Showing papers on "Field (physics) published in 1975"

Random-Field Instability of the Ordered State of Continuous Symmetry

Abstract: Phase transitions are considered in systems where the field conjugate to the order parameter is static and random. It is demonstrated that when the order parameter has a continuous symmetry, the ordered state is unstable against an arbitrarily weak random field in less than four dimensions. The borderline dimensionality above which mean-field-theory results hold is six. (auth)

Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations

Abstract: A numerical method is described for the solution of the electromagnetic fields within an arbitrary dielectric scatterer of the order of one wavelength in diameter. The method treats the irradiation of the scatterer as an initial value problem. At t = 0, a plane-wave source of frequency f is assumed to be turned on. The diffraction of waves from this source is modeled by repeatedly solving a finite-difference analog of the time-dependent Maxwell's equations. Time stepping is continued until sinusoidual steady-state field values are observed at all points within the scatterer. The envelope of the standing wave is taken as the steady-state scattered field. As an example of this method, the computed results for a dielectric cylinder scatterer are presented. An error of less than /spl plusmn/10 percent in locating and evaluating the standing-wave peaks within the cylinder is achieved for a program execution time of 1 min. The extension of this method to the solution of the fields within three-dimensional dielectric scatterers is outlined.

Concept of Nonintegrable Phase Factors and Global Formulation of Gauge Fields

Abstract: Through an examination of the Bohm-Aharonov experiment an intrinsic and complete description of electromagnetism in a space-time region is formulated in terms of a nonintegrable phase factor. This concept, in its global ramifications, is studied through an examination of Dirac's magnetic monopole field. Generalizations to non-Abelian groups are carried out, and result in identification with the mathematical concept of connections on principal fiber bundles.

From Maxwell to paraxial wave optics

Abstract: In this paper we are concerned with the propagation of a light beam through an inhomogeneous, isotropic medium with a possibly nonlinear index of refraction. The customary paraxial approximations of neglecting grad $\mathrm{div}\mathcal{E}$ and seeking a plane-polarized solution are shown to be incompatible with the exact Maxwell equations. By starting from Maxwell's equations, and scaling transverse and longitudinal distances by the beam waist ${w}_{0}$ and diffraction length $l$, respectively, an expansion procedure in powers of $\frac{{w}_{0}}{l}$ is developed. The exact equations obeyed by the zeroth-order fields are not Maxwell's equations but the customary paraxial approximation to Maxwell's equations. Equations for the first-, second-, and third-order fields are developed. The first-order field is found to be a longitudinal field. It is solved for explicitly in terms of the zeroth-order field which is transverse. Thus a precise knowledge of the meaning and accuracy of paraxial wave optics is obtained.

Relativistic limitations on runaway electrons

Abstract: The non-relativistic theory of a plasma in an electric field E predicts that there will always be runaway electrons, although their number will be exponentially small for fields less than the Dreicer field ED. However, when E/ED ~ kT/mec2, the ratio of the electron thermal energy to the rest mass energy, relativistic effects become important. After comparing earlier non-relativistic calculations we extend the approach of Kruskal and Bernstein to take account of relativistic effects and also to investigate the influence of impurities. It is found that below the critical electric field ER = ED (kT/mec2) absolutely no runaways are generated. In addition, the number of runaway electrons produced by electric fields in excess of ER is calculated and we find significant modifications to the non-relativistic estimates when (ED/E)2 (kT/mec2) > 1.

Lee waves in stratified flows with simple harmonic time dependence

Abstract: The process of internal gravity wave generation by the simple harmonic flow (U = U0, cos ω0t) of a stably stratified fluid (Brunt–Vaisala frequency N) over an obstacle is investigated in some detail. Attention is primarily directed to the behaviour of the solution in various limiting cases, and to estimating the flux of energy into the internal wave field. In general, waves are generated not only at the fundamental frequency ω0, but also at all of its harmonics. But, for values of ω0/N greater than about one half, the waves of fundamental frequency are dominant. For values of ω0/N, less than about one half, the quasi-static approximation, in which the problem is considered as a slowly-varying version of the classical lee wave problem, is found to provide a viable estimate for the wave field. The general solution is found to compare favourably with the limited available experimental data.

