Theoretical analysis of the microwave-drill near-field localized heating effect

The microwave-drill principle [Jerby et al., Science 298, 587 (2002)] is based on a localized hot-spot effect induced by a near-field coaxial applicator. The microwave drill melts the nonmetallic material locally and penetrates mechanically into it to shape the hole. This paper presents a theoretical analysis of the thermal-runaway effect induced in front of the microwave drill. The model couples the Maxwell’s and heat equations including the material’s temperature-dependent properties. A finite-difference time-domain algorithm is applied in a two-time-scale numerical model. The simulation is demonstrated for mullite, and benchmarked in simplified cases. The results show a temperature rise of $\sim {10}^3\mathrm{K}∕\mathrm{s}$ up to $1300\mathrm{K}$ within a hot spot confined to a $\sim 4\text{-}\mathrm{mm}$ width ($\sim 0.1$ wavelength). The input-port response to this near-field effect is modeled by equivalent time-varying lumped-circuit elements. Besides the physical insight, this theoretical study provides computational tools for design and analysis of microwave drills and for their real-time monitoring and adaptive impedance matching.