Penetration of waves in global stochastic conducting media

Abstract

The attenuation in the propagation of a plane wave in conducting media has been studied. We analyzed a wave motion suffering dissipation by the Joule effect in its propagation in a medium with global disorder. We solved the stochastic telegrapher’s equation in the Fourier-Laplace representation allowing us to find the space penetration length of a plane wave in a complex conducting medium. Considering fluctuations in the loss of energy, we found a critical value kc for Fourier’s modes, thus if |k| < kc the waves are localized. We showed that the penetration length is inversely proportional to kc. Thus, the penetration length L = k−1 c becomes an important piece of information for describing wave propagation with Markovian and non-Markovian fluctuations in the rate of the absorption of energy τ −1. In addition, intermittent fluctuations in this rate have also been studied.