Showing papers on "Dipole model of the Earth's magnetic field published in 1989"

Computational modeling of magnetic fields in solar active regions

Abstract: The magnetic field plays an important role in various solar activities. This paper reviews techniques for computational modeling of magnetic fields in solar active regions. The input data are photospheric magnetic fields supplied by magnetograph observations. The field above the photosphere is computed by assuming an equation for the magnetic field. Three classes of magnetic fields, namely current-free fields, constant-α force-free fields, and general force-free fields are considered. Their physical/mathematical significances and computational procedures are systematically presented.

Small-scale magnetic structures on the Sun

Abstract: The Sun provides us with a unique astrophysics laboratory for exploring the fundamental processes of interaction between a turbulent, gravitationally stratified plasma and magnetic fields. Although the magnetic structures and their evolution can be observed in considerable detail through the use of the Zeeman effect in photospheric spectral lines, a major obstacle has been that all magnetic structures on the Sun, excluding sunspots, are smaller than what can be resolved by present-day instruments. This has led to the development of indirect, spectral techniques (combinations of two or more polarized spectral lines), which overcome the resolution obstacle and have revealed unexpected properties of the small-scale magnetic structures. Indirect empirical and theoretical estimates of the sizes of the flux elements indicate that they may be within reach of planned new telescopes, and that we are on the verge of a unified understanding of the diverse phenomena of solar and stellar activity. In the present review we describe the observational properties of the smallscale field structures (while indicating the diagnostic methods used), and relate these properties to the theoretical concepts of formation, equilibrium structure, and origin of the surface magnetic flux.

On field line resonances of hydromagnetic Alfven waves in dipole magnetic field

Abstract: Using the dipole magnetic field model, we have developed the theory of field line resonances of hydromagnetic Alfven waves in general magnetic field geometries. In this model, the Alfven speed thus varies both perpendicular and parallel to the magnetic field. Specifically, it is found that field line resonances do persist in the dipole model. The corresponding singular solutions near the resonant field lines as well as the natural definition of standing shear Alfven eigenfunctions have also been systematically derived. 11 refs.

Polar Anglo-American Conjugate Experiment

Abstract: Study of the near-Earth plasma environment and its interactions with the solar wind has reached a stage where major progress will come only from taking a global view of the interactions and coupling between different regions of the magnetosphere and ionosphere. An important aspect o f this global approach is coordinated investigation of ionospheric processes in both polar regions. The coupling between the two polar regions is determined in large part by Earth's magnetic field. Processes that occur at opposite ends of field lines are called conjugate. (Roederer [1969] has given a more complete definition and classification of conjugacy.)

Electrodynamics of moving dipoles: The case of the missing torque

Abstract: In a recent article, Bedford and Krumm [‘‘On the Origin of Magnetic Dynamics,’’ Am. J. Phys. 5 4, 1036 (1986)], examine in detail the interaction between a moving line of charges and a magnetic dipole consisting of a conducting ring of current from the point of view of different frames of reference. One particular orientation of the magnetic dipole leads to an apparently paradoxical situation of a torque acting in one inertial frame but not in another. These authors explain the situation by considering the rate of change of mass of the charge carriers and a wall force that prevents them from accelerating in the direction of their motion. They also hint at an intriguing analogy with some kind of inertial or fictitious force such as occurs in noninertial frames. First, the general expression is derived for the torque on a moving magnetic dipole in any orientation and the term representing the missing torque is explicitly revealed. Then the physical origin of this torque is investigated in the particular case considered by Bedford and Krumm, where the magnetic dipole consists of a small current‐carrying conducting loop. It appears that, in this case, the elusive torque arises from the interaction between the current carriers in the magnetic dipole loop and the magnetic field due to the surfacecurrentgenerated by the motion of the induced charges on the surface of the conducting loop.

Beam instability of the Z mode in the solar wind

Abstract: The instability of the slow extraordinary wave (z mode) caused by a tenuous population of energetic electrons, n(e), in the presence of a weak magnetic field and a cold plasma background, n(0), is investigated. The growth rate of the z mode was calculated within linear Vlasov theory and assuming that, for a weak magnetic field, the growth rate coincides with that of the electrostatic Langmuir wave, i.e., when the magnetic field is neglected for the cold background but retained for the energetic electrons. The analytical expression for the case of a thermal beam is deduced and numerically evaluated for some typical solar wind plasma conditions. The effects of the beam density, direction of propagation, and magnetic field on the observable polarization is discussed.

