Классикаци дбиижэхий в обобщэхной плоцкой задачэ трех неподБижнΨη цэнтпов

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On the classification of motion in the generalized two-dimensional problem of three fixed centres

A qualitative analysis and classification of forms of motion in the problem under consideration have been carried out using a method (applicable to any case of integrability) due to Liouville. All the forms of the two-dimensional motions for any masses (negative and complex as well) at fixed centres corresponding to the real potential have been considered.

     

εлектроны космических лучей радиогало галактики

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Effects of Hall current on hydromagnetic free-convective flow through a porous medium

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     

The prominence-corona interface compared with the chromosphere-corona transition region

The intensities of 52 EUV emission lines from each of 9 hedgerow prominences observed at the limb with the Harvard experiment on ATM-Skylab have been compared with intensities from the interior of network cells at the center of the disk, in order to compare the prominence-corona (P-C) interface with the chromosphere-corona (C-C) transition region. The intensity ratio I _cell/I _prominence for each line varies systematically (in all of the prominences observed), with the temperature of formation of the line as T ^–0.6. The density sensitive C iii (formed at T 9 × 10⁴ K) line ratio I ₁₁₇₅/I ₉₇₇ implies an average density 1.3 × 10⁹ electrons cm^–3 in the P-C interface and 4 times this value in the C-C transition of the cells. The total optical thickness at the head of the Lyman continuum is 10 in most of the prominences studied; in two of the prominences, however, we cannot reject the possibility that _o is large. Methods of analysis of these EUV data are developed assuming both a resolved and an unresolved internal prominence structure. Although the systematic differences between the P-C interface and the C-C transition are stressed, the similarities are probably more remarkable and may be a result of fine structure in the C-C transition.Currently on leave from the Institute of Astronomy, Hawaii; at the Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado, 80309.     

Complete determination of the magnetic field vector and of the electron density in 14 prominences from linear polarizaton measurements in the HeI D3 and Hα lines

The present paper is devoted to the interpretation of linear polarization data obtained in 14 quiescent prominences with the Pic-du-Midi coronagraph-polarimeter by J. L. Leroy, in the two lines Hei D₃ andH quasi-simultaneously. The linear polarization of the lines is due to scattering of the anisotropic photospheric radiation, modified by the Hanle effect due to the local magnetic field. The interpretation of the polarization data in the two lines is able to provide the 3 components of the magnetic field vector, and one extra parameter, namely the electron density, because the linear polarization of H is also sensitive to the depolarizing effect of collisions with the electrons and protons of the medium. Moreover, by using two lines with different optical thicknesses, namely Hei D₃, which is optically thin, and H, which is optically thick ( = 1), it is possible to solve the fundamental ambiguity, each line providing two field vector solutions that are symmetrical in direction with respect to the line of sight in the case of the optically thin line, and which have a different symmetry in the case of the optically thick line.It is then possible to determine without ambiguity the polarity of the prominence magnetic field with respect to that of the photospheric field: 12 prominences are found to be Inverse polarity prominences, whereas 2 prominences are found to be Normal polarity prominences. It must be noticed that in 12 of the 14 cases, the line-of-sight component of the magnetic field vector has a Normal polarity (to the extent that the notion of polarity of a vector component is meaningful; no polarity can be derived in the 2 remaining cases); this may explain the controversy between the results obtained with methods based on the Hanle effect with results obtained through the Zeeman effect. A dip of the magnetic field lines across the prominence has been assumed, to which the optically thick H line is sensitive, and the optically thin Hei D₃ line is insensitive.For the Inverse prominences, the average field strength is 7.5±1.2 G, the average angle,, between the field vector and the prominence long axis is 36° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 29° ± 20°, and the average electron density is 2.1 × 10¹⁰ ± 0.7 × 10¹⁰ cm^–3. For the Normal prominences, the average field strength is 13.2±2.0 G, the average angle,, between the field vector and the prominence long axis is 53° ± 15°, the average angle, , between the outgoing field lines and the solar surface at the prominence boundary is 0° ± 20° (horizontal field), and the average electron density is 8.7 × 10⁹ ± 3.0 × 10⁹ cm^–3.     

