Advanced Theory of Diffraction by a Semi-infinite Impedance Cone

Download or read book Advanced Theory of Diffraction by a Semi-infinite Impedance Cone written by J.M.L Bernard and published by ALPHA SCIENCE INTERNATIONAL LIMITED. This book was released on 2014-07-11 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mathematical problem concerning the diffraction by a semi-infinite cone with circular cross section for the Helmholtz equation, which has well-known solutions for Dirichlet and Neumann boundary conditions, is here considered for the more general boundary condition of constant impedance type. As previously stated by D.S. Jones, the problem then changes in complexity, beginning with the difficulty of obtaining the uniqueness of the solution. An exact analytical method is developed to reduce this problem to the determination of the solution of a well-posed non-oscillatory integral equation, of which the solution can be directly used to express the field in an integral form. Some generalization, in particular to the electromagnetic case, are also given.