Showing papers on "Scalar potential published in 1975"

A quantitative magnetospheric model derived from spacecraft magnetometer data

Abstract: Quantitative models of the external magnetospheric field were derived by making least-squares fits to magnetic field measurements from four IMP satellites The data were fit to a power series expansion in the solar magnetic coordinates and the solar wind-dipole tilt angle, and thus the models contain the effects of seasonal north-south asymmetries The expansions are divergence-free, but unlike the usual scalar potential expansions, the models contain a nonzero curl representing currents distributed within the magnetosphere Characteristics of four models are presented, representing different degrees of magnetic disturbance as determined by the range of Kp values The latitude at the earth separating open polar cap field lines from field lines closing on the dayside is about 5 deg lower than that determined by previous theoretically-derived models At times of high Kp, additional high latitude field lines are drawn back into the tail

Thin Fiim Acoustic Surface Waveguides on Anisotropic Media

Abstract: Abslrucl-Mm loaded rMp, slot, and Av/v surface acoustic waveguides on anisotropic substrates are ?heoretidy analyzed using a single scalar potential and wave equation. The scalar theory has the advantages of mathematical simplicity and can be applied with generality to the practical case of very thin films. A variety of surface waveguide problems can be described and analyzd in termcl of several 5xed parameters which are well known or easily measured. Waveguide dispersion curves and coupling coefficients for parallel waveguides are given. Experimental results for waveguides on LiNbO, and Bil,GeOl are prenented which substantiate the theory’s Validity.

Scalar binding of quarks

Abstract: A scalar potential which is linear in the radius is used to confine relativistic individual quark states. Calculation results are compared with those of the "bag" model.

Analytic expression for the fringe field of finite pole-tip length recording heads

Abstract: Previous computations based on a conformal transformation are used as a guide in selecting a plausible magnetic scalar potential at the surface of the head. An analytic expression for the horizontal component of the field is obtained from this potential. Certain characteristics of the potential and field are discussed.

3-dimensional computation of transformer leakage fields and associated losses

Abstract: Numerical methods, based on a magnetic scalar potential function, have been used to compute three-dimensional leakage fields and leg-plate losses in large power transformers. Fast convergence is obtained. The currents induced in the leg-plate are calculated by a simple modification of the static scalar-potential formulation. This includes three-dimensional, flux perturbation, and plate edge effects. The results show that two-dimensional approximations are unsatisfactory.

Quantitative models of magnetic and electric fields in the magnetosphere

Abstract: In order to represent the magnetic field B in the magnetosphere various auxiliary functions can be used: the current density, the scalar potential, toroidal and poloidal potentials, and Euler potentials -- or else, the components of B may be expanded directly. The most versatile among the linear representations is the one based on toroidal and poloidal potentials; it has seen relatively little use in the past but appears to be the most promising one for future work. Other classifications of models include simple testbed models vs. comprehensive ones and analytical vs. numerical representations. The electric field E in the magnetosphere is generally assumed to vary only slowly and to be orthogonal to B, allowing the use of a scalar potential which may be deduced from observations in the ionosphere, from the shape of the plasmapause, or from particle observations in synchronous orbits.

The field of gravitating bodies

Abstract: This chapter presents the field of gravitating bodies. The potential energy of a particle in a gravitational field is equal to its mass multiplied by the potential of the field, in analogy to the fact that the potential energy in an electric field is equal to the product of the charge and the potential of the field. Therefore, for the potential energy of an arbitrary mass distribution the gravitational energy of the body is obtained. For the Newtonian potential of a constant gravitational field, at large distances from the masses producing it, the expansion obtained is analogous to that obtained for the electrostatic field. Thus, in the case of the gravitational field, the dipole terms can always be eliminated.

Determining equations are obtained in covariant form for the coordinates of a differential symmetry operator of second order of a nonparabolic equation. The possibility of construc

Abstract: In the study of the algebraic properties of a linear differential second-order equation and, in particular, in the problem of separation of variables, one requires determining equations for the coordinates of the symmetry operators expressed in covariant form. This is also necessary to solve a problem that is of interest not only in the mathematieal but also the physical respect: Can one, in a preassigned Riemannian space, construct a second-order scalar differential operator having the complete symmetry of the space? One imagines that such an operator would be a good generalizatton of the Laplace operator for the Riemannian space:. Covariant determining equations for differential symmetry operators of first order are known [1]. In this paper, we obtain covariant determining equations for a differential operator of second order allowed by a scalar equation of the form {gu (x) O'lOx ~ OxS + b ~ (x) O,'Ox' + b (x)} ? (x) = 0, (i = 1 ..... n), where gij = gji, det(gij) # 0. Since we are concerned with the local properties of the equation, we assume that all functions are sufficiently smooth in the neighborhood of the point (x). Suppose V n is a Riemannian space with metric; tensor gij(x): ~,ir~, . - ai. ~rj - "], ~i is the operator of covariant differentiation in V n with respect to variable i. Clearly, this equatibn can be written in the form F~ =-- {g'J (x) P~ PS + V(x)} ~ (x) = 0; (1) here and below Pr - --iar + Ar(x), and the functions At(x) and V(x) can be determined in an obvious manner in terms of br(x) and b(xL Since F is a scalar operator, A r are the covariant components of a vector, and V(x) is a scalar. We shall call the vector A r, the scalar V, and the tensor Fij = Aj, i -- Ai, j the vector potential, the scalar potential, and the tensor of the field of the operator F, respectively. Obviously, an arbitrary scalar differential operator of second order X can be written in the form X = Pi X u (x) P/q- X i (x) Pi 4- ;((x), (2)

Transient response of thick axially symmetric monopoles

Abstract: The steady-state results for thick hemispherically capped monopoles with or without conical feed sections are used to construct the transient response of such monopoles. For a voltage pulse excitation, file transient waveforms for the transmitted-reflected feed currents, the radiated fields in different directions, and the instantaneous currents on the monopoles are calculated and presented. Steady-state results are obtained by solving the scalar potential integral equation with the axis extended boundary condition using the moment method.