Showing papers on "Field (physics) published in 1972"

Rotating black holes: separable wave equations for gravitational and electromagnetic perturbations.

Abstract: Separable wave equations with source terms are presented for electromagnetic and gravitational perturbations of an uncharged, rotating black hole. These equations describe the radiative field completely, and also part of the nonradiative field. Nontrivial, source-free, stationary perturbations are shown not to exist. The barrier integral governing synchrotron radiation from particles in circular orbits is shown to be the same as for scalar radiation. Future applications (stability of rotating black holes, "spin-down," superradiant scattering, floating orbits) are outlined.

Topological dissipation and the small-scale fields in turbulent gases.

Abstract: It is shown that a large-scale magnetic field possesses a hydrostatic equilibrium only if the pattern of small-scale variations is uniform along the large-scale field. Thus equilibrium obtains only if the variations in the field consist of simple twisting of the lines, with the twists extending uniformly the full length of the field. Any more complicated topology, such as two or more flux tubes wrapped around each other to form a rope, or braided or knotted flux tubes, is without equilibrium, no matter what fluid pressures are applied along the individual lines of force. The result is rapid dissipation and field-line merging, which quickly reduces the topology to the simple equilibrium form. The effect explains the absence of strong small-scale fields in the solar photosphere and in interstellar space in spite of the vigorous turbulence.

Atomic Coherent States in Quantum Optics

Abstract: For the description of an assembly of two-level atoms, atomic coherent states can be defined which have properties analogous to those of the field coherent states. The analogy is not fortuitous, but is shown to be related to the group contraction of exponential operators based on the angular momentum algebra to exponential operators based on the harmonic-oscillator algebra. The derivation of the properties of the atomic coherent states is made easier by the use of a powerful disentangling theorem for exponential angular momentum operators. A complete labeling of the atomic states is developed and many of their properties are studied. In particular it is shown that the atomic coherent states are the quantum analogs of classical dipoles, and that they can be produced by classical fields.

The hydrodynamic interaction of two small freely-moving spheres in a linear flow field

Abstract: Two rigid spheres of radii a and b are immersed in infinite fluid whose velocity at infinity is a linear function of position. No external force or couple acts on the spheres, and the effect of inertia forces on the motion of the fluid and the spheres is neglected. The purpose of the paper is to provide a systematic and explicit description of those aspects of the interaction between the two spheres that are relevant in a calculation of the mean stress in a suspension of spherical particles subjected to bulk deformation. The most relevant aspects are the relative velocity of the two sphere centres (V) and the force dipole strengths of the two spheres (S′ij, S″ij), as functions of the vector r separating the two centres.It is shown that V, S′ij and S″ij depend linearly on the rate of strain at infinity and can be represented in terms of several scalar parameters which are functions of r/a and b/a alone. These scalar functions provide a framework for the expression of the many results previously obtained for particular linear ambient flows or for particular values of r/a or of b/a. Some new results are established for the asymptotic forms of the functions both for r/(a + b) [Gt ] 1 and for values of r − (a + b) small compared with a and b. A reasonably complete numerical description of the interaction of two rigid spheres of equal size is assembled, the main deficiency being accurate values of the scalar functions describing the force dipole strength of a sphere in the intermediate range of sphere separations.In the case of steady simple shearing motion at infinity, some of the trajectories of one sphere centre relative to another are closed, a fact which has consequences for the rheological problem. These closed forms are described analytically, and also numerically in the case b/a = 1.

Stimulated Emission and Absorption near Resonance for Driven Systems

Abstract: The rate of absorption of energy from a weak signal field by an atom driven by a strong pump field is evaluated. The pump field and the signal field are assumed to induce transitions between the same pair of states, and their frequencies are both assumed to lie near the atomic resonance frequency for the transition in question. We find that the signal-field absorption line-shape function takes on negative values, representing stimulated emission rather than absorption, even though population inversion does not occur. This amplification of the signal field, which is most pronounced at high pump intensities, is shown to occur primarily at the expense of the pump field, which suffers an increased rate of attenuation. The results are discussed in the context of a theorem which expresses the absorption line-shape function for general atomic systems in terms of a suitable atomic correlation function.

