Self-Consistent Calculation of the Interaction of an 83 GHZ Beam with a Ceramic Cylinder

Summary form only given. The high power millimeter-wave beams that can be generated by CW gyrotrons represent a promising energy source for rapid, high-temperature processing of materials. A program is under way at the Naval Research Laboratory to investigate the heating of ceramic tubes and cylinders using an 83 GHz beam for joining and sintering applications. Thermal gradients produced by non-uniform heating and losses play an important role in these processes. In this presentation we analyze the scattering and absorption of a millimeter-wave beam by a ceramic cylinder or tube and calculate the temperature profile. The analysis includes the temperature dependence of the dielectric properties, an effect that can dramatically alter the microwave coupling during the heating process. The workpiece is assumed to be rotating fast enough to obtain sufficiently azimuthally uniform heating that only the radial dependence of the dielectric properties and radial heat flow need be included. In the analysis the workpiece is subdivided into thin concentric tubes in which the dielectric and other material properties are held constant. Maxwell´s equations are solved by expanding the RF fields in cylindrical waves. Matching the boundary conditions at the tube interfaces leads to a set of equations for the expansion coefficients. The radial heat-conduction equation is nonlinear and is solved numerically. When solving the heat conduction equation, the tube dielectric and thermal parameters, and the RF field expansion coefficients are recalculated after each time step or iteration. This leads to a self-consistent RF-thermal solution. The solutions provide the transient and steady-state temperature profiles for a given beam power density and polarization. Calculations for an alumina cylinder show several features believed to be typical for millimeter-wave heating of low-loss oxide ceramics: 1) at low temperatures (up to several hundred degC), where the loss-tangent is low, the cylin- er acts like a high-refractive index lens focusing the beam to a region near the center of the cylinder. In addition, the temperature dependence of the permittivity causes resonance effects leading to sudden variations in power deposition with temperature. 2) At intermediate temperatures (~400-1200degC), the rapid increase in the loss tangent leads to rapid heating with little or no increase in the applied beam power (thermal runaway effect). 3) At high temperatures (~1200-2000degC) the loss tangent is so large that the microwaves are absorbed in the outer region of the cylinder.