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This article deals with the experimental verification of a theoretical radial model, developed by the authors, for the sheath that surrounds a cylindrical Langmuir probe immersed in a plasma in which the positive ion temperature, Ti, is not negligibly small compared to the electron temperature, Te. The theoretical model is a generalization of the classical one developed for cold ions by Allen, Boyd, and Reynolds for the case of spherical probes, and extended by Chen for cylindrical ones. According to our theory, due to the positive ion thermal motion the ion current collected by the probe is increased with respect to the case of cold ions, so its influence must be considered in plasma diagnosis. An experimental device to accurately measure the I-V characteristic of a cylindrical probe in plasma, for which Ti/Te ≠ 0, has been developed. Very good agreement has been found between the theoretical positive ion I-V probe characteristic and the experimental values by using a Sonin plot.

We solve a radial theoretical model that describes the ion sheath around a cylindrical Langmuir probe with finite non-zero ion temperature in which singularity in an a priori unknown point prevents direct integration. The singularity appears naturally in fluid models when the velocity of the ions reaches the local ion speed of sound. The solutions are smooth and continuous and are valid from the plasma to the probe with no need for asymptotic matching. The solutions that we present are valid for any value of the positive ion to electron temperature ratio and for any constant polytropic coefficient. The model is numerically solved to obtain the electric potential and the ion population density profiles for any given positive ion current collected by the probe. The ion-current to probe-voltage characteristic curves and the Sonin plot are calculated in order to use the results of the model in plasma diagnosis. The proposed methodology is adaptable to other geometries and in the presence of other presheath mechanisms.

This article shows a transition in the behavior of the positive ions movement around a cylindrical Langmuir probe which we have experimentally observed in a low pressure plasma. In the case of helium plasma, depending on the plasma conditions, the ion current collected by the probe behaves as predicted by a radial motion theory, by an orbital motion theory, or by none of them when the transition between the two behaviors takes place. In the case of argon and neon plasmas, the ion current is well described by radial motion theories. The knowledge of the positive ions behavior is essential to diagnose the plasma parameters by using the ion saturation zone of the current-voltage characteristic curve. The use of this zone is one of the less intrusive in probe plasma diagnostics methods providing local information about the plasma parameters, since the charge drained from the plasma is very low.

This paper analyzes the results of accurate measurements of the ion current collected by a cylindrical Langmuir probe immersed in cold argon, neon, and helium plasmas. These measurements make it possible to study the influence of the positive ion-to-electron temperature ratio β = T + /T e on the collected ion current, providing valuable information about the trajectory described by the positive ions when falling toward the probe. Several criteria have been applied to discriminate whether the ion current is described by using the orbital motion limited theory or the radial motion theory. In all the studied argon and neon plasma discharge conditions, the criteria indicate that the positive ion current collected by the probe is appropriately described by the radial motion theory; however, as β increases, some criteria indicate a trend toward the orbital theory. In contrast, for the studied helium plasmas discharge conditions, a transition from radial to orbital motion has been measured.