摘要：Context. We consider a weakly to moderately active comet and make the following simplifying assumptions: (i) The partial ionization frequencies are constant throughout the considered part of the coma. (ii) All species move radially outward with the same constant speed. (iii) Ion-neutral reactions affect the chemical composition of the ions, but ion removal through dissociative recombination with free electrons is negligible.Aims. We aim to derive an analytical model for the radial variation of the abundances of various cometary ions.Methods. We present two methods for retrieving the ion composition as a function ofr. The first method, which has previously been used frequently, solves a series of coupled differential equations. The new method introduced here is based on probabilistic arguments and is analytical in nature.Results. For a pure H2O coma, the resulting closed-form expressions yield results that are identical to the standard method, but are computationally much less expensive.Conclusions. In addition to the computational simplicity, the analytical model provides insight into how the various abundances depend on parameters such as comet production rate, outflow speed, and reaction rate coefficients. It can also be used to investigate limiting cases. It cannot easily be extended to account for a radially varying flow speed or dissociative recombination in the way a code based on numerical integrations can.
