Anisotropy Vector Research Articles

Propagation of solar-flare cosmic rays along corotating interplanetary flux-tubes

The propagation of solar-flare cosmic rays along a corotating spiral mean interplanetary magnetic flux-tube is investigated under a variety of initial, inner and outer boundary conditions, by solving the transport equations numerically. The inner boundary condition is shown to have negligible effects on the redistribution of the cosmic rays in interplanetary space, apart from a proportionality constant. The diffusion coefficients have been classified into type I and type II: for type I the peakalong-spiral stays at a finite heliocentric distance, while for type II it travels to infinity. The time dependence of the anisotropy vector is characteristically different in each type and in the case of type I is a function of the observation point. The general propagation characteristics with a free-escape outer boundary are like those of type I. It is shown that closely exponential decay can be produced without a free-escape boundary. The concept of an ‘equilibrium shape’ at late time is introduced. With a source that decays slowly, a maximum and minimum pair appears in the spatial distribution; the maximum subsequently propagates outward and the minimum inward. The impulsive models given do not reproduce satisfactorily all the observed characteristics of solar burst events and a solar source extended in time appears to be indicated.

Anisotropies in the interplanetary intensity of solar protonsEp> 0.3 Mev

By using Explorer 35 interplanetary observations of solar protons of Ep > 0.3 Mev during ten selected solar events (1967-1970) the time dependence of intensity and of the angular distribution of intensity has been studied for the first time in the sub-Mev range of energy. The respective contributions of diffusive and convective transport are resolved. Results are qualitatively similar to those of McCracken et al. (1968, 1971) in the energy range 7.5 < Ep < 45 Mev; but, as was expected, convective transport is found to be relatively more important at the lower energies. The convective component of the anisotropy vector yields values of the solar wind velocity in good agreement with directly measured values.

Solar flare particle propagation: Comparison of a new analytic solution with spacecraft measurements

A new radial solution has been obtained to the Fokker-Planck equation for solar flare particle propagation that includes the effects of convection, energy change, and anisotropic diffusion with κγ = constant. It is assumed that the particles are injected impulsively at a single point and that there is a free escape boundary. In addition, the azimuthal solution derived by Burlaga, which was based on κθ ∝ γ², has been modified to include some of the effects of solar rotation. With an outer boundary at ∼2.7 AU, a solar wind velocity of ∼400 km/sec, and κγ ≈ 2 to 8 × 1020 cm²/sec, the complete solution gives reasonable fits to the time profiles of 1- to 10-Mev protons from ‘classical’ flare-associated events observed with the Caltech solar and galactic cosmic ray experiment aboard Ogo 6. It is not necessary to invoke a scatter free region near the sun in order to reproduce the fast rise times observed for west limb events, indicating that κγ = constant is a better description of conditions inside 1 AU than is κγ ∝ γ. The radial solution also provides insight into the possible dependence of the observed decay times on various parameters and can be used as the basis for an illustrative calculation of the evolution of the vector anisotropy.

The propagation of solar cosmic-ray bursts

A model is presented in which we show analytically the three phases of anisotropy which occur during solar cosmic-ray events observed in the 7.5 MeV to 21 MeV kinetic-energy interval and reported by McCracken et al. (1971): (i) a highly anisotropic, near field-aligned, initial phase, (ii) a convective phase, and (iii) a late-time phase in which the anisotropy is approximately perpendicular to the mean interplanetary magnetic field. The model is based on the cosmic-ray particles being convectively transported out from the Sun, undergoing anisotropic diffusion along the interplanetary magnetic-field lines, and losing energy by adiabatic deceleration or by collision processes. The event is seen simply as a pulse moving outward from the Sun after a cosmic-ray burst with a negative density-gradient in front of it and a positive gradient behind. The convective phase (ii) occurs as the spatial peak moves past the observer and has a propagation speed V d associated with it; the anisotropy vector late in the decay phase (iii) is the result of a residual ‘balance’ between the radial outward convection and the inward radial component of the anisotropic diffusion. The mathematical solutions are based upon a diffusion coefficient proportional to heliocentric radius and independent of energy and are thus rather special. However they yield formulae for the propagation speed of the convective phase and the direction in space of the long-time anisotropy which are useful as a guide to the dependence of these quantities on the solar wind speed V, the diffusion coefficient κ and the spectral index μ. In this model V d increases with V, κ, and μ; and θ′, the angle between the anisotropy vector at infinite time and the outward radial direction increases with κ/V and decreases as μ is increased. These predictions of the dependence of θ and′ V d upon V, κ, and μ are open to observational verification.

Magnetic Steering of Magnetostatic Waves in Epitaxial YIG Films

High quality epitaxial YIG films grown on gadolinium gallium garnet have certain geometrical advantages over flux-grown material for refined investigation of basic magnetic wave propagation phenomena. Better uniformity of internal field under magnetic bias and convenience for placement of spatially periodic current-carrying couplers on the free YIG surface, ensures enhanced field uniformity by confining the region of propagation. Surface magnetostatic waves are dispersive and exhibit wave vector anisotropy so that, in general, the phase and group velocity vectors are noncollinear, with the beam steering angle variable by the magnetic bias field. Scanning magnetic probe experiments were conducted at 3 GHz on 10-μm thick films wherein beam steering angles were observed up to ∼50° for a wave number approximating 830 cm−1, for a 10° rotation of the bias field from the collinear situation. Use of the theoretical model applicable to thin film media, which neglects exchange effects, led to good agreement with the experimental results within measurement error.

Sidereal time variation of high-energy cosmic rays observed by an air Cerenkov telescope

Using the cosmic-ray telescope No. 3 (air Cerenkov telescope) at Nagoya, observations of high-energy (~200 GeV) cosmic rays were continued during the period from February 1964 to March 1966. The observations were made at a fixed zenith angle Z = 60° and at two azimuths A = 72° and 288°. With this setting, the celestial sphere was scanned in the declination band between 25° and 40 °N. Using the difference between the two diurnal vectors observed at 72° (east) and 288° (west), the anisotropy, free from any diurnal variation of meteorological origin, was obtained corresponding to each of four seasons. From these four anisotropy vectors, the solar anisotropy was found to be insignificant, but the sidereal anisotropy was as follows:[Formula: see text]

The Dislocation Image Force in Cubic Polycrystals

AbstractThe image force on a screw dislocation in an anisotropic cubic polycrystal is examined as a function of elastic anisotropy and Burgers vector. For iron it is shown that the screw glide dislocation is always repelled from a grain boundary but for copper there can be either an attraction or repulsion depending on the misorientation across the grain boundary.