Physics of solar prominences

Summary Conclusion This colloquium on solar prominences - the first ever held - has shown that a major part of activity in prominence research in recent years concentrated on both observation and computation of the magnetic conditions which were found to play a crucial role for the development and the maintainance of prominences. Remarkable progress was made in fine-scale measurements of photospheric magnetic fields around filaments and in internal field measurements in prominences. In addition, important information on the structure of the magnetic fields in the chromosphere adjacent to the filaments may be derived from high resolution photographs of the H fine structure around filaments which have become available recently; unfortunately, an unambiguous determination of the vector field in the chromosphere is not yet possible.It is quite clear, now, that stable filaments extend along neutral lines which divide regions of opposite longitudinal magnetic fields. Different types of neutral lines are possible, depending on the history and relationship of the opposite field regions. There is convincing evidence that the magnetic field in the neighbouring chromosphere may run nearly parallel to the filament axis and that there are two field components in stable prominences: an axial field dominant in the lower parts and a transverse field dominant in the higher parts.Methods for the computation of possible prominence field configurations from measured longitudinal photospheric fields were developed in recent years. In a number of cases (e.g. for loop prominences) the observed configuration could be perfectly represented by a force-free or even a potential field; poor agreement was found between computed and measured field strengths in quiescent prominences. In order to reconcile both of them it is necessary to assume electric currents. Unambiguous solutions will not be found until measurements of the vector field in the photosphere and in the prominences are available.The two-dimensional Kippenhahn-Schlüter model is still considered a useful tool for the study of prominence support and stability. However, a more refined model taking into account both field components and considering also thermal stability conditions is available now. It was proposed that quiescent prominences may form in magnetically neutral sheets in the corona where fields of opposite directions meet.As for the problem of the origin of the dense prominence material there are still two opposite processes under discussion. The injection of material from below, which was mainly applied to loop prominences, has recently been considered also a possible mechanism for the formation of quiescent prominences. On the other hand, the main objections against the condensation mechanism could be removed: it was shown that (1) sufficient material is available in the surrounding corona, and that (2) coronal matter can be condensed to prominence densities and cooled to prominence temperatures in a sufficiently short time.The energy balance in prominences is largely dependent on their fine structure. It seems that a much better radiative loss function for optically thin matter is now available. The problem of the heat conduction can only be treated properly if the field configuration is known. Very little is known on the heating of the corona and the prominence in a complicated field configuration. For the optically thick prominences the energy balance becomes a complicated radiative transfer problem.Still little is known on the first days of prominence development and on the mechanism of first formation which, both, are crucial for the unterstanding of the prominence phenomenon. As a first important step, it was shown in high resolution H photographs that the chromospheric fine structure becomes aligned along the direction of the neutral line already before first filament appearance. More H studies and magnetic field measurements are badly needed.Recent studies have shown that even in stable prominences strong small-scale internal rotational or helical motions exist; they are not yet understood. On the other hand, no generally agreed interpretation of large-scale motions of prominences seems to exist. A first attempt to explain the ascendance of prominences, the Disparitions Brusques, as the result of a kink instability was made recently.New opportunities in prominence research are offered by the study of invisible radiations: X-rays and meterwaves provide important information, not available otherwise, on physical conditions in the coronal surroundings of prominences; EUV observations will provide data on the thin transition layer between the cool prominence and the hot coronal plasma.Mitt. aus dem Fraunhofer Institut No. 111.     

Космическое черенковское излучение

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On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE _n which is denoted as _n (). The main result of this analysis enables us to establish a two-term recurrence formula for _n (0) and a three-term recurrence formula for _n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.     

