High-Frequency Currents on a Strongly Elongated Spheroid

The problem of high-frequency diffraction by a strongly elongated spheroid is considered. The field in the boundary layer near the surface is represented as a sum of Fourier harmonics with respect to the angle of revolution. Every harmonics is approximated by the sum of forward and backward waves. The forward waves are represented asymptotically by rapidly converging integrals involving Whittaker functions. The amplitudes of forward waves are determined by matching with the incident plane wave. To find the amplitudes of backward waves, the surface of strongly elongated spheroid near its rear tip is approximated by a paraboloid, and the solution proposed by Fock is used. At large distances from the tip, this solution transforms to the sum of incoming and outgoing waves, which are matched to the forward and backward waves, respectively. This defines the amplitudes of backward waves. Finally, the field of backward waves, initially given in the form of a series with respect to the solutions of a complicated dispersion equation, is represented in the form of an integral similar to that for the forward waves. The asymptotic results are compared with a number of numerical tests, which confirm good approximating properties of the derived asymptotic representations.