Showing papers on "Scalar potential published in 1979"

On the use of the total scalar potential on the numerical solution of fields problems in electromagnetics

Abstract: SUMMARY The paper summarizes the formulation of a set of computer algorithms for the solution of the three-dimensional non-linear Poisson field problem. Results are presented that were obtained by applying algorithms to the analysis of two-dimensional magnetostatic fields. Scalar and vector potentials were used, and it is shown that the convenient single valued scalar potential associated with the induced sources gives severe accuracy problems in permeable regions. The results become as good as those obtained using vector potential if the scalar potential associated with the total field is used for permeable regions. The combination of two scalar potentials has a significant advantage for three-dimensional problems. The non-linear Poisson equation occurs in many areas of physics and engineering. The equation is relatively easy to solve compared to other defining equations, but for many applications the solutions must be very accurate. In magnetostatic problems, for example, the geometry of boundaries and surfaces separating differing media is often complicated and field accuracies of the order of 0.1 per cent and higher are essential. These conditions are frequently encountered in the wide range of electromagnets associated with the design of charged particle accelerators, spectrometers, detectors, focusing devices and plasma containment experiments used in physics and also in the broad spectrum of machines, transformers, etc. used in electrical engineering. Although the methods discussed in this paper are of general applicability they are looked at with particular reference to electromagnetics. Both differential and integral operator formulations have been used to solve the magnetostatic problem. Many well established programs solve the two-dimensional cases using differential formulations based directly on the defining equation usually in terms of the single component vector potentiaI. 1 - 3 These programs are capable of giving high accuracy although the position of the far field boundary can have a significant effect on the results. This latter difficulty has been overcome at the expense of increased computational cost by solving the integral form of the equations in terms of field components directly. An added advantage of this approach is that only regions containing material media (e.g., iron) are discretised. This is very useful in extending to three dimensions where the need to have a mesh of elements connecting many different regions of complex shape is seen as a limitation of the differential approach. This difficulty is avoided in programs based on integral formulations 4-6 and at the present time these provide a general technique for solving non-linear three-dimensional magnetostatic problems providing high accuracy is not required.

Dynamic Response of Inhomogeneous Fermi Systems.

Abstract: This paper presents a theory of the linear density response to an external time-dependent scalar potential for a Fermi system whose unperturbed density varies slowly. Simple local-density-functional response theory is valid except in a region of small $q$ and $\ensuremath{\omega}$ (wave number and frequency of the perturbation). For this region we have worked out a generalization, to the case of inhomogeneous systems of Landau Fermi-liquid theory.

Magnetic multipole expansions using the scalar potential

Abstract: Using the magnetic scalar potential, the multipole expansion is derived for the magnetostatic field outside a localized current distribution.

Plane symmetric static fields in Brans-Dicke theory of gravitation

Abstract: An explicit form of the relationship between g00 and the Brans–Dicke scalar potential φ in the interior of a perfect fluid with an equation of state p=eρ as well as in the matter free space, is obtained assuming functional dependence of g00 on φ. Plane symmetric static perfect fluids in Brans–Dicke theory of gravitation are discussed. Explicit solutions are also obtained for a fluid with e=1/3, that is, for a disordered radiation and some of its properties studied.

Point charge in a static, spherically symmetric Brans-Dicke field

Abstract: We determine in closed form the electrostatic potential of a point test charge held at rest in a static, spherically symmetric Brans-Dicke field. This result is a generalization of the previously obtained expression for the potential of a test charge at rest near a Schwarzschild black hole. Moreover, our solution is valid for the coupled gravitational and massless scalar fields.

Decomposition of vector fields by scalar potentials

Abstract: Details of a decomposition of an arbitrary vector field by scalar potentials are given Known expansions for divergence-free fields, curl-free fields and transverse fields are shown to be special cases

Axisymmetric and three dimensional electrostatic field solutions by the finite element method

Abstract: Axisymmetric and Three Dimensional Finite Element solutions of the scalar potential problem are described. The method of application to the Electrostatic Field problem in Electrical Machinery and Devices is indicated.

Finite elements for magnetostatic fields with distributed current densities

Abstract: This paper presents a general finite element method for the solution of fields due to general three-dimensional vector-valued sources in terms of the magnetic scalar potential, between boundaries of axisymmetric shape. In the space occupied by the sources, and there only, a correction field defined by a vector quantity must be added. This correction field is obtained by using a vector potential Ā, subject to the Coulomb convention. The latter convention may be relaxed to allow Ā to be divergenceless in the mean. In many magnetic field problems, the sources (current-carrying coils), occupy only a small part of the problem region. Since the correction field is non-zero only in the current-carrying space, it is computationally relatively cheap to find. Use of the procedure is illustrated by the end winding model of an electric machine.

Numerical treatment of transverse edge effects in linear induction motors

Abstract: A 3-dimensional-field analysis is presented for the treatment of finite-width effects in linear induction motors (LIM). Account is taken of the effects of stator fringing and rotor-end-portion leakage. The model allows for a finite iron height and width, an arbitrary lateral secondary displacement, and the secondary iron width different from the primary iron width. The method used involves numerical solution of difference equations for the magnetic vector potential as well as a scalar potential. The performance such as thrust, real and reactive power are obtained from the vector potential, and the induced primary voltage. An equivalent circuit with a secondary leakage reactance and modified finite-width correction factors is proposed.

Design of High-Perveance Confined-Flow Guns for Periodic- Permanent-Magnet-Focused Tubes

Abstract: An approach to the design of high perveance, low compression guns is described in which confinement is used to stabilize the beam for subsequent periodic-permanent-magnet focusing. The computed results for two cases are presented. A magnetic boundary value problem was solved for the scalar potential from which the axial magnetic field was computed. A solution was found by iterating between Poisson's equation and the electron trajectory calculations. Magnetic field values were varied in magnitude until a laminar beam with minimum scalloping was produced.