Shear angle of magnetic fields

In this paper we introduce a new parameter, the shear angle of vector magnetic fields, , to describe the non-potentiality of magnetic fields in active regions, which is defined as the angle between the observed vector magnetic field and its corresponding current-free field. In the case of highly inclined field configurations, this angle is approximately equal to the angular shear, , defined by Hagyardet al. (1984). The angular shear, , can be considered as the projection of the shear angle, , on the photosphere. For the active region studied, the shear angle, , seems to have a better and neater correspondence with flare activity than does . The shear angle, , gives a clearer explanation of the non-potentiality of magnetic fields. It is a better measure of the deviation of the observed magnetic field from a potential field, and is directly related to the magnetic free energy stored in non-potential fields.     

Influence du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité

Résumé On étudie l'effet du champ magnétique terrestre sur le mouvement d'un satellite autour de son centre de gravité. Le satellite possède une symétrie dynamique et un moment magnétique propre dirigé suivant l'un des axes principaux d'inertie; le champ magnétique terrestre est assimilé au champ d'un dipôle dont les pôles coïncident avec les pôles terrestres. On néglige les perturbations de la trajectoire du satellite qui est supposée circulaire. La position du satellite par rapport à son centre de gravité est repérée dans un système d'axes lié au plan de l'orbite et le mouvement est décrit à l'aide des angles d'Euler , , . La symétrie sphérique et le choix du moment magnétique sur l'un des axes d'inertie permettent d'éliminer l'angle .La solution pour et peut se développer en séries de puissance d'un petit paramètre . Les séries convergent pour ||<1.Lorsque le moment magnétique est faible on la rotation du satellite rapide, est faible. Les développements sont calculés effectivement jusqu'à ².La comparaison des résultats avec l'intégration numérique du système d'équations différentielles est satisfaisante.

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The effect of the Earth's magnetic field on the motion of a satellite around its centre of mass is investigated. The satellite is assumed to be dynamically symmetric and to be magnetized in the same direction as that of a principal axis. The Earth's magnetic field is assumed to be a dipole field whose poles coincide with the rotation poles of the Earth. The satellite's orbit is circular and perturbations are neglected. The position of the satellite with respect to its centre of mass is given with respect to a coordinate system fixed in the orbital plane and the motion is described by Euler's angles , , . The spherical symmetry and the coincidence of the magnetic moment with a principal axis allow one to eliminate the angle .The solution for and , can be expanded in power series for small parameter .The series converge for <1. is small for a small magnetic moment or a high angular velocity of the rotating satellite. The terms of the expansion of the series are calculated up to ².The comparison of the results with those obtained by numerical integration of the differential equation is satisfactory.

     

Theory of the Trojan asteroids,IV

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 m_j(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 .     

Energy supply processes for magnetospheric substorms and solar flares: Tippy bucket model or pitcher model?

In the past, both magnetospheric substorms and solar flares have almost exclusively been discussed in terms of explosive magnetic reconnection. Such a model may conceptually be illustrated by the so-called tippy-bucket model, which causes sudden unloading processes, namely a sudden (catastrophic, stochastic, and unpredictable) conversion of stored magnetic energy. However, recent observations indicate that magnetospheric substorms can be understood as a result of a directly driven process which can conceptually be illustrated by the pitcher model in which the output rate varies in harmony with the input rate. It is also possible that solar flare phenomena are directly driven by a photospheric dynamo. Thus, explosive magnetic reconnection may simply be an unworkable hypothesis and may not be a puzzle to be solved as the primary energy supply process for magnetospheric substorms and solar flares.     

