Determination of the Collision Parameters by Means of Langmuir Probes

The current collected by Langmuir probes in the ion saturation regime is affected by collisions among ions and with neutrals. This effect depends not only on the Debye length and the various mean free paths involved, but also on the geometry, size, and biasing potential of the probes. Two or more independent measurements thus afford means for determining the collision parameters and related quantities, such as the ion temperature, the chemical composition of the plasma, and the density of the background gas. Good agreement is obtained between theory and experimental data taken in quite distinct physical situations, by using a hypersonic shock tunnel and a laser discharge. The method presented here could be applied to the determination of ion-neutral collision cross sections in the transition region between the D and E layers of the ionosphere. Nomenclature e = electronic charge, base of natural logarithms erf = error function h = altitude above ground / = current / = normalized current k = Boltzmann constant Lp = probe length m = particle mass N = number density p = pressure r = spherical radial coordinate R — molecule radius T = temperature u = directed velocity x = normalized inverse radius Z = ion valence a. = spherical correction index /S = cylindrical correction index X = mean free path \D = Debye length v = collision frequency p = cylindrical radial coordinate

ion current