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Spherical and cylindrical many-particle models are used to simulate rf (radio frequency) discharges in which the rf powered and the grounded electrodes have different areas. This asymmetry determines the magnitude of the average plasma-to-electrode voltage I', (the ion bombarding energy) at the smaller powered electrode, which is a critical process parameter. A collisionless uniform ionization discharge model predicts that the voltage ratio V,/V, scales as the fourth power of the electrode areadoi:10.1063/1.348436 fatcat:rhaigwhysjhzllshqvfycqcaia