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.     

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.     

Electrical conductivity of neutron star cores in the presence of a magnetic field

General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities ₀, where ₀ = 2.8×10¹⁴ g cm^–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of ^–-hyperons at > _c , where _c 4₀. The electric resistivities along and acrossB, and , and the Hall resistivity _H are calculated and fitted by simple analytical formulae at _c and > _c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If _c , one has = [1 + (B/B ₀)²] for the normal neutrons, and for the superfluid neutrons, while _H = B/B _e for both cases. HereB _e 10⁹ T ₈ ² G,B ₀10¹¹ T ₈ ² G, andT ₈ is temperature in units of 10⁸ K. Accordingly for the normal neutrons atBB ₀, the transverse resistivity suffers an enhancement, _{1/4 1}. When 5₀ andB varies from 0 toBB _p 10¹³ T ₈ ² G, increases by a factor of about 10³–10⁴ and _H changes sign. WhenBB _p , remains constant for the superfluid neutrons, and _H B ² for the normal neutrons, while _H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.     

Magnetic fields and flares in the region CMP 20 September 1963

The position of bright knots of 30 flares at their very beginning relative to the high-resolution isogauss maps of the longitudinal component (H ) and maps of the transverse component (H ) of magnetic field are considered for seven days during the passage of the active and large spot group in Sept. 1963 (see Table I and maps on Figures 1–8).The flare bright knots occur simultaneously in regions of opposite magnetic polarity, and the majority of these knots are adjacent to neutral line H = 0, although not coinciding precisely with this line (Figure 9). Lenticular form of flare knots and the motions of bright material of flares is restrained by transversal field H . Also flares are closely associated (83%) with so-called bifurcated regions, where specific crossing of transverse components takes place (Figures 4–5). There is well-expressed (80%) coincidence of flare knots with the strongest (positive or negative) electric currents as determined from the relation j = c/4 rot H. The relation of results obtained to some existing theories of flares is briefly discussed.U.S. Nat. Acad. of Science - U.S.S.R. Acad. Nauk. Exchange Scientist Program; now at CSIRO Division of Physics, Australia.     

Thermalization of solar wind

Three kinetic equations describing the linear and non-linear wave-particle interaction for an anisotropic solar wind plasma have been developed. These equations have been solved numerically to find the variation inT /T with respect to time, whereT andT are the perpendicular and parallel temperatures with respect to the ambient magnetic field of the solar wind. For wave energy greater than a critical value (strong turbulence), non-linear wave-particle interactions are important but do not lead to thermalization. On the other hand, weak nonlinear interactions tend to increaseT /T , but make only a negligible contribution in the quantitative sense. Thus, only the linear wave-particle interaction remains as the significant contributer to the increase ofT /T .     

Explorer 34 magnetic field measurements near the tail current sheet and auroral activity

Explorer 34 (Imp 4) 2.56 s magnetic data during 131 traversals of the tail current sheet are presented along with simultaneous 2.5 min auroral electrojet indices AE and AL. The normal magnetic field,B , satellite crossing times and positions are tabulated for these 131 crossings.B is defined in the center of the sheet: it is the vector magnetic field at the time of field minimum during the crossing (B _x component changes sign). It is remarkable that the only normal components too large in magnitude to be classified as fine structure occur near the time of onset of an AE event. Cases are discussed where the normal component, defined near the plasma sheet edges, has the opposite sign compared to the normal component defined at the sheet center. For quiet times, the current sheet may be only about 1000 km thick within a 3R _e (Earth-radii) plasma sheet, and may carry some 10–15% of the total tail current.     

