An experimental study of plasma density determination by a cylindrical Langmuir probe at different pressures and magnetic fields in a cylindrical magnetron discharge in heavy rare gases

This article presents an experimental study that contributes to the problem of interpretation of cylindrical Langmuir probe data obtained in a non-isothermal tow-temperature plasma in magnetic field. A discussion on the influence of positive ion-neutral collisions on the charged particle density estimation is also given and the effect is demonstrated on the experimental data. A Maxwellian electron energy distribution is assumed throughout the present study. The Langmuir probe data are obtained in a cylindrical magnetron discharge in argon at pressures from 1.5 to 6 Pa and magnetic fields between 100 and 500 G. The radially movable Langmuir probe was made of either 100 mu m or 41 mu m diameter tungsten wire in order to investigate the effect of the probe dimensions on the estimated plasma density. The electron density is calculated from the electron current at the space potential (used as a reference) and from the OML collisionless theory. The ion density is calculated by using ABR-Chen theory without and with the correction due to the collisions of positive ions in the probe sheath. Also, the recent collisional positive-ion-collection-theory is used for comparison. The resulting numerical values of plasma density are compared over more than one order of magnitude change in the plasma density given by its radial dependence in the cylindrical magnetron discharge. Optical measurements were made in order to quantitatively assess the neutral gas temperature in the discharge and the density of particles in excited states that could induce secondary electron emission from the probe surface and thus apparently enhance the positive-ion density estimated from the probe positive-ion current. The effect of secondary electron emission from the probe surface on the probe data interpretation has been found small compared to the experimental error limits and consequently not substantial for our experimental conditions. In the range of our experimental conditions the ABR-Chen theory with the collisional correction gives the best agreement of the estimated numerical values of ion and electron densities in the whole range of its investigated change. Also from our results it follows that the effect of the magnetic field on the thinner-probe-electron-current at the space potential and hence on the reference-electron-density-estimation is negligible within the experimental uncertainties up to a magnetic field strength of 500 G which was the maximum used in our experimental study.