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## Creator

Haruumi Yamamoto, Daiki Kobayashi, [Kyohei Natsume](https://orcid.org/0000-0003-3949-6923), [Koji Kamiya](https://orcid.org/0000-0002-6765-4485)

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[Study on a Stationary Metamagnetic AMR System Using AC Superconducting Magnet](https://mdr.nims.go.jp/datasets/0e8edaf0-07ef-4d22-99ae-dc5bea59ecbe)

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財務省主計局高田主査 所管事項説明資料© NIMS All Rights Reserved.*Haruumi Yamamoto1, Daiki Kobayashi1, Kyohei Natsume1, Koji Kamiya1 1. National Institute for Materials Science (Japan)Study on a Stationary Metamagnetic AMR System Using AC Superconducting Magnet38th International Symposium on Superconductivity (ISS2025)@DEJIMA MESSE NAGASAKI4 December 2025AP8-07 Magnet science and technology 2© NIMS All Rights Reserved.Outline1. What are “Magnetic Refrigeration” and “AMR”2. Concept of Stationary Metamagnetic AMR System3. Design and AC Loss on Superconducting Magnet4. Scalability of Stationary Metamagnetic AMR System1© NIMS All Rights Reserved.Outline1. What are “Magnetic Refrigeration” and “AMR”2. Concept of Stationary Metamagnetic AMR System3. Design and AC Loss on Superconducting Magnet4. Scalability of Stationary Metamagnetic AMR System2© NIMS All Rights Reserved.1. What are “Magnetic Refrigeration” and “AMR”What is Magnetic refrigeration?Magnetocaloric effect (MCE): Magnetic entropy changes by applying magnetic fieldMagnetic refrigeration utilizes MCE combined with heat exchangeGas: 𝒅𝑼 = 𝑻𝒅𝑺 − 𝒑𝒅𝑽(Work with compression and expansion)Magnetic material: 𝒅𝑼 = 𝑻𝒅𝑺 + 𝝁𝟎𝑯𝒅𝑴(Work with magnetization and demagnetization)3Advantages of Magnetic refrigeration (In comparison with gas refrigeration)Reversible cooling cycle: Magnetic Carnot cycle satisfied theoretical efficiencyEnvironmental safety: No use of Freon or any other refrigerants to produce CO2N SDemagnetizationMagnetizationExpansionCompressionGas Refrigeration Magnetic Refrigeration© NIMS All Rights Reserved.Active Magnetic Regenerative Refrigeration (AMR) SystemMagnetic material functions as regenerator in addition to refrigerant.It can extend operating temperature range.1. Magnetization 2. Heat dissipation(Cold to Hot flow)3. Demagnetization 4. Heat absorption(Hot to Cold flow)Cold stage(H2liquefaction vessel)Upper AMR bedLower AMR bed Tandem AMR and H2 Liquefaction vessel4Particles of Magnetic material1. What are “Magnetic Refrigeration” and “AMR”© NIMS All Rights Reserved.Recent progress on AMR system for Hydrogen liquefactionNIMS successfully demonstrated world’s first liquefaction by AMR. [1]Achieved % Carnot 60% (FOM 0.6). [2]1.31.351.41.451.51.551.61.651.71.751.8101214161820222426-20 30 80 130 180Silicon diode output(V)Cold stage