A study of the accuracy of various Langmuir probe theories

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Abstract
Ion and electron densities have been measured in long, low pressure, cylindrical nitrogen and helium dc discharges using computer-controlled Langmuir probes. Cylindrical probe data have been analyzed with a variety of theories in order to determine the latter’s accuracy. Electron densities were obtained from the electron saturation currents using orbital motion limited (OML) theories, and from the electron retardation region of the probe trace by integration of the second derivative of the probe current. Ion densities were obtained from both OML and radial motion analysis of the ion saturation currents. Line integrated microwave interferometry and discharge current continuity considerations in the positive column have been used to obtain two independent electron density measurements. While both probe electron density methods agree very well with each other and reasonably well with the independent density measurements, the OML theory applied to the ions overestimates the plasma density by up to a factor of 10. The radial motion theory yields ion densities that show considerably better agreement with the electron densities than the OML theory. Ion and electron densities have also been measured with planar probes, but they were found to perturb the surrounding plasma more than the cylindrical ones.