Polar cap currents for different directions of the interplanetary magnetic field in the Y‐Z plane

Abstract: During intervals of a steady state condition of the interplanetary magnetic field the geomagnetic variations at the polar cap have been examined as a function of the direction of the interplanetary field in the Y-Z plane of the geocentric solar magnetospheric coordinate system. A prominent feature of the equivalent current patterns during a positive B/sub z/ steady state is the total vanishing of the well-known two-cell current system, which is generally considered to be related to the convection across the polar cap. Another significant effect for a northward interplanetary magnetic field is a poleward shift of the B/sub y/ associated currents at the day side of the polar cap, with no decrease of the current strength. The existence of these currents even during the absence of the two-cell current system indicates that the explanation proposed by Heppner (1972) of the currents' being due to a shift toward the dawn or the dusk of the polar cap convection is not exhaustive. Rather, the magnetic perturbations for a positive B/sub z/ may correspond to merging of the northward interplanetary magnetic field with the open geomagnetic field lines at the poleward boundary of the cusp as suggested by Burch (1973). A pronounced decreasemore » of the B/sub y/ related magnetic perturbations from summer to winter compared to the seasonal variation of the B/sub z/ related disturbances at the polar cap indicates a different origin of the associated currents. (auth)« less

First order transitions in ACo 2 compounds

Abstract: Some magnetic properties of ACo2 compounds, where A is a heavy rare earth metal, are shown to be related to properties of YCo2 In particular the existence of first order transitions for A=Er, Ho, Dy, but second order transitions for A=Tb, Gd, implies a special temperature dependence of the Landau parameter B which appears in the expansion of the free energy of YCo2 in powers of the magnetization B changes from negative to positive with increasing temperature and this is verified experimentally by measurements of the field dependence of the susceptibility of YCo2 at 42, 77 and 300K in field up to 150 kOe It is estimated that an applied field of about 1400 kOe would be required to produce itinerant electron metamagnetism in YCo2 and the magnetization of GdxY1-xCo2, where the 'applied' field is the molecular field due to Gd moments, is discussed from this point of view Stoner theory is used to relate the behaviour of B to the existence of a maximum in the susceptibility of YCo2 as a function of temperature

Engineering Electromagnetic Fields and Waves

Abstract: Vector Analysis and Electromagnetic Fields in Free Space Vector Differential Relations and Maxwell's Differential Relations in Free Space Maxwell's Equations and Boundary Conditions for Material Regions at Rest Static and Quasi-Static Electric Fields Static and Quasi-Static Magnetic Fields Wave Reflection and Transmission at Plane Boundaries The Poynting Theorem and Electromagnetic Power Mode Theory of Waveguides TEM Waves on Two-Conductor Transmision Lines Phasor Analysis of Reflective Transmision Lines Radiation from Antennas in Free Space Appendixes Index.

Observations of oceanic internal and surface waves from the earth resources technology satellite

Abstract: Periodic features observed on the ocean surface from the Earth Resources Technology Satellite 1 have been interpreted as surface slicks due to internal wave packets. They appear to be generated at the edge of the continental shelf by semidiurnal and diurnal tidal actions and propagate shoreward. Nonlinear effects apparently distort the wave packets as they progress across the shelf. This observational technique constitutes a new tool for delineating two dimensions of the internal wave field under certain limited conditions.

