Temporal Cavity Oscillations Caused by a Wide-band Waveform

Excitation of the electromagnetic fields by a wide-band current surge, which has a beginning in time, is studied in a cavity bounded by a closed perfectly conducting surface. The cavity is filled with Debye or Lorentz dispersive medium. The fields are presented as the modal expansion in terms of the solenoidal and irrotational cavity modes with the time-dependent modal amplitudes, which should be found. Completeness of this form of solution has been proved earlier. The systems of ordinary differential equations with time derivative for the modal amplitudes are derived and solved explicitly under the initial conditions and in compliance with the causality principle. The solutions are obtained in the form of simple convolution (with respect to time variable) integrals. Numerical examples are exhibited as well.