Modification to the Nyquest Thermal Noise Equation for Plasma Circuit Elements - a high frequency cut off

The Nyquest Thermal Noise Equation for circuit elements is given as $\frac{2}{\pi }RKT$ where R is the resistance in Ohms, K is Boltzmann's constant (Joules per degree Kelvin) and T is the temperature in degrees Kelvin. When applied to plasma circuit elements such as plasma antennas\footnote{ Recent Results for Plasma Antennas, Igor Alexeff, Ted Anderson, Esmaeil Farshi, Naresh Karnam, and Nanditha Reddy Pulsani, Physics of Plasmas 15, 057104-1 (2008).}, this equation predicts a large amount of thermal noise, since plasmas are in general much hotter than metal circuit elements. However, this equation is an approximation in that it assumes that the electron collision frequency in the conductor is much higher than the frequency being studied. We have extended this equation as follows $\frac{2RKT}{\pi }(\frac{1}{1+(\frac{2\pi \nu }{\nu _c })^2})$ where $\nu$ is the frequency of interest and $\nu _c$ is the electron collision rate. Actually in our research in the 2 GHz frequency region, we find that the electron collision rate is much lower than the applied frequency. This results theoretically in a plasma antenna having much less thermal noise than a metal antenna.