An analytical study of dynamic response and nonequivalence of an absolute active cavity radiometer operating at cryogenic temperatures

Abstract

A finite-element model describing the dynamic thermal response of an absolute active cavity radiometer is developed. The model considers thermal conduction, diffuse-specular thermal radiation and electrical heat generation. The analysis of diffuse-specular radiation is made possible by the use of the Monte Carlo method.

The model is used to analyze both the steady-state and transient instrument response for operating temperatures of 5, 70 and 300 K using a 465-node system. The temperature is monitored at the locations where resistance thermometers would be mounted on thermal impedance members. Steady-state relationships between radiative input energy from a uniform diffuse source field and temperature drop between the resistance thermometers and the heat sink are found to be linear. The steady-state sensitivity of the model to a diffuse input field, determined by relating electrical input energy to radiative input energy, is found to be a function of the placement of the heater wire on the cavity but is independent of operating temperature.

The transient response of the instrument to a step increase in radiative input energy is examined in both passive and active operation, and in the latter case with feedback control of the electrical heating. In passive operation, the time constants of the thermal circuit of the model are determined to be 0.35 ms, 5.38 s and 17.80 s for the operating temperatures of 5, 70 and 300 K, respectively. The effects of the electrical substitution heater feedback circuit time constant on overall model performance are determined from closed-loop active operation. Overdamped, underdamped and nearly critically damped model response is obtained for selected values of the electrical circuit time constant.