambert's Law. To account for the increasing reflectivity of the Earth toward the poles, its albedo is assumed to have a latitudinal dependence given bya=a 0 +a 2 sin2. The effect of the terminator on the perturbations has been neglected. The perturbations within a particular revolution are given analytically, while the long-range perturbations are obtained by accumulation.  相似文献   

8.
The growth of two-dimensional axisymmetric perturbations in the motion of a neutral shell formed in the interstellar medium when an ionization-shock front exits at the surface of a cloud is simulated numerically. The perturbations are assumed to emerge when the shock ahead of the ionization front reaches the cloud boundary. For long-wavelength perturbations, the accumulation of mass has been found to take place in radially oriented condensations in the shape of a rod pointed toward the star and widened at the opposite end as a result of instability. The shell fragmentation is accompanied by supersonic spouting of a hot plasma into a low-density medium. Flow nonstationarity is shown to affect significantly the gas density and velocity distributions both inside and in the immediate vicinity of the condensation. As one recedes from the ionization front, the density of charged particles changes only slightly, which is inconsistent with the power law of density decrease with increasing distance from the condensation center commonly used in interpreting observations.  相似文献   

9.
The gravitational instability of an incompressible, infinitely conducting plasma layer of finite thickness surrounded a non-conducting matter has been investigated taking into account the effect of the finite Larmor radius. The magnetic field is assumed to be directed parallel to the interfaces. Only the perturbations transverse to the magnetic field are considered, though both the symmetric and asymmetric nature of the perturbations are taken into account. Using the normal mode technique, dispersion relations are obtained.It is found that the finite larmor radius has, in general, a stabilizing influence on the configuration. Even when the system is thoroughly unstable, it has been shown that there exists a critical value of the wave-number, such that the motion is stabilized for wave-numbers of perturbations exceeding this critical value.  相似文献   

10.
We have performed a series of experiments examining the properties of high Mach number blast waves. Experiments were conducted on the Z-Beamlet laser at Sandia National Laboratories. We created blast waves in the laboratory by using ∼1000 J laser pulses to illuminate millimeter scale solid targets immersed in gas. Our experiments studied the validity of theories forwarded by Ryu and Vishniac (1987, 1991) and Vishniac (1983) to explain the dynamics of perturbations on astrophysical blast waves. These experiments consisted of a systematic scan of the decay rates of perturbations of known primary mode number induced on the surface of blast waves by means of a regularly spaced wire array. The amplitude of the induced perturbations relative to the radius of the blast wave was tracked and fit to a power law in time. Measurements were taken for a number of different mode numbers in a mixed gas consisting of 7.5 Torr xenon and 2.5 Torr nitrogen and the results are compared to theoretical predictions. It is found that two of the three mode numbers imply one polytropic index while the third case, which is the most complicated for several reasons, implies a higher polytropic index.  相似文献   

11.
The motion of a lunar satellite   总被引：2，自引：0，他引：2  
Presented in this theory is a semianalytical solution for the problem of the motion of a satellite in orbit around the moon. The principal perturbations on such a body are due to the nonspherical gravity field of the moon, the attraction of the earth, and, to a lesser degree, the attraction of the sun. The major part of the problem is solved by means of the celebrated von Zeipel Method, first successfully applied to the motion of an artificial earth satellite by Brouwer in 1959. After eliminating from the Hamiltonian all terms with the period of the satellite and those with the period of the moon, it is suggested to solve the remaining problem with the aid of numerical integration of the modified equations of motion.This theory was written in 1964 and presented as a dissertation to Yale University in 1965. Since then a great deal has been learned about the gravity field of the moon. It seems that quite a number of recently determined gravity coefficients would qualify as small quantities of order two. Hence, according to the truncation criteria employed, they should be considered in the present theory. However, the author has not endeavored to update the work accordingly. The final results, therefore, are incomplete in the lunar gravitational perturbations. Nevertheless, the theory does give the largest such variations and it does present the methods by which perturbations may be derived for any gravity terms not actually developed.  相似文献   

12.
An improved linear stability theory of small-amplitude oscillations of a self-gravitating, infinitesimally thin gaseous disk of spiral galaxies has been developed by Bertin, Lau, Lin, Mark, Morozov, Polyachenko, and others in the approximation of moderately tightly wound gravity perturbations. In this regime, the generalized Lin–Shu type dispersion relation was also found by including higher order terms in the small parameter 1/kr for wavenumber k and radius r. It was shown that in the differentially rotating disks for nonaxisymmetric (spiral)perturbations Toomre's modified critical Q-parameter is larger than the standard one: the fact that the spiral perturbations in the nonuniformly rotating system are more unstable than the axisymmetric ones is taken into account in this modified local stability criterion. We use hydrodynamical simulations to test the validity of the modified local criterion. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

13.
《Planetary and Space Science》1999,47(3-4):545-555
We consider the inductive interaction between a conducting body and a magnetizedincompressible plasma in relative uniform motion, which has application to the Io–Jupitersystem, for example. An incompressible plasma only supports one mode of propagation, namelythe Alfvén mode. In the case of free oscillations, this mode propagates the perturbations in themagnetic field and in the plasma velocity unattenuated along the direction of the backgroundfield, while the plasma pressure balances the magnetic pressure. The situation changes in thepresence of source currents and in a flowing plasma. In particular, the parallel plasma vorticityand parallel plasma current are propagated unattenuated along the familiar Alfvéncharacteristics, while the field and velocity perturbations suffer Laplacian decay in the near field.We study these perturbations in the frame of the body and compare them to the case of no sourceterms.  相似文献   

