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.