Comparative analysis and approximations of space-charge formation in Langmuir probes with plane, cylindrical and spherical electrodes including temperature effects

In this paper the space-charge effects in Langmuir probes are compared for different kinds of symmetries: plane, cylindrical and spherical. A detailed analysis is performed here including temperature effects, and therefore kinetic theory is used instead of fluid equations as used by other authors. The nonlinear equations obtained here have been solved first by numerical computation and later by approximations using Bessel functions. The accuracy of each approximation is also discussed. Space-charge effects are more important in plane geometries than in the case of cylindrical or spherical symmetries.