There is growing interest in the use of microwaves to process materials. The main application of microwave processing of materials is in heating. The most important characteristic of microwave heating is {\it volumetric} heating, which is quite different from conventional heating where the heat must diffuse in from the surface of the material. Volumetric heating means that materials can absorb microwave energy directly and internally and convert it to heat. It is this characteristic that leads to advantages such as rapid, controlled, selective, and uniform heating.

However, some problems hinder the widespread use of microwave energy. One of these problems is called thermal runaway, which is a type of thermal instability due to the interaction between the electromagnetic waves and materials. As thermal runaway occurs, the temperature of the heated material rises uncontrollably. The normal consequence of thermal runaway is the damage of the processed materials.

The origins of thermal runaway are different under different processing conditions. When processing ceramic materials, thermal runaway is mainly due to the positive temperature dependence of dielectric loss of the material. These materials absorb more microwave energy as they are being heated. The most plausible explanation of this phenomenon is the so-called "S-curve" theory. However, prior to this work, no direct experimental evidence has been published to verify this theory.

In this dissertation, we report the direct experimental evidence of the so-called "S-curve" by heating thermal runaway materials in a microwave resonant cavity applicator. A complete discussion of how the experimental results were achieved is presented. From the experimental results, we find that by the use of the cavity effects thermal runaway can be controlled.

To explain the experimental findings, a theoretical model based on equivalent circuit theory is developed. Also, a coupled heat transfer and electromagnetic field model is developed to simulate the heating process. Both models give reasonably good comparison with our experimental results. Finally, a method to control thermal runaway is described.