Simple 1.5 dimensional thermal model for CKM cavities
Inputs: Phonon Kapitza Rbcs model
peak conductance Nb (srimp=H,
He temp Ro fudge fudge thickness Solyak=S,
(K) (nOhm) factor factor (mm) Eq4.43=T)
1.800 49.4 20 1 2.20 S
Outputs: 60000
For 3.9 GHz, BCS surface resistance is
51.1 nOhm; with Ro, 100.5 nOhm Q of 2.27E+09
For 80 mT field power is 203.58 W/sq. meter
Kapitza conductance H = 6092 W/K-sq.meter, so outer
surface is at 1.833 K, & inner surface is 1.846 +- Columns G on have scratch data.
(at RRR = 300 ). 0.000 K 1.3E-06 5.5
Algorithm is to evaluate conductanc
Tinr 1.800 1.841 1.845 1.846 dZ slice to get dT, which is added t
Rbcs(srimp) 45.1 55.4 56.5 56.7 at end of slice. Kappa' then is cond
Rbcs(Hasan) 27.6 33.6 34.3 34.4 slice. The average of kappa & kap
Rbcs(Nick) 40.5 49.9 51.0 51.1 Then scale for area to get dT'. Rep
Rs 89.9 99.3 100.3 100.5
P 182.2 201.2 203.3 203.6 kappa T+dT
Z T(1) T(2) T(3) T(3) 45.8226 1.8303
2.200 1.800 1.800 1.800 1.800 19 45.8661 1.8308
2.200 1.830 1.833 1.833 1.833 18 45.9104 1.8312
2.090 1.830 1.834 1.834 1.834 17 45.9557 1.8317
1.980 1.831 1.834 1.834 1.834 16 46.0019 1.8322
1.870 1.831 1.835 1.835 1.835 15 46.0492 1.8326
1.760 1.832 1.835 1.835 1.835 14 46.0975 1.8331
1.650 1.832 1.836 1.836 1.836 13 46.1469 1.8336
1.540 1.833 1.836 1.836 1.837 12 46.1974 1.8341
1.430 1.833 1.837 1.837 1.837 11 46.2492 1.8347
1.320 1.834 1.837 1.838 1.838 10 46.3022 1.8352
1.210 1.834 1.838 1.838 1.838 9 46.3565 1.8357
1.100 1.835 1.838 1.839 1.839 8 46.4123 1.8363
0.990 1.835 1.839 1.839 1.839 7 46.4695 1.8369
0.880 1.836 1.840 1.840 1.840 6 46.5282 1.8375
0.770 1.836 1.840 1.841 1.841 5 46.5886 1.8381
0.660 1.837 1.841 1.841 1.841 4 46.6507 1.8387
0.550 1.838 1.842 1.842 1.842 3 46.7147 1.8393
0.440 1.838 1.842 1.843 1.843 2 46.7806 1.8400
0.330 1.839 1.843 1.843 1.843 1 46.8486 1.8407
0.220 1.840 1.844 1.844 1.844
0.110 1.840 1.844 1.845 1.845
0.000 1.841 1.845 1.846 1.846
G on have scratch data.
0.6
m is to evaluate conductance kappa at start of
o get dT, which is added to T(start) to get T
slice. Kappa' then is conductance at end of
e average of kappa & kappa'is used for dT'.
le for area to get dT'. Repeat 4 times.
