Wave Guiding Properties of Large Low-Conductivity Cylinders

Using the FDTD method for solving Maxwell's equations, we have studied wave guiding properties of a large cylinder, having a radius of 100 m, ϵ = ϵ 0 , and μ = μ 0 , for four values of conductivity, σ = ∞, 10 −3 S/m, 10 −4 S/m, and 10 −5 S/m. The cylinder was excited by a Gaussian voltage pulse whose half-peak width (HPW) was 1, 3 or 10 μs. In all considered cases, traveling waves were observed and the longitudinal Poynting vector P z on the cylinder surface was greater than (or comparable to for HPW = 1 μ s) the radial Poynting vector P r . The wave propagation speeds were of the order of 10 8 m/s. Even for σ = ∞, traveling current waves exhibited attenuation, which was not much different for σ = 10 −3 S/m and was noticeably stronger for lower values of σ . After propagation over 400 m, the current peak was about 70% to 90% of its original value for σ = ∞, about 60% to 80% for σ = 10 −3 S/m, about 40% to 60% for σ = 10 −4 S/m, and about 10% to 20% for σ = 10 −5 S/m. The current attenuation distances, over which the amplitude decreases to 1/ e (about 37%) of its original value, for σ = 10 −5 S/m were roughly 120, 170, and 220 m for HPW = 1, 3, and 10 μ s, respectively. The results imply that essentially cold and, hence, low-conductivity compact intracloud discharges (CIDs), whose lengths are usually a few hundreds of meters may involve traveling wave phenomena, such as reflections.