Evolution of an ion admixture in an AC RF electric field

We consider the spatially homogeneous problem of the behavior of an ion admixture after the application of a harmonic electric field for various laws of interaction of ions with atoms. The expansion is performed in parameter $\alpha$, which turns out to be small for a low electric field strength or at a high frequency. We use the special normalization that has been introduced earlier, in which the mobility in a weak electric field is equal to unity. It is shown that the time dependences of electric current at any frequency for any total energy acquired by ions at high frequencies become universal in this normalization and are independent of the interaction cross section. It is shown how the correction to the transverse energy of ions is accumulated. The behavior of the ion distribution function is analyzed. A simple method is proposed for determining the effective time between collisions for any law describing the interaction.