Hydromagnetic Ekman layer on free convection past an infinite porous flat plate

Free convection in a conducting liquid past an infinite porous vertical flat plate in a rotating frame of reference when the Hall current is present is considered. Exact solutions for the velocity and temperature fields have been derived. The effects ofM (Hartmann number),m (Hall parameter), andE (Ekman number) on the velocity field are discussed.Nomenclature C _p specific heat at constant pressure - g acceleration due to gravity - E Ekman number - G Grashof number - H ₀ applied magnetic field - j _x ,j _y ,j _z components of the current densityJ - k thermal conductivity - M Hartmann number - m Hall parameter - P Prandtl number - Q heat flux per unit area - T temperature of the fluid near the plate - T _w temperature of the plate - T temperature of the fluid in the free-stream - u, v, w components of the velocity fieldq - U uniform free-stream velocity - w ₀ suction velocity - x, y, z Cartesian coordinates - z dimensionless coordinate normal to the plate Greek symbols coefficient of volume expansion - _e cyclotron frequency - _e electron collision time - _u skin friction in the direction ofu - _v skin friction in the direction ofv - dimensionless temperature - density of the fluid - kinematic viscosity - _e magnetic permeability - electrical conductivity of the fluid - angular velocity     

Central holes in disks of spiral galaxies

On the basis of the solutions obtained in the previous paper, the changes in the scenario of the standard model of the Big Bang are found. The chaos degree (constrainst on fluctuation spectra) is obtained, which could be still preserved by the initially completely chaotic Universe at the time of light elements nucleosynthesist _es. The time boundaries of hadron and lepton eras and the time the electron neutrinos and neutrons become frozen in reactions of weak interaction may be shifted up to 1.4 times. The corresponding temperatures may shift off from the standard ones 0.88 times if the mean-square level of fluctuations is close to unity. If the density of the energy of fluctuations concentrated in the short-wave region of the spectrum is less than 1.5 ^– , the nucleosynthesis leads to a helium abundance coinciding with the observe one. If at the timet _es the maximum of the spectral density of the energy is in the long-wave region, that is _max ct _es the level of the chaos during the period of nucleosynthesis is restricted to 1.76 (where |C _K |² d³ K,C _K is Fourier component of the amplitude of metric fluctuations). In particular, the protogalactic vortical disturbances with a wide spectrum 4 × 10^{3 -1}( = K/K, = /_crit) are compatible with the observed helium abundance.     

Basic concepts in the electrodynamics of the auroral ionosphere

Equations governing the large-scale electrodynamic processes in the auroral ionosphere are systematically discussed and the limits to drawing conclusions from incomplete sets of equations are evaluated. The vectors of electic current density,j, and electric field,E, are expressed as explicit functions of the densities, pressures and velocities of the constituents of the ionosphere.The equation div (·E)=0 is an identity satisfied by any solution of the full set of equations governing the problem and cannot be treated as a differential equation forE in which the components of the conductivity tensor are given parameters. The concept of the height-integrated conductivities and the conclusions based on it are inconsistent with the equations of momentum balance for the ionospheric constituents.The global structure of the auroral ionosphere is determined by the state of equilibrium between the pressure gradients, the inertial forces and thej×B-force associated with the auronal electrojets flowing along the auroral oval. The time-averaged, global, electric field is directed across the auroral oval. Its value is substantially affected by the motions of neutral particles. The velocity vector of the neutrals has a substantial component directed across the oval.     