Polar-cap electric field distributions related to the interplanetary magnetic field direction

Abstract: The correlations between the azimuthal direction of the interplanetary magnetic field and the most simple polar cap signatures are discussed. Only the spatial distribution of the dawn-dusk polar cap field is considered. For each OGO 6 traverse across the northern or southern polar cap, the simultaneous values of the interplanetary magnetic field in solar-equatorial coordinates were recorded by the Explorer 33 magnetometer. Histograms of these values are presented and are discussed. The high degree of correlation with the longitudinal angle indicates that the relative geometry of the interplanetary magnetic field and magnetospheric magnetic fields must be fundamental to explaining the distribution of polar cap electric fields. The sign of the solar-equatorial component perpendicular to the sun-earth line appears to be a more critical parameter than the sign of the component toward the sun. The Svalgaard-Mansurov correlation and the correspondence between fast convection and parallel magnetospheric and interplanetary magnetic fields are described.

Two-dimensional discrete Markovian fields

Abstract: A definition of discrete Markovian random fields is formulated analogously to a definition for the continuous case given by Levy. This definition in the homogeneous Gaussian case leads to a difference equation that sets forth the state of the field in terms of its values on a band of minimum width P , where P is the order of the process. The state of the field at position (i,j) is given by the set of values of the nearest neighbors within distance P of the point (i,j) . Conversely, given a difference equation satisfying certain conditions relating to stability, there corresponds a homogeneous discrete Markov random field. This theory is applied to the problem of obtaining spectral estimates of a two-dimensional field, given observation over a limited aperture.

Nonspherical Perturbations of Relativistic Gravitational Collapse. II. Integer-Spin, Zero-Rest-Mass Fields

Abstract: A nearly spherical star collapses through its gravitational radius. Nonspherical perturbations exist in its density, pressure, electromagnetic field, and gravitational field, and in other (hypothetical) zero-rest-mass, integer-spin fields coupled to sources in the stars. Paper I analyzed the evolution of scalar-field and gravitational-field perturbations. This paper treats fields of arbitrary integer spin and zero rest mass, using the Newman-Penrose tetrad formalism. The analysis of each multipole ($\mathrm{order}=l$) of each field ($\mathrm{spin}=s$) is reduced to the study of a two-dimensional wave equation, with a "curvature potential" that differs little from one field to another. The analysis of this wave equation for the scalar case ($s=0$) carries over completely to fields of arbitrary spin $s$. In particular, any radiatable multipole ($l\ensuremath{\ge}s$) gets radiated away completely in the late stages of collapse; if the multipole is static prior to the onset of collapse, it will die out as ${t}^{\ensuremath{-}(2l+2)}$ at late times. Nonradiatable multipoles ($lls$) are conserved. This paper also treats gravitational perturbations in the Newman-Penrose framework, and supplies some technical details missing in the gravitational-perturbation analysis of Paper I.

Quasilinear Diffusion of an Axisymmetric Toroidal Plasma

Abstract: In a toroidal plasma with axial symmetry, the three adiabatically invariant actions of a particle are the magnetic moment, the canonical angular momentum, and the toroidal flux enclosed by the drift surface. Resonant interactions between particles and the normal modes of collective oscillation produce mode growth or decay and random changes in the actions. This random walk is represented by a diffusion equation in action space. Both the diffusion tensor and the growth rate depend upon a coupling coefficient which represents the work done by a normal‐mode field eigenfunction on the current density of an unperturbed particle orbit. The diffusion of the plasma causes adiabatic changes in the electric and magnetic self‐consistent fields. Accordingly, energy is not conserved, but is exchanged with external currents.

Theory of Phase Space Density Granulation in Plasma

Abstract: A novel state of turbulent plasma characterized by small scale phase‐space granulations called “clumps” is proposed. Clumps are produced when regions of different phase space density are mixed by the fluctuating electric field. They move along ballistic orbits and drive the turbulent field in a manner similar to that in which thermal fluctuations are driven by particle discreteness. In the coherent wave limit the clumps become the familiar trapped particle eddies of a Bernstein‐Green‐Kruskal mode. The turbulent state can exist in the absence of linear instability although it is more likely to occur in a linearly unstable plasma. The spectrum contains a ballistic portion as well as resonances at the wave (collective) frequencies. The discreteness of the clumps produces collision‐like process. For example, the average distribution function satisfies a Fokker‐Planck equation instead of a quasilinear diffusion equation.