Flaring arches

Flaring arches is a name assigned to a particular component of some flares. This component consists of X-ray and H emission which traverses a coronal arch from one to the other of its chromospheric footpoints. The primary footpoint is at the site of a flare. The secondary footpoint, tens of thousands of kilometers distant from the source flare, but in the same active region, brightens in H concurrent with the beginning of the hard X-ray burst at the primary site. From the inferred travel time of the initial exciting agent we deduce that high speed electron streams travelling through the arch must be the source of the initial excitation at the secondary footpoint. Subsequently, a more slowly moving agent gradually enhances the arch first in X-rays and subsequently in H, starting at the primary footpoint and propagating along the arch trajectory. The plasma flow in H shows clearly that material is injected into the arch from the site of the primary footpoint and later on, at least in some events, a part of it is also falling back.Thus a typical flaring arch has three, and perhaps four consecutive phases: (1) An early phase characterized by the onset of hard X-ray burst and brightening of the secondary footpoint in H. (2) The main X-ray phase, during which X-ray emission propagates through the arch. (3) The main H phase, during which H emitting material propagates through the arch. And (4) an aftermath phase when some parts of the ejected material seem to flow in the reverse direction towards the primary site of injection.An extensive series of flaring arches was observed from 6 to 13 November, 1980 at the Big Bear Solar Observatory and with the Hard X-Ray Imaging Spectrometer (HXIS) on board the SMM in a magnetically complex active region. The two most intense arches for which complete H and X-ray data are available and which occurred on 6 November at 17 21 UT (length 57000 km) and on 12 November at 16 57 UT (length 263 000 km) are discussed in this paper.     

Pulsar radio emission. I. Oblique rotator

The problem of pulsar radio emission for the case of a coaxial rotator was investigated in our preceding paper [G. S. Sahakian, Astrofizika,38, 143 (1995)]. In this paper it is solved for the realistic case in which the star's magnetic axis does not coincide with its rotational axis (an inclined rotator). It is shown that above the star's magnetic cap a special region, called a magnetic funnel, is formed in which vigorous processes of particle multiplication occur. The height of this region is h 8·10^60.2 ₃₀ ^1/3 R ₆ ^1.3 cm and its radius r(r/c)^0.5 depends little on the inclination angle a ( is the angular rotation rate, is the magnetic moment, R is the star's radius, and r is distance from the center of the star). It is shown that the pulsar radio emission is produced in the magnetic funnel. Here, in the course of active radiative processes, two main particle fluxes with a high ultrarelativistic energy are formed: an upward electron flux and a positron flux falling onto the star's magnetic cap. These main fluxes are accompanied by individual narrow strips of positron and electron fluxes with a relatively low energy, which are fairly powerful, coherent radio sources. Such secondary fluxes are formed immediately after the annihilation of photons of curvature radiation emitted by particles of the main fluxes. The pulsar's radio luminosity is estimated to be L7.4·10^233.52 ₃₀ ^8/3 (a), where (a) is a known function (1 for a<50°). Equating the theoretical and observed radio luminosities L and L₀, we obtain the formula ₃₀P^1.32R ₆ ^0.4 (2.1·10^–27L₀/)^3/8 for the magnetic moment of the pulsar's neutron star, where P is the pulsar's period. The magnetic moments of slow pulsars calculated from this formula turn out to be considerably larger than those of fast pulsars. This means that the masses of slow pulsars are larger, on the average, than those of fast pulsars. The magnetic funnel operates with interruptions, periodically undergoing a discharge, so that the production of pulsar radio emission operates with interruptions. The durations of the production of radio emission and of the interruptions between those processes are on the order of h/c2.7·10^–40.2 ₃₀ ^1/3 sec, i.e., pulsar radio emission has a microstructure. Consequently, a study of the microstructure of the profiles of observed radio pulses enables one to obtain additional information about the magnetic moments of the neutron stars.Translated from Astrofizika, Vol. 39, No. 2, pp. 313–335, April–June, 1996.     

Cosmic ray origin above 1018 eV: Galactic or extragalactic?

An analysis is made of the implications of assuming that suprathermal dust grains (a3×10⁸ cm) of intergalactic origin may acquire cosmic ray energies as high as 10²⁰ eV. These dust grains may attain suprathermal energy (v _g3×10⁸ cm s^–1) by the Fermi process. Initially the dust grains are accelerated by the radiation pressure against the drag of the ambient gas of the medium, but once these dust grains attain a terminal velocity (U10⁵ cm s^–1), then they may be expelled out of the galactic region into the intergalactic medium and finally acquire high energy     

Medium resolution EUV observations and network structure

Medium resolution observations have been used to find the fractional emitting area in three transition region lines. It is found that is given by DI _{mg x} ^k where k varies from 0.78 to 0.51 in the temperature range 2 × 10⁵ to 7 × 10⁵ K. The average emitting area in O vi deduced by this method is in good agreement with the results from ATM observations. The fractional emitting areas at different values of the Mg x intensity and at different temperatures are combined to find the variation of the areas with height. This variation is in good agreement with Giovanelli's model of the fractional area of cross-section of a magnetic tube of force in the transition region.     

