SC issues for TM 110 cavities

1. SC issues for TM110 cavities • The TM110 mode and cavity measurements • Construction of a heuristic heat flow model • Data that doesn't match it • Wild Eyed Speculation Leo Bellantoni U.W. Visit 21 November 2003

2. TM110 mode concentrates B field in iris Our BMAX is about 80mT "State of the art" is about 166mT EMAX is much smaller than in typical TM010 mode cavities Out of concern for thermal limits our initial design had thin (1.62mm) walls – but it is not structurally sound & we are looking at thicker walls

3. Basic measurement scheme Power into cavity less reflected power is power dissipated in Nb Ringdown time when RF power is shut off is Q/ From Q and P, obtain U, the stored energy in the cavity From U, via Finite Element Analysis of the RF fields, obtain electric and magnetic fields, accelerating potentials etc.

4. A heuristic model of heating Kapitza conductance from Nb to He: From a fit to published data, with Fudge factor that could easily be off by 50% in W/ m2-K Boucheffa et.al., in 7th Workshop on RF Superconductivity (1995)

5. A heuristic model of heating Collapse of e- into Cooper pairs permits phonons to move freely Bulk thermal conductance in Nb: Published data show a range of values and effects in W/ m-K Müller, in 3th Workshop on RF Superconductivity (1988) From fit by DESY to their RRR=380 data & more Fudge

6. A heuristic model of heating Surface resistance at RF frequencies for Nb: I take R 0 as a free parameter Using the obviously heuristic 0.3nHEXT(mOe) f(GHz) and our measured HEXT in the Dewar, 18n is reasonable RSURF = R0 + RBCS For RBCS I have two forms: 1. A fit of a polynomial to SRIMP.F, a code based on Halbritter's thesis of ~1970, with these values: Tc = 9.2K /kTC = 1.86 L = 33nm 0 = 40nm e = 5.99nm(RRR) = 5.99nm x 270 = 1617nm Except for the RRR, these are the default values in the code 2. A very phenomenological equation based on that thesis and the work of Turneaure, modified for mean free path of the electron (Padamsee, Knobloch, Hays, pg. 88)

7. A heuristic model of heating The polynomial to SRIMP.F is of the form The phenomenological equation is and is only valid for RRR~300 At 1.8K, 3.9GHz, these forms give: 31n TESLA data, scaled by 2 45n SRIMP.F 41n Phenomological formula before e correction 27n Phenomological formula with e correction However, temperature drop across the Nb is a significant effect

8. Model says… With phenomenological RBCS: 22mK from Nb to He 103mK across Nb 66n at 80mT, 1.925K With SRIMP.F RBCS: 45mK from Nb to He 183mK across Nb 134n at 80mT, 2.082K Variation of 50% in Kapitza conductance changes RSURF <4% with phenomenological RBCS, <9% with SRIMP version

9. Model says… Increased thermal conductance due to phonon peak can help a lot, particularly if true RBCS is high. Lower thermal conductance is really bad in all cases. 1

10. Model says… SRIMP Phenomenological Measurement at low field!

11. Model says… We do have some measurement issues, but basically we do not see the droopy characteristic that one would expect from large heat loading across the Nb.

12. Thoughts & Observations • The Q vs T curve can be accommodated by abandoning the SRIMP prediction and letting R0 float up to 85n. But – In TM010 mode, which is at about 2.8GHz, we measure about 65n. Multiply by (3.9/2.8)2 and you get a fairly reasonable 125n. That means that the mystery R0 term is specific to either TM110 mode or to 3.9GHz. We do have a correction already applied to the data shown here that is specific to the TM110 mode. • The correction is for RF fields dissipating power in the steel flanges. It has been obtained in two different ways: first by covering (most) of the flanges with Nb and secondly by calculating the power dissipated in the steel using a FEM of the RF fields and published data on the resistivity of cold steel. The result is the same both ways… still could be wrong.

13. Thoughts & Observations • The Q vs EDEFL curve can be accommodated by imagining that the thermal conductivity is large – i.e., by letting the bulk thermal conductivity go up by, say, a factor of 10. It is true that we have welds in the iris regions and that recrystallization after welding leaves larger grains, possibly purer material and therefore, perhaps, better thermal conductivity. That would imply I think that the true RBCS is higher than the phenomenological model says it is.However, we do not see an increase in RRR in the weld region of our samples.Perhaps what is happening is that heat is flowing down out of the iris regions to other parts of the structure where it then is transferred into the LHe.

14. Thoughts & Observations • If the phenomenological model is right, R0 is 85n, and a cavity made of 2.2mm thick material will have RSURF of 220n.If we just let the bulk thermal conductivity go up by a factor of 10, to model either SRIMP or sideways heat flow, we should see a very low RSURF of 50n, where we actually see 170n. The next question is, do we model that higher RSURF with a higher RBCS, or with a higher R0? • • Suppose a higher RBCS, using the form from SRIMP. That gives values close to the measurement at higher temps, but leaves only 72n at 1.8K. So we would need to postulate also that R0 is near 100n to fit the data. In this scenario, the thick wall cavity will show RSURF = 170n. • • Suppose the lower RBCS. Then R0 must be 130n to fit the data at 1.8K. The high temp curve is still close to the data, and in this scenario, the thick wall cavity will still show RSURF = 170n.