Showing papers on "Field (physics) published in 1973"

Nonuniqueness of canonical field quantization in Riemannian space-time.

Abstract: We point out and discuss an ambiguity which arises in the quantum theory of fields when the background metric is not explicitly Minkowskian-in other words, when an external gravitational field, real or apparent, is present. A general theory of a canonical neutral scalar field in a static universe, including the construction of a Fock space, is presented. It is applied to a portion of two-dimensional flat space-time equipped with a non-Cartesian space-time coordinate system with respect to which the metric is nonetheless static. The resulting particle interpretation of the field is shown to be different from the standard one in special-relativistic free-field theory. The ambiguity frustrates an attempt to define uniquely the energy-momentum tensor by the usual method of normal ordering. We discuss various suggestions for (1) distinguishing a unique correct quantization in a given physical situation, or (2) reinterpreting seemingly inequivalent theories as physically equivalent. In passing it is shown that the vacuum state and the energy density of a free field in a box with periodic boundary conditions differ from those associated with a region of the same size in infinite space; this result should be of interest outside the gravitational context.

Phase Transition in the Dicke Model of Superradiance

Abstract: A system of $N$ two-level atoms interacting with a quantized field, the so-called Dicke model of superradiance, is studied. By making use of a set of Glauber's coherent states for the field, the free energy of the system is calculated exactly in the thermodynamic limit. The results agree precisely with those obtained by Hepp and Lieb, who studied the same model using a different method. The exhibition of a phase transition of the system is presented mathematically in an elementary manner in our approach. The generalization to the case of finitely many radiation modes is also presented.

Self‐consistent calculation of the motion of a sheet of ions in the magnetosphere

Abstract: Time-dependent magnetospheric electric fields have been computed, including the effects of Birkeland currents from the inner edge of a sheet of ions that moves under the influence of the computed electric fields. Ionospheric currents are also taken self-consistently into account with the use of a time-independent model of ionospheric conductivity that includes day-night asymmetry and auroral enhancements but neglects electric fields parallel to the magnetic field. Ion precipitation and neutral winds are also neglected. The behavior and effects of the ion sheet are studied in a series of model calculations, with the following results. (1) In agreement with the conclusions of E. T. Karlson, L. P. Block, V. M. Vasyliunas, and D. W. Swift, Birkeland currents from the Alfven layer (inner edge of the ion sheet) are found to reduce the electric field earthward of the Alfven layer to a small value by the time a steady state is reached; however, different parts of the electric field earthward of the Alfven layer are eliminated at different rates; one component of the nightside field relaxes to near its low asymptotic value in a few minutes, whereas the dayside field takes hours to relax. (2) If the ion sheet is brought in from the tail by a large cross-tail electric field that stays large, the inner edge of the sheet generally touches the magnetopause boundary layer; however, a decrease in the cross-tail field can cause the Alfven layer to contract and form a complete ring. (3) For the parameters used, a cross-tail potential of 134 kv will bring a sheet of ring current protons in to about L = 4; the results of the model calculations support the idea that convection electric fields bring low-energy ions in from the tail to form the storm time ring current; the minimum geocentric distance to which convection fields can bring the ions is found to be roughly proportional to (ημ/Φ0σρ)1/3, where η is the number of ions per unit magnetic flux, μ is the ion magnetic moment, Φ0 is the cross-tail potential, and σρ is an average height-integrated Pedersen conductivity on the dayside. (4) The nightside Alfven layer naturally produces a dividing line near local midnight, such that particles arriving west of the line drift to the west, whereas those arriving east of the line drift east; this characteristic is often observed in motions of barium clouds and auroral arcs.

Theory of Isothermal Currents and the Direct Determination of Trap Parameters in Semiconductors and Insulators Containing Arbitrary Trap Distributions

Abstract: Equations are presented that permit the calculation of the isothermal current- (I) vs-time ($t$) characteristics for defect insulators and semiconductors in which the field is sufficiently high and the active region sufficiently thin so that recombination of free carriers is negligible. More important, however, it is shown that by plotting $\mathrm{It}$ vs ${log}_{10}t$ the resulting characteristic is either (a) in the case of distributed traps, a direct image of the trap distribution, or (b) in the case of discrete traps, exhibits a number of sharp maxima at various times, depending on the trap parameters. The technique permits the direct determination of the trap distribution without having to have an a priori knowledge of the trap parameters and without the necessity of laborious analyses.

A field study of hearing in the cod,Gadus morhua L.