temperature (K)Time (sec)LH2 reachedLevel sensor 1 (top)LH2 reachedLevel sensor 2 (middle)LH2 reachedLevel sensor 3 (bottom)Upper AMRLower AMRCold stage(LH2vessel inside)Onset of AMR cycle0Level sensor 3 (bottom)Level sensor 2 (middle)Level sensor 1 (top)HeaterLH2LevelLH2 vessel5[1] Koji Kamiya et al 2022 Appl. Phys. Express 15 053001[2] Koji Kamiya et al Cryogenics 152 (2025) 104205Heat exchange gas(Cold Helium) Hydrogen gasLH2 vessel1. What are “Magnetic Refrigeration” and “AMR”© NIMS All Rights Reserved.Expected Applications of AMR Highly efficient liquefaction for coming hydrogen societyHydrogen liquefaction for utilization of water on the Moon etc.Issues of AMR system High magnetic field (~5 T) is necessary.It requires a mechanical drive.65 T Nb-Ti DC Superconducting Solenoid for AMR(Field variation is generated by moving magnetic materials inside the magnet)Liquefaction efficiency, cost, demand0.3 million ton$3 $2$10H2 cost100 million tonDemand of Hydrogen1. What are “Magnetic Refrigeration” and “AMR”© NIMS All Rights Reserved.Outline1. What are “Magnetic Refrigeration” and “AMR”2. Concept of Stationary Metamagnetic AMR System3. Design and AC Loss on Superconducting Magnet4. Scalability of Stationary Metamagnetic AMR System7© NIMS All Rights Reserved.2. Concept of Stationary Metamagnetic AMR SystemProperty of Metamagnetic materialConventional magnetic material: Large MCE with large magnetic field fluctuation Metamagnetic material: Abrupt magnetic transition, Large MCE with small magnetic field change𝑻𝟐Temperature 𝑻𝟏Magnetic field 𝝁𝟎𝑯Magnetization 𝑴Large field change(5 T)Conventional magnetic material Metamagnetic material𝑻𝟐𝑻𝟏Area: Proportional to MCESmall field change(1 T)8Magnetization 𝑴Magnetic field 𝝁𝟎𝑯© NIMS All Rights Reserved. 9Existing Metamagnetic materialsMany metamagnetic materials are found in wide temperature range and magnetic field range.Holmium for wide temperature range and low magnetic field suitable for Hydrogen liquefaction2. Concept of Stationary Metamagnetic AMR System© NIMS All Rights Reserved.Estimation of MCE on Metamagnetic HolmiumMagnetic entropy change: ∆𝑆 = 𝜇0𝐻1׬𝜇0𝐻2 𝜕𝑀𝜕𝑇𝑑 𝜇0𝐻Metamagnetic Ho with 0.5 to 1.5 T (1 T) exhibits almost same MCE as HoAl2 with 0 to 5 T (5 T)Required field variation reduced to 1/5.Magnetocaloric effect ofmetamagnetic Ho[𝟏𝟎𝟏𝟎] (Δμ0H =1 T)Magnetocaloric effect of conventional magnetic refrigeration materials(μ0H=0-5 T)00.20.40 20 40 60 80 100GGIG(Fe50%)ErAl2HoAl2Ho0.5Dy0.5Al2DyAl2GdNi2Gd5(Si0.0825Ge0.9175)4ErCo2S (J/cm3 K)Temperature (K)B: 0-5 T102. Concept of Stationary Metamagnetic AMR System-0.18-0.16-0.14-0.12-0.1-0.08-0.06-0.04-0.0200 20 40 60ΔS[J/(cm3K)]Temperature[K]HoAl2(0-5T) Ho(0.5-1.5 T)© NIMS All Rights Reserved.Controllability of temperature rangePeak of ∆𝑺 changes