Integral transforms and the regularisation method in the time‐domain excitation of open PEC slotted cone scatterers

Abstract

An initial-boundary value problem for the transient electromagnetic field in the presence of a complicated-shape scatterer is studied. The considered biconical zero-thickness and perfectly conducting surface with periodic longitudinal slots has many special cases, each of which is of separate practical interest. A new analytical-numerical technique is presented that is based on the Mehler–Fock integral transform and the method of analytical regularisation. The source of excitation of the slotted bicone is a radial electric dipole with an arbitrary time dependence on the field. The proposed method makes it possible to obtain an analytical and numerical solution of the problem to carry out a qualitative and numerical analysis, and to study the characteristic features of the main scattering. Due to the use of the method, the initial-boundary value problem is reduced to a Fredholm type of the second kind system of linear algebraic equations (SLAE-2). The dependences of the condition number on the problem parameters and the estimation of the SLAE-2 convergence with larger truncation orders are given. The far-field radiation patterns are plotted for various values of the problem parameters, the behaviour of the near field at the apex of the slotted cone is studied, and the regime of the slot wave propagation is analysed.