The High Frequency Behavior of a Plasma

An analogue for a uniformly ionized gas on the basis of the known formula Kₚ=1-ω₀²ω² for its specific inductive capacity is found in a shunt-tuned circuit. In that formula ω₀²=4πNe²m and ω 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 Kₚ=-1. 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.The theoretical variation of Kₚ was checked in the range ω₀²>2ω² by the hyperbolic relation between change in condenser reactance and arc current there. Resistance measurements on the Lecher system, used in connection with a more detailed analysis, allowed calculation of relative electron density in the range from one-half to five times that giving resonance, checking the actual values. In the same range, the resistance to electron motion varied considerably. The maximum value occurred near resonance and checked, roughly, the value calculated from free path considerations. The alternating fields in the plasma varied from 0.17 to 1.2 v cm^-1 and the maximum amplitude of electron motion was 2.1×{}10^-3 cm.A transverse magnetic field was found to double the resonance as H. Gutton has found. The separation of resonances accords with theory.