Plasma inhomogeneity caused by standing-wave effects in rf parallel plate reactors can be removed if one of the electrodes is replaced by a shaped electrode. The proposed shape is calculated using Maxwell's equations in vacuum. In this solution, the electric field has a radially uniform vertical component, and a radial component which remains negligible for a plasma gap small compared to the quarter wavelength. Perturbations to this vacuum solution in presence of a plasma should remain small if the damping length due to dissipation in the plasma is large compared to the reactor radius and if the rf skin depth remains large compared to the plasma thickness. (C) 2003 American Institute of Physics.