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 Thu Aug 5 11:53:26 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Wed Aug 11 14:58:47 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Wed Aug 11 18:00:19 2021, Koji, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 13 15:14:14 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 13 21:01:42 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Thu Aug 19 14:34:10 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 20 13:44:58 2021, rana, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS Fri Aug 20 14:05:45 2021, Radhika, DailyProgress, Cryo vacuum chamber, Cooldown model fitting for MS
Message ID: 2647     Entry time: Thu Aug 19 14:34:10 2021     In reply to: 2644     Reply to this: 2648
 Author: Radhika Type: DailyProgress Category: Cryo vacuum chamber Subject: Cooldown model fitting for MS

Building on [2643], I realized that the conductive cooling term proportional to $(T_{coldplate} - T_{testmass})$ was also negligible. I added back in physical parameters for the 2 radiative terms (one from the cold plate, one from 295K) and used the emissivities of the test mass and inner shield as fit parameters:

$F_e = (\frac{1}{e_{tm}} + (\frac{1}{e_{is}} - 1) \frac{A_{testmass}}{A_{innershield}})^{-1}$

$P_{rad} = F_e A_{testmass} \sigma (T_{coldplate}^4 - T_{testmass}^4)$

$F_{e295} = (\frac{1}{e_{tm}} + (\frac{1}{e_{is}} - 1) \frac{A_{testmass}}{A_{aperture}})^{-1}$

$P_{rad295} = F_{e295} A_{testmass} \sigma (295^4 - T_{testmass}^4)$

I used Koji’s input to model radiative heating from 295K. I approximated the radius of the aperture (from which room temperature could be exposed) to be 3cm, and assumed radiative heat is emitted from this circle.

The result of this fit can be seen in Attachment 1: [e_testmass, e_innershield] = [0.59736291, 0.20177643]. This would imply that Aquadag has an emissivity of about 0.6, and that the emissivity of rough aluminum is much higher than expected at 0.2.

I then used these parameters to model the cooldown, given: 1. both the test mass and inner shield surfaces are painted in Aquadag; 2. only the inner shield surface is painted in Aquadag. These models are shown in Attachment 2.

Painting the inner shield in addition to the test mass would yield marginal improvement, as expected. However, painting the inner shield while removing Aquadag from the test mass would, according to this model, weaken the coupling further compared to the reverse case. This makes sense, since in Fe the effect of the inner shield’s emissivity is scaled by the ratio $\frac{A_{testmass}}{A_{innershield}}$, which is quite small. Increasing the emissivity of the test mass therefore makes more of a difference in the coupling.

 Attachment 1: model_fit_tm_painted.pdf  42 kB  Uploaded Fri Aug 20 15:54:58 2021
 Attachment 2: models_painted.pdf  25 kB  Uploaded Fri Aug 20 15:55:09 2021
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