Theory is presented, based on the lack of crystal orientation dependence of the oxidation rate, for the anodisation of silicon in an oxygen plasma. It is demonstrated that the diffusion of oxygen is unlikely to control the process rate in either the linear or parabolic regions of growth. The drift of ions and electrons is controlled by the need for a constant field at the silicon surface and the build up of ionic space charge in the oxide continues at the expense of that within a boundary layer throughout the constant rate regime. As this boundary layer becomes depleted, a parabolic region of growth is predicted. This theory is found to be consistent with growth occurring in a microwave-stimulated plasma of oxygen.