Analysis of Ionic Recombination Including Ion Production during Measurement

The differential equations governing the removal of ions by recombination in competition with time-dependent production or exchange processes are solved for three different important cases. Firstly, the gradual transformation from one type of carrier into another is discussed where the two types of carriers may have widely differing recombination coefficients. A relatively simple solution is given if the rate of decay of the first type is dominated by the rate of transformation. In the two other cases ion production caused by collisions of metastable atoms is considered. It is reasoned that the rate of production may either decrease exponentially just as the concentration of metastables or the rate of production may decrease quadratically if the removal of metastables is controlled by ionizing collisions between the metastables. Both cases can be solved rigorously.