kappa' dT' dT'' kappa T+dT kappa' dT' dT'' kappa T+dT
45.8656 0.0004 0.0004 46.1307 1.8335 46.1782 0.0005 0.0005 46.1651 1.8339
45.9091 0.0004 0.0005 46.1786 1.8340 46.2261 0.0005 0.0005 46.2136 1.8344
45.9535 0.0004 0.0005 46.2275 1.8345 46.2750 0.0005 0.0005 46.2630 1.8349
45.9987 0.0004 0.0005 46.2775 1.8350 46.3249 0.0005 0.0005 46.3135 1.8354
46.0450 0.0004 0.0005 46.3284 1.8355 46.3759 0.0005 0.0005 46.3650 1.8359
46.0922 0.0004 0.0005 46.3805 1.8360 46.4279 0.0005 0.0005 46.4176 1.8364
46.1405 0.0004 0.0005 46.4338 1.8366 46.4812 0.0005 0.0005 46.4715 1.8369
46.1899 0.0004 0.0005 46.4882 1.8371 46.5356 0.0005 0.0006 46.5265 1.8375
46.2404 0.0004 0.0005 46.5440 1.8377 46.5913 0.0005 0.0006 46.5828 1.8381
46.2921 0.0004 0.0005 46.6010 1.8382 46.6483 0.0005 0.0006 46.6405 1.8386
46.3451 0.0004 0.0005 46.6594 1.8388 46.7068 0.0005 0.0006 46.6996 1.8392
46.3995 0.0004 0.0006 46.7193 1.8394 46.7667 0.0005 0.0006 46.7601 1.8398
46.4552 0.0004 0.0006 46.7808 1.8400 46.8281 0.0005 0.0006 46.8222 1.8405
46.5124 0.0004 0.0006 46.8438 1.8407 46.8911 0.0005 0.0006 46.8859 1.8411
46.5711 0.0004 0.0006 46.9086 1.8413 46.9558 0.0005 0.0007 46.9514 1.8418
46.6315 0.0004 0.0006 46.9751 1.8420 47.0224 0.0005 0.0007 47.0187 1.8424
46.6936 0.0004 0.0006 47.0436 1.8427 47.0908 0.0005 0.0007 47.0879 1.8431
46.7575 0.0004 0.0007 47.1141 1.8434 47.1613 0.0005 0.0007 47.1591 1.8438
46.8234 0.0004 0.0007 47.1867 1.8441 47.2339 0.0005 0.0007 47.2325 1.8445
46.8914 0.0004 0.0007 47.2616 1.8448 47.3088 0.0005 0.0008 47.3082 1.8453
kappa' dT' dT'' kappa T+dT kappa' dT' dT''
46.1651 0.0005 0.0005 46.1690 1.8339 46.1690 0.0005 0.0005
46.2136 0.0005 0.0005 46.2175 1.8344 46.2175 0.0005 0.0005
46.2630 0.0005 0.0005 46.2670 1.8349 46.2670 0.0005 0.0005
46.3135 0.0005 0.0005 46.3175 1.8354 46.3175 0.0005 0.0005
46.3650 0.0005 0.0005 46.3691 1.8359 46.3691 0.0005 0.0005
46.4176 0.0005 0.0005 46.4219 1.8365 46.4219 0.0005 0.0005
46.4715 0.0005 0.0006 46.4757 1.8370 46.4757 0.0005 0.0006
46.5265 0.0005 0.0006 46.5308 1.8375 46.5308 0.0005 0.0006
46.5828 0.0005 0.0006 46.5872 1.8381 46.5872 0.0005 0.0006
46.6405 0.0005 0.0006 46.6450 1.8387 46.6450 0.0005 0.0006
46.6996 0.0005 0.0006 46.7041 1.8393 46.7041 0.0005 0.0006
46.7601 0.0005 0.0006 46.7647 1.8399 46.7647 0.0005 0.0006
46.8222 0.0005 0.0006 46.8269 1.8405 46.8269 0.0005 0.0006
46.8859 0.0005 0.0007 46.8907 1.8411 46.8907 0.0005 0.0007
46.9514 0.0005 0.0007 46.9562 1.8418 46.9562 0.0005 0.0007
47.0187 0.0005 0.0007 47.0236 1.8425 47.0236 0.0005 0.0007
47.0879 0.0005 0.0007 47.0929 1.8432 47.0929 0.0005 0.0007
47.1591 0.0005 0.0007 47.1642 1.8439 47.1642 0.0005 0.0007
47.2325 0.0005 0.0008 47.2377 1.8446 47.2377 0.0005 0.0008
47.3082 0.0005 0.0008 47.3135 1.8454 47.3135 0.0005 0.0008
1.900
1.850
1.800
T(K)
1.750
1.700
1.650
1.600
0.000 0.500 1.000 1.500 2.000 2.500
Z(mm)