Showing papers on "Scalar potential published in 1971"

The Magnetic Scalar Potential

Abstract: We obtain closed expressions for scalar magnetic potentials due to an arbitrary static current density J(x). Simple prescriptions are given for forbidden regions where B ≢ −∇ψ; these forbidden regions make the potential single valued where it can be used. Finally, the complete multipole expansion of the magnetostatic field is derived in a few simple steps.

Some Results on the Magnetic Field of Electric Currents Induced in a Thin Hemispherical Shell of Finite Conductivity, with Geomagnetic Applications

Abstract: Summary We consider the induction of electric currents in a thin uniformly conducting hemispherical shell by axisymmetric time-varying fields. A method of successive approximation to the solution is developed; the first approximation corresponds to the perfectly conducting shell. Using the vector potential of the fields, the first and second approximations are obtained for certain external fields. The results for the first approximation agree with those obtained by Ashour using the scalar potential. However, the analysis given here is simpler. The results are applied to electromagnetic induction in a large ocean and to the effect of the concentration of the induced currents near the edge. For variations of periods up to 24 h, the second approximation is found adequate. The calculations made for a varying field of 24 h period show that the vertical component of the induced field is enhanced near the coastline in both sea and land, and is reversed in direction on crossing the coast. The horizontal (tangential) component of the field is enhanced near the edge in the sea.

The Radiation of Love Waves from an Oscillating Cylinder

Abstract: We consider the radiation of Love waves from a rigid circular cylinder imbedded part way into the upper solid layer overlying a semi‐infinite solid and oscillating sinusoidally about its vertical axis. Only the radial component of the vector potential exists, and this is transformed into a scalar potential satisfying Helmholtz's equation; the boundary conditions are unusual for propagation in a fluid. Because the boundary values on the cylinder are mixed and the cylinder is finite in length, the mathematical formulation is converted into a pair of integral equations by means of a Green's function. The latter is obtained in two ways: using Hankel transforms, and using Weyl expansion for the source. In either case, the final integration is obtained by closing a contour. The contributions from the poles have the characteristics of Love waves. The contributions from the deformation of the contour about branch cuts have the property of lateral waves. The evaluation of the Green's functions on the surface of the cylinder enables us to replace the dual integral equations approximately by two sets of simultaneous algebraic equations for the unknown wavefield or its normal derivative. Lastly, the Green's integral is integrated numerically.

Huygens Principle and the Rubinowicz-Kirchhoff Theory of Diffraction

Abstract: In discussing diffraction, we shall frequently use the language of optics and talk about a shadow boundary, an illuminated space, light sources, and screens (boffles). A block body is an ideally absorbent body. This language is natural because most of the original work has been done for light diffraction. However, there is no difference between the computations for light and for sound waves, as long as both are based on the assumption of a scalar potential. Using a scalar and a vector potential optical computations have also been performed for boundary conditiosn that apply to electrical waves. Such computations have no bearing on sound waves and are not discussed in this book.

The reconstruction theorem with external sources

Abstract: Wightman’s reconstruction theorem for a neutral scalar field is extended to permit external interactions as well. The result is illustrated for a neutral scalar field interacting with a c-number source only.

Computer Method for the Analysis of Axisymmetrical Magnetic Fields for an Accelerator

Abstract: A computer code has been set up for use in calculating the magnetic field distribution for a circulator accelerator. The code calculates axisymmetrical three-dimensional magnetostatic fields, including the effect of coil current distribution. The modified scalar potential for axisymmetrical fields is derived to solve the boundary value problem of Poisson's equation. Magnetic fields for betatron poles have been computed. The results are in agreement with meas - urements.