Langmuir probe characteristic modulated with random fluctuations

Abstract

Distortion of the Langmuir probe characteristic due to random fluctuations is investigated theoretically and experimentally. A statistical method is newly introduced to reasonably take account of the effects of statistically random processes. When the fluctuations in the plasma parameters and the current flowing to a Langmuir probe are ergodic, the time-averaged probe current is obtained by taking an ensemble average of the probe current weighted by the probability density function of fluctuating parameters. Therefore, the analysis is valid only for fluctuation spectra with frequencies small compared with the ion plasma frequency. Calculations are made for the distortion of the electron probe current due to Gaussian or periodic fluctuations in number density, space potential, and electron temperature. Previous results based on the usual time average can be deduced from the statistical method as special cases. The method is also examined experimentally by applying broadband Gaussian or periodic potential fluctuations to the plasma of a mercury discharge tube. It is found that Gaussian fluctuations in the plasma parameters bring about greater distortion to the electron probe characteristic than periodic ones, such as sinusoidal, rectangular, triangular waves.