The goal of this study was to determine the critical ion-radiation conditions under which heavy ion beams can induce DNA double-strand breaks. Helium, nitrogen and argon-ion beams in the energy range of 20 eV to 2 keV were used to irradiate naked DNA plasmid pGFP to fluences of 1, 2 and 4 × 10¹⁵ ions/cm². The topological forms of DNA were subsequently analyzed using gel electrophoresis. The DNA forms were changed from the original supercoiled to damaged relaxed and linear forms, depending on the ion mass, energy, fluence and inertia. We found ion energy and fluence thresholds above which direct double-strand breaks can occur. The threshold is discussed in terms of the areal ion-energy density and the cross-section.