Limitations of the Microwave Cavity Method of Measuring Electron Densities in a Plasma

Abstract

The limitations of the conventional microwave cavity method of measuring the electron density are derived. The conventional method permits the electron density to be measured over a range of approximately two decades. The upper limit of the measurement of the electron density, roughly 5×${10}^9$ ${\mathrm{cm}}^{-3\mathrm{}}$, is caused by plasma resonance due to the macroscopic polarization of the plasma and by the overlapping from higher order modes. The lower limit of the measurement of the electron density, roughly 5×${10}^7$ ${\mathrm{cm}}^{-3\mathrm{}}$, is determined by how accurately the resonant frequency can be measured. The macroscopic electric polarization can be eliminated and the overlapping modes suppressed by designing the cavity so that the probing microwave field and the plasma have rotational symmetry around the same axis. The electric polarization limit is then replaced by a magnetic polarization limit and the available range is increased approximately one additional decade at 3000 Mc/sec. By decreasing the frequency from 3000 Mc/sec to 1 Mc/sec and by measuring the $Q$ or the losses of the plasma in a properly designed solenoid instead of a cavity the magnetic polarization limit can be raised even more. At 1 Mc/sec and at a pressure of 1 mm Hg the electron density corresponding to the magnetic polarization limit is ${10}^{15}$ to ${10}^{16}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The lower limit for the measurable electron density or the conductivity is determined by the sensitivity of the detecting arrangement, and the noise originating in the electron-ion plasma and is probably ${10}^4$ to ${10}^5$ times less than the maximum measurable electron density.