Theoretical aspects of a new technique for the MeV ion microbeam are described in detail for the first time. The basis of the technique, termed scanning ion deep level transient spectroscopy (SIDLTS), is the imaging of defect distributions within semiconductor devices. The principles of SIDLTS are similar to those behind other deep level transient spectroscopy (DLTS) techniques with the main difference stemming from the injection of carriers into traps using the localized energy-loss of a focused MeV ion beam. Energy-loss of an MeV ion generates an electron-hole pair plasma, providing the equivalent of a DLTS trap filling pulse with a duration which depends on space-charge screening of the applied electric field and ambipolar erosion of the plasma for short ranging ions. Some nanoseconds later, the detrapping current transient is monitored as a charge transient. Scanning the beam in conjunction with transient analysis allows the imaging of defect levels. As with DLTS, the temperature dependence of the transient can be used to extract trap activation levels. In this, the first of a two-part paper, we introduce the various stages of corner capture and derive a simple expression for the observed charge transient. The second paper will illustrate the technique on a MeV ion implanted Au-Si Schottky junction.