Showing papers on "Field (physics) published in 1976"

Theory of plasma transport in toroidal confinement systems

Abstract: The dissipation induced by coulomb-collisional scattering provides an irreducible minimum, and thus a useful standard for comparison, for transport processes in a hot, magnetically confined plasma. The kinetic description of this dissipation is provided by an equation of the Fokker-Planck form. As in the standard transport theory for a neutral gas, approximate solution of the Fokker-Planck equation permits the calculation of transport coefficients, which linearly relate the fluxes of particles, energy, and electric charge, to the density and temperature gradients, and to the electric field. The transport relations are useful in studying the confinement properties of present and future experimental devices for research in controlled thermonuclear fusion. The transport theory for a magnetized plasma (in which the Larmor radius is much smaller than gradient scale lengths describing the plasma fluid) departs from the theory for a neutral gas in several fundamental ways. Thus, transport coefficients for a magnetized plasma can be calculated even when the collisional mean free path is much longer than the gradient scale length (as would pertain in thermonuclear regimes). Such transport coefficients are generally nonlocal, being defined in terms of averages over surfaces with macroscopic dimensions. Furthermore, when the mean free path is long, the magnetized-plasma transport coefficients depend crucially upon the magnetic field geometry, the effects of which must be treated at the kinetic level of the Fokker-Planck equation. The results display several novel couplings between collisional dissipation and the electromagnetic field. The present review of magnetized-plasma transport theory is intended to be as widely accessible as possible. Thus the relevant features of magnetic confinement in closed (toroidal) systems, and of charged particles in spatially varying fields, are derived, at least in outline, from first principles. Although consideration is given to "classical" transport in which most field geometric effects are omitted, major emphasis is placed on the "neoclassical" theory which has been developed over the last decade. Neoclassical transport coefficients are specifically relevant to a magnetically confined plasma, rather than to just a magnetized plasma; their unusual features, such as nonlocality and geometry dependence, become particularly important in the high temperature regime of proposed thermonuclear reactors. The area of neoclassical theory which seems most complete---its application to axisymmetric tokamak-type confinement systems---is correspondingly stressed.

On the duality condition for quantum fields

Abstract: A general quantum field theory is considered in which the fields are assumed to be operator‐valued tempered distributions The system of fields may include any number of boson fields and fermion fields A theorem which relates certain complex Lorentz transformations to the T C P transformation is stated and proved With reference to this theorem, duality conditions are considered, and it is shown that such conditions hold under various physically reasonable assumptions about the fields Extensions of the algebras of field operators are discussed with reference to the duality conditions Local internal symmetries are discussed, and it is shown that these commute with the Poincare group and with the T C P transformation

On a Lagrangean for classical field dynamics and renormalization group calculations of dynamical critical properties

Abstract: From the path probability density for nonlinear stochastic processes a Lagrangean for classical field dynamics is derived. This formulation provides a convenient approach to the mode coupling equations and the renormalization group theory of critical dynamics. An application is given for the time-dependent isotropic Heisenberg ferromagnet. The dynamical exponent $$z = \frac{{d + 2 - \eta }}{2}$$ is derived aboveT c for all dimensionsd>2.

A Climatological Spectral Study of the 500 mb Geopotential Height of the Northern Hemisphere.

Abstract: A 10-year record of the 500 mb geopotential height for the Northern Hemisphere has been expanded into spherical harmonics and filtered in the time domain. Maps of the root-mean-square (rms) height have been constructed corresponding to different spatial scales and frequency bands. The spatial scales and frequency bands were chosen to emphasize blocking and cyclogenesis and to help isolate spurious, high-frequency parts of the field from the physically meaningful parts. We find that low-frequency fields are dominated by planetary-scale waves at high latitudes and by synoptic-scale waves at mid-latitudes. The medium-frequency fields get substantial contributions from the waves of synoptic scale and shorter. Power spectra of the spherical harmonic expansion coefficients are presented, as well as quadrature spectra for each pair of cosine and sine expansion coefficients. We find large-scale waves have a large amount of low-frequency power and a spectrum rapidly decreasing with frequency. Shorter wave...

