Abstract
The Langmuir probe technique is not suitable for measuring ion densities above 1 mm Hg pressure because the probe dimensions approach those of the ionic and electronic mean free paths. In addition to the invalidity of the Langmuir theory for this case, such a probe also causes a great disturbance of the discharge.
In this paper a detailed examination is made of the possibility of using a probe collecting positive ions as a means of finding ion densities
It has been found possible to calculate the potential distribution, outside a space-charge sheath around a spherical probe, if the radius of the sheath is known From this the current of positive ions to the probe may be found Curves are given to facilitate this calculation.
It is found that, depending on the ion concentration and pressure, there are two rather different sets of conditions around the probe. If the ion density is high (greater than about 108/mean free path (in cm)) a thin sheath will form on the probe and a complete solution of the problem is possible Under such conditions the energies of the diffusing ions in the neighbourhood of the probe greatly exceed the thermal energies of the gas particles At the lower ion densities normally encountered, a thick `diffusion' sheath occurs and the problem can now only be solved if the sheath thickness is known The ion energies may or may not greatly exceed the thermal energies, depending on conditions.
These results contradict one of the basic assumptions made by Davydov and Zmanovskaja in their approach to the same problem They assume a thin sheath with the ions in thermal equilibrium with the surrounding gas As a result their conclusion is in conflict with the conclusion of this paper, that in most circumstances it is not possible to use a negative probe to measure ion densities unless an additional means of determining the sheath thickness is available.