Brian Jeffs3.4 Thermal Model for the ALPACA Cryostat
Requirements
The cryogenic system for ALPACA shall:
- be a closed-cycle cryogenic system ("dry dewar")
- keep dual-polarization dipoles and low noise amplifiers (LNAs) at ~20 K physical temperature throughout the GBT environmental operating conditions
Baseline Model
- Cornell Astronomy has 30+ years of experience modeling heat budget across multiple types of instruments, from mK to 100 K
- Accounts for conduction (wiring & structure) and radiative loads, as well as Joule heating (LNAs)
- Supplemented with thermal finite-element analysis (FEA) for more complex items (e.g. 3D conduction through foam; dipole radiation loading)
- Experience carried over from AO-19 prototype success
- Assume 305 K ambient air / exterior surface temperature
- Required cooling is achieved via three CTI 1020CS cold heads (one per trient) from Trillium
Results
- 84 W on 1st cold stage, operating at 99 K
- 10 W on 2nd cold stage, operating at 19 K
- Heat loads broken down by major source are graphically illustrated below:
Figure 1: The heat load contribution from various components on the first stage (top) and the second cold stage inside the ALPACA instrument (bottom) is shown here.
- LNAs thermally anchored to 19-20 K
- Uniform temperature achieved across the array using high conductivity Aluminum (1000 Series) for 2nd cold stage base plate. Figure 2 shows < 1 K temperature variation across 2nd cold stage base plate
Figure 2: This figure shows the results from a simplified model that was used to evaluate material choices for the 2nd stage base plate with particular emphasis on the temperature variation across the plate. We applied a cold sink at 15K (dark blue), and a heat load at each dipole base based on the operating power draw of two LNAs and overall heat load estimated from the thermal model referenced here is distributed over the plate surface. We observed that using 1000 series aluminum offers significant temperature uniformity, with ΔT<1K, when compared with 6061 aluminum which results in a ΔT~5K. The absolute temperatures shown here should not be taken as operating temperatures of 2nd cold stage.
- Expected operating point for CTI-1020 cold heads:
Figure 3: The standard performance curve for a CTI-1020 cold head provided by Trillium is shown here. The available cooling power and operating temperature of the cold stage are related as shown. Based on the thermal budget and accounting for ample overheads, the operating point for ALPACA is clearly marked above. The information shown here is for a single CTI-1020 and all three cold heads in the instrument would be operating under identical conditions.
- Foam conduction and radiation dominates 1st and 2nd cold stage loadings, respectively
- In general, the foam radiative heat transfer is greater than the foam conductive heat transfer, so light-weighting the foam pieces does not reduce (and indeed increases) the thermal load on the cryogenic stage
- Temperature distribution of the 4-layer foam stack, shown for a single trient in Figure 4.
Figure 4: The overall temperature distribution through the four layer foam stack is shown here. The thermal model is setup with the top layer of the foam seeing ambient temperature (fixed at 305K, shown in red) and the bottom layer is in contact with the the ground plane at the first thermal stage (fixed at 95K, shown in blue) inside the instrument. The dipoles pass through the lowest layer of the foam stack and the temperature distribution across it would provide the effective radiative heat load on the dipoles.
- View into dipole pockets in foam from the ground plane showing pocket temperature variation across a trient (dipole radiative load thus varies by position)
Figure 5: Looking at the temperature distribution through the bottom face of the ground plane. The dipoles pass through the holes shown in the figure above and and connect to the 20K stage. This view captures the variation in the temperature of the the foam radially. Each dipole sees the foam surrounding it and the simulation here shows that the temperature of the foam changes from ~207 K for dipoles in the center to ~239 K for dipoles towards the edge.