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Measurements with electric probes, called Langmuir probes, are the oldest and most often used procedures for low-temperature plasmas. The method was developed by Irving Langmuir and his co-workers in the 1920s, and has since been further developed in order to extend its applicability to more general conditions than those presumed by Langmuir. Langmuir probe measurements are based on the estimation of current versus voltage characteristics of a circuit consisting of two metallic electrodes that are both immersed in the plasma under study. Two cases are of interest: (a) The surface areas of the two electrodes differ by several orders of magnitude. This is known as the single-probe method. (b) The surface areas are very small in comparison with the dimensions of the vessel containing the plasma and approximately equal to each other. This is the double-probe method.
Conventional Langmuir probe theory assumes collisionless movement of charge carriers in the space charge sheath around the probe. Further it is assumed that the sheath boundary is well-defined and that beyond this boundary the plasma is completely undisturbed by the presence of the probe. This means that the electric field caused by the difference between the potential of the probe and the plasma potential at the place where the probe is located is limited to the volume inside the probe sheath boundary.
The general theoretical description of a Langmuir probe measurement requires the simultaneous solution of the Poisson equation, the collision-free Boltzmann equation , and the continuity equation with regard to the boundary condition at the probe surface and requiring that, at large distances from the probe, the solution approaches that expected in an undisturbed plasma.
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