Bidimensional spectroscopy of network bright points

We develop an automatic, computer controlled procedure to select and to analyze the Network Bright Points (NBPs) on solar images. These have been obtained at the Sac Peak Vacuum Tower Telescope by means of the Universal Birefringent Filter and Zeiss H filters, tuned, respectively, along the profiles of the H, Mg-b1, Na-D2, and H lines.A structure is identified as an NBP if at the wavelength H- 1.5 A its maximum intensity is greater than I + 3 and its area is greater than 1.5 arc sec² at I + 1.5, where I is the mean value and the standard deviation of the intensity distribution on the image. Each detected NBP is then searched and confirmed in all the remaining 31 images at different wavelengths.For each NBP several parameters are measured (position, area, mean and maximum contrast, Dopplergram velocity, compactness, and so on) and some identification constraints are applied.The statistical analysis of the various parameter distributions, for NBPs present within an active region and its surroundings, shows that two types of NBPs can be identified according to the value of their mean contrast C _min the H- 1.5 Å image (C _m 0.1 type I, C _m> 0.1 type II). The type I NBPs (all occurring on the boundaries of the supergranular network) appear to be much more frequent (180/26) than the type II ones.The size A of type I NBPs is less than 1.0 arc sec for H/H wings but of the order of 1.2 arc sec for Na-D2 and Mg-bl. The mean contrast C _m is around the value of 10% along the Na-D2 and Mg-bl profiles and of 20% along the H/H wings.The C _m - A scatter diagrams show, for the photospheric radiation (h < 100 km), a narrow range of variability for C _min correspondence with a wide range for A. For radiation orginated at higher levels (h > 200 km), the C _m- A scatter diagrams seem to indicate, even if with a large variance, that the highest C _m's tend to correspond to the highest A values.The mean Doppler shift is close to zero for Na-D2 and Mg-bl lines but negative (downward motion) for H and H lines.The type II NBPs tends to be preferentially located in the neighbourhood of small, compact sunspots and their detectability is almost constant through all the 4 studied line profiles. No conclusions can be derived on the mean size, contrast and Doppler shift values because their distributions are too dispersed. The only positive information is that its C _m- A scatter diagram, in H and H wings, indicates a wide range of variability for C _m in correspondence with very narrow range of variability for A.     

An observation on the inverse extended problem of Szebehely

Through the use of Jacobi's formulation of the least action principle, differential equations for Szebehely's problem extended to a holonomic system with n degrees of freedom are obtained.

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Sunto Si riottengono le equazioni differenziali relative al problema di Szebehely esteso ad un sistema olonomo ad n gradi di libertà utilizzando il principio di minima azione nella formulazione di Jacobi.

     

Космическое черенковское излучение

, . N/E, E _r, (E _r)=1. , (, ) . .     

The influence of satellite flexibility on orbital motion

The orbital perturbations induced by the librational motion and flexural oscillations are studied for satellites having large flexible appendages. Using a Lagrangian procedure, the equations for coupled motion are derived for a satellite having an arbitrary number of appendages in the nominal orbital plane and two flexible members normal to it. The formulation enables one to study the influence of flexibility on both the orbital and attitude motions. The orbital coordinates are expanded as perturbation series in =(l/a ₀)²,l anda ₀ being a characteristic length of the satellite and unperturbed semi-major axis of the orbit, respectively. The first order perturbation equations are solved in terms of elastic deformations and librational angles using the WKBJ method in conjunction with the variation of parameter technique. Existence of secular perturbations is noted for certain librational flexural motions. Three specific examples, Alouette II, Radio Astronomy Explorer and Tethered Orbiting Interferometer, are considered subsequently and their possible secular drifts estimated.List of Symbols A _ij, B_ij coefficients in the eigenfunction expansion ofv _i andw _i respectively, Equation (10) - C _k, D_k constants, Equation (21) - EI _i flexural rigidity of theith appendage - E(u₀) ²(1+e ₀ cosu ₀)² h ₀ ³ - F(u₀) perturbation function, Equation (17b) - F ,F ,F functions of librational angles and flexural displacements, Equation (11i) - F ,F ,F F ,F ,F with change of independent variable fromt tou ₀ - I _xx, I_yy, I_zz principal moments of inertia of the undeformed satellite - [J ⁱ] inertia dyadic of the deformedith appendage - [J _d] inertia dyadic of the deformed satellite - M mass of the satellite - P _R, P_u functions of librational angles and flexural displacements, Equation (15d) and (15e), respectively - R _c magnitude ofR _c - R _c0, R₁ unperturbed value and first order perturbation ofR _c, respectively - R _c ,R ₀ position vectors of the c.m. of the deformed and undeformed satellite, respectively - T kinetic energy of the satellite - U potential energy of the satellite - U _e, U_g elastic and gravitational potential energy, respectively - X, Y, Z orbital co-ordinate axes, located at the c.m. of the deformed satellite - Y ₁(u₀), Y₂(u₀) functions ofu ₀, Equation (18b) and (18c), respectively - a semi-major axis - a ₀ unperturbed value ofa - e eccentricity - e ₀ unperturbed value ofe - h ₀ unperturbed angular momentum per unit mass of the satellite - i inclination of the orbital plane to the ecliptic - i, j, k unit vectors alongx (or ),y (or ) andz (or ) axes, respectively - l characteristic length of the satellite - l _i length of theith appendage - [l ⁱ] matrix of direction cosines ofx _i, v_i andw _i - l ,l ,l direction cosines ofR _c - m ₀, m_i mass of the main body andith appendage, respectively - p _i ² - q _m, Q_m generalized co-ordinate and force, respectively - r ₁ R ₁/R_c0 - r position vector of an element of the body referred toxyz axes - r _u position vector of an element after deformation, referred to axes - r _c x _c i+y _c j+z _c k, position vector of the c.m. of the deformed body referred toxyz axes - s x _i/l_i - t time - u true anomaly - u ₀, u₁ unperturbed value and the first order perturbation ofu, respectively - u elastic displacement vector - u _c u–r _c - velocity of an element relative to axes - v _i, w_i flexural deformations - x, y, z body co-ordinate axes with origin at the c.m. of the undeformed satellite - x _i distance of an element of theith appendage from the root - _j jth eigenfunction (normalized) of a cantilever - angle between the line of nodes and vernal equinox - , , components of nondimensionalized angular velocity of the satellite - , , pitch (spin), yaw and roll, respectively - _i nominal inclination of theith appendage in the orbital plane - - small parameter, (l/a ₀)² - _j jth eigenvalue of a cantilever - gravitational constant - _jk constant, Equation (11j) - , , body co-ordinate axes with origin at the c.m. of the deformed satellite - ( i + j + k), angular velocity of the satellite     