14.
We consider the interaction of an ionization-shock front with isothermal waves in an H I region. Based on a two-front model in the linear approximation, we have detected a significant (approximately by an order of magnitude) periodic amplification of perturbations as they penetrate from the interstellar medium into an H II region. Numerical simulations have revealed that even when the shock-and ionization-front velocities differ and the relative density perturbations in the interstellar medium are ～10?1, the variations in gas parameters near the ionization front are comparable to those observed at the boundaries of H II regions.  相似文献   

15.
On the surface of a degerate star, a slow nuclear combustion process with a wake of escaping matter can exist. The evolution of this process has been studied by solving the nonadiabatic, time-dependent hydrodynamic equations. It has been found that this flow is almost stationary and is stable against small spherical symmetric perturbations.  相似文献   

16.
Assigning to the equivalent gravitational parameter of a two-body dynamic system, a periodic change of a small amplitude B and arbitrary frequency and phase, the behaviour of an elliptic-type orbit is studied. The first order (in B) perturbations of the orbital elements are determined by using Delaunay's canonical variables. According to the value of the ratio between oscillation frequency and dynamic frequency, three cases (non-resonant (NR), quasi-resonant (QR), and resonant (R) ones) are pointed out. The solution of motion equations shows that only in the QR and R cases there are elements (argument of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order of pericentre and mean anomaly) affected by secular perturbations. The solutions are valid over prediction times of order B−1 in the NR case and B−1/2 in the QR and R cases.  相似文献   

17.
Numerical simulations of the magnetic reconnection process in a current sheet show that, in some cases, MHD shocks appear to be attached to edges of the sheet. The appearance of the shocks may be considered to be a result of splitting of the sheet. In the present paper we suppose that this splitting takes place in consequence of non-evolutionarity of the reconnecting current sheet as a discontinuity. The problem of time evolution of small perturbations does not have a unique solution for a non-evolutionary discontinuity, and it splits into other (evolutionary) discontinuities. Such an approach allows us to determine conditions under which the splitting of the-sheet occurs. The main difficulty of this approach is that a current sheet is not reduced to a classified 1D discontinuity, because inhomogeneity of flow velocity inside the sheet is two-dimensional. To formulate the non-evolutionarity problem, we solve the linear MHD equations inside and outside the sheet and deduce linearized 1D boundary conditions at its surface. We show that for large enough conductivity, small perturbations exist which interact with the sheet as with a discontinuity. Then we obtain a non-evolutionarity criterion, with respect to these perturbations, in the form of a restriction on the flow velocity across the surface of the sheet.  相似文献   

18.
《New Astronomy》2002,7(6):283-292
A local perturbation analysis is performed on a realistic background accretion flow in a global magnetic field. The adopted background model is an analytic solution to the resistive MHD equations and describes magnetically-controlled advection-dominated accretion flows (ADAFs) with an accuracy to the first order in the resistive corrections. The results show that there are three independent wave modes, which may be called the Rayleigh, Balbus–Hawley and resistive modes. Within our resistive-MHD corrections to the ideal-MHD limit, a Balbus–Hawley-like criterion for the instability of axisymmetric perturbations appears as a consequence of the competition between damping due to magnetic diffusion and excitation due to shear flow. As for non-axisymmetric perturbations, the former two modes are likely to be unstable in the presence of shears because the magnetic diffusion acts as a stabilizer only to axisymmetric perturbations within our approximation.  相似文献   

19.
The orbital accelerations of certain balloon satellites exhibit marked oscillations caused by solar radiation impinging on the surface of the satellites, which, once spherical, have assumed a spheroidal shape producing a component of force at right-angles to the Sun-satellite direction. Given the characteristics and orientation of the satellite, the equations of force are determined by the formulae of Lucas. Otherwise the phase-angle and magnitude of the right-angle force are determined by trial and error, or best-fit techniques. Using a variation of the approach developed by Aksnes, a semi-analytical algorithm is presented for evaluating the perturbations of the Keplerian elements by direct solar radiation pressure on a spheroidal satellite. The perturbations are obtained by summing over the sunlit part of each orbit and allow for a linear variation in the phase-angle. The algorithm is used to determine the orbital accelerations of 1963-30D due to direct solar radiation pressure, and these results are compared to the observed values over two separate periods of the satellite's lifetime.  相似文献   

20.
T.A. Heppenheimer 《Icarus》1974,22(4):436-447
A theory is presented for determining regions where planets may form in binary star systems. Planet formation by accretion is assumed possible if mean planetesimal collision velocities do not exceed a critical value. Collision velocities are increased by perturbations due to the companion star, treated by secular perturbation theory. Collision velocities are damped by aerodynamic drag within the solar nebula, taken as the linear case of Cameron and Pine.A general feature of planetary systems in binary stars is the existence of two zones. The inner zone has enough damping to permit unimpeded growth by accretion; in the outer zone, growth proceeds to a limited diameter, beyond which damping is insufficient. It is shown that the asteroids could not have failed to coalesce due to Jupiter perturbations in the primitive solar nebula. Binary star systems with semimajor axis < 30AU are not likely to have planets; these include Alpha Centauri and 70 Ophiuchi. Systems possibly possessing planets include Eta Cassiopeiae, 40 Eridani, and Σ 2398. Epsilon Eridani is a marginal case.  相似文献   

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