Abstract: 1. Field measurements of hearing in the cod,Gadus morhua L., have shown that these fish are sensitive to pure tones in the frequency range from 30 to 470 Hz with greatest sensitivity in the range 60 to 310 Hz. At the most sensitive frequencies the mean thresholds varied between -18 and -26 dB/μbar (Fig. 4). 2. Variation in the thresholds at most frequencies was related to changes in the level of ambient sea noise (Figs. 5–7). Only in calm sea conditions were unmasked thresholds obtained. The masking effect of noise was confirmed by raising the level artificially. The thresholds increased in proportion to the increase in noise level. 3. The thresholds were largely independent of the distance of the sound source over the range from 1.7 to 50m, suggesting that cod are sensitive to acoustic pressure. However, a changeover to particle displacement sensitivity was noted at frequencies below 50 Hz when the sound source was moved to within l m of the fish (Fig. 9). 4. It is concluded that the swimbladder plays an accessory role in hearing. Differences obtained in the thresholds at different sound source distances may be explained in terms of the displacement sensitivity of the otolith organs. These respond to displacements re-radiated from the swimbladder in the far-field, and to the greater incident displacement in the near-field at very low frequencies.

Field singularities and related integral representations

Abstract: This chapter is concerned with certain stress fields in isotropic elastic bodies. Assumed will be the laws of linear elasticity where the stresses and strains are related to one another by Hooke’s law. Emphasis will be placed on field singularities due to cracks. Moreover the analysis will be confined to fields of plane strain and to special cases of axial symmetry. The results for plane strain apply to cases of plane stress, if the familiar approximation is admitted whereby a field of plane strain can be interpreted as one of plane stress for different elastic parameters.

Theory of space‐charge polarization and electrode‐discharge effects

Abstract: A combined, general treatment of intrinsic and extrinsic conduction in a liquid or solid is presented. Positive and negative species of mobile charge of arbitary valences and mobilities are assumed present, together with homogeneous immobile charge in the extrinsic case. The general equations are specialized to a one‐dimensional situation and then to that where both position‐dependent static and much smaller sinusoidally time‐varying components of charge, field, and current are simultaneously present. Sufficiently general boundary conditions are used that any condition from complete blocking to free discharge of positive and negative mobile carriers separately can occur at the electrodes. For the flat‐band condition (zero static field; in the binary electrolyte case, coincidence of the zero charge potential and the equilibrium potential) exact equivalent circuits and an exact expression for the small‐signal impedance are obtained. Relatively simple, closed‐form expressions for the zero‐frequency limiting ...

A qualitative study of the reconnection between the Earth's magnetic field and an interplanetary field of arbitrary orientation

Abstract: To the present date only the reconnection process for exactly antiparallel fields has been discussed in detail. In magnetospheric terms this restricts us to the consideration only of southward interplanetary fields. The qualitative study presented here shows how reconnection takes place between arbitrarily oriented fields in infinite and finite geometries. The process may best be thought of as a continuous exchange of field-line partners during the time a field line maps into the diffusion region. In a finite geometry the diffusion regions lie on field lines which connect neutral points of the field configuration, and along which a potential drop is imposed. Although the discussion here centers principally on the magnetosphere, the described reconnection process and field topology should also be applicable to other astrophysical problems.

Generation of stationary Einstein‐Maxwell fields

Abstract: The Einstein‐Maxwell field equations in the presence of one Killing vector are shown to possess covariance under an eight‐parameter group of linear substitutions in the field variables. This internal symmetry group is isomorphic to SU(2,1). Three of the degrees of freedom correspond to gage transformations, but the remaining ones allow us to generate a five‐parameter family of solutions given a single solution.

An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack

Abstract: This paper contains an asymptotic treatment, consistent with the fully nonlinear equilibrium theory of compressible elastic solids, of the stresses and deformations near the tip of a traction-free crack in a slab of all-around infinite extent under conditions of plane strain. The loading applied at infinity is taken to be one of uniform uniaxial tension at right angles to the faces of the crack. For the particular class of elastic materials considered the tensile stress in large homogeneous uni-axial extension is asymptotic to a continuously adjustable power of the corresponding principal stretch. The asymptotic analysis of the foregoing crack problem is reduced to a nonlinear eigenvalue problem, the solution of which is established in closed form, in terms of elementary functions and a transcendental integral of such functions. This solution involves two arbitrary constants, one of which governs the amplitude of the ensuing elastostatic field near the tip of the crack. A precise estimate of the amplitude parameter, valid at sufficiently small load intensities, is deduced with the aid of a known conservation law. The remaining arbitrary constant, which is left indeterminate by the present lowest-order asymptotic analysis, does not affect the dominant behavior of the field quantities of primary physical interest. II-lustrative numerical results, appropriate to both hardening and softening materials, are presented.

