Derivation of a new expression relating the ion density to the ion current from a langmuir probe

Abstract

For a plasma, consisting of electrons and singly ionized ions an expression is derived relating the ion current, at a given probe voltage, to the ion density. The derivation is valid in the limiting case of low ion temperature (Ti<<Te), a high value of the negative probe-potential (|qVp|>>kTe), a high value of the formula is discussed. The results are compared with computer calculations of different author and the difference is within 10% in the considered range. The ion densities, calculated with our formula, agree very well with electron densities, calculated from the same probe characteristics (standard deviation 10%), taking into account the secondary emission of the ions. The measurements are performed in the positive column of a helium discharge.