Radiation from a moving mirror in two-dimensional space-time conformal anomaly

Abstract: The energy-momentum tensor is calculated in the two dimensional quantum theory of a massless scalar field influenced by the motion of a perfectly reflecting boundary (mirror). This simple model system evidently can provide insight into more sophisticated processes, such as particle production in cosmological models and exploding black holes. In spite of the conformally static nature of the problem, the vacuum expectation value of the tensor for an arbitrary mirror trajectory exhibits a non-vanishing radiation flux (which may be readily computed). The expectation value of the instantaneous energy flux is negative when the proper acceleration of the mirror is increasing, but the total energy radiated during a bounded mirror motion is positive. A uniformly accelerating mirror does not radiate; however, our quantization does not coincide with the treatment of that system as a 'static universe'. The calculation of the expectation value requires a regularization procedure of covariant separation of points (in products of field operators) along time-like geodesics; more naive methods do not yield the same answers. A striking example involving two mirrors clarifies the significance of the conformal anomaly.

Vacuum expectation value of the stress tensor in an arbitrary curved background: The covariant point-separation method

Abstract: A method known as covariant geodesic point separation is developed to calculate the vacuum expectation value of the stress tensor for a massive scalar field in an arbitrary gravitational field. The vacuum expectation value will diverge because the stress-tensor operator is constructed from products of field operators evaluated at the same space-time point. To remedy this problem, one of the field operators is taken to a nearby point. The resultant vacuum expectation value is finite and may be expressed in terms of the Hadamard elementary function. This function is calculated using a curved-space generalization of Schwinger's proper-time method for calculating the Feynman Green's function. The expression for the Hadamard function is written in terms of the biscalar of geodetic interval which gives a measure of the square of the geodesic distance between the separated points. Next, using a covariant expansion in terms of the tangent to the geodesic, the stress tensor may be expanded in powers of the length of the geodesic. Covariant expressions for each divergent term and for certain terms in the finite portion of the vacuum expectation value of the stress tensor are found. The properties, uses, and limitations of the results are discussed.

Theory of resonance fluorescence

Abstract: The problem of the interaction between a two-level atom and a quantum electromagnetic field is treated without the use of perturbation theory, without introduction of classical fields or factorization conditions for the states, and without assumptions about loss of memory. The calculation is carried out in the Heisenberg picture, without mode decomposition, and the conclusions all refer to physically measurable quantities, such as the fluorescence detected in the far field of the atom. It is shown that in a coherent field of constant amplitude the system always settles down to a quasistationary state, and that the stationarity is a manifestation of the quantum fluctuations. A solution for the growth of the fluorescent light intensity is presented that holds for any coherent exciting field. The two-time correlation function and the spectral density of the fluorescence are calculated, and are found to agree in the long-time limit with earlier results of Mollow. The two-time intensity correlation function of the field is derived, which corresponds to measurable photoelectric pair correlations, and it is found that this reflects several quantum features of the field. It is shown that quantum fluctuations are manifest more explicitly in two-time correlations in the steady state than in transient effects, like spontaneous emission in the vacuum. The measurement of such correlations therefore presents an opportunity for further experimental tests of quantum electrodynamics.

Lowering of Dimensionality in Phase Transitions with Random Fields

Abstract: We prove that to all orders in perturbation expansion, the critical exponents of a phase transition in a $d$-dimensional ($4ldl6$) system with short-range exchange and a random quenched field are the same as those of a ($d\ensuremath{-}2$)-dimensional pure system. Heuristic arguments are given to discuss both this result and the random-field Ising model for $2ldl6$.

