Heating of an oculus concentrator

An oculus concentrator must stand off from the oculus to reduce the intensity of its heating.

Sunlight must pass through the oculus at high concentration because there is a high level of radiant flux inside the hot space which will be leaking out the same opening the sunlight enters. At the empty storage temperature of 1250 °C, the blackbody radiant flux inside the hot space is 305 kw/m2, and 72% of this is outside the 0.35-2.0 micron passband of glass; at the full storage temperature of 1800 °C, the radiant flux inside the hot space is 1047 kw/m2, and 49% of this is outside the passband of glass. Thus a hypothetical glass window covering the oculus would be absorbing between 220 and 513 kw/m2 of back-radiation depending on the hot space temperature. And the heating from the concentrated sunlight may be comparable. With 8000 kw/m2 of solar flux at the oculus, an absorption of just 2% in the optics would amount 160 kw/m2 of additional  heating.

Due to the heating of the optics, it is necessary to separate an oculus concentrator by some distance from the oculus itself. Mirror optics would have the advantage that special arrangements for cooling can be made on the dark face, transmissive optics are practically limited to radiant and air convection cooling. A tolerable heating flux on transmissive optics may be 10 kw/m2, which requires standing off till the flux is reduced to 1/75 the flux at the oculus. For example, an oculus concentrator that is a hemisphere of area 2πR^2 =75 * π *r^2, so R/r = sqrt(75/2) = 6, where R is the radius of the oculus concentrator and r is the radius of the oculus.