Simultaneous radio and white light observations of the 1984 June 27 coronal mass ejection event

We present the two-dimensional imaging observations of radio bursts in the frequency range 25–50 MHz made with the Clark Lake multifrequency radioheliograph during a coronal mass ejection event (CME) observed on 1984, June 27 by the SMM Coronagraph/Polarimeter and Mauna Loa K-coronameter. The event was spatially and temporally associated with precursors in the form of meter-decameter type III bursts, soft X-ray emission and a H flare spray. The observed type IV emission in association with the CME (and the H spray) could be interpreted as gyrosynchrotron emission from a plasmoid containing a magnetic field of 2.5 G and nonthermal electrons with a number density of 10⁵ cm^–3 and energy 350 keV.On leave from Indian Institute of Astrophysics, Kodaikanal, India.     

Free-convection effects on MHD flow past a porous plate with step function change in suction velocity

Free convection effects on MHD flow past a semi infinite porous flat plate is studied when the time dependent suction velocity changes in step function form. The solution of the problem is obtained in closed form for the fluid with unit Prandtl number. It is observed that for both cooling and heating of the plate the suction velocity enhances the velocity field. The heat transfer is higher with increase in suction velocity.Notations B intensity of magnetic field - G Grashof number - H magnetic field parameter,H=(M+1/4) ^1/2–1/2 - M magnetic field parameter - N _u Nusselt number - P Prandtl number of the fluid - r suction parameter - T temperature of the fluid - T _w temperature of the plate - T temperature of the fluid at infinity - t time - t non-dimensional time - u velocity of the fluid parallel to the plate - u non-dimensional velocity - U velocity of the free stream - suction velocity - ₁ suction velocity att0 - ₂ suction velocity att>0 - x,y coordinate axes parallel and normal to the plate, respectively - y non-dimensional distance normal to the plate - coefficient of volume expansion - thermal diffusivity - kinematic viscosity - electric conductivity of the fluid - density of the fluid - non-dimensional temperature of the fluid - shear stress at the plate - non dimensional shear stress - erf error function - erfc complementary error function     

Filter observations of prominences in the D3 and Hα lines

D₃ and H pictures of prominences were obtained with a 21-in. Lyot coronograph and a Fabry-Perot etalon used as a narrow band filter. The monochromatic images of quiescent, quasiquiescent and loop-prominences were studied. The comparison of the isophotes of quiescent and quasi-quiescent prominences in D₃ with those in H shows the similarity of the prominence structure at both wavelength, although there is a strong tendency for an increase in the intensity ratio D₃/H in the upper region of prominences. It seems that it is due to lower temperature in the upper regions of prominences. Probably, the relaxation processes establishing ionization equilibrium play some role. Measurements of the knot intensities of the loop-prominence show strong variations of the intensity ratio D₃/H (more than one order of magnitude).     

The behaviour of the infrared lines of neutral oxygen and the balmer lines of hydrogen in the spectra of early-type stars with emission lines

The equivalent widths of the oxygen lines at 7774 and 8446 and of H (and some H) have been measured for 22 early-type, emission-line stars. A strong correlation between H and 8446 intensities has been found, although there is no such correlation between H and 7774. This confirms the probability that Bowen's mechanism is operative (the neutral oxygen 3³ D state is overpopulated because the excitation energy of Ly- nearly coincides with that of theOi 1025 line). The possibility of using 8446 and H equivalent widths for a comparison of oxygen to hydrogen abundances in these stars is discussed.