The effect of positive ions on Langmuir probe electron energy distributions

The results of a theoretical study of the effect of positive ions on electron energy distributions derived from spherical Langmuir probe second derivative characteristics are presented. The ion contribution to the probe second derivative causes the density of electrons in the high energy tail of the distribution to be overestimated. The second derivative of the ion current characteristic has been obtained by numerical double differentiation of characteristics calculated from the theory of Allen et al. (1957) these are presented in a dimensionless form suitable for application to a wide range of experimental conditions. A probe second derivative characteristic has been calculated for a helium plasma with a Maxwellian electron energy distribution and a ratio of probe radius to Debye length (rP/λD) of unity. It is shown that the errors in the electron density and mean energy obtained from the probe energy distribution are negligible ; however, there is a large error in the ionization rate. These errors will decrease with increasing rP/λD and ionic mass. It is concluded that a correction for the effect of the-ions must be made in calculations of the ionization rate from probe electron energy distributions.