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 and the spectral index . In this model V _d increases with V, , and ; and , the angle between the anisotropy vector at infinite time and the outward radial direction increases with /V and decreases as is increased. These predictions of the dependence of and V _d upon V, , and are open to observational verification.     

Heat loss and tectonic style of Venus

The tectonic style of a terrestrial planet depends strongly on the mechanisms of heat release from the mantle through the lithosphere to the surface. Three types of lithospheric heat transfer have been proposed. (1) Lithospheric conduction, (2) (hot spot) volcanism, (3) plate recycling (mainly at spreading plate margins). In the case of the Earth the total heat flow is determined by plate recycling 65%, heat conduction through the lithosphere 20%, decay of radioactive elements in the crust 15%, hot spot volcanism <1%. Scaling the mean surface heat flow density of the Earth to venusian conditions leads to 66 mW/m². In the case of Venus plate tectonics play only a minor role. Thus, two processes remain for heat release: (hot spot) volcanism and conduction. The term hot spot is written in brackets because volcanism on Venus occurs globally, not necessarily associated with hot spots.The volcanic lava production has been estimated from Venera 15/16 scenes. Arecibo and Magellan images revealed that the surface character south of 30° N is very similar to the area covered by Venera. The main results of the estimation are: (i) The maximum thickness of the plain lavas is 3 km. (ii) With plain lava thicknesses larger than 200 m the lava production from central volcanoes is negligible, (iii) Two age models have been used for the mean age of the area obseved: t ₁ = 10⁹ a, t ₂ = 400 x 10⁶ a. t ₁ leads to the maximum lava production rate of 3 km³/a compared to 20 to 25 km³/a of the Earth; this gives a maximum contribution of 0.75mW/m² to the heat flow density of Venus, i.e. about 1%. This implies that either heat conduction is the only dominating process for heat release or there is a hidden reservoir of the missing basalt somewhere or there is another unknown tectonic process. Assuming pure conduction and correcting the surface heat flow density for radioactive elements in the crust leads to a thickness of the thermal lithosphere of 45km. A reservoir for the missing basalt could be basaltic underplating to a depth of 100 km. This gives a contribution of about 20 mW/m² with the age model t ₂ to the heat flow density from first order calculations.While the tectonic style of the Earth can be described to be linear formed at the plate margins, the surface of Venus is characterized by global spotty volcanism. The surface is more dominated by volcanic landforms than in the case of the Earth despite the relatively low lava production rate with a maximum of 3 km³/a. As plate tectonics is a minor process on Venus, conduction through a rather thin lithosphere should play an important role for heat release.Contribution No. 437, Institut für Geophysik der Universität Kiel, Germany.     

