[en] Transformation of the different types of the ion beam phase density distribution by non-linear quadrupole probe forming systems was considered. Phase density distributions were specified by multiparticle approximation (∼10⁷). Nonlinearities caused by probe forming system aberrations were taken into account to the third order inclusive. Using three probe forming systems was showed that non-linear character of the phase coordinates transformation from the object to the target plane leads to the pronounced peak of the beam density distribution