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Magnetic Refrigeration Down to 1.6 K for the Future Circular Collider E+ E

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Magnetic Refrigeration Down to 1.6 K for the Future Circular Collider E+ E PHYSICAL REVIEW ACCELERATORS AND BEAMS 20, 041001 (2017) Magnetic refrigeration down to 1.6 K for the future circular collider e + e − † Jakub Tkaczuk,* François Millet, Jean-Marc Duval, and Bernard Rousset Univ. Grenoble Alpes, INAC-SBT, F-38000 Grenoble, France CEA, INAC-SBT, F-38000 Grenoble, France (Received 14 July 2016; published 11 April 2017) High-field superconducting rf cavities of the future circular collider eþe− may require a kW-range superfluid helium refrigeration down to 1.6 K. Magnetic refrigeration operating below 4.2 K can be an alternative to the compression/expansion helium refrigeration. A significant difference between this application and previous magnetic refrigerator studies is its large cooling power, up to 103 times larger than the other designs. Principles of magnetic refrigeration are described and various technical solutions are compared. A numerical model for the static magnetic refrigerator is presented, validated, and adapted to the needs of the positron-electron version of the future circular collider. A preliminary design of magnetic refrigerator suitable for low temperature, kW-range cooling is studied. DOI: 10.1103/PhysRevAccelBeams.20.041001 I. INTRODUCTION II. MAGNETIC REFRIGERATION THEORETICAL PRINCIPLES High field superconducting rf cavities of the future circular collider eþe− (FCC) may require a kW-range Magnetic refrigeration is a cooling method based on superfluid helium refrigeration down to 1.6 K. Indeed, the magneto-caloric effect: a reversible variation of internal to cool down superconducting rf (SRF) cavities, helium energy in suitable material when external magnetic field cooling is classically used in normal state (4.5 K) or in is modified. The magnetic refrigerator working principle superfluid state (T<2.1 K). The SRF cavities operating depends on the technical solution, the one studied below temperature is selected to minimize the cost and the energy follows a Carnot-like cycle. If the magnetic field increases, consumption of the whole accelerator infrastructure [1] depending on whether the transformation is adiabatic or including SRF cavities and cryogenic cooling as shown isothermal, either the material temperature increases (phase in Fig. 1. 1 in Fig. 2) or the magnetic moments align (phase 2 in If one would like to operate at optimal temperature— Fig. 2) [2]. 1.6 K (the refrigeration cost minimum in Fig. 1) the The magneto-caloric material and the type of thermo- compression/expansion cycle with several cryogenic cen- dynamical cycle with a practical design should be carefully trifugal compressors pumping in series is the current design chosen depending on the specific application. A relevant for kW-range superfluid helium refrigeration. However, magneto-caloric material has to be selected for the designed this solution presents some obvious disadvantages such as temperature range (4.5 K − 1.6 K). Material commonly complex control of the cold compression train and long downtime after stops. It might be possible to replace the cold compressors by magnetic refrigeration or to add one magnetic refrigeration stage to an already existing system to reduce the number of cold compressors in series. Magnetic refrigerator operating below 4.2 K could be therefore an alternative to the compression/expansion helium refrigeration. A preliminary design of magnetic refrigerator suitable for low temperature, kW-range cooling is detailed in the following work. *[email protected] † [email protected] Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distri- bution of this work must maintain attribution to the author(s) and FIG. 1. Optimal operating temperature for superconducting rf the published article’s title, journal citation, and DOI. cavities [1]. 2469-9888=17=20(4)=041001(8) 041001-1 Published by the American Physical Society TKACZUK, MILLET, DUVAL, and ROUSSET PHYS. REV. ACCEL. BEAMS 20, 041001 (2017) issue but leak-tightness remained essential in the operation phase. The use of stationary magnets and the construction itself put limitations on magnetic field profile—in none of the positions zero field could have been obtained. C. Hitachi static magnetic refrigerator Another magnetic refrigerator constructed by Hitachi was based on static GGG and pulsed superconducting FIG. 2. Adiabatic demagnetization refrigerator cycle. magnet [7,8]. The design took advantages of efficient heat transfer during the phase transition in “isothermal” trans- used for refrigeration down to 1 K is gadolinium gallium formations. It was assumed that stratified helium inside garnet, Gd3Ga5O12 or GGG [3]. the heat sources can work as a static heat switch between While choosing the technical implementation for the GGG and the helium bath. While no moving parts brought FCC application, the following objectives need to be the benefits of high reliability, high heat losses to the warm considered: large cooling