Theory of Saturated-Absorption Line Shapes

Abstract: A general theory of the saturated-absorption phenomenon in a two-level atomic system is developed, in which the phase relationships between the oscillating atomic dipoles as well as the population differences between energy levels are taken into account. The absorbing gaseous medium considered in this theory is subjected to irradiation by a quasi-running-wave composed of a strong pump field and a weak probe field propagating in opposite directions. Some new interesting results, not predicted by the so-called hole-burning or rate-equation model, are obtained. In particular, the probe-field-transmission peak line shape is found to be markedly different from what is expected according to the rate equations. For finite Doppler widths and a strong saturating pump field, absorption of the probe field can even change sign, and amplification of this field can actually occur. All these features are explained by a close inspection of the evolution of each atomic ensemble of given velocity. Detailed comparison with similar phenomena already observed in rf experiments is presented and permits us to clarify the new predicted effects.

Force-free magnetic-field structures and their role in solar activity.

Abstract: Magnetic-field structures in solar active regions are expected to be substantially force-free. A method is proposed for calculating such structures by numerical methods. The method is applied to the study of the magnetic-field pattern associated with a sunspot of one polarity surrounded by a magnetic region of opposite polarity when the sunspot rotates with respect to the surrounding region. Rotation introduces a toroidal component of magnetic field, and the associated pressure leads to inflation of the magnetic field pattern. If the differential rotation exceeds about 180 deg, the force-free magnetic field has energy greater than that of an open magnetic-field configuration with the same photospheric boundary conditions. It is concluded that, beyond this point, the force-free field structure is metastable and can be converted into an open field structure by an explosive MHD instability.

Some crystalline field effects in metals

Abstract: We discuss different physical effects which are caused by the crystalline electric field splitting of rare earth ions in metals. Thus, the rare earth ions may be impurities dissolved in a metallic matrix or they may form a regular lattice. In the former case we distinguish between the cases of a normal conducting and a superconducting matrix. The influence of the crystalline field splitting on the properties of the conduction electrons is calculated. In the case of a normal matrix anomalous behaviour of the thermoelectric power is found due to the impurity levels. If the matrix is superconducting large deviations result from the theory of Abrikosov and Gorkov which describes the influence of non-split magnetic impurities on superconductivity. A comparison of the theory with available experiments is presented. For the case that the rare earth ions form a regular lattice we discuss various aspects of the collective excitations in the paramagnetic state. Special attention is paid to the soft mode pr...

Energy-Conservation Considerations in the Characterization of Impact Ionization in Semiconductors

Abstract: A simple expression for the ionization coefficient of charged carriers in a semiconductor as a function of electric field and lattice temperature has been developed by simultaneously fitting three physical asymptotic cases to Baraff's result. These cases are for low field (Shockley), high field (Wolff), and limitations imposed by energy conservation at high electric field or when the energy loss by phonon scattering is negligible. Given the threshold energy for ionization and the optical-phonon energy, our expression requires a single additional parameter to predict experimental results. Although the final expression is thus essentially a one-point fitting, it reproduces experimental data over as much as four decades of ionization coefficient with better accuracy than frequently used empirical two-parameter expressions. Excellent fits with much of the existing electric field dependence of the ionization coefficients for electrons and holes in Ge, Si, GaAs, and GaP were obtained. The temperature dependence was examined in the cases of GaAs and Si and excellent agreement was obtained in the case of GaAs. Some data on Si were found to be in considerable error in the sense that the data do not appear to be consistent with energy conservation.

Resonant Nonlinear Optical Susceptibility: Electroreflectance in the Low-Field Limit

Abstract: A theory of the electric field effect on the dielectric function of solids is developed by means of a perturbation treatment similar to that used to describe nonlinear optical phenomena. The field-induced change in the dielectric function is given directly as a Brillouin-zone integral over a fourth-power resonant denominator. It is shown that electric field modulation results in spectra nearly proportional to the third derivative of the unperturbed dielectric function for common experimental conditions. The perturbation treatment is related to the standard (high-field) Franz-Keldysh theories. The differences between the two approaches is discussed in physical terms. Simplified expressions for parabolic critical points are developed and used to discuss experimental criteria for the validity of the perturbation theory. Application to band-structure analysis is discussed. In particular, critical-point parameters (energy, broadening, etc.) enter nearly independently, and the mathematical form of the fourth-rank tensorial line shape is simple enough to permit the calculation of electroreflectance spectra from existing band-structure calculations.

