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In this paper we present a time domain (TD) transient analysis of electromagnetic (EM) fields scattered from a perfectly conducting parabolic reflector, when it is illuminated by EM fields of a general astigmatic Gaussian beam (GB). The analysis employs physical optics (PO) approximation and analytic time transform (ATT) to treat complex time delays that result from the GB's complex phase variations along its propagation axis in the frequency domain (FD). This work exhibits two advantages. First, within the validity of the paraxial approximation of the GB fields, this TD-PO quasi-analytic solution is highly efficient in reducing the numerical surface integration into a one-dimensional angular integration, which remains fairly independent of reflector sizes in most practical applications. Second, the nature of the PO approximation assists in avoiding ray-caustic problems encountered in most asymptotic solutions. Numerical examples are presented to illustrate the phenomena of GB scattering, as well as the uses of the described solution.