capacity, high reliability, high source were identified at the same time. They significantly efficiency, and compact construction. The factors allowing reduced the cooling capacity and cycle efficiency (<15%). comparing various designs in terms of efficiency and size (material cost) are cycle efficiency ηc [W=W] and D. CERN magnetic refrigerator 3 _ volumetric cooling capacity [W=dm ]—cooling capacity Q At CERN a magnetic refrigerator with superconducting 4 referred to the volume of magneto-caloric material VG, pulsed magnets, static GGG and circulating He was ideally both coefficients should be maximized. The largest constructed [9]. It was designed to reach a cooling power magnetization, hence the largest entropy change is char- of more than 10 W at 1.8 K. Due to large losses caused by η acterized by the highest cycle efficiency c value. A constant presence of liquid helium inside the GGG (large comparison of various designs is performed in order to dead volume), the refrigerator was limited in performance. select the most suitable magnetic refrigerator technical The research activity was stopped before global perfor- solution for the FCC. mance measurements, after identifying the main limita- tions: negative influence of helium dead volume inside III. TECHNICAL SOLUTIONS the GGG on cooling capacity and superfluid transition of Several technical solutions have been developed in the helium present inside the magneto-caloric material occur- past and are analyzed in terms of scaling to large cooling ring in every cycle. capacity. E. MIT tandem active magnetic A. CEA double acting reciprocating regenerative refrigerator magnetic refrigerator The magnetic refrigerator designed in MIT worked in tandem mode (two GGG cores operating in counterphase) In the design developed in CEA-Grenoble in the 1980s, 3 two stationary magnets and two moving GGG single with pulsed superconducting magnets and He circulation crystals were operated in reciprocating mode [4,5]. [10]. Helium gas, in comparison to liquid, has minor influence on dead volume because of significantly lower Working pressure of two heat sources (He-I on the warm 4 3 side and He-II on the cold side) were similar in order to mass. Unlike He, He has no superfluid transition during 3 limit the leaks. Very large cycle efficiency (>50%)was the whole cycle. However, using gaseous He imposes low obtained thanks to the direct contact between GGG and working pressure (50 mbar for operating at 1.8 K) and heat sources only during the ‘isothermal’ transformations. results in unsatisfying heat exchange conditions for rea- The need of moving magneto-caloric material brings into sonable pressure drop. Experiments showed significantly question the refrigerator reliability. Increasing magneto- lower cooling capacity and cycle efficiency (<15%)in caloric material mass might lead to additional problems comparison with the calculated values. with leaks and inertia. F. Studied solution B. Hitachi rotary magnetic refrigerator The main parameters and a summary of described design The rotary magnetic refrigerator was using 12 GGG performances are presented in Table I. A design with high pieces installed in a rotor. Thanks to this design the cooling volumetric cooling capacity and high cycle efficiency production was almost continuous and reasonable perfor- should be developed for FCC_ee. However, a solution mances were obtained (ηc > 30%) [6]. In comparison to the which is reliable and easily scalable has to be selected. reciprocating magnetic refrigerator inertia was not a critical Therefore, the Hitachi static magnetic refrigerator is studied 041001-2 MAGNETIC REFRIGERATION DOWN TO 1.6 K … PHYS. REV. ACCEL. BEAMS 20, 041001 (2017) TABLE I. Comparison of various technical solutions. A. CEA B. Hitachi rotative C. Hitachi static D. CERN E. MIT Cold source temperature [K] 1.8 1.8 1.8 1.8 1.8 Warm source temperature [K] 4.2 4.2 4.2 4.5 4.2 External field variation [T] 0–4 0.5–30–30–3.5 0–2.8 Frequency [Hz] 0.8 0.5 0.4 0.2–1 0.1 Cooling capacity [W] 1.35 1.8 0.5 10a 0.012 _ 3 75 612250 a 0 7 Q=VG½W=dm . - . a Cycle efficiency ηc [W=W] 0.53 0.34 0.13 - 0.12 aResults not published. in detail with objectives to improve its efficiency and demagnetization (phase 4 in Fig. 2) heat is transferred from volumetric cooling capacity. the cold source to GGG throughout condensation. As mentioned before, GGG is a magneto-caloric material When the GGG temperature is larger than the cold source commonly used for refrigeration in 5 K − 1 K temperature temperature (phases 1, 2, 3 in Fig. 2), insulation of the He-II range. Its entropy can be reasonably well described using bath is provided thanks to stratification in gaseous helium. the free ion model [11]. It was compared with experimental As the gas conductivity is small (around 0.01 W=mK), values [12,13] and is presented in Fig. 3. the losses to the cold source have little impact on general Other important GGG properties used in the following performance. calculations are thermal conductivity, magnetization, and When GGG is colder than the warm source, the specific heat [13–16].
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