High frequency diffraction by a soft circular disc

Abstract

The problem is governed by a Jones integral equation and the solution is shown to depend upon a single function which occurs naturally after a contour deformation has produced extensive cancellation in the work. The far-scattered field off the axis of symmetry is found in detail, yielding terms which are believed to be new.

Radiation from a Point Charge Moving through a Circular Aperture in a Screen

“…Inversion of (6.3) and application of the condition that wf(w) should be zero at the origin shows that Jones (1965a) has also devised a special iterative procedure to obtain a solution of (6.4) for large a. To obtain the first iteration is rather difficult; see also Thomas (1968) and Newby (1972). Williams (1972) has shown that the first iteration can be obtained in a more direct way, related to trivial boundary value problems, which arise in the absence of the diffracting screen.…”

“…The integral equation is of the same form as the one occurring in the diffraction of a scalar plane wave by a soft disk. In the latter problem, techniques are used which transform the integral equation to one especially suitable either for handling low frequencies (Jones, 1956;Collins, 1961;Williams, 1962) or for handling high frequencies (Jones, 1965a;Newby, 1972;Williams, 1972). An extension of these techniques to our problem of the diffraction radiation from a point charge yields solutions for small a and large a.…”

“…132-134) and the other integrals can be rewritten as integrals from 1 to infinity (Newby, 1972), and hence,…”