An exact solution for the impulse response of a uniform plasma half space

A horizontally polarized impulsive plane wave is incident on a uniform half space of cold lossless plasma. The exact form of the resultant impulse response is found for any depth in the plasma in terms of two integer-order Bessel functions by inverting an appropriate Laplace transform. It is shown that as the observer's position in the plasma is increased, the frequency and relative amplitudes of the oscillations of the impulse response increase in a corresponding fashion. Numerical results are presented to illustrate these effects.