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Der Einfluß des Entladungsgefäßes auf die Bestimmung der Plasmaelektronendichte mit Hohlraumresonatoren / The Influence of the Discharge Tube on the Determination of the Plasma Electron Density by Means of Cavity Resonators

Abstract The eigenvalue equation of a plasma-discharge tube configuration in a cylindrical microwave cavity is derived and solved numerically by an exact theory for TMlm0 , TM0mn, and TE0mn resonance modes. The radial and axial electron density profiles are assumed to be homogeneous. The factors of proportionality between electron density and shift of the resonance frequency derived from the linear perturbation theory are compared with the exactly computed eigenvalues. Hence the range of validity of the linearly computed factors of proportionality (geometry factors) can be established. By considering the influence of the discharge tube the geometry factors are altered and consequently the sensitivity of the measurement. The influence of the discharge tube can be taken into account by means of suitable correction factors.