On the structure of the magnetotail current sheet

Abstract: A self-consistent tail current sheet model described by an exact analytic solution of the time-independent Vlasov-Maxwell equations is presented. The model has a 'slingshot' field configuration with field lines outside the plasma sheet slightly flared in the antisolar direction. It is pointed out that when the model parameters are adjusted to agree with the spatial variation along the tail the required thickness of the neutral sheet must be about 2.5 earth radii, instead of less than or equal to 1 earth radius, as indicated by observations. Furthermore, it is shown qualitatively that a considerable velocity shear must be present in the tail current sheet if the plasma sheet is indeed much thicker than the neutral sheet.

On the generation of potential differences across the membranes of ellipsoidal cells in an alternating electrical field.

Abstract: Particles with a nonconducting membrane, oriented in an alternating electrical field, will show the behaviour of electrical dipoles. Across the membranes there will be generated alternating electrical potential differences, which may be calculated for confocal ellipsoidal cells by solving Laplace's equation. We have evaluated a formula valid generally for single confocal ellipsoidal cells under physiological conditions, the cells being placed with one of their semi-axes parallel to an external electrical field. The values of the generated potential difference, considered at the position of their maximum values, are dependent on the shape and size of the cells, on their orientation to the electrical field and on the frequency and strength of the field. The relaxation frequency depends also on cell shape, size and orientation, but furthermore on the membrane properties and on the conductivities inside and outside the cells. For simple cases like spheres and cylinders perpendicular to the electrical field, our formula will correspond to known expressions. Values for the generated potential differences, form-factors and relaxation frequencies are given for different types of spheroids and at different orientations. Of some practical importance are long prolate spheroids with their long semi-axes parallel to the external field, because only small field strengths are necessary in order to generate large potential differences which may evoke action potentialse.g. in muscle or nerve cells. The significance of this mechanism concerning the determination of protection and safeguard standards for the exposure to low-frequency electrical fields is discussed.

Theory of gyrotrons with a nonfixed structure of the high-frequency field

Abstract: In a gyrotron (amplifier or oscillator) having an electrodynamic system in the form of a slightly irregular waveguide having a low effective Q, the frequency of the variable field is close to the critical frequency of one of the natural waves of the waveguide in operating modes having a high efficiency; as consequence of this: 1) a fairly accurate determination of the optimal parameters of the system may be accomplished by extrapolation of the results of the theory based on the fixed-variable-field-structure approximation; 2) a constraint on the output power exists which is caused on the one hand by mode competition and on the other hand by rebunching of electrons in an excessively powerful variable field, which according to the constraint imposed by the diffraction Q(1), may develop in the electrodynamic system of a gyrotron when a powerful electron beam is injected into it.

Nonlinear perturbation theory for cosmic ray propagation in random magnetic fields

Abstract: A nonlinear perturbation theory is applied to the problem of pitch angle diffusion of energetic particles in random magnetic fields. To keep the analysis simple, the discussion is restricted to fluctuation fields, consisting of Alfven waves. It is shown that the failure of quasilinear theory at small particle velocities parallel to the average field can be overcome by a statistically exact treatment of the particle orbits in the first order fields. In fact, for spherical power spectra which, in addition, do not fall off too steeply with increasing frequency, the conventional perturbation theory also leads to formally convergent expressions for the scattering mean free path. These results are shown to be quite satisfactory, even in a quantitative sense. For more general physically realistic power spectra, however, a divergence-free diffusion theory is indispensible. A simple representation for the resulting pitch-angle diffusion coefficient is suggested.

Theory of the magnetic viscosity of lunar and terrestrial rocks

Abstract: Lunar materials exhibit two distinct types of viscous or time-dependent magnetic behavior. Igneous rocks and largely recrystallized breccias, whose magnetic properties are due to multidomain iron, typically have weak magnetic viscosity, but decay persists for very long times following even a brief exposure to a field. Lunar soils and low metamorphic grade breccias, which contain an important fraction of metallic iron of single-domain and superparamagnetic size, generally acquire an anomalously strong viscous remanence, whose decay time is about equal to the time of exposure to the field. Four theories of magnetic viscosity are reviewed in this paper in an attempt to interpret the very different viscous properties of these two types of rocks. The Richter (1937) and Neel (1949) theories are appropriate to soils and low-grade breccias, whereas igneous and recrystallized rocks are better described by the multidomain theories of Neel (1950) and Stacey (1963). Both the Stacey and Neel theories correctly predict logarithmic magnetic viscosity, in spite of the fact that the central role played by the internal demagnetizing field in multidomain grains is ignored in Neel's formulation. This apparent paradox has been resolved. Analysis of the particularly simple case of a two-domain particle shows that the distribution of asymmetrical nonidentical potential barriers required by Neel is automatically generated from the simpler distribution of symmetrical identical barriers proposed by Stacey through the action of the demagnetizing field. Experimental evidence on many facets of viscous magnetization, from terrestrial as well as lunar materials, is reviewed in detail before a final evaluation of the various theories is made. One interesting conclusion is that the magnetic viscosity of multidomain particles, although relatively weak, is still too strong to be explained by displacements of entire domain walls. Either displacements of small wall segments or rotation of pseudo-single-domain moments could account for the enhancement of magnetic viscosity in these particles.

