1. Magnetic Refrigeration down to 1.6K for FCC_ee Jakub Tkaczuk Supported by: DRF Energy Program – DESA41K CERN FCC Collaboration Francois Millet, Jean-Marc Duval Mathematical modeling for

2. Contents Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design 2FCC Week 2016 - J. Tkaczuk

3. Contents 3FCC Week 2016 - J. Tkaczuk Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design

4. Magnetic refrigeration – Theoretical principle Magnetic refrigeration is based on the Magneto-Caloric Effect (MCE) (reversible variation of internal energy when applied magnetic field in a suitable material) Remove magnetic field temperature decreases spins randomize Apply magnetic field temperature increases spins align - Gadolinium Gallium Garnet – typical material for 1.5K – 4.5K temperature range. 4FCC Week 2016 - J. Tkaczuk

5. Magnetic refrigeration – Ideal Carnot cycle 2 adiabatic transformations 2 isothermal transformations Typical entropy-temperature diagram for magneto-caloric material. 5FCC Week 2016 - J. Tkaczuk

6. Contents 6FCC Week 2016 - J. Tkaczuk Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design

7. Technical solutions – Various possibilities CEA design Hitachi rotating design Hitachi static design CERN design MIT design 7FCC Week 2016 - J. Tkaczuk A. Lacaze, 1981 Y. Hakuraku, 1985 M. Schmidt, 1992 S. Jeong, 1992 Moving GGG Rotating GGG Simple construction Void fraction - critical Heat exchange with He-3

8. See presentation: FCC Week 2015 Technical solutions – Design performances Cold source Temperature [K]1.8 1.8*1.8 Cooling capacity [W]1.351.80.510*0.012 Volumetric cooling capacity [W/l]75.612.25.0?0.7 Carnot efficiency0.530.340.13?0.12 External magnetic field variation [T]0 – 40.5 – 30 – 30 – 3.50 – 2.8 Frequency [Hz]0.80.50.20.2 – 10.1 8FCC Week 2016 - J. Tkaczuk (*) results not published

9. Contents 9FCC Week 2016 - J. Tkaczuk S. Jeong, 1992 Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design

10. Active Magnetic Regenerative Refrigerator - Principle SMR Static Magnetic Refrigerator AMRR Active Magnetic Regenerative Refrigerator Every part of magneto-caloric material goes through its own cycle 10FCC Week 2016 - J. Tkaczuk S. Jeong, 1992 Y. Hakuraku, 1985

11. Active Magnetic Regenerative Refrigerator - Cycle Input x = 0 x = 1 x = 0 Cold source temperature [K]1.6 Warm source temperature [K]4.2 GGG mass [kg]1000 Core diameter [m]0.29 Core length [m]2.35 Diameter of channels [mm]9 Number of channels600 Magnetic field variation [T]0 - 4 11FCC Week 2016 - J. Tkaczuk 0.01.0 S. Jeong, 1992

12. Output Warm source temperature [K]4.22.1 Cycle frequency [Hz]0.1 Cooling capacity [W]9595300 Volumetric cooling capacity [W/l]0.62.1 Maximal overall efficiency0.120.21 Active Magnetic Regenerative Refrigerator - Performance Large DT possible, but: More material needed Very low heat transfer 12FCC Week 2016 - J. Tkaczuk Fundamental limitation of AMRR cycle makes it impractical for FCC application Conclusion from our design:

13. Contents 13FCC Week 2016 - J. Tkaczuk Y. Hakuraku, 1985 Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design

14. Static Magnetic Refrigerator – Heat exchange Condensation in superfluid is limited by Kapitza resistance Nucleate Boiling is described by Kutateladze correlation Stratification used for insulation 14FCC Week 2016 - J. Tkaczuk

15. Static Magnetic Refrigerator – Heat exchange & losses Impact of the heat exchange conditions: 30% smaller Impact of the heat losses from the warm source: 45% smaller 15FCC Week 2016 - J. Tkaczuk Impact of other heat losses: Largest heat losses: GGG – warm source < 1% smaller

16. Output Input Warm source temperature [K]4.2 Cold source temperature [K]1.8 GGG mass [kg]0.7 Length to diameter ratio1 Core length [cm]5 Frequency [Hz]0.2 Overall heat losses [W]1.0 Cooling capacity [W]0.55 Volumetric cooling capacity [W/l]5.0 Overall efficiency0.12 Static Magnetic Refrigerator – Model validation Input fixed by Y. Hakuraku (Hitachi) Calculations results Thermal part of the model has been validated 0.5 W 0.13 Hitachi experimental results 16FCC Week 2016 - J. Tkaczuk Y. Hakuraku, 1986

17. Static Magnetic Refrigerator – Magnet design validation AC losses 17FCC Week 2016 - J. Tkaczuk Magnet simulation based on Hitachi design Low AC losses wire: fine filament, Cu-Ni matrix Hitachi experimental results: GGG SC Magnet Smaller impact for larger scale Axis of symmetry Hitachi cooling capacity:

18. Contents 18FCC Week 2016 - J. Tkaczuk Magnetic refrigeration Technical solutions Active Magnetic Regenerative Refrigerator Static Magnetic Refrigerator Path to FCC design

19. Path to FCC design – Experimental prototype 19FCC Week 2016 - J. Tkaczuk Next step Small scale FCC prototype for laboratory validation: 0.3 W @ 1.6K cooling (56 ml of GGG).

20. Path to FCC design Paramagnetic material properties and geometry optimization Collaboration with material laboratory Heat transfer optimization Conceptual and experimental study underway 20FCC Week 2016 - J. Tkaczuk Magnet design study: (field profile, AC losses) Contact with magnet companies

21. Thank you 21FCC Week 2016 - J. Tkaczuk

22. 50 µm Gas heat switch “off ” conduction is satisfying “on” conduction is not satisfying – 1-2 µm heat switch required – technically impossible Heat switch design 22FCC Week 2016 - J. Tkaczuk