Laboratory simulation of the large-scale Birkeland current system in the polar region with northward interplanetary magnetic field

Abstract: The large scale Birkeland current system in the polar region has been studied by using the UCR-T1 space simulation facility (diameter 1.3 m, length 11 m). Intense plasma flow simulating the solar wind interacts with the terrella magnetic field which simulates the planetary dipole field. The northward interplanetary magnetic field (B{sub 1MF}) is simulated by an externally applied uniform magnetic field throughout the interaction chamber. Magnetic field measurements above the polar cap show that for the northward interplanetary magnetic field, a stable well-developed W pattern in the transverse component of magnetic field, prevails for the entire period of the interaction. These results have a remarkable similarity with the space observations obtained from the Magsat satellite data. The W pattern can be interpreted as an evidence for a large-scale Birkeland current system which may be associated with the field line reconnection in the magnetotail.

Steady hydromagnetic flows in open magnetic fields. III. Allowing for variations of density with latitude and nonalignment of velocity with magnetic field

Abstract: A steady hydromagnetic stellar wind flowing in a rotating axisymmetric partially open magnetic field is modeled under the assumptions that the density is a function of radial distance only and that the flow is everywhere aligned to the local magnetic field. The model illustrates that monotonic acceleration of the wind speed in the polar region requires a decrease of density toward the stellar pole at fixed radial distance. In the presence of rotation, a nonalignment between the flow velocity and the magnetic field is found to be necessary for the acceleration of the poloidal flow speed from below to above the Alfven speed defined in terms of the poloidal part of the magnetic field. 13 refs.

A Model of Astrophysical Tori with Magnetic Fields

Abstract: A steady axisymmetric model of magnetohydrodynamical tori is con­ structed under the assumptions that the specific angular momentum is constant in whole space and the magnetic field has only the toroidal component. Furthermore, the gas is assumed to be polytropic and the magnetic field is supposed to be expressed by a power of the density"and the radius in some specified manner. The relativistic effect is simulated by use of a pseudo-Newtonian potential. It is found that the configuration of the torus with a toroidal magnetic field is elongated along the symmetry axis because of the dominance by the magnetic field far from the axis. Furthermore, the position of the bottom where the density is maximum approaches the center in comparison with the case without magnetic field, although the shape of the funnel and the location of the cusp do not change. In order for such MHD tori to exist, the values of the parameters, e.g., the specific angular momentum and the Alfven speed at the bottom are restricted in some ranges.

Large-scale fluid motion in the earth's outer core estimated from non-dipole magnetic field data.

Abstract: Fluid motion in the Earth's outer core can be estimated from magnetic field data at the Earth's surface based on some assumptions, without which no unique solution to this inverse problem is likely to be derived. Our basic standpoint is that the non-dipole magnetic field is generated by the interaction between a strong toroidal magnetic field, created by differential rotation, and convective motion in the outer core. We consider large-scale convective motion and express it in terms of the poloidal velocity field expanded into a series of spherical harmonics of degree up to five. We first estimate the radial distribution of differential rotation from the balance between the effective couple due to angular momentum transfer and the electromagnetic couple. Then the radial dependence of the toroidal magnetic field is derived from the interaction between the differential rotation thus estimated and the dipole magnetic field within the outer core. For magnetic field data we use our secular variation model, in which fluctuations of the standing and the drifting parts of the non-zonal magnetic field are taken into account. The velocity field in the outer core is estimated for two cases: first, the non-zonal magnetic field is considered to be in the steady state at various epochs (the quasi-steady case) and next, timedependence of the non-zonal magnetic field is incorporated into equations to be solved (the non-steady case). It turns out that the pattern of convective motion is generally characterized by large-scale motion for the quasi-steady and the nonsteady cases; a pair of upwelling and downwelling motions is seen at the equator near the core surface for the standing and the drifting non-zonal fields, respectively. In the non-steady case, the magnitude of the velocity field is much larger, indicating a more dynamical feature.

