Abstract The present GAMMA10 experiment suggests that the ions trapped in the thermal barrier cell escape from there radially, although the mechanism of the radial loss of ions is unknown. But, a numerical calculation by the drift equation suggests that the existence of non-axisymmetric potential is one of the leading causes of the radial loss of ions in the axisymmetric end-mirror cells. Because it is difficult to analyze the orbits of ions in the actual magnetic field in GAMMA10, the qualitative approach by mapping equation is adopted. The mapping equation obtained is investigated for its properties by comparison with the standard mapping. In the result, it is confirmed that the existence of the small perturbations with high mode numbers in the electrostatic potential affects the orbits of ions greatly.