Bipolar high-power impulse magnetron sputtering (HiPIMS) is used to achieve ion acceleration for ion bombardment of dielectric thin films. This is realized by increasing the plasma potential (U-p), during the interval in-between the HiPIMS-pulses, using a positive reversed voltage (U-rev). As long as the film surface potential (U-s) is maintained low, close to ground potential, this increase in U-p results in ion-acceleration as ions approach the film surface. The effect of U-rev on the ion bombardment is demonstrated by the growth of dielectric (Al,Cr)(2)O-3 films on two sets of substrates, Si (001) and sapphire (0001) utilizing a U-rev ranging from 0 to 300 V. A clear ion bombardment effect is detected in films grown on the conductive Si substrate, while no, or a very small, effect is observed in films grown on the dielectric sapphire substrate. This is ascribed to the changes in U-s when the substrate is subjected to the bombardment of positive ions. For a film surface that has a high capacitance to ground, U-s remains close to ground potential for an extended time in-between the HiPIMS pulses, while if the capacitance is low, U-s quickly attains floating potential (U-float) close to U-p. The simulated temporal evolutions of U-s for the films by using capacitors show that for a 1 mu m thick (Al,Cr)(2)O-3 film on a conductive substrate, U-s is maintained close to ground potential during the entire 20 mu s that U-rev is applied after the HiPIMS pulse. On the other hand, when a capacitance corresponding to the 0.5 mm thick sapphire substrate is used, U-s rapidly attains a potential close to U-rev.