Ion‐ion recombination in dilute and dense plasmas

Theory of ion-ion recombination in a gas is provided as a function of gas density N, ion density N±, and time. An approximate analytical solution to the generalized time-dependent Debye-Smoluchowski equation for reaction and diffusional drift under general ion-ion field is provided for an initial Boltzmann distribution of ions. The transition in the time-dependent rates α(t) of recombination from reaction to the rate limiting step of reaction and transport is illustrated for various N, together with the variation of the steady-state limit α with N. The method and results are of basic significance for situations ranging from medical radiological and biophysics to the rate of disappearance of ionization tracks.