Magnetic merging in a collisionless plasma

Abstract: This paper examines the problem of magnetic merging in a fully collisionless plasma, i.e., a plasma of noninteracting charged particles, explicitly avoiding the fluid (MHD) approximation. The Alfven self-consistency criterion that relates the plasma density to the electric and magnetic fields is shown to be equivalent, when suitably generalized, to the stress-balance requirement discussed by Rich, Vasyliunas, and Wolf. From this criterion the self-consistent electric field and the magnetic merging speed are obtained as functions of the magnetic field configuration and of the incident plasma parameters. The merging speed obtained for equal antiparallel fields is within a factor of 2 of the result of fluid theory if the incident plasma pressure is initially isotropic. The merging speed is respectively reduced or enhanced when the incident parallel plasma pressure P∥ is greater than or less than the incident transverse pressure P⊥. When P∥ - P⊥ = B²/µ0 (the marginal fire hose stability condition), merging ceases. For the more general field configuration wherein the opposing magnetic fields B1 and B2 have arbitrary magnitudes and directions the merging electric field is shown to have a maximum value when the fields are antiparallel and to decrease monotonically to zero as the angular separation of the fields decreases to arccos (B1/B2). The expected merging electric field at the day side magnetopause as a function of the strength and direction of the interplanetary magnetic field is presented in a form that can be compared directly with observations. Although a detailed comparison is not feasible, the general results of the analysis are compatible with available observations in the magnetosphere and solar wind.

On Phillips' Theory of Equilibrium Range in the Spectra of Wind-Generated Gravity Waves

Abstract: Phillips' hypothesis concerning the equilibrium range in the spectrum of wind-generated surface waves in deep water can be expressed either in the frequency form S(ω)∝ω−5 or the wavenumber form Ψ(k)k−4 If one adopts the wavenumber form as universal, it can then be shown that for shallow water S(ω)∝ω−3, a relation supported by observations It is noted that deviations from the S(ω)∝ω−5 relation can be introduced not only by finite depth but also by permanent currents, as well as by the presence of long-wave components in the sea wave spectrum In the latter case determination of S(ω) has to include both the Doppler effect, due to orbital displacements of liquid particles in long waves, as well as the effect of additional vertical acceleration in short waves propagating along the surface of the long-wave field The article also gives calculations that illustrate the significance of the foregoing effects on deviations from the Phillips −5 power law in the frequency spectrum S(ω)

Geomagnetic secular variation over the past 5 m.y.

Abstract: The study of the geomagnetic secular variation in prearcheological times is based upon investigations of the angular dispersion of paleomagnetic results and its variation with latitude. The westward drift of the geomagnetic field observed in historic times and apparently confirmed by archeomagnetic data back 1000 years or more suggests the way in which the present geomagnetic field may be analyzed for comparison with paleomagnetic results. Generalized models of paleosecular variation suppose that the angular dispersion arises from two contributions, one due to variations in the dipole field (dipole wobble) and one due to variations in the nondipole field. Attempts at distinguishing between these two contributions are inherently nonunique. To overcome the nonuniqueness problem, we have proposed a model for paleosecular variation (model M) that fits both the paleomagnetic data and the variation expected from analysis of the present field and that is also compatible with current theories of the origin of secular variation. This results in an average dipole wobble of 9$sup 0$ over the past 5 m.y. The best fit to the nondipole dispersion then arises from a combination of two mechanisms for the origin of secular variation. The major contribution arises from a nondipole field that originates frommore » some sort of interaction with the main poloidal field, probably akin to Hide's magnetohydrodynamic wave mechanism. The secondary contribution, about two-thirds the magnitude, arises from a fixed field whose intensity is independent of latitude compatible with Bullard's mechanism of fluid eddies interacting with the toroidal field near the core-mantle boundary. The two types of nondipole field are compatible with Yukutake's subdivision into drifting and standing parts, respectively, and provide a possible physical basis for his analysis. During a polarity transition the standing part of the nondipole field should predominate. (auth)« less

Audio-frequency magnetotellurics with a grounded electric dipole source

Abstract: The conventional audio‐frequency magnetotelluric method has been useful in problems of shallow exploration to depths of a few kilometers. Because the natural sources are unpredictable in strength and direction, we have examined the possibility of doing magnetotelluric sounding utilizing the ratio of horizontal electric field to horizontal magnetic field from a controlled source. The source chosen for this study was a grounded electric dipole. The equations for the electric and magnetic fields around this antenna as a function of range and azimuth have been calculated for a half‐space and for a one‐layered earth. These calculations were checked for the half‐space case with an analog model and in the field at the Bonneville Salt Flats. In addition, layered cases were calculated, and a field example near Timmins, Ont., studied. Provided the distance of the observation point from the source is three skin depths (relative to the greatest resistivity in the section) or more, the conventional magnetotelluric int...

