Power flow from a short antenna in a lossy uniaxial medium

The power flow from a short linear current element is computed by integrating the Poynting's vector over concentric cylindrical surfaces of various radii ρ. An effective antenna resistance is defined as the ratio between the integrated power flow and the mean square source current. In a lossless medium the integrated power flow is independent of ρ, and the conventional expression is obtained for the radiation resistance. In a slightly iossy medium, and at moderate distances ρ the effective resistance R remains unaltered for frequencies ω above the plasma frequency ωp. For ω < ωp, a simple asymptotic approximation shows that R which is inversely proportional to the antenna length ℓ for ρ small is gradually changed to R ∼ ℓ²/ ρ³ with increasing values of ρ. There is an optimum antenna length ℓ ∼ ρ which maximizes the power flow for this value of ρ. For very large distances from the source the power flow is proportional to ℓ²/ρ⁴ and it remains of the same form for frequencies above and below the plasma frequency.