1. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Typical insulations for Rutherford cables Heat transfer model Heat flux comparison same operating conditions specific operating conditions Potential for enhanced insulation for NbTi Porosity checker Preliminary results Conclusions Improving heat transfer from cable to HeII

2. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Typical Cable Insulations The first barrier to the removal of the heat generated in a coil is the electrical insulation: ~100-200 V between adjacent turns ~100-200 V between adjacent turns ~5 kV to ground ~5 kV to ground up to 200 MPa up to 200 MPa Nb-Ti: All polyimide insulation: semi- permeable to He II Nb 3 Sn (wind & react): mineral fiber cloth wrapping & Epoxy resin impregnation: impermeable to He II Courtesy of F. Rondeaux (CEA)

3. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 NbTi : all PI

4. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Nb3Sn : S2 glass +resin G.Dambrosio&D.Chichili

5. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Heat Transfer Model No He II reaches the strands Heat goes through solid conduction first, then to He II R Insulation Kapton R Kapitza Kapt.-He II. Cable, T c =T b +  T He II bath, T b =1.9 1) Q a Vs Q b depends on insulation porosity 2)Q a & Q b are non linear 3)Q b has saturation level R Kapitza Cu-He II He II is in direct contact with the strands Heat flux is shared by two parallel paths ( a & b ). Nb-Ti (porous insulation) Nb 3 Sn (sealed insulation) He II channels Q a : Q a : Solid Conduction TbTbTbTb TCTCTCTC TbTbTbTb TCTCTCTC Q b : Q b : Superfluid Conduct. QaQaQaQa QbQbQbQb Q R He II Channel Cable, T c =T b +  T He II bath, T b =1.9 R insulation Ep.+G.Fiber R Kapitza Epoxy.-He II. Q : Solid Conduction a b

6. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Equivalent Thermal Resistances Bulk resistance of 0.1 mm thick Kapton ~2 times larger than 0.2 mm thick epoxy+fiberglass Bulk resistance of 0.1 mm thick Kapton [7] ~2 times larger than 0.2 mm thick epoxy+fiberglass [2] Boundary resistance (Kapitza): Kapton (& Ep.+F.) ~6 times larger than Cu Boundary resistance (Kapitza): Kapton [8] (& Ep.+F.) ~6 times larger than Cu [9] HE II channel resistance: -depends on insulation porosity (channel lengths and cross-areas) -is always smaller than Kapton and epoxy+fiberglass but is limited by saturation

7. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Experimental (B. Baudouy et al Experimental (B. Baudouy et al Cryogenics 39, 921 (1999) SSC dipole LHC dipole Solid Conduction Superfluid Conduction Predominance:

8. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Comparison for Operating Conditions: Same or Specific  We consider two coils in a He II bath (T b =1.9) :  Nb 3 Sn with sealed insulation  Nb-Ti with porous insulation  We impose the same eng- ineering current density J eng and operative peak field B  We get the temperature margin  T=T c -T b we combine it with the heat transfer correlations and we obtain the corresponding heat flux  We impose J and B ult specific of their practical use

9. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Temperature Margin Comparison for Same B (9T) and J eng T b =1.9 Cu/Sc Nb-Ti1.5 Nb 3 Sn1

10. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Maximum Heat Flux for Same B (9T) and J eng Cu/Sc Nb-Ti1.5 Nb 3 Sn1 Bare cable asymptotic limit Nb 3 Sn Enhanced SSC dipole LHC dipole SSC dipole LHC dipole Enhanced Bare cable Nb 3 Sn

11. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Maximum Heat Flux for Specific Conditions Bare cable asymptotic limit Nb 3 Sn Enhanced SSC LHC Main J/J c (T b,B ult ) B= 9 T for NbTi B= 13.5 T for Nb3Sn

12. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 it corresponds to ~ 220 mW/m per cable it corresponds to ~830 mW/m per cable

13. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Enhanced porosity

14. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Enhanced Insulation Details 3 layers with gaps Overlap between 1 st and 3 rd ( ) Overlap between 1 st and 3 rd ( detached overlap ) All polyimide insulation No special manufacturing or additional cost 1 st layer with gap 3 nd layer with gap 2 rd layer with gap Dedicated He II channels of finite size ExampleThickness [  m] Width[mm]Gap[mm] 1 st 24.5112 2 nd 752.51.5 3 rd 55.4112 1 tape 4 tapes1 tape

15. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Porosity checker Air enters the stack of cable longitudinally (A) and can exit longitudinally (C), without crossing the insulation or radially (B) crossing the insulation. Insulation porosity is evaluated from the comparison between radial and longitudinal flow A C B Flow out (B) Flow in (A) Flow out (C)

16. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007

17. Tests Results/1 Vertical compression 10 MPa

18. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Tests Results/2

19. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Heat transfer tests

20. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007Summary For same B and J eng, Nb 3 Sn coils made by Rutherford cables can draw one order of magnitude more heat than typical LHC Nb-Ti coils thanks to : For same B and J eng, Nb 3 Sn coils made by Rutherford cables can draw one order of magnitude more heat than typical LHC Nb-Ti coils thanks to : Greater temperature margin Greater temperature margin Thermal conductivity of epoxy+fiberglass higher than Kapton Thermal conductivity of epoxy+fiberglass higher than Kapton For the same margin to critical surface (specific operating conditions), Nb 3 Sn coils made by Rutherford cables can draw three times more heat than typical LHC Nb-Ti coils For the same margin to critical surface (specific operating conditions), Nb 3 Sn coils made by Rutherford cables can draw three times more heat than typical LHC Nb-Ti coils…however… there is a large potential to increase the dimension of the cooling channels thus moving their saturation at higher heat fluxes The use of this potential in HeII provides a spectacular increase of heat evacuation capabilities of NbTi coils

21. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 References 1. 1.C. Meuris, B. Baudouy, D. Leroy, B. Slezess, Heat transfer in electrical insulation of LHC cables cooled with superfluid Helium, Cryogenics 39, 921 (1999) 2. 2.L. Imbasciati et al.,Thermo-mechanical Characterization of Insulated and Epoxy- Impregnated Nb 3 Sn composites, IEEE Trans. on Appl. Supercond., Vol. 13, Issue 2, 1788 (2003) 3. 3.D.S. Matsumoto, C.L. Reynolds Jr., A.C. Anderson, Thermal Boundary Resistance at Metal Epoxy Interfaces, Phys. Rev. B, Vol. 16 n.8, 15 Oct. 1977. 4. 4.F. Rondeaux, P. Bredy, J.M. Rey, Thermal Conductivity Measurements of Epoxy Systems at Low Temperatures, Adv. Cryo. Eng. 48A (Materials), 197 (2002) 5. 5.J. Gorter, J. H. Mellink, On the Irreversible Processes in Liquid Helium II, Physica 15, 285 (1949) 6. 6.V. Arp, Heat transport through Helium II, Cryogenics 10, 96 (1970) 7. 7.J. Lawrence, A.B. Paterl, J.G. Brisson, The Thermal Conductivity of Kapton HN between 0.5 and 5 K, Cryogenics 40, 203 (2000) 8. 8.B. Baudouy, Kapitza Resistance and Thermal Conductivity of Kapton in Superfluid Helium, Cryogenics 43, 667 (2003) 9. 9.A. Kashani, S.W. Van Sciver, Kapitza Conductance of Technical Copper with Several Different Surface Preparations, Cryogenics 25, 238 (1985) 10. 10.E. Todesco, J.P. Koutchouk, Scaling Laws for  * in the LHC Interaction Regions, CARE Workshop LUMI-06, 17th October 2006, Valencia, Spain. 11. 11.N. Kimura et al., Heat Transfer from Insulated Rutherford Type Cables Immersed in Pressurized He II, Adv. Cryo. Eng. 43

22. Davide Tommasini Improving heat transfer from cable to HeII LIUWG 15 November 2007 Comparison for Specific Operating Conditions  We consider the coils of two alternative designs * (same l*,  *) of triplets for LHC IR upgrade:  Nb 3 Sn with sealed insulation  Nb-Ti with porous insulation  We impose to each coil the corresponding B po and J and we get the T c  We compare the heat flux that can pass through each insulation for the corresponding temperature margin  T=T c -T b :   T Nb3Sn =T cNb3Sn -T b for sealed insulation   T NbTi =T cNbTi -T b for porous insulation l*=23 m,  *=0.28 cm, T b =1.9K Nb-Ti Nb 3 Sn G154258[T/m] Bore9481[mm] B pc 10.315.0[T] B po 8.212.0[T] J c (B pc,T b )15832156[A/mm 2 ] (IR upgrade, E.Todesco LUMI06) Assuming 95% of the maximum gradient/aperture ratio achievable [X] we come up with the following designs: *