Nonlinear behavior of acoustic waves in combustion chambers

Abstract: This paper is concerned with the general problem of the nonlinear growth and limiting amplitude of acoustic waves in a combustion chamber. The analysis is intended to provide a formal framework within which practical problems can be treated with a minimum of effort and expense. There are broadly three parts. First, the general conservation equations are expanded in two small parameters, one characterizing the mean flow field and one measuring the amplitude of oscillations, and then combined to yield a nonlinear inhomogeneous wave equation. Second, the unsteady pressure and velocity fields are expressed as syntheses of the normal modes of the chamber, but with unknown time-varying amplitudes. This procedure yields a representation of a general unsteady field as a system of coupled nonlinear oscillators. Finally, the system of nonlinear equations is treated by the method of averaging to produce a set of coupled nonlinear first order differential equations for the amplitudes and phases of the modes. These must be solved numerically, but results can be obtained quite inexpensively. Subject to the approximations used, the analysis is applicable to any combustion chamber. The most interesting applications are probably to solid rockets, liquid rockets, or thrust augmentors on jet engines. The discussion of this report is oriented towards solid propellant rockets.

Apparatus for generating a nutating electromagnetic field

Abstract: A field (e.g., a magnetic field) which nutates about a pointing vector is used to both track or locate an object in addition to determining the relative orientation of this object. Apparatus for generating such a field includes mutually orthogonal coils and circuitry for supplying an unmodulated carrier, hereafter called DC signal, to one coil and an AC modulated carrier signal, hereafter called AC signal, to at least one (usually two) other coil, such that the maximum intensity vector of a magnetic field produced by the currents in the coils nutates about a mean axis called the pointing vector direction of the field.

Linear transformations of gravity and magnetic fields

Abstract: The spectral representation of gravity and magnetic fields shows that the mathematical expressions describing these fields are the result of convolution of factors which depend on the geometry of the causative body, the physical properties of the body and the type of field being observed. If a field is known, it is possible to remove or alter these factors to map other fields or physical parameters which are linearly related to the observed field. The transformations possible are: continuation, reduction to the pole, converting between gravity and magnetic fields, converting between components of measurement, calculation of derivatives, and mapping magnetization and density distribution, relief on interfaces, and vertical thicknesses of layers.

Non-Abelian gauge fields as Nambu-Goldstone fields

Abstract: Gauge invariance is obtained as a consequence of the spontaneous breaking of a larger symmetry. The Yang--Mills gauge fields are the corresponding Nambu--Goldstone fields. This involves the study of field theories in a space with more than four dimensions. In a ''cylindrical'' sector these field theories reduce to new non-Abelian generalizations of Jordan--Brans--Dicke theory. The nonobservability of the excess dimensions (while a difficulty for theories in which these dimensions are bosonic) should cause no problems if the higher dimensions are fermionic. In the latter case, field theories in which all basic fields are at the same time Nambu--Goldstone and Yang--Mills fields become possible. The relation of this work to recent work on gravitation theory by Yang is explored.

A study of geomagnetic storms

Abstract: Twenty-one geomagnetic storm events during 1966 and 1970 were studied by using simultaneous interplanetary magnetic field and plasma parameters. Explorer 33 and 35 field and plasma data were analyzed on large-scale (hourly) and small-scale (3 min.) during the time interval coincident with initial phase of the geomagnetic storms. The solar-ecliptic Bz component turns southward at the end of the initial phase, thus triggering the main phase decrease in Dst geomagnetic field. When the Bz is already negative, its value becomes further negative. The By component also shows large fluctuations along with Bz. When there are no clear changes in the Bz component, the By shows abrupt changes at the main phase onet. On the small-scale behavior of the magnetic field and electric field (E=-VxB) studied in details for the three events, it is found that the field fluctuations in By, Bz and Ey and Ez are present in the initial phase. These fluctuations become larger just before the main phase of the storm begins. In the largescale behavior field remains quiet because the small scale variations are averaged out.

