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 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.

The floating potential of a Langmuir probe immersed in an electronegative plasma is studied theoretically under the assumption of radial positive ion fluid movement for non-zero positive ion temperature: both cylindrical and spherical geometries are studied. The model is solvable exactly. The special characteristics of the electronegative pre-sheath are found and the influence of the stratified electronegative pre-sheath is shown to be very small in practical applications. It is suggested that the use of the floating potential in the measurement of negative ions population density is convenient, in view of the numerical results obtained. The differences between the two radial geometries, which become very important for small probe radii of the order of magnitude of the Debye length, are studied.

This paper presents an experimentally observed transition from the validity of the radial theories to the validity of the orbital theories that model the ion current collected by a cylindrical Langmuir probe immersed in low-pressure, low-temperature helium plasma when it is negatively biased with respect to the plasma potential, as a function of the positive ion-neutral collision mean free path to the Debye length ratio Λ=λ+/λD. The study has been also conducted on argon and neon plasmas, which allows a comparison based on the mass of the ions, although no transition has been observed for these gases. As the radial or orbital behavior of the ions is essential to establish the validity of the different sheath theories, a theoretical analysis of such a transition not only as a function of the parameters Λ and β=T+/Te, T+ and Te being the positive ion and electron temperature, respectively, but also as a function of the ion mass is provided. This study allows us to recognize the importance of the mass of the ion as the parameter that explains the transition in helium plasmas. Motivated by these theoretical arguments, a novel set of measurements has been performed to study the relationship between the Λ and β parameters in the transition that demonstrate that the effect of the ion mean free path cannot be completely ignored and also that its influence on the ion current collected by the probe is less important than the effect of the ion temperature.

A radial Langmuir probe sheath model is used to make a prediction of the floating potential of a Langmuir probe immersed in an electronegative plasma. The new electronegative plasma sheath model takes into account the positive ion and the negative ion thermal energies and is valid for any ion temperature value. The values predicted can be used for diagnosing and controlling an electronegative plasma, and we compare them with measurements of the floating potential in an Argon plasma and in a Neon plasma with with two distinct electron populations at different temperatures. We have found that the agreement is very good in a wide range of plasma pressure and discharge current values, and thus the model is applicable for electronegative plasmas. Moreover, the model can be used to measure the energy with which the ions will collide with the surface of the probe.