Calculation of radiation heating in a microwave Luneberg lens

A microwave Luneberg lens is heated by radiation from the feed. The resultant temperature rise is calculated in terms of the thermal conductivity and electric dissipation factor of the lens dielectric for the wavelength of the microwave radiation. The temperature rise at the center of a lens is calculated, taking into account the varied properties of the dielectric within the lens. The spherical symmetry of the lens substantially simplifies this calculation. The temperature distribution within the lens is calculated, neglecting the varied thermal conductivity and dissipation factors of the lens. A spherical inversion (Kelvin transform), centered at the feed, is used to transform the lens surface to a plane so that the heat flow may be calculated. The hottest point is at the feed; the temperature rise being about twice that at the center. In the limit of low dissipation factor, the lens diameter has no effect on temperature because of the compensating effects of thermal resistance and dissipated power variations with lens size.