Diffraction of waves by screens (apertures in screens) with time-varying dimensions. Time-varying Kirchhoff's integral representation for moving boundaries

The diffraction of electromagnetic waves by screens (apertures in screens) with time-varying dimensions is studied. The generalized vector Kirchhoff's representation for this case is obtained. It is also shown that with accuracy up to the terms of the order of v/c<<1, the expressions for the scattered wave and instantaneous power can be derived from the appropriate expressions for a stationary case by substituting the time-dependent parameters of the screen dimensions (e.g. time-dependent radius) for constant parameters of screen dimensions (e.g., the screen radius) appearing in the formulas describing the stationary case.