The reconnection rate of magnetic fields.

Abstract: Rapid reconnection of magnetic lines of force occurs whenever two regions of opposite field are pressed together without sufficient fluid pressure between to keep them apart. It has been suggested that rapid reconnection is the basis for solar flares, and that in the magnetopause and the neutral sheet of the geomagnetic tail it plays an essential role in geomagnetic activity. It is pointed out that the escape of fluid from between the fields is the result of magnetohydrodynamic exchange instabilities, leading to reconnection rates which are generally some fraction of the Alfven speed.

Power Deposition in a Spherical Model of Man Exposed to I-20-MHz Electromagnetic Fields

Abstract: The induced fields and the associated power deposition in mail exposed to HF electromagnetic (EM) fields have been investigated theoretically using spherical models. The induced electric fields inside the model exposed to either plane wave or near fields can be described adequately by a combination of quasi-static electric and magnetic induction solutions. It is shown that for field impedances less than 1200/spl pi//spl Omega/ the magnetically induced energy absorption predominates. Therefore, H fields must be measured to obtain any estimate of the hazards due to HF exposure. For a 70-kg model of man exposed to a plane wave field, the theory indicates that the time-average power absorption per unit volume is less than 2.5x10/sup -3/ mW/g for each milliwatt per square centimeter incident at 20 MHz and below. This suggests that the thermal safe-exposure levels for the HF band are many orders of magnitude in excess of the 10-mW/cm/sup 2/ level recommended for the microwave region.

Intrinsic photoconduction in anthracene single crystals: Electric field dependence of hole and electron quantum yields

Abstract: For electric fields up to 2 × 104 V/cm applied normal to the a b plane of virgin anthracene crystals, both the hole and electron photocarrier quantum yields increase linearly with field Field‐dependence plots exhibit a slope to intercept ratio of 31 × 10−5 cm/V, a value which is in quantitative agreement with that predicted by Onsager's theory of geminate recombination In nonvirgin crystals, sharply reduced photocarrier quantum yields at low fields are found to result from recombination of free carriers with oppositely charged trapped carriers left behind in the excitation region from previous experiments The free carrier‐trapped charge recombination rates are found to be diffusion controlled

High latitude electric fields and the modulations related to interplanetary magnetic field parameters

Abstract: The meaning and characteristics of basic and average convection (i.e., electric field) patterns are described. The continuous existence of the basic convection pattern argues against treating magnetic field merging mechanisms as the fundamental cause of magnetospheric convection. However, whether related to merging or to some other mechanism, interplanetary magnetic field conditions significantly modulate the distribution, magnitudes, and boundaries of the convection pattern. A previous correlation between azimuthal angles of the interplanetary magnetic field and asymmetries in polar cap electric field distributions as seen by OGO-6 is reviewed. A new approach is taken to reveal correlations with the north-south angle and magnitude of the interplanetary field as well as additional features which correlate with the azimuthal angle. Both significant correlations and conditions which show a lack of correlation are found. Several aspects of the correlations appear to be particularly important.

Monte-Carlo investigations of the motion of gaseous ions in electrostatic fields

Abstract: The motion of gaseous ions in arbitrarily strong electrostatic fields has been studied by Monte-Carlo simulation techniques, assuming various forms of the ion-neutral interaction law. Approximate expressions for the mobility and the mean square velocity suggested by Wannier (1953) were in most cases found to predict the correct values within 20%. The lateral diffusion coefficient to mobility ratio Dperpendicular to / mu was in all cases studied found to be remarkably accurately connected to the mean square velocity normal to the electric field through a generalized Nernst-Townsend relation. The longitudinal diffusion coefficient D/sub /// does not, on the other hand, seem to be simply related in any way to the mean square random velocity in the field direction, except near thermal energies. For hard sphere interaction and non-vanishing fields the lateral diffusion coefficient is always larger than the longitudinal one.

