Transient signal propagation in lossless, isotropic plasmas

The asymptotic behavior of transient signal propagation in lossless, isotropic plasmas is discussed for a typical input signal of a step modulated sine wave. A generalized saddlepoint integration is carried out which gives a continuous solution for the dispersed signal everywhere except at the signal wavefront. The solution which is valid at the signal wavefront is obtained by using a high-frequency expansion technique. Universal curves are presented for the behavior of the distorted signal as a function of the plasma frequency, signal frequency, and propagation distance. The solution is a good approximation for the case of plasma propagation lengths which are long compared to a free space wavelength and for the operating frequency near the plasma frequency. This solution is useful since the available exact solutions for this case converge too slowly to be practically computed.