Parallel-Plate Plasma Problem

The parallel-plate plasma problem is considered under the assumption of uniform density and a specular reflection boundary condition at the plates. The impedance of the device is derived for several different models of the plasma medium. The impedance of a hydromagnetic medium exhibits resonances whenever the plate separation is an odd multiple of a half-wave-length, as defined by the dispersion relation, while the Boltzmann equation yields similar results which include, however, the presence of losses in a collisionless plasma. The predicted resonances in the impedance can most likely be observed at high frequencies where only electron motion is important. The low-frequency resonances would be difficult to observe in gas-discharge plasmas because of the high collision frequencies and because the resonances occur at small wavelengths.