Natural-mode representation of transient scattered fields

Abstract: Electromagnetic scattering from a perfectly conducting body of finite extent is considered from an integral equation point of view. It is shown that the operator inverse to the integral operator of the magnetic field formulation is an analytic operator-valued function in the complex frequency plane except at certain points (the natural frequencies) where it has poles. Furthermore, a representation of the inverse operator in terms of the natural frequencies and the nontrivial solutions of the homogeneous integral equation is given. Explicit expressions for the scattered field in terms of exponentially damped sinusoidal oscillations are given for the special case where the incident wave is a delta-function plane wave and the inverse operator has only simple poles.

Numerical Solutions of the Kinematic Dynamo Problem

Abstract: The expansion method of Bullard & Gellman is used to find numerical solutions of the induction equation in a sphere of conducting fluid. Modifications are made to the numerical methods, and one change due to G. O. Roberts greatly increases the efficiency of the scheme. Calculations performed recently by Lilley are re-examined. His solutions, which appeared to be convergent, are shown to diverge when a higher level of truncation is used. Other similar dynamo models are investigated and it is found that these also do not provide satisfactory steady solutions for the magnetic field. Axially symmetric motions which depend on spherical harmonics of degree n are examined. Growing solutions, varying with longitude, $\phi $, as e$^{\text{i}\phi}$, are found for the magnetic field, and numerical convergence of the solutions is established. The field is predominantly an equatorial dipole with a toroidal field symmetric about the same axis. When n is large the problem lends itself to a two-scale analysis. Comparisons are made between the approximate results of the two-scale method and the numerical results. There is agreement when n is large. When n is small the efficiency of the dynamo is lowered. It is shown that the dominant effect of a large microscale magnetic Reynolds number is the expulsion of magnetic flux by eddies to give a rope-like structure for part of the field. Physical interpretations are given which explain the dynamo action of these motions, and of related flows which support rotating magnetic fields.

Asymptotic theory for inhomogeneous waves

Abstract: The conventional asymptotic theory for propagation of high-frequency fields is based on a local description in terms of homogeneous plane waves A(r) exp [ik_{0}S(r)] , where k_{0} is the (large) free space wavenumber, A(r) is a spatially dependent amplitude, and the phase S(r) is real. The conventional theory does not accommodate the more general class of fields that behave locally like inhomogeneous plane waves with complex phase S(r)= R(r) + iI(r) , where R determines the propagation of the equiphase surfaces and I describes the attenuation. This paper develops an asymptotic theory for inhomogeneous wave fields in lossless media, to be termed evanescent fields. Such fields are encountered, for example, in connection with Gaussian beams and with phenomena on the exterior of surface wave structures or on the dark side of caustics. The scalar wave equation is used to derive eikonal and transport equations for S and A , respectively, and it is shown how the latter equations may be integrated with the aid of trajectories tangent to the direction of ablaR , which differs slightly from that for the local power flow. Detailed application of the theory is made to two-dimensional scattering of a weakly evanescent incident plane wave by a curved boundary in a homogeneous medium. The phase propagation paths for the reflected field are determined explicitly and are found to possess curvature and points of inflection; these characteristics are shown to be predictable from basic attributes of evanescent wave propagation. For the special case of a circular cylinder, the subsequently constructed reflected field is found to agree with the asymptotic expansion of the rigorous solution, thereby confirming the validity of the theory for weakly evanescent fields. The rigorous solution, valid for arbitrary evanescent decay and obtained from known results for ordinary plane wave scattering by analytic continuation of the incidence angle to complex values, reveals that both the reflected and creeping wave fields should be viewed in a restrictive manner when the evanescent decay is large. However, for weak evanescent decay, these fields retain their customary significance and permit their construction by local evanescent field tracking. It is interesting to observe that in contrast to the nonevanescent case, the creeping waves provide a field contribution exceeding that of the incident or reflected waves in certain portions of the illuminated region.

A stereo field map with implications for disparity processing.

Abstract: The neural basis for stereopsis may be divided into at least two components: one mechanism that processes divergent disparities and a second mechanism that processes convergent disparities. The most clearcut evidence for the presence of these two components is the finding that some individuals lack either one or the other. However, when the ability to process both convergent and divergent disparities is present in the same individual it is more difficult to demonstrate the presence of two separate mechanisms. In this paper, the mechanisms for stereopsis are shown to consist of at least two components in the same individual. This demonstration is based upon a new kind of perimetry whereby field maps for stereopsis are plotted for both convergent and divergent disparities. Extensive measurements on one observer show that the zone of the visual field over which convergent disparities are processed may differ quite distinctively from the zone of the visual field over which divergent disparities are processed.