Showing papers on "Scalar potential published in 1983"

An optimal method for 3-D eddy currents

Abstract: A novel formulation for eddy current calculations in 3-D is derived.The method promises to require the minimum set of degrees of freedom, and also to be numerically Stable. A magnetic vector potential is used inside conducting regions, and it is shown that the gauge of this potential is implicit in the formulation. In non-conducting regions a magnetic scalar potential is used. The vector and scalar potentials are coupled on the interface between the two regions by the field continuity conditions, which implies zero current flow across the interface Computed results are compared with the analytic solutios of a conducting permeable sphere in an external field, and with measurements on a conducting block is a spatially varying field.

Derivation of the Power-Zienau-Woolley Hamiltonian in Quantum Electrodynamics by Gauge Transformation

Abstract: The different forms of Hamiltonian for the coupled system consisting of the electromagnetic field and a non-relativistic charged particle are considered in the context of gauge-transformation theory. The conventional Lagrangian of the system in an arbitrary gauge is converted to a new form by transformation to another arbitrary gauge, and a new formulation of the theory is obtained by expressing the new Lagrangian in terms of the initial potentials. Thus different gauge transformations produce different momenta $\pi$ conjugate to the initial vector potential $\mathbf{A}$, and hence different forms of Hamiltonian. The transformations that produce the Coulomb-gauge and Power-Zienau-Woolley (P.Z.W.) Hamiltonians are considered in detail. It is shown that $\Pi$ is transverse in both cases and only the transverse part of $\mathbf{A}$ is accordingly involved in the field quantization; neither the longitudinal part of A nor the scalar potential appears explicitly, the instantaneous Coulomb energies being included via an electronic polarization determined by the gauge generator. The transformations between gauges are illustrated by simple diagrammatic representations of $\mathbf{A}$ and $\Pi$. Compararison with the commonly used unitary transformation derivation of the P.Z.W. Hamiltonian emphasizes the need for a careful reinterpretation of the physical significance of $\Pi$ after the unitary transformation has been made.

A three dimensional eddy current formulation using two potentials: The magnetic vector potential and total magnetic scalar potential

Abstract: A formulation of the three dimensional eddy current problem is presented. The magnetic vector potential is used in regions with source currents and conducting material and the total magnetic scalar potential is employed elsewhere. The continuity of the normal component of flux density and tangential component of field intensity are used to couple the two potentials on the interface between regions. The formulation leads to a symmetric system amenable to traditional solution techniques. The formulation is also valid for static problems with modification that are easily implemented.

Vector and scalar confining potentials and the Klein paradox

Abstract: Confining potentials in euqations involving the interaction of fermions lead to no Klein paradoxes if the strength of the vector potential is appropriately limited compared to the scalar potential For linear potentials the Regge trajectories are asymptotically like those of the harmonic oscillator, namely, ${E}^{2}\ensuremath{\sim}j$

Relativistic corrections in potential models

Abstract: Following the method of Gromes, we calculate effective Hamiltonians for the scalar and an electrostatic potential. By comparing two-particle corrections to the Dirac limit, we eliminate an ambiguity in the corrections to the static propagator. We find that the spin-independent corrections to the scalar potential given by Gromes do not yield the proper Dirac limit, and we present an effective scalar Hamiltonian which does.

Spherical harmonic representation of the magnetic field in the presence of a current density

Abstract: Summary. Spherical harmonic expansions are derived to represent arbitrary current densities and magnetic fields in a spherical region. The expansions can be viewed as a generalization of the spherical-harmonic, scalar-potential theory to include regions where spatially distributed current densities exist. The new expansions are found in terms of the eigenfunctions of the curl curl operator. It is found that four basic field forms may be present ; one of these is the well-known scalar potential expansion originated by Gauss. Electric and magnetic field boundary conditions appropriate to a conducting spherical shell including the case of anisotropic conductivity are presented. They are discussed in terms of their ability to couple the four field forms. It is pointed out that the four field forms can be expressed in five other orthogonal curvilinear coordinate systems.

An accurate scalar potential finite element method for linear, two‐dimensional magnetostatics problems

Abstract: We have assessed the accuracy of a commercially available computer software package for finite element method calculations of magnetostatic fields. The computer program, MSC/NASTRAN,11 is well known for its wide applicability in structural analysis and heat transfer problems. We exploit the fact that the differential equations of magnetostatics are identical to those for heat transfer if the magnetic field problem is formulated with the reduced scalar potential.1 Consequently, the powerful, optimized numerical routines of NASTRAN can immediately be applied to two- and three-dimensional linear magneto-statics problems. Application of the NASTRAN reduced scalar potential approach to a ‘worst case’ two-dimensional problem for which an analytic solution is available has yielded much better accuracy than was recently reported2 for a reduced scalar potential calculation using a different finite element program. Furthermore, our method exhibits completely satisfactory performance with regard to computational expense and accuracy for a linear electromagnet with an air gap. Our analysis opens the way for large three-dimensional magnetostatics calculations at far greater economy than is possible with the more commonly used vector potential and boundary integral methods.

On eddy currents in thin plates

Abstract: A method of calculation of eddy currents in thin plates is presented. The stationary eddy-current problem is solved by using a scalar potential. The reaction of the eddy currents on the magnetic field is taken into account by application of an integral equation. Further, a combination of finite elements with the integral equation is presented to calculate an approximated solution for optional configuration of the plate. The paper is a continuation of [2].

