Theory on conductivity measurement technique for Langmuir probes in the stratosphere

In this work, a theoretical development related to the technique of stratospheric conductivity measurments using Langmuir probes is presented. Such a technique, which was used in measurements on board stratospheric balloons, involves the determination of the relaxation time-constant associated with the probes. Considering a horizontal stratified atmosphere, this technique consists in shorting during a time interval two probes at different altitudes and then determining a time constant when the probes are refloated to the initial potentials. Although this technique was used by several authors, the exact relation between the relaxation time and the conductivity is not determined yet. This work determines such a relation showing also when this technique gives the total conductivity or only the positive or negative ones.