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The centroid and envelope dynamics of a high-intensity charged-particle beam are investigated as a beam smoothing technique to achieve uniform illumination over a suitably chosen region of the target for applications to ion-beam-driven high energy density physics and heavy ion fusion. The motion of the beam centroid projected onto the target follows a smooth pattern to achieve the desired illumination, for improved stability properties during the beam-target interaction. The centroid dynamics is controlled by an oscillating "wobbler," a set of electrically biased plates driven by rf voltage.