Fourier techniques for an analysis of eclipsing binary light curves: III

The aim of the present paper will be to present a new approach to the light changes of eclipsing binary systems. The light changes have been expanded into the Fourier-Bessel and Dini series. The coefficients of these expansions which are the Hankel transforms of the order of the loss of light (1–l) have been expressed in terms of the eclipse elements. These discrete Hankel transformsH (j _m ) andH ( _m ) valid for only the positive real zerosj _m and _m of the functionsJ and [xJ(x)+J (x)] have been generalized for any positive value of andy. Thus, these general expressions for the Hankel transforms of the light curves which are valid for all types of eclipses, for any arbitrary degree of the adopted limb-darkening law and, moreover, for any positive value of the free parameters andy, may be used for the solution of the elements of eclipsing binary systems.     

A search for discrete gamma-ray sources of energy greater than 2×1012 eV

The results of the observations to search gamma-ray sources with the energy greater than 2×10¹² eV, which were made in Crimean Astrophysical Observatory during the years 1969–73 are presented. A technique of the detection of the EAS Cerenkov flashes was used.The quality of the data obtained is analysed. The criteria for the selection of the data free from meteorological variations are considered.It was shown that two objects, namely, Cyg X-3 and Cas -1, may be the sources of high-energy gamma quanta. It is probable that the object with the coordinates =05^h15^m, =+1° is the source of gamma-rays as well. An unidentified object Cas -1 is variable: gamma-ray flux was observed twice — in Sepember–October 1971 and in December 1972. It is possible that the flux from Cyg X-3 has a period of 4.8 hr.

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I I , I I , - >2.10¹² . I . I , I I, I ., - -1 Cyg -3- -I . , =0515 ·=+1° -.I -1 I: I J I- - 1971 1972 . Cyg -3, , - T=4.8 .

     

The effect of chemical abundance oscillations on the pulsational properties of A 5M ⊙ hydrogen-helium star

A model of a first generation intermediate star of 5M , with Z=0 has been considered. The model is at an advanced stage of its evolution and has a double shell burning. It burns helium in the inner shell, and hydrogen, via CNO cycle, in the outer shell. =(log/log) _T and _T =(log/logT) were computed allowing for the oscillations of the relative mass abundance of the reagents in nuclear reactions. Including =(log/log) _T and =(log/logT) of mean molecular weight and the effect of the oscillations of abundances due to nuclear reactions, stability was studied. Contrary to the results of the static calculations, we found that instability due to the excitation mechanism provided by the high temperature sensitivity of energy generation rate propagates up to the surface. Thus the model in question was found to be unstable against radial adiabatic pulsations, in its fundamental mode.     

Ultraviolet observations of β Persei, μ1 Scorpii and γ2 Velorum with the TD-1A satellite

This paper reports on the results of a study of S59 ultraviolet spectral scans of the spectroscopic binaries Persei, ¹ Scorpii and ₂ Velorum. In the case of ¹ Sco it was found that the Mgii doublet at 2800 Å undergoes intensity variations that may be indicative of variable emission in the photographic spectrum. The continuum in the 2490–2590 Å range deviates from the continuum of the comparison stars. In ₂ Vel, flux variations in the 2770–2870 Å region have been detected.Member of the Carrera del Investigador Cientifico, CONICET, Argentina. Guest Investigator of the S59 experiment on board the TD-1A satellite.