Determining charged-particle concentrations from the ion current to a cylindrical probe in a weakly ionized low-pressure plasma

An experimental study has been performed on the applicability of collision-free theories of the ion current to a Langmuir probe over a wide range in the ratios of the radius of the probe to the Debye screening radius $\xi = R/\lambda_D$, and also over wide ranges in the ion mean free path $\lambda_i$ and in the ratio of the probe length L to the radius of the spacecharge layer s: $(10^{-2}<R/\lambda_D<10^1,10^{-1}<\lambda_i s \le 10^1, 1<L/s\le 10^1)$. For $\lambda_i\ge s$, it is found that for values of $\xi$ satisfying the criterion for distruption of the orbital motion $\frac{\lambda_i}{s}<\frac{\xi}{5\gamma^{1/2}} \eta^{1/2}$ $(\eta=\frac{eV}{kT_e}, \gamma=\frac{T_i}{T_e})$, the ion-current density is close to that calculated from Chen's radial-motion theory; at lower $\xi$, the ion-current density in the orbital-motion mode is dependent on $\lambda_i/s$ and L/s. A close fit to Laframbolse's calculations is to be expected for $\lambda_i/s \gg 10^1$ and $L/s \gg 10^1$.