A global magnetic anomaly map

Abstract: A subset of POGO satellite magnetometer data has been formed that is suitable for analysis of crustal magnetic anomalies. Using a thirteenth order field model, fit to these data, magnetic residuals have been calculated over the world to latitude limits of plus 50 deg. These residuals averaged over one degree latitude-longitude blocks represent a detailed global magnetic anomaly map derived solely from satellite data. Preliminary analysis of the map indicates that the anomalies are real and of geological origin.

Visually evoked magnetic fields of the human brain.

Abstract: Magnetic field variations from the human brain produced by visual stimulation have been observed in a normal laboratory setting with a superconducting quantum interference device and no magnetic shielding of the subject. Previously unknown temporal and spatial features of the field near the scalp are reported.

Spatial aspects of the electric fields generated by weakly electric fish

Abstract: 1. The electric fields of four species of wave type, gymnotid fishes were measured and mapped using a technique that allowed accurate assessment of small electric fields, free of unknown field compression and distortion artifacts. 2. Dipole moment values were calculated for each fish's electric field from measurements made at a sufficient distance (Table 1). A dipole moment is an absolute evaluation of the electric fish's field strength that can be used for quantitative, intraspecific and interspecific comparisons. 3. The electric fish, as a field source, represents a distributed rostral pole and a point-like caudal pole (Fig. 2). Deviations of a fish's electric field from that of a dipole field increase with fish size, decreasing water resistivity, and decreasing distance from the fish. 4. Apteronotid species maintain a constant current electric organ output (dropping less than 5%) in water of resistivity up to 15 kOhm · cm, whereas rhamphichthyid species maintain a constant current output only in water up to 10 kOhm · cm (Fig. 6). Within each family, the larger fish maintained their current output level in higher water resistivities than did smaller fish. 5. Electrocommunication distances for the individual fishes are predicted based upon their measured electric field magnitudes and the known electrosensitivities of these species (Table 2); consequences of the geometry of the fishes' electric fields on object detection and object resolution are discussed.

Quantum Electrodynamical Effects in Kerr-Newmann Geometries

Abstract: Following the classical approach of Sauter, of Heisenberg and Euler and of Schwinger the process of vacuum polarization in the field of a "bare" Kerr-Newman geometry is studied. The value of the critical strength of the electromagnetic fields is given together with an analysis of the feedback of the discharge on the geometry. The relevance of this analysis for current astrophysical observations is mentioned.

The effect of adiabatic focusing upon charged particle propagation in random magnetic fields

Abstract: This paper describes the effects of strong adiabatic focusing in terms of eigenfunctions of an operator which incorporates both scattering by random fields and focusing by a spatially inhomogeneous guiding field. It is found that focused transport differs from rectilinear transport in the following ways: (1) the coherent velocity toward stronger fields is larger than that toward weaker fields; (2) coherent effects are more prominent relative to diffusive effects when focusing is present; and (3) initial anisotropies at injection have a minimal influence upon rectilinear transport but they have a pronounced effect on focused transport. These features explain certain well-known discrepancies between the diffusive picture and the observed profiles of solar particle events. In particular, they explain the so-called scatter-free propagation of kilovolt flare electrons.

Theory of the hydromagnetic generator

Abstract: It is shown that in a homogeneous medium, a magnetic field may generate helical motion in a cylinder with constant angular and axial velocities. The generation problem is solved exactly, and analytic expressions for the magnetic field are found. At high velocities the increment of field growth is maximal when the ratio of the velocities is of the order of unity. The maximum increment and frequency are of the order of the velocity to the two-thirds power. The field distribution has the form of a surface wave. The field decay decrement for departure from the cylinder surface is proportional to the square root of its increment.