Wave propagation in a switched-on time-varying plasma medium

The interaction of an electromagnetic wave with a switched-on time-varying plasma medium is considered. The characteristic features of wave propagation in such a medium are the conservation of wave number and the generation of new waves having frequencies different from that of the incident wave. Initially, a plane wave is assumed to be propagating in free space, and at time t=0 the entire space is converted to a plasma having a time-varying number density. The solution to this problem is obtained through a WKB (Wentzel-Kramer-Brillouin) approximation. The condition of validity of the solution is discussed. Identification of the reflected and transmitted waves constitutes the chief advantage of the method. The ratio of the amplitudes of the electric fields of the reflected and the transmitted waves is shown to depend upon the initial rate of rise of the particle density. This result is useful in diagnosing the initial rate of rise of the number density. To illustrate the method, an exponentially varying number density is considered. Numerical results of the solution of the time-varying differential equations are found to be in good agreement with the proposed solution