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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 116 (1985), S. 107-129 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we review the drift theory of charged particles in electric and magnetic fields. No new physical interpretations are added to this classical topic, but through an alternative, simplified derivation of the guiding centre velocity, several complexities are eliminated and possible misconceptions of the theory are clarified. It is shown that: (i) The curvature/gradient drift velocity in the magnetic field, averaged over a particle distribution function is to lowest order in the direction of∇×B/B 2, while the average particle velocity is in the direction ofB×∇ P withP the scalar particle pressure. (ii) These drift directions are correct for first-order expansions of the particle distribution function, and only second-order or higher expansions change these directions. (iii) The∇×B/B 2 drift, which is the standard gradient plus curvature drift, and which is usually considered as a ‘single particle’ drift, need not be ‘reconciled’ with theB×∇ P, or ‘macroscopic, collective’ drift, as is often asserted in the literature. They are in fact related per definition and we show how. (iv) When viewed in fixed momentum intervals (p,p+dp), the so-called Compton-Getting factor enters into the electric field (E×B)/B 2 drift term. (v) The results are independent of the scale length of variation ofE andB, in contrast to existing drift theory. We discuss the implications of this result for three important cases.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 58 (1978), S. 21-39 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A clarification and discussion of the energy changes experienced by cosmic rays in the interplanetary region is presented. It is shown that the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system is 〈p〉 =p V·G/3 (p=momentum,V is the solar wind velocity andG=cosmic-ray density gradient). This result is obtained in three ways: (i) by a rearrangement and reinterpretation of the cosmic-ray continuity equation; (ii) by using a scattering analysis based on that of Gleeson and Axford (1967); (iii) by using a special scattering model in which cosmic-rays are trapped in ‘magnetic boxes’ moving with the solar wind. The third method also gives the rate of change of momentum of particles within a moving ‘magnetic box’ as 〈p〉ad = −p ∇·V/3, which is the adiabatic deceleration rate of Parker (1965). We conclude that ‘turnaround’ energy change effects previously considered separately are already included in the equation of transport for cosmic rays.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 70 (1980), S. 3-31 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we discuss the particle flow or streaming and energy changes of cosmic rays in the interplanetary region via flow lines in momentum-position space. We consider the steady-state case where particles are released monoenergetically from the Sun or from infinity and study the cosmic-ray ‘traffic pattern’ in momentum and position arising from monoenergetic sources. The analysis makes extensive use of the result $$\left\langle {\dot p} \right\rangle = \tfrac{1}{3}pV {\text{ }}G$$ (wherep is the particle momentum,V the solar wind velocity andG the cosmic-ray density gradient) for the mean time rate of change of momentum of cosmic rays reckoned for a fixed volume in a reference frame fixed in the solar system, developed by us in several recent papers.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 80 (1981), S. 323-335 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract 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 κ=κ0 r (κ0 constant), and in the second solution κ=κ0= 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 50 (1977), S. 205-223 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Green's Theorem is developed for the spherically-symmetric steady-state cosmic-ray equation of transport in interplanetary space. By means of it the momentum distribution functionF o(r,p), (r=heliocentric distance,p=momentum) can be determined in a regionr a≤r≤rbwhen a source is specified throughout the region and the momentum spectrum is specified on the boundaries atr a andr b . Evaluation requires a knowledge of the Green's function which corresponds to the solution for monoenergetic particles released at heliocentric radiusr o , Examples of Green's functions are given for the caser a =0,r b =∞ and derived for the cases of finiter a andr b . The diffusion coefficient κ is assumed of the form κ = κo(p)r b . The treatment systematizes the development of all analytic solutions for steady-state solar and galactic cosmic-ray propagation and previous solutions form a subset of the present solutions.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 50 (1977), S. 349-360 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract A non spherically-symmetric monoenergetic-point-source solution of the steady-state equation of transport for cosmic-rays in the interplanetary region, in which monoenergetic particles are released isotropically and continuously from a fixed heliocentric position is derived by a Laplace transform method. The solution is for a spherically-symmetric model of the propagating region incorporating anisotropic diffusion, with a diffusion tensor symmetric about the radial direction, and the solar wind velocity is radial and of constant speedV. The spherically-symmetric monoenergeticsource solution of Webb and Gleeson (1973) and of Toptygin (1973) is regained from the spherically-symmetric component of the point-source solution.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 60 (1979), S. 335-351 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract In this paper we provide two new alternative derivations of the equation of transport for cosmic-ray particles in the interplanetary region. Both derivations are carried out by using particle positionr and timet in a frame of reference fixed in the solar system, and the particle momentump′ is specified relative to a local frame of reference moving with the solar wind. The first derivation is carried out by writing down a continuity equation for the cosmic rays, taking into account particle streaming and energy changes, and subsequently deriving the streaming and energy change terms in this equation. The momentum change term in the continuity equation, previously considered to be due to the adiabatic deceleration of particles in the expanding magnetic fields carried by the solar wind, appears in the present analysis as a dynamic effect in which the Lorentz force on the particle does not appear explicitly. An alternative derivation based on the ensemble averaged Liouville equation for charged particles in the stochastic interplanetary magnetic field using (r, p′,t) as independent coordinates is also given. The latter derivation confirms the momentum change interpretation of the first derivation. We also provide a new derivation of the adiabatic rate as a combination of inverse-Fermi and betatron deceleration processes.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Astrophysics and space science 81 (1982), S. 215-220 
    ISSN: 1572-946X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract The one-dimensional, steady-state equation of transport for cosmic rays including convection, diffusion and adiabatic deceleration is separated for a spatial diffusion coefficient with an arbitrary momentum dependence and for an arbitrary spatial dependence of the convection velocityV, and applies for planar, cylindrical and spherical geometries. As an application, the previously obtained spherically symmetric steady-state Green's functions, describing the propagation of cosmic rays in interplanetary space, are generalized to the case where the convection velocity is a function of position.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Solar physics 106 (1986), S. 287-313 
    ISSN: 1573-093X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Solar physics 127 (1990), S. 229-252 
    ISSN: 1573-093X
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Physik
    Notizen: Abstract Solutions of the sine-Poisson equation are used to construct a class of isothermal magnetostatic atmospheres, with one ignorable coordinate corresponding to a uniform gravitational field in a plane geometry. The distributed current in the model j is directed along the x-axis, where x is the horizontal ignorable coordinate. The current j varies as the sine of the magnetostatic potential and falls off exponentially with distance vertical to the base with an e-folding distance equal to the gravitational scale height. We investigate in detail solutions for the magnetostatic potential A corresponding to the one-soliton, two soliton, and breather solutions of the sine-Gordon equation. Depending on the values of the free parameters in the soliton solutions, horizontally, periodic magnetostatic structures are obtained possessing either (a) a single X-type neutral point, (b) multiple neutral X-points, or (c) solutions without X-points. The solution cases (b) and (c) contain two families of intersecting current sheets, in which the line of intersection forms flux concentration points (or singularities) for the magnetic field. The solutions illustrate the contribution of the anisotropic J × B force (B, magnetic field induction), the gravitational force, and the gas pressure gradient to the force balance.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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