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

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

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

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 J. Tkaczuk

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

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

Technical solutions – Various possibilities CEA design Hitachi rotating design Hitachi static design CERN design MIT design 7FCC Week 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

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

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

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 J. Tkaczuk S. Jeong, 1992 Y. Hakuraku, 1985

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] FCC Week J. Tkaczuk S. Jeong, 1992

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

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

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 J. Tkaczuk

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 J. Tkaczuk Impact of other heat losses: Largest heat losses: GGG – warm source < 1% smaller

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 J. Tkaczuk Y. Hakuraku, 1986

Static Magnetic Refrigerator – Magnet design validation AC losses 17FCC Week 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:

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

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

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

Thank you 21FCC Week J. Tkaczuk

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 J. Tkaczuk