The stability of short waves on a straight vortex filament in a weak externally imposed strain field

Abstract: The stability of short-wave displacement perturbations on a vortex filament of constant vorticity in a weak externally imposed strain field is considered. The circular cross-section of the vortex filament in this straining flow field becomes elliptical. It is found that instability of short waves on this strained vortex can occur only for wavelengths and frequencies at the intersection points of the dispersion curves for an isolated vortex. Numerical results show that the vortex is stable at some of these points and unstable at others. The vortex is unstable at wavelengths for which ω = 0, thus giving some support to the instability mechanism for the vortex ring proposed recently by Widnall, Bliss & Tsai (1974). The growth rate is calculated by linear stability theory. The previous work of Crow (1970) and Moore & Saffman (1971) dealing with long-wave instabilities is discussed as is the very recent work of Moore & Saffman (1975).

Spin from Isospin in a Gauge Theory

Abstract: We show that in an SU(2) quantum gauge field theory, with isospin symmetry broken spontaneously by a triplet of scalar mesons, isospinor degrees of freedom are converted into spin degrees of freedom in the field of a magnetic monopole.

Functional organization in the visual cortex of the golden hamster

Abstract: The visual cortex of the golden hamster was studied by means of multi-unit and single unit recording, which revealed three separate retinotopic maps of the visual field in the posterior cortex. V1, corresponding to cyto-architectonic area 17, has the contralateral temporal field represented medially, the central visual field (extending about 10 deg ipsilateral) represented laterally and the lower field anteriorly. The borders of the map, especially for the upper field, seem to be more restricted than the whole visual field available to the contralateral hemiretina: V1 probably does not represent the extreme periphery of the field. A large fraction of V1 has binocular input, for up to about 50 deg lateral to the vertical midline. There is a retinotopic reversal near the representation of the vertical midline where V1 meets V2 (corresponding to the more lateral "area 18a"). There is another retinotopic reversal at the extremity of the contralateral field representation, where V1 meets Vm (the medial visual area, corresponding to "area 18"). V2 and Vm each contain a reduced mirror image version of the map in V1. Almost all isolated single units in V1 have receptive fields that can be classified as radially symmetrical (60%) or asymmetrical (35%). Symmetrical fields have ON (13%), OFF (4%), ON-OFF (30%) or "SILENT" (12%) central areas when plotted with flashing spots. There are minor but not striking differences between these groups in their field sizes, velocity preferences and so on. They almost invariably prefer moving to stationary stimuli but are not selective for orientation or direction of movement. Asymmetrical fields are of four types, three of which (type 1, 11%; type 2, 17%; and type 3, 2%) are orientation selective and resemble simple, complex and hypercomplex cells in the cat cortex. Some of these have direction as well as orientation preference. Axial movement detectors (5%) have a selectivity for one axis of motion, and thus prefer one orientation of edge, but respond equally well to movement of a spot. Vertical and horizontal orientation preferences, especially the latter, are much the most common. There is some evidence of clustering of cells according to receptive field type and, possibly, preferred orientation. Asymmetrical cells are, relatively somewhat rarer in the deeper cortical layers. Within the binocular segment, fully 89% of cells are binocularly driven and the receptive fields are similar in the two eyes. Receptive fields tend to increase in size away from the area centralis representation and, in a complementary fashion, the magnification factor decreases from up to 0.1 mm/deg at the area centralis representation to about 0.02 mm/deg for the peripheral field.

Theory of nonresonant multistable optical devices

Abstract: We show that a Fabry‐Perot interferometer filled with a Kerr medium has a multiple‐valued transmission‐intensity characteristic. ’’On’’ and ’’off’’ field for bistable operation are estimated, and a simple but accurate approximate theory is described.

Influence of nonuniform field distribution on frequency limits of GaAs field-effect transistors

Abstract: A simple model which describes well the nonequilibrium electron transport in GaAs using the fit to the equilibrium Monte Carlo data is suggested In the frame of this model, the cutoff-frequency/gate-length curves are calculated for uniform and nonuniform channel field distribution in GaAs fets The results show that the nonhomogeneity of the electric field in the channel can considerably decrease (by 30%) the maximal frequency of GaAs fets

Transport properties of molten alkali halides

Abstract: The transport properties of molten alkali halides have been calculated in molecular dynamics "experiments" based on rigid-ion pair potentials of the Huggins-Mayer form with parameters proposed by Tosi and Fumi. The coefficients of shear viscosity and electrical conductivity are obtained by computing the response of the system to a small applied field of the appropriate type, and the extension of the method to the calculation of current-current correlation functions of acoustic and optic character is also considered. Comparison with experimental data shows that the electrical conductivities are very well reproduced, but systematic discrepancies are found for diffusion coefficients and viscosities.