following the “Offset” field.0.2-1.2 T (“0.2 T offset”): Suitable for 20 K range 1.2-2.2 T (“1.2 T offset”): Suitable for 50 K range -0.18-0.16-0.14-0.12-0.1-0.08-0.06-0.04-0.0200 10 20 30 40 50 60ΔS[J/(cm3K)]Temperature[K]0.2-1.2 T0.4-1.4 T0.6-1.6 T0.8-1.8 T1-2 T1.2-2.2 T11Estimation of cooling capacity of Holmium Cooling capacity: 𝑸𝒕𝒉𝒆𝒐𝒓𝒚 W = ∆𝑺 ΤJ 𝑐𝑐 ∙ 𝐾 ∙ 𝑻𝒄𝒐𝒍𝒅 K ∙𝑽𝒐𝒍𝒖𝒎𝒆 cc𝑻𝒄𝒚𝒄𝒍𝒆 sHo can cover 20-50 K range with∆𝑺 ≥ 0.1 ΤJ cc ∙ KRequired volume:𝑽𝒐𝒍𝒖𝒎𝒆 =𝑸𝒕𝒂𝒓𝒈𝒆𝒕∙𝑻𝒄𝒚𝒄𝒍𝒆∆𝑺 ∙𝑻𝒄𝒐𝒍𝒅=𝑸𝒕𝒂𝒓𝒈𝒆𝒕∙𝑻𝒄𝒚𝒄𝒍𝒆0.1 ΤJ 𝑐𝑐∙𝐾 ∙20 K2. Concept of Stationary Metamagnetic AMR System© NIMS All Rights Reserved.Concept of Stationary Metamagnetic AMR System (Meta-AMR)Metamagnetic material can reduce required magnetic field variation.-> Making stationary design (field sweep) more realisticTemperature range of MCE can be controlled by magnetic field offset.-> Wide operating temperature range is achievable with single material.Magnetic Field Generation for Meta-AMRAC superconducting magnet: Control of AMR cycleDC superconducting magnet: Control of temperature range    ✓Lightweight superconducting magnet    ✓No need for heavy actuators, improved reliability    ✓High frequency, Downsizing×AC loss, AC Magnet power supply2. Concept of Stationary Metamagnetic AMR SystemAC SC Magnet(1T class)DC SC Magnet(Offer offset field)Metamagnetic MaterialHot End(High offset field)Cold End(Low offset field)Heat ExchangeFluid12© NIMS All Rights Reserved. 13Target value for Meta-AMR designCapacity: 200 W@20 K(Equivalent to ~25 kg/day hydrogen liquefaction)Temperature range: 20 K(Cold end)-50 K(Hot end)Cycle time: 10 s/cycle (0.1 Hz)Required volume:𝑽𝒐𝒍𝒖𝒎𝒆 =𝑸𝒕𝒂𝒓𝒈𝒆𝒕∙𝑻𝒄𝒚𝒄𝒍𝒆0.1 ΤJ 𝑐𝑐∙𝐾 ∙20 K=200W∙10 s0.1 ΤJ 𝑐𝑐∙𝐾 ∙20 K= 1000 ccTandem metamagnetic material bed of~1500 cc (𝝓𝟖 × 𝟑𝟎 𝐜𝐦)×2 is employed.2. Concept of Stationary Metamagnetic AMR SystemTandem Meta-AMR System© NIMS All Rights Reserved.Outline1. What are “Magnetic Refrigeration” and “AMR”2. Concept of Stationary Metamagnetic AMR System3. Design and AC Loss on Superconducting Magnet4. Scalability of Stationary Metamagnetic AMR System14© NIMS All Rights Reserved.3. Design and AC Loss on SC MagnetDC Superconducting MagnetApplying a DC offset magnetic field 0.2 T(Cold end, 20 K)～1.2 T(Hot end, 50 K)15AC Superconducting MagnetA time-varying magnetic field of 0⇔1 T is applied to the entire magnetic material (0.1 Hz).Electromagnet design of one side of 200 W class Meta-AMRMagnet design parameters of 200 W Meta-AMRWire: 4 mm-w REBCO tape @20 K(Je>1.4×105 A/cm2)AC Magnet DC MagnetOperating current 0 100 A 100 ANumber of turns (1000+800+800+1000)×2 3200×2Inductance 1.1 H×2 2.8 H×2Tape c axis direction(Vertical ⊥ direction)© NIMS All Rights Reserved.00.511.522.5-0.3 -0.15 0 0.15 0.3Magnetic field [T]Axial position [m]MagnetizedDemagnetizedMagnetