Advanced Theory of the Diffraction by a Semi-infinite Impedance Cone

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, which solution can be directly used to express the field in an integral form. Some elements of a generalization to the Maxwell case are given.

Introduction / About the Representation of the Field in Scalar Case / Determination of G(v) / Some Elements of a Generalization to Maxwell Case / Asymptotics and Numerical Applications / Conclusion / Appendices / References.