A percolation treatment of high-field hopping transport

Abstract: A previous percolation theory for hopping conduction is extended to high fields, and applied specifically to the Mott (1969) model (a constant density of states). The importance of nearest-neighbour pair correlations, the local chemical potential, and certain spatial correlations are discussed. The directional constraints created by the spatial correlations and by the nature of the percolation cluster are included approximately. The effect of the local chemical potential is included in an approximation similar to the mean field approximation. The theory is worked out primarily in the moderate field regime. The conductance is found to be proportional to exp (-A+eFl/kT), where exp(-A) is the low field conductance, F the electric field, and l a fraction of the characteristic low-field hopping distance rm. For three dimensions, l=0.17 rm, and for two dimensions, l=0.18 rm. Expressions are also derived for the high-field limit, and agree functionally with derivations by others.

Electromagnetic fields in the presence of rotating bodies

Abstract: Field calculations in the presence of rotating bodies with symmetry of revolution can be performed in the (inertial) laboratory frame of reference. Specific results are presented for a rotating circular cylinder immersed in a plane wave of the E or H type. Particular emphasis is put on the low-frequency limit, but some numerical data are also given for a typical frequency in the "resonance" region. The analysis becomes more complicated in the absence of symmetry of revolution. It is then necessary to solve the problem in a rotating system of coordinates. Maxwell's equations are written in these coordinates, together with the relevant constitutive equations and boundary conditions. The general formalism is applied to a typical two-dimensional configuration, viz., a cylinder immersed in an incident E wave. Considerable simplification obtains if all material velocities are negligible with respect to c, a condition which is always met in practice. Even simpler results are obtained if the cross-sectional dimensions of the cylinder are small with respect to λ. Some numerical results are presented, at low frequencies, for a dielectric cylinder of rectangular cross section.

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

Abstract: Charged particles propagating along the diverging lines of force of a spatially inhomogeneous guiding field were considered as they are scattered by random fields. Their longitudinal transport is described in terms of the eigenfunctions of a Sturm-Liouville operator incorporating the effect of adiabatic focussing along with that of scattering. The relaxation times and characteristic velocities are graphed and tabulated. The particle density is evaluated as a function of space and time for two different regimes. In the first regime (relatively weak focussing), a diffusive mode of propagation is dominant but coherent modes are also dominant. In the second regime (strong focussing), diffusion does not occur and the propagation is purely coherent. This supercoherent mode corresponds exactly to the so-called scatter-free propagation of kilovolt solar flare electrons. On a larger scale, focussed transport provides an interpretation of many observed characteristics of extragalactic radio sources.

Equations of state and renormalization-group recursion relations

Abstract: Renormalization-group recursion relations are used to construct equations of state to first order in $\ensuremath{\epsilon}=4\ensuremath{-}d$ for continuous spin models of critical behavior. The recursion relations map Hamiltonians out of the critical regime into regions of small correlation length, where Landau theory with fluctuation corrections is employed. This technique is used to discuss critical behavior along a $\ensuremath{\lambda}$ line of critical points, together with the effect of imposing an ordering field. An application of the method to tricritical phenomena is described briefly.

Nonlinear Electromagnetic Properties of Semiconductors with a Superlattice

Abstract: The nonlinear high-frequency conductance of superlattices due to the nonparabolicity of minizones has been investigated. Exact expressions for the current excited with a harmonic electric field are obtained. A selftransparence effect is predicted. It is shown that in the presence of a strong high-frequency field the increase of the low-frequency oscillations is possible. The frequency doubling and the high-frequency signal detection in the presence of a strong constant electric field is also investigated. [Russian Text Ignored].