*Takeaway*: The current 1D cooling model is getting closer to matching our observed cooling trends, mainly in the lower temperature limit. The predicted time constant is still much smaller than we are seeing in reality (by about a factor of 3), but this can potentially be improved by revising specific heat values and/or dimensional estimates for chamber components.
The model uses the known cooling power of the cold head [attachment 2] and considers radiative heat from the outer shield, baseplate (bottom lid), and mylar wrapping around braid. I increased the complexity of the script by solving a system of ODEs (for braid and coldplate temperature) simultaneously instead of assuming the temperatures are equal at all times, and solving only 1 ODE. This resulted in the model's lower temperature limit prediction matching our observed data, at ~66 K.
The model still predicts a much smaller time constant than we are seeing. This is affected by specific heat values for Cu and Al, along with dimensional estimates of the coldplate and braid (AKA how much mass is being cooled). It is possible that these values are being underestimated in the model, which would lead to the smaller time constant. Currently the model uses constant values for the specific heat of Cu and Al (room temperature). But since specific heat increases with temperature, accounting for temperature dependence would lower the specific heat values and shift the model in the opposite direction (towards an even smaller time constant). Therefore I suspect the model is underestimating the mass of the coldplate, though I am unsure if this would completely correct the discrepancy.
If the term (specific_heat * density * volume) of the coldplate (Al) is increased by a factor of 4, the model resembles the data well [attachment 3]. |