Time-dependent Green's functions of the cosmic ray equation of transport

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.     

Topology of magnetotail fieldlines and current lines

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.     

Charged particle transport in turbulent magnetic fields: The perpendicular diffusion coefficient

The diffusion of charged particles in a static turbulent magnetic field, which is superimposed on a constant magnetic fieldB ₀ k, is considered. Previous calculations of the particle flux in a direction perpendicular tok have related the fluxS to the particle number densityf byS = – (f) where is found from the power spectrum of the turbulent magnetic field. It is shown that this formula is inconsistent with the notion, developed by Jokipii and Parker (1969), that the perpendicular particle flux primarily arises because of random-walking of magnetic field lines across the directionk. For a simple example of a turbulent magnetic field it is shown that the above expression forS is incorrect; the particle fluxS is recalculated and a new relationship betweenS andf is found. This new expression forS is shown to be consistent with particle diffusion across the directionk being due to random-walking of the magnetic field lines.     

Stellar wind for non-negligible gravitational potential of the atmosphere

We consider a spherically symmetric, isothermal and stationary stellar atmosphere whose gravitational potential cannot be neglected. If , the ratio of the density on the base of the corona to the mean density of the star is not zero, the density vanishes at infinity for any solution of the hydrodynamic equations. We deduce the maximum mass loss depending on two dimensionless parameters, the ratio of the gravitational to the thermal energy and . This mass loss has itself a maximum for =1/3.     

On practical representation of magnetic field

Various manners of determination of a magnetic field are reviewed briefly from the standpoint of practicality and uniqueness. Then a practical representation of magnetic fields in terms of a class of force-free magnetic field is described. The proposed scheme is based on the physical consideration that in the chromosphere and lower corona a quasistatic magnetic field must be nearly force-free and that for the class of force-free magnetic field, i.e., ×B=B with = constant, the magnetic field can be determined uniquely from the observed distribution of the vertical component of a magnetic field. The applicability of the representation is demonstrated by examples and the limitations are discussed.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Determination of constant α force-free solar magnetic fields from magnetograph data

At first it is shown that a magnetic field being force-free, i.e. satisfying × B = B, with = constant ( 0) in the whole exterior of the Sun cannot have a finite energy content and cannot be determined uniquely from only one magnetic field component given at the photosphere. Then the boundary value problem for a semi-infinite column of arbitrary cross section is solved by a Green's function method.     

On the Stability of the Terrestrial Planets as Models for Exosolar Planetary Systems

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.     

On the reconstruction of the nonlinear force-free coronal magnetic field from boundary data

Using a simple model in which the corona is represented by the half-space domain = {z > 0} and the photosphere by the boundary plane = {z = 0}, we discuss some important aspects of the general problem of the reconstruction of the magnetic field B in a small isolated coronal region from the values of the vector B¦ measured by a magnetograph over its whole basis. Assuming B to be force-free in : (i) we derive a series of relations which must be necessarily satisfied by the boundary field B¦ , and then by the magnetograph data if the force-free assumption is actually correct; (ii) we show how to extract directly from the measured B¦ some useful informations about the energy of B in and the topological structure of its field lines; (iii) we present a critical discussion of the two methods which have been proposed so far for computing effectively B in from B¦ .     

Calculation of force-free magnetic field with non-constant α

A numerical method is developed for solving the force-free magnetic field equation, × B = B, with spatially-varying . The boundary conditions required are the distribution of B _n (viz. normal component of the field on the photosphere) as well as the value of in the region of positive (or negative) B _n . Examples of calculations are presented for a simple model of a solar bipolar magnetic region. It is found that the field configuration and the energy stored in the field depend crucially on the distribution of . The present method can be applied to a more complex configuration observed on the Sun by making use of actual magnetic field measurements.On leave of absence from Department of Astronomy, University of Tokyo.     

Approximate expressions for Gyrosynchrotron radiation in Transverse Propagation

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.     

Implications of a strongly peaked polar magnetic field

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.     

Фотогаирование Луны Со Зтездами Метофом Ррзделенных Пластинок Для Определения Координат Опорных Точек

. . .     

Force-free equilibrium at magnetic neutral points

It is shown that, at neutral points of force-free magnetic fields, the electric current density must vanish. This property is independent of whether the neutral points are isolated or (e.g.) fill lines or surfaces. One implication is the fact that in a cold pressureless plasma the formation of neutral current sheets cannot be adiabatically slow. The field-line topology in the neighbourhood of neutral points is discussed. At neutral points of force-free magnetic fields in general three constant- surfaces, defined by the equation ×B=B, with the same value of intersect orthogonally. If, during a time-development, the magnetic field gradient matrix B _i/x _j becomes singular at a neutral point, the field topology can change qualitatively — in general connected with the merger of two or more neutral points into one and/or the splitting up of one neutral point into several others. This can be interpreted as implying the transition from a quasi-static evolution to a dynamical state in which magnetic energy is released.     

New System of Coordinates for Tokamaks

A new system of coordinates for tokamak is presented here. They are described by the usual toroidal angle and coordinates in the meridian plane using the projection of the magnetic field lines and families of orthogonal lines. The number of families depends on the number of magnetic axis, and in this way the number of regions in the meridian plane are also defined. The differential operators are obtained using the curvatures _s and of each family. Grad–Safranov equation, poloidal field equations and Pfirsch–Schlüter transport are described in a general way using this kind of coordinates.     

О ФОрРИРОВНИИИ диаграммы излучения пульсаров

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On the stability of small quasiperiodic motions in the hamiltonian systems

Orbital stability of quasiperiodic motions in the many dimensional autonomic hamiltonian systems is considered. Studied motions are supposed to be not far from equilibrium, the number of their basic frequencies may be not equal to the number of degrees of freedom, and the procedure of their construction is supposed to be converged. The stability problem is solved in the strict nonlinear mode.Obtained results are used in the stability investigation of small plane motions near the lagrangian solutions of the three-dimensional circular restricted three-body problem. The values of parameters for which the plane motions are unstable have been found.

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εлектроны космических лучей радиогало галактики

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Аккреция вещества с магнитным полем на коллапсирующую звезду. II. Самосогласованная стационарная картина

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Sur les solutions Lagrangiennes et euleriennes du probleme generalise des trois corps en axes absolus

Résumé Le présent travail est une continuation d'un autre, publié plus tôt (Doubochine, 1970). On montre ici, que les propriétés des mouvements Lagrangiens et Euleriens établies en mécanique céleste classique sont vraies aussi dans les cas plus généraux, envisagés dans le travail indiqué. On montre de plus, que les trajectoires des points en ces mouvements en axes absolus sont les spirales infinies s'enroulant sur les surfaces des cylindres curvilignes infinis.

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An example for solar flares caused by magnetic field non-equilibrium

Using a photospheric magnetogram of the solar activity complex HR 16862, 16863, 16864 at the end of May 1980 as boundary data a sequence of three-dimensional force-free magnetic fields with spatially constant ( defined by the equation × B = B) is calculated, including numerical field-line tracing. The field is assumed not to be frozen-in and ¦¦, which is a measure of the magnetic free energy, is assumed to increase with time due to some dynamo mechanism. Variation of , starting from = 0, produces a catastrophe-like change of the topology of a field-line system corresponding to an arch filament system connecting the leading spot of HR 16863 with the trailing spot of HR 16862. This topological change is interpreted as causing a series of large homologous flares with synchronous flaring in the two spots. The catastrophe-like behaviour of the field topology is attributed to the nonlinear field-line equations.