Model for Anomalous Power Dependence of Microwave Heating in Ceramic Materials

A model is presented to explain the anomalous power dependence of microwave heating in ceramic materials. The anomaly considered consists of a saturation effect wherein the dependence of the heating rate on microwave power becomes sublinear. Our proposed explanation is based on the idea of spatial confinement of the absorbing charges in grain boundary regions. The mechanism of saturation, more generally, of a decrease in absorption efficiency, arises from a mismatch of two lengths, one of which measures the maximum distance an absorbing charge travels under the combined action of damping and of the oscillating microwave field, and the other measures the spatial extent of the confining region. Explicit calculations for a simple model are presented and the results are examined in the light of observations on ferric oxide.