Two-Dimensional Mapping of Dayside Convection

Abstract: Millstone Hill radar azimuth scans have been used to map the large-scale features of the ionospheric convection pattern in the vicinity of the cusp and cleft. Each scan covers 5 hours of MLT and 20° of invariant latitude, Λ, with 30 minute temporal resolution Individual “snapshots” of the convection pattern for disturbed conditions on 31 January 1982 span the entire region of convection convergence near noon and compare favorably with average model representations of the dayside region. The characteristic features of ion and electron precipitation observed during satellite overflights of the radar field of view are used to identify the cusp and cleft and to relate the location of these magnetospheric features to the pattern of ionospheric convection electric field. Cusp precipitation is seen at 70°Λ and 09 MLT at the sunward/anti-sunward convection reversal immediately after a sudden turning of interplanetary magnetic field (IMF) By from -5 nT to +5 nT while IMF Bz was-10 nT.

Splitting of normal modes and travel time anomalies due to the magnetic field of the Earth

Abstract: We examine the effects of a toroidal magnetic field on two types of seismic data: first, on splitting of normal modes and, second, on body wave travel times. The main contribution of this paper is the derivation of formulas for these problems. Comparison between data and theory indicates that the magnitude of the toroidal magnetic field (T20) has to be as large as 250 T (tesla) to explain the data. There are, however, some inconsistencies among the fit to the data set. For example, some modes require a strong magnetic field near the core mantle boundary, while other modes require a weak field. Also the travel time difference between polar and equatorial paths is not explained by the T10 or T20 field. A field with odd angular degree 𝓁 (T𝓁0 or S𝓁0) is needed to produce the travel time difference between the polar and equatorial paths. We also point out that ohmic dissipation due to a strong magnetic field with 100 T is about 4–5 orders of magnitude larger than the present heat flow output of the Earth. The analysis suggests that the magnetic field in the outer core is not the cause of seismic anomalies.

Calculation of induced modes of magnetic field in the geodynamo problem.

Abstract: In the dynamo problem, the calculation of induced modes is of vital importance, because the interaction of fluid motions with the magnetic field induces specific types of fields which are, in many cases, different either from the type of velocity field or from the original magnetic field. This special induction relationship, known as “selection rules”, has so far been derived by calculating Adams-Gaunt integrals and Elsasser integrals.In this paper, we calculate the induced modes in a more direct way, expressing the magnetic fields and the velocity in a spherical harmonic series. By linearizing the product terms of spherical harmonic functions, which appear in interaction terms between the velocity and the magnetic field, into a simple spherical harmonic series, we have derived the induced magnetic modes in a simple general form.When the magnetic field and the velocity are expressed by toroidal and poloidal modes, four kinds of interaction are conceivable between the velocity and the magnetic field. By each interaction, two modes, the poloidal and toroidal, are induced, except in the interaction of the toroidal velocity with the toroidal magnetic field, which induces only the toroidal mode. In spite of the diversity of interaction processes, the induced modes have been found to be expressed simply by two types. For a velocity of degree l and order k interacting with a magnetic field of degree n and order m, one type is the mode with degree and order of n+l-2t, |m±k| for an integer t, and the other with n+l-2t-1, |m±k|.

The Magnetic Field Dependence of Brightness Temperatures at Frequencies Microwave Absorption

Abstract: The dependence of microwave brightness temperatures on the earth's magnetic field at frequencies within a few megahertz of the O2 absorption line centers is examined in detail. The aLimuthal angular dependence i5 shown to factor from the radiative transfer equation while the dependence on the angle between the propagation direction and the earth's field direction is described hj a linear or quadratic poljnomial in the square of the cosine of this angle in some tjpical cases of potential interest for a mesospheric sounder. Dependencies of the brightness temperature matrix on the magnitude of the earth's field are derived and shown to he different according to whether linear or circular polari7ation is used. I. INTRODUCTION ONSIDERABLE interest is developing in obtaining C remotely sensed air temperature soundings of the earth's mesosphere and upper stratosphere. To accom- plish this goal by means of satellite-borne microwave ra- diometers, one must use frequencies lying within a few megahertz of the oxygen absorption line centers near 60 or 1 18 GHz. At these frequencies the Zeeman splitting of the lines arising from the interaction of the oxygen mol- ecule's magnetic dipole moment with the earth's magnetic field plays an important role in determining the absorption and emission behavior of the atmosphere. Early works by Lenoir (l), (2) have discussed a number of phenomena that must be considered in studying microwave brightness temperatures for mesospheric sounders. More recently, Rosenkranz and Staelin (3) have considered certain re- finements to Lenoir's work and looked at the use of cir- cular polarization. However, no studies of actual bright- ness temperature inversion algorithms have been published to date, nor has there been any discussion of how the magnetic field effects may be accounted for in an inversion algorithm. It is the purpose of this paper to describe the depen- dence of the microwave brightness temperature on the earth's magnetic field in some detail. The general situa- tion that will arise in practice with a scanning radiometer is considered so that a slight generalization of Lenoir's equations including all of the relevant angles-angle of incidence and the two angles describing the orientation of the earth's field with respect to the triad consisting of the