Solution of quasi-stationary field problems by means of magnetic scalar potential

Abstract: A numerical method is described for computing eddy currents in thin conductors arbitrarily shaped and placed in a source harmonic field. The magnetic scalar potential is used to represent eddy currents and a set of integro-differential equations is solved using the finite element method. Eddy currents in a thin cylinder are calculated to test the method. Finally the method is used for rectangular conducting plates.

Geomagnetism of Earth's core

Abstract: Instrumentation, analytical methods, and research goals for understanding the behavior and source of geophysical magnetism are reviewed. Magsat, launched in 1979, collected global magnetometer data and identified the main terrestrial magnetic fields. The data has been treated by representing the curl-free field in terms of a scalar potential which is decomposed into a truncated series of spherical harmonics. Solutions to the Laplace equation then extend the field upward or downward from the measurement level through intervening spaces with no source. Further research is necessary on the interaction between harmonics of various spatial scales. Attempts are also being made to analytically model the main field and its secular variation at the core-mantle boundary. Work is also being done on characterizing the core structure, composition, thermodynamics, energetics, and formation, as well as designing a new Magsat or a tethered satellite to be flown on the Shuttle.

The Galerkin method of weighted residuals applied to the restricted magnetostatic scalar-potential boundary-integral equation in three dimensions

Abstract: The point-matching method for the numerical solution of the magnetostatic scalar-potential boundary-integral equation in three dimensions has been found to suffer from limited accuracy and heavy computational costs. Experiments with the Galerkin weighted-residual scheme show significant improvements in accuracy for a given amount of computation. The formulation is restricted to the situation where currents are excluded from magnetized regions; the latter are restricted to constant permeability in this report.

Solution of three dimensional electromagnetic field problems on a mini-computer

Abstract: The finite element solution of three dimensional magnetostatic problems using a scalar potential on computers with limited memory and speed is described. The paper concentrates on three main aspects of a solution system; namely the interactive mesh generator, a soft-failing solver algorithm and the output display. Each of these is discussed in detail with regard to the limitations of the hardware system.

The H-gradient method for magnetostatic field computations

Abstract: A new method for approximating magnetostatic field problems is given in this paper. The new method approximates the scalar potential for the magnetic intensity and is based on a volume integral formulation. The corresponding algorithm is similar to that obtained from coupled differential and boundary integral approaches. Convergence results in computations are compared with results for the usual volume integral method used in GFUN3D.

3-dimensional eddy-current calculation by the network method. formulation using magnetic scalar potential for nonconducting regions

Abstract: A network model for the representation of the general 3-dimensional electromagnetic field has been presented in previous publications. Solution of the network was performed by an all mesh variable method. A method is described in the paper for the solution of the linked network model in terms of a scalar potential in the magnetic part of the field, and the mesh currents in the electric part. The validity of the solution method is confirmed by a comparison of calculations with experimental results, for a full 3-dimensional problem. The new node-mesh method is shown to give rise to considerably less variables than the all mesh variable method for the solution of the linked-network problem. A comparison is also made between the number of variables required by the node-mesh method and that required by some other differential equation formulations of the 3-dimensional eddy-current problem.

Ideal fluid with short range scalar interactions in the field of a plane gravitational wave

Abstract: An exact solution of the self-consistent equations of relativistic hydrodynamics and the scalar field equation is obtained. The solution describes motion of a fluid with short-range scalar interactions in the field of a plane gravitational wave.

A Solution for the Electromagnetic Fields Close to a Lightning Discharge

Abstract: : A solution is presented for the electromagnetic fields produced by a current pulse propagating along a filamentary path apropos of lightning return strokes. This solution includes the effects of charge transfer by the pulse. It is obtained following traditional procedures, but modifying the electric scalar potential to insure conservation of charge at the filament's ends, and employing a relativistically correct relationship between charge and current. Conventional solutions can be obtained from this solution by employing conservation of charge to rewrite it in terms of current only; however, this form has computational advantages over other formulations very close to the channel. (Author)

2D and 3D static field computation with the codes VEPO2 and POFEL3

Abstract: The field computation codes VEPO2 and POFEL3 have been developed and used extensively over the past decade for designing electric and electromagnetic devices for the cyclotron facilities currently under construction at the NAC near Cape Town [1]. In VEPO2 scalar or vector potential formulations and a rectangular mesh are used to solve linear and non-linear static field problems in two dimensions for various boundary conditions. Dirichlet boundary problems can be solved with POFEL3 for a scalar potential and polar mesh or cylindrical (r,θ,z) grid. Novel finite-difference representations and special concepts employed in these codes are presented and discussed together with various results obtained for typical applications.

Relativistic tidal forces

Abstract: The post-Newtonian, relativistic (1/c/sup 2/) tidal force is calculated within the general PPN framework of all metric theories of gravity. There are no relativistic tides in general relativity, but they are generally nonzero in other metric theories of gravity, including scalar-tensor theories. In close binaries (GM/c/sup 2/Rroughly-equal10/sup -6/), such as the binary pulsar system PSR 1913+16, the relativistic tides can be orders of magnitude larger than Newtonian tides. In ''preferred frame'' theories of gravity in which the PPN coefficient ..cap alpha../sub 1/ is nonzero, the relativistic tidal field is not the gradient of a scalar potential, but includes also a circulating, nonconservative field in a body.

Fluid-dynamical representations of the Dirac equation

Abstract: A relative kinetic mass operator is defined bym =c −2·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H 2 + molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.