Hydromagnetic convection in a rapidly rotating fluid layer

Abstract: The linear stability of a rotating, electrically conducting viscous layer, heated from below and cooled from above, and lying in a uniform magnetic field is examined, using the Boussinesq approximation. Several orientations of the magnetic field and rotation axes are considered under a variety of different surface conditions. The analysis is, however, limited to large Taylor numbers, T , and large Hartmann numbers, M . (These are non-dimensional measures of the rotation rate and magnetic field strength, respectively.) Except when field and rotation are both vertical, the most unstable mode at marginal stability has the form of a horizontal roll whose orientation depends in a complex way on the directions and strengths of the field and angular velocity. For example, when the field is horizontal and the rotation is vertical, the roll is directed parallel to the field, provided that the field is sufficiently weak. In this case, the Rayleigh number, R (the non-dimensional measure of the applied temperature contrast) must reach a critical value, R c , which is O ( T 2/5 ) before convection will occur. If, however, the field is sufficiently strong [ T = O ( M 4 )], the roll makes an acute angle with the direction of the field, and R c = O ( T 1/2 ), i.e. the critical Rayleigh number is much smaller than when the magnetic field is absent. Also, in this case the mean applied temperature gradient and the wavelength of the tesselated convection pattern are both independent of viscosity when the layer is marginally stable. Furthermore, the Taylor-Proudman theorem and its extension to the hydromagnetic case are no longer applicable even qualitatively. Over the interior of the layer, however, the Coriolis forces to which the convective motions are subjected are, to leading order, balanced by the Lorentz forces. The results obtained in this paper have a bearing on the possibility of a thermally driven steady hydromagnetic dynamo.

Measurements of the electrical properties of dust storms

Abstract: Characteristics of the electrification in dust storms have been studied by making field observations at different places in the southwestern United States. Measurements consisted of the atmospheric electric potential gradient at ground level, space charge and wind speed (both at 1.25 meters above the ground), atmospheric temperature and relative humidity, and size distribution of dust particles at ground level. It has been observed that during dust storms both signs of potential gradient can occur at ground level, and any sign of potential gradient can be associated with the same or opposite sign of space charge at 1.25 meters above the ground. Potential gradients of many kilovolts per meter are not uncommon during these dust storms, and sometimes these high values can be sustained for many minutes, The space charge values at 1.25 meters above the ground associated with these high values of potential gradient can be as high as 105–106 el cm−3. In some dust storms the polarities of potential gradient and space charge have been observed to change if the blowing dust, rather than reach high altitudes, is raised because of low wind speeds only to lower levels. Size distributions of different types of dust particles collected at ground level are also given.

Turbulent fluid and particle interaction

Abstract: Main attention will be paid to the more basic aspects following from the interaction between fluid and discrete particles. First we will consider a single particle in a turbulent-flow field. The basic equation describing the motion of a particle has a number of terms which can either be given in a formal way only, or which contain parameters that depend strongly on the nature of both the particle and the fluid, and on the turbulent fluid motion. A description of the behaviour of the particle depending on the magnitude of those parameters and in the light of the ratio between response time and the many characteristic times of the turbulence will be given. The study of the long-time behaviour of the particle following the Lagrangian description leads to considering the turbulent diffusion of the particle relative to that of the fluid. Some attention will be paid to the effect of spatial inhomogeneity of the mean flow field. In the case of many discrete particles in a turbulent-flow field, an additional important parameter is the concentration by volume of the particles. Direct and indirect interaction of particles will be considered and their effects on the dynamic behaviour of the particulate phase and on the turbulence of the fluid. The merits and shortcomings of the continuum concept for the particulate phase, and of the concept of an eddy diffusion coefficient, will be discussed.

Indefinite-Metric Quantum Field Theory

Abstract: Some recent progress in the quantum field theory based on the indefinite- metric Hilbert space is reviewed in a systematic way. Various problems (as shown in the table of contents below) are discussed extensively. The selection of topics is, however, dependent on the present author's interest; undescribed topics are not necessarily meant to be unimportant. An almost complete exposition is given concerning the finite-dimensional indefinite-metric space. On the indefinite-metric quantum field theory, the problem of interpretation and the unltarity of the physical S-matrix are discussed in detail. Also included are a number of new results and remarks on various existing theories. Some of them are construction of a field theory having only one Feynman integral, critical remarks on the quantization of a purely imaginary-mass field and a criticism of the renormalization procedure of the Gupta-Bleuler quantum electrodynamics. (auth)

Effect of the magnetic field ripple on diffusion in Tokamaks

Abstract: The magnetic field modulation due to the discrete nature of the field coils in a Tokamak leads to additional particle trapping. The resulting diffusion is evaluated and compared with the neoclassical diffusion. The two diffusion rates are found to be comparable in existing Tokamaks. The limit on the field ripple below which ripple diffusion should be negligible in the next generation of machines is evaluated.