The High Frequency Behavior of a Plasma

An analogue for a uniformly ionized gas on the basis of the known formula $K_p=1-\frac{{{\omega }_0}^2}{{\omega }^2}$ for its specific inductive capacity is found in a shunt-tuned circuit. In that formula ${{\omega }_0}^2=\frac{4\pi N{e}^2}{m}$ and $\omega$ is the impressed angular frequency. This formula is extended to two simple cases of non-uniform ionization, with the conclusion that non-uniformity may be indistinguishable from large energy dissipation, insofar as reactive effects are concerned. Formulas have been derived for calculating the conductivity and specific inductive capacity of a cylindrical plasma (positive column of an arc) between parallel condenser plates from the measured impedance of this condenser by using a modification of Mossotti's Theory. The natural period of such a condenser occurs very nearly when $K_p=-1\mathrm{}$. For a fixed frequency the reactance of such a composite condenser was followed for varying arc current by observing the length of Lecher System connected to the condenser plates which was required to cause circuit resonance. Two and sometimes three resonances were found. They occurred in the neighborhood of the calculated plasma-electron resonance as determined from electron density measurements, and varied with impressed frequency according to theory.