Solar and Stellar Magnetic Fields and Structures: Observations

Abstract: This review of stellar magnetic field measurements is both a critique of recent spectral diagnostic techniques and a summary of important trends now appearing in the data. I will discuss both the Zeeman broadening techniques that have evolved from Robinson’s original approach and techniques based on circular and linear polarization data. I conclude with an ambitious agenda for developing self-consistent models of the magnetic atmospheres of active stars.

Theoretical and experimental research on the second-order magnetic field

Abstract: This article deals with the second-order magnetic field, which appears significant in inhomogeneous current systems, where the total electric current has a zero value. The origin of this field is affected by the different drift velocities of the charge carriers in the individual parts of the system. The field is of a relativistic nature. This work describes suitable current systems as the origins of this field. Their main component is a semiconductor or superconductor bar, or if need be a beam of accelerated charged particles (electrons). The induction of this field in direct and alternating systems is calculated. The most significant component of this field is the acceleration boundary field, which appears in the thin boundary layers between the conductors with different drift velocities. The electromagnetic induction method of measuring the alternating second-order magnetic field is described. The article also gives an account of a successful experiment, which has confirmed the existence of this field with fast electrons in both a qualitative and quantitative way. The work discusses the possibilities of realisation of the current system with the semiconductor or superconductor and their application in the research of transport phenomena.

Radar studies of high-latitude ionospheric flows

Abstract: Strong interactions occur between the solar wind and the Earth’s magnetic field which result in the convection of ionospheric plasma over the polar cap regions. This generally forms a two-cell pattern with westward and eastward flows in the pre- and post-midnight sectors respectively. The flow pattern is sensitive to the flux of the solar wind and the direction of the interplanetary magnetic field. Observations of the flow pattern are thus of considerable value in the interpretation of the magnetosphere-ionosphere coupling processes and in identifying the influence of the solar wind on the Earth’s environment. The plasma convection can be observed by ground-based coherent and incoherent scatter radars and the flow vectors determined. Measurements for a range of flow conditions are presented. These are interpreted in terms of the interactions of the solar wind with the magnetosphere and the resulting electric fields which drive the plasma flows in the ionosphere.

Analysis of alternating magnetic field location technology of buried pipe lines

Abstract: The magnetic field induced by currents flowing through the ground between a buried pipe and an earth contact electrode is analyzed and numerically evaluated under the assumptions of homogeneous soil of pure resistance and quasi-steady field in order to clarify and to increase the accuracy of alternating magnetic field location technology. An effective formula for the evaluation of the magnetic field induced by underground current is developed. The theory evaluates the magnetic field with about 80% accuracy, providing more precise location. The time required for the evaluation is greatly reduced by the development of a table lookup algorithm. Experimental measurement of magnetic fields on an open space agree well with the numerical evaluations in spite of the use of idealized assumptions. >

Solar force-free magnetic fields on and above the photosphere

Abstract: If the problem of a magnetic field being force-free with α = constant (α ≠ 0) is solved by some previously published methods, then the field obtained in the whole exterior of the Sun cannot have a finite energy content and the solution cannot be determined uniquely from only one magnetic field component given at the photosphere. A magnetic field in the volume between two parallel planes has been investigated by us (Chen and Wang, 1986).

Threshold of stochastic motion of charged par-ticles in gradient magnetic field by electrostatic wave

Abstract: Nonlinear effects of the gradient inhomogeneity of the magnetic field on the stochastic motion of charged particles due to an electrostatic wave propagated arbitarily relative to the m-agnetic field are considered in this paper. A sequence of canonical transformations is preformed to obtain a Hamiltonian explicitly exhibiting the possibility of the resonance between the periodic motion of particles and oscillation in the wave. The theoretical analysis shows that, due to the inhomogeneity of the magnetic field, the threshold for the onse of the stochasticity is changed and, in the case of weak inhomogeneity of the magnetic field, it is lowered, which means that the stochasticity appears more easily than in the case of uniform magnetic field.