Nonstationary plane wave incidence on the perfectly conducting structures. Part 2. Diffraction of a nonstationary plane wave on the perfectly conducting sphere

The paper considers the incidence of a nonstationary plane wave on a perfectly conducting sphere. To find the current on the surface of the sphere, the well-known solution of the problem in the frequency domain has been used and the transition from the real frequency to the complex variable has been performed. Expressions for calculating the current on the sphere have been obtained using the residue formula. Graphs and vector images of the current have been plotted, which make it possible to observe its changes during the propagation of the incident wave. You can specify the following time intervals, differing in current distribution. At 0 < t < a/c, the current on the illuminated part of the sphere is close to the current determined in the geometrical optics approximation. In this case, there is naturally no current in the shadow region. For a/c < t < a/c + (π/2)a/c, a diffraction current appears in the shadow region, which turns out to be small compared to the current in the illuminated region. In the a/c + (π/2)a/c < t < a/c + πa/c, the current distribution on the sphere surface rapidly approaches the steady-state distribution. In the steady state, the streamlines represent circles obtained by sectioning the sphere with planes orthogonal to the magnetic field of the incident wave. At t > a/c + πa/c, the current practically does not change, and the steady-state distribution is preserved.