International audienceThe ion foreshock located upstream of the Earth's shock front is populated with ions having interacted with the shock and then are reflected back with an high energy gain. In situ spacecrafts measurements have firmly established the existence of two distinct populations in the foreshock usptream of quasi-perpendicular shock region (i.e. for 45° ≤ ΘBn ≤ 90°, where ΘBn is the angle between the shock normal and the upstream magnetostatic field): (i) field-aligned (FAB) ion beams characterized by a gyrotropic distribution, and (ii) gyro-phase bunched (GPB) ions characterized by a NON gyrotropic distribution, which exhibit a non-vanishing perpendicular bulk velocity. Then, the purpose of the present wo...