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1.
The componentsj andj of the current densityj are expressed in terms of the torsion and curvature of the magnetic lines of force and a relation between and equivalent to divj=0, is pointed out.Assuming that the magnetotail neutral line is not a straight line parallel to the (solar magnetospheric)y-coordinate and that loops of closed fieldlines may be formed in the distant magnetotail, we discuss the topological features of the corresponding current system. We find that the perpendicular current is diverted into the direction ofB and that enhancements and depletions ofj along the Sun-Earth line are generated. Arguments usual in current diversion analyses imply a possibility of disintegration of the magnetotail.It is ponted out that the simply connected surfaces containing both vectors,j andB, are unlikely to exist in the magnetotail. The concept of current sheets containing the vector lines ofB is mathematically, and consequently also physically, not feasible.  相似文献   

2.
Using the flux-transport equation in the absence of sources, we study the relation between a highly peaked polar magnetic field and the poleward meridional flow that concentrates it. If the maximum flow speed m greatly exceeds the effective diffusion speed /R, then the field has a quasi-equilibrium configuration in which the poleward convection of flux via meridional flow approximately balances the equatorward spreading via supergranular diffusion. In this case, the flow speed () and the magnetic field B() are related by the steady-state approximation () (/R)B()/B() over a wide range of colatitudes from the poles to midlatitudes. In particular, a general flow profile of the form sin p cos q which peaks near the equator (q p) will correspond to a cos n magnetic field at high latitudes only if p = 1 and m = n /R. Recent measurements of n 8 and 600 km2 s–1 would then give m 7 m s–1.  相似文献   

3.
We present the use of the analytical solutions of the planets and of the Moon's motion in the determination of the quantities which relate the barycentric and the geocentric coordinate systems and of the expressions of precession-nutation. The computation of the precession and nutation quantities are built with the analytical theories of the motion of the Moon, the Sun and the planets of the Bureau des longitudes. We take into account the influence of the Moon, the Sun and all the planets on the potential of the Earth limited to C j,0 for j from 2 to 5, C 2,2, S 2,2, C 3, S 3, , for from 1 to 3 and C 4,1, S 4,1. We determine the 3 Euler angles , , and 2 calculating the components of the torque of the external forces with respect to the geocenrer in the case of the rigid Earth. The equations are solved by iterations and so are taken into account the nutations-on-the-nutations effects. We have determined the analytical variations of the angles and w fixing the equator with respect to the ecliptic J2000. We find, in w, a secular term of –26.5026 mas per century. The analytical solution of the precession-nutation has been compared to a numerical integration over the time span 1900–2050. The differences do not exceed 16 µas for and 12 µas for .  相似文献   

4.
Two spherically symmetric time-dependent Green's functions of the equation of transport for cosmic rays in the interplanetary region are derived by transform techniques. The solar wind velocity is assumed radial and of constant speedV. In the first model the radial diffusion coefficient =0 r (0 constant), and in the second solution =0= constant. The solutions are for monoenergetic, impulsive release of particles from a fixed heliocentric radius. Integration of the solutions over timet, fromt=0 tot=, gives the steady-state Green's functions obtained previously.  相似文献   

5.
A two-stage model of the propagation of 1–50 MeV solar-flare cosmic rays is presented. The first stage consists of a thin spherical shell of radius r a near the Sun which feeds particles into interplanetary space (the second stage) where they propagate along the Archimedean mean interplanetary magnetic field under the influences of anisotropic diffusion, convection, and energy changes. To calculate the time dependence at a fixed point in space, account is taken of the corotation of flux tubes past the observer.It is shown that the well-known east-west effect of the time-to-maximum cannot be obtained if the injection from the first stage is impulsive and thus a time and longitude dependent release for the second stage is essential. This is achieved by treating the first stage as a thin, spherical, diffusing shell of radius r a with diffusion coefficient s, from which particles leak into interplanetary space at a rate determined by the leakage coefficient .With this model we are able to reproduce simultaneously four principal features of solar events observed at r = 1 AU: (i) the east-west effect, i.e. the time-to-maximum as a function of flare longitude; (ii) the three phases of the anisotropy vector variation; (iii) the time-to-convective-phase as a function of flare longitude; and (iv) the longitudinal distribution of the differential intensity. Our best estimates of the parameters of the near-Sun propagation are that 0.01 hr–1 s/r a 2 0.02 hr–1 and 1/15 hr–1 1/10 hr–1. For the interplanetary propagation we estimate /V - 1.2AU with , the effective cosmic-ray diffusion coefficient and V, the solar-wind speed.  相似文献   

6.
An analysis of the effects of Hall current on hydromagnetic free-convective flow through a porous medium bounded by a vertical plate is theoretically investigated when a strong magnetic field is imposed in a direction which is perpendicular to the free stream and makes an angle to the vertical direction. The influence of Hall currents on the flow is studied for various values of .Nomenclature c p specific heat at constant pressure - e electrical charge - E Eckert number - E electrical field intensity - g acceleration due to gravity - G Grashof number - H 0 applied magnetic field - H magnetic field intensity - (j x , j y , j z ) components of current densityJ - J current density - K permeability of porous medium - M magnetic parameter - m Hall parameter - n e electron number density - P Prandtl number - q velocity vector - (T, T w , T ) temperature - t time - (u, v, w) components of the velocity vectorq - U 0 uniform velocity - v 0 suction velocity - (x, y, z) Cartesian coordinates Greek Symbols angle - coefficient of volume expansion - e cyclotron frequency - frequency - dimensionless temperature - thermal conductivity - coefficient of viscosity - magnetic permeability - kinematic viscosity - mass density of fluid - e charge density - electrical conductivity - e electron collision time  相似文献   

7.
All results, achieved up to now, show the long term stability of our planetary system, although, especially the inner solar system is chaotic, due to some specific secular resonances. We study, by means of numerical integrations, the dynamical evolution of the planetary system where we concentrate on the stability of motion of the terrestrial planets Venus, Earth and Mars. Our model consists of a simplified planetary system with the inner planets Venus, Earth and Mars as well as Jupiter and Saturn. A mass factor was introduced to uniformly change the masses of the terrestrial planets; Jupiter and Saturn were involved in the system with their actual masses. We integrated the equations of motion with a Lie-integration method for a time interval of 107 years. It turned out that when 220 < < 245 and > 250 the system became unstable due to the strong interactions between the planets. We discuss the model planetary systems for small mass-factors 0.5 10 and large ones 160 270 with the aid of several different numerical tools. These results can be applied to recently discovered exoplanetary systems, which configuration is comparable to our own.  相似文献   

8.
Analytic structure of high-density steady isothermal spheres is discussed using the TOV equation of hydrostatic equilibrium which satisfies an equation of state of the kind:P = K g , = g c 2.Approximate analytical solutions to the Tolman-Oppenheimer-Volkoff (TOV) equations of hydrostatic equilibrium in (, ), (,U) and (u, v) phase planes in concise and simple form useful for short computer programmes or on small calculator, have been given. In Figures 1, 2, and 3, respectively, we display the qualitative behaviours of the ratio of gas density g to the central density gc , g / gc ; pressureP to the gc ,P/ gc ; and the metric componente –, for three representative general relativistic (GR) isothermal configurations =0.1, 0.2, and 0.3. Figure 4 shows the solution curve (, ) for =0.1, 0.2, and 0.3 (=0 represents the classical (Newtonian) curve). Numerical values of physical quantitiesv (=4r 2 P *(r)), in steps ofu (=M(r)/r)=0.03, and the mass functionU, in steps of =0.2 (dimensionless radial distance), are given, respectively, in Tables I and II. Other interesting features of the configurations, such as ratio of gravitational radius 2GM/c 2 to the coordinate radiusR, mass distributionM(r)/M, pressure (or density) distributionP/P c , binding energy (B.E.), etc., have also been incorporated in the text. It has further been shown that velocity of sound inside the configurations is always less than the velocity of light.Part of the work done at Azerbaijan State University, Baku, U.S.S.R., and Mosul University, Mosul, Iraq, 1985-1986  相似文献   

9.
Multiple expansion of the tidal potential   总被引：1，自引：0，他引：1  
The Earth tidal deformation causes an additional gravitational potential. Its effect on the Moon orbital motion has been studied by several authors.In this contribution, we develop this additional potential without specifying the inertial frame chosen.For this purpose, we use the properties of the representation of rotation groups in 3 dimensions space. We finally obtain the interaction potential between the distorted Earth and the Moon which is a necessary preliminary to the study of the evolution of the Earth-Moon system.Nomenclature T.R.O Tide raising object - (, , ) Spherical coordinates of the T.R.O. - (J, E ) Earth spin axis orientation. E is the longitude of the ascending node of Earth's equator on thexy-plane - (a ,I ,e , , ,M ) Elliptics elements of the T.R.O  相似文献   

10.
We present here a very simple model that could explain the relatively high eccentricities and inclinations observed in the minor planet belt. This model is based upon the sweeping of the secular resonances 6 and 16 through the belt due to the gravitational effect of the dissipation of a primitive solar nebula. The sweeping of the 16 secular resonance (responsible for the high inclinations) is very sensitive to the density profile of the nebula. For the model to work we need a density profile proportional to –k with between 1.0 and 1.5.  相似文献   

11.
In a previous publication (1977) the author has constructed a family () of long-periodic orbits in the Trojan case of the restricted problems of three bodies. Here he constructs the domain of the analytical solution of the problem of the motion, excluding the vicinity of thecritical divisor which vanishes at the exact commensurability of the natural frequencies 1 and 2. In terms of thecritical masses mj(2), or the associatedcritical energies j 2 (m), is the intersection of the intervals ofshallow resonance, of the form. Inasmuch as the intervals |2– j 2 |<j ofdeep resonance aredisjoint, it follows that (1) the disjointed family () embraces the tadpole branch, 021, lying in: and (2) despite the clustering of j 2 (m) atj=, the family () includes, for 2=1, an asymptoticseparatrix that terminates the branch in the vicinity of the Lagrangian pointL 3.In a similar manner, the family () can be extended to the horseshoe branch 1<2 2 2 .  相似文献   

12.
Infinite series expansions are obtained for the doubly averaged effects of the Moon and Sun on a high altitude Earth satellite, and the results used to interpret numerically integrated examples. New in this paper are: (1) both sublunar and translunar satellites are considered; (2) analytic expansions include all powers in the satellite and perturbing body semi-major axes; (3) the fact that retrograde orbits have more benign eccentricity behavior than direct orbits should be exploited for high altitude satellite systems; and (4) near circular orbits can be maintained with small expenditures of fuel in the face of an exponential driving force one forI ab, whereI b=180°–I a andI a is somewhat less than 39.2° for sublunar orbits and somewhat greater than 39.2° for translunar orbits.Nomenclature a semi-major axis - A lk coefficient defined in Equation (11) - B lk coefficient defined in Equation (24) - C km coefficient defined in Equation (25) - D, E, F coefficients in Equations (38), (39) - e eccentricity - H k expression defined in Equation (34) - expression defined in Equation (35) - I inclination of satellite orbit on lunar (or solar) ring plane - J 2 coefficient of second harmonic of Earth's gravitational potential (1082.637×10–6 R E 2 ) - K k, Lk, Mk expressions in Section 4 - expressions in Section 4 - p=a(1–e 2) semi-latus rectum - P l Legendre polynomial of degreel - q argument of Legendre polynomial - radial distance of satellite - R E Earth equatorial radius (6378.16 km) - R, S, W perturbing accelerations in the radial, tangential and orbit normal directions - syn synchronous orbit radius (42 164.2 km=6.6107R E) - t time - T satellite orbital period - T orbital period of perturbing body (Moon) - T e period of long periodic oscillations ine for |I|<I a - T s synodic period - U gravitational potential of lunar (or solar) ring - x, y, z Cartesian coordinates of a satellite with (x, y) being the ring plane - coefficient defined in Equation (20) - average change in orbital element over one orbit (=a, e, I, , ) - 1,23 unit vectors in thex, y, z coordinate directions - r , s , w unit vectors in the radial, tangential and orbit normal directions - =+ angle along the orbital plane from the ascending node on the ring plane to the true position of the satellite - angle around the ring - gravitational constant times mass of Earth (3.986 013×105 km s–2) - gravitational constant times mass of Moon (or Sun) - m gravitational constant times mass of Moon (/81.301) - s gravitational constant time mass of Sun (332 946 ) - ratio of the circumference of a circle to its diameter - radius of lunar (or solar) ring - m radius of lunar ring (60.2665R E) - s radius of solar ring (23455R E) - true anomaly - argument of perigee - 0 initial value of - i critical value of in quadranti(i=1, 2, 3, 4) - longitude of ascending node on ring plane This work was sponsored by the Department of the Air Force.  相似文献   

13.
Ai-Hua  Zhou  Guang-Li  Huang  Xin-Dong  Wang 《Solar physics》1999,189(2):345-356
Two sets of accurate approximate expressions for the gyrosynchrotron radiation in the transverse propagation case are presented for the first time. They contain emissivity –/BNand absorptivity – B/Nfor e-mode, effective temperature T effand frequency of peak brightness p. The expressions are designed for the range 2 to 7 of electron energy spectral index and for the ranges from 2 to 10 and 10 to 100 of harmonic numbers s(=/B). Their statistical error is, respectively, ±18% and ±29% for –/BNand – B/Nfor 10/B100, ±128% and and ±170% for 2/B10.  相似文献   

14.
R. Grant Athay 《Solar physics》1988,116(2):223-237
An attempt is made in this paper to determine the coefficient a in a power-law relationship of the form V ~T between the r.m.s. velocity fluctuation, V for raster images with 3 resolution and the temperature, T of line formation using SMM solar data. For T between 8000 and 105 K, the data suggest a best fit with 3/4 < 1. It is argued, however, that unresolved fine structure tends to reduce the observed value of V and that higher resolution data may yield different values for . Skylab data have shown that the non-thermal line broadening velocity, , is proportional to T 1/2. Also, for all temperatures less than 105 K, V . This latter result, however, is again dependent on spatial resolution and may not be true in observations made with sufficient spatial resolution. The magnitudes of both V and indicate that bulk motions play important roles in the structure of the solar atmosphere as well as in its energy and momentum balance. It is important, therefore, to identify the true nature of such motions with better accuracy than is possible with currently available data.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

15.
The velocity gradients of the contrastreaming electron beams observed in the Earth's magnetosphere can excite three types of ordinary mode instabilities, namely (i) B-resonance electron instability, (ii) ion cyclotron instability, and (iii) unmagnetized ion instability. The B-resonance electron instability occurs at small values of the shear parameter 10–4<S<10–3, whereS = [(1/e){dU o(x)}/(dx)] (U 0(x) and e being the streaming velocity of the electron beams and the electron cyclotron frequency, respectively). Near the equatorial plane of the bouncing electron beams region, this instability can generate electromagnetic waves having frequenciesf(0.045–0.2) Hz and wavelentghs (0.5–10)km, and the wave magnetic field is polarised in a radial direction. This instability can also occur in the plasma sheet region during the earthwards and tailwards plasma flows events and can generate waves, with wave magnetic field polarised along north-south direction, in the frequency rangef(0.007–0.02) Hz with (10–100)km nearR=–35R E . For 10–3<S<10–2, the ion cyclotron instability is excited and it can generate waves up to 5th harmonic or so of ion cyclotron frequency. ForS>10–2, the unmagnetized ion instability is excited which can generate electromagnetic waves having frequences from 5 to 50 Hz and typical wavelengths (0.5–6)km. The growth rates of all the three velocity shear driven instabilities are reduced in the presence of cold background plasma. The turbulence generated by these instabilities may give rise to enhanced effective electron-electron and electron-ion collisions and broaden the bouncing electron beams.  相似文献   

16.
We compare microphotometer intensity traces perpendicular to dispersion in simultaneous spectrograms of good spatial resolution traced at various 's in each of the lines. Cross correlations between the different traces show the following: (a) For each K there is a corresponding b 1at which the coefficient of correlation, r, is a maximum, usually > 0.8. (b) No such high correlations are found between H and H. (c) Comparison of traces in the continuum and at all observed 's in K, H, b1, b2 show a range of 's in each line over which r is very significantly negative, while H shows no such peculiarity.  相似文献   

17.
I. D. Palmer 《Solar physics》1973,30(1):235-242
A simple model of solar cosmic ray propagation which includes diffusion, convection, and energy loss by adiabatic deceleration is studied. A Monte Carlo technique is employed to investigate the variation of mean particle energy in the interplanetary medium after the impulsive release of mono-energetic particles at the Sun. At 1 AU typical energy losses are 43% at 20 h and 64% at 60 h after particle release for a diffusion coefficient (r)= 0r with =+1/2 and 0=1.33 × 1021 cm2 s–1. When 0 in this model is reduced by a factor of 4, the energy loss is greater by a factor of 2 at 60 h after particle release. When is increased, the energy losses are greater. Using the model parameters above, an increase in solar wind speed from 300 to 600 km s–-1 gives rise to energy losses that are greater again by factor of 2 at a time of 60 h. Results are compared with an observation by Murray et al. (1971) of a knee in the energy spectrum of solar protons. It is not considered likely that the change in the energy of the knee with time requires, in addition to adiabatic deceleration, another energy change process which acts to increase the energy of particles.Part of this work was performed while the author was at CSIRO, Division of Radiophysics, Epping, NSW, Australia; also supported in part by the U.S. Atomic Energy Commission.  相似文献   

18.
Computations of polarization and intensity of radiation from a unit stellar surface area are presented, as well as a study of the numerical characteristics of atmospheres — single-scattering albedo and the initial source function(), which define the polarization behaviour of atmospheres. The radiatively stable models of stellar atmospheres presented by Kuruczet al. (1974) and Kurucz (1979) have been used for calculations. Since the versus optical depth dependence is rather weak, it has been assumed that (=cost. With a fixed effective temperatureT eff maximum values of are characteristic of stars featuring the lowest surface gravity accelerationg. Among stars with radiatively stable atmospheres, maximum values of (=5000 Å) 0.4–0.6 are exhibited by supergiants withT eff=8000–20 000 K. The plot of () is characterized by discontinuities at the boundaries of spectral series for hydrogen and, sometimes, for helium. Maximum are attained in the Lyman region of =912–1200 Å, where can reach the value 0.7–0.9 for supergiants, this value being 0.3 for Main-Sequence stars. For stars withT eff 35 000 K, high values of also are attained for <912 Å. Within the infrared region, is always small because of bremsstrahlung absorption.A rapid growth of the source functionB with < typical for ultraviolet range (within the Wien part of spectrum), together with high values of results in the strong polarization of emission from a unit stellar surface element, sometimes exceeding the values for the case of a pure electron scattering. For longer wavelengths, where the limb-darkening coefficient is smaller, the plane of polarization abruptly turns 90° in the central parts of the visible stellar disk.  相似文献   

19.
I give an interpretation of a result of Simpsonet al. (1988) on the variation with kinetic energyT i of the mean pathlengthX m (T i ) of the galactic cosmic rays (CGRs) in the range 0.1T i 10.0 GeV nucl–1. I argue that the data onX m (T i ) may be interpreted in terms of a model of GCR diffusion on the one-dimensional Alfvén-wave turbulence, having a cutoff in the spectrum at frequencies h , where h is the proton gyrofrequency. The cutoff results in changing of the character of variation of the GCR diffusion coefficientD(T i )T a in the rangeT i 1 GeV nucl–1 towards some more complicated variation at 0.1T i 1.0 GeV nucl–1 due to the peculiarities of the pitch-angle scattering at 900.  相似文献   

20.
Resume On étudie les solutions périodiques d'un système Hamiltonien au voisinage des résonances i/j Ni et Nj sont des nombres entiers premiers entre eux.Dans le cas ou l'hamiltonien à la forme H=H0+H1, une procédure générale est donnée pour trouver les familles de solutions périodiques. Le développement asymptotique de la solution peut être calculé explicitement. L'étude de la stabilité est traitée (Stellmacher, 1984).Une application aux problèmes de dynamique galactique pour un système à trois degrés de liberté est faite pour le voisinage de la résonance 221.
Hamiltonian systems in the neighbourhood of an equilibrium solution. I:Periodic orbits in cases of resonance
We study the periodic solutions of an Hamiltonian system with n degrees of freedom, near an equilibrium point, in the vicinity of the resonances i/jNi/Nj. Ni/Nj are fractions in their lowest terms for any pair (i, j).In this case, a general procedure to find the families of periodic solutions is given. The asymptotic solutions can explicitly be calculated including the periods. (The stability will be presented in Stellmacher (1984).) An application to a galactic dynamics problem in a system with three degrees of freedom near the resonances 221, is analytically treated in detail.
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