The bombardment of condensed matter by low energy ion beams induces ion transport through the material. A general theory for bombardment induced ion transport (BIIT) based on numerical solutions of the well known Nernst-Planck-Poisson equations is presented. The theory is applicable to polymer membranes as well as ion-conducting glasses with the implementation of appropriate boundary conditions. The fundamental properties of the theory, i.e. the capability to describe the potential, the field and the concentration/charge density profile within the two classes of materials mentioned above are demonstrated. In particular, the theory is capable of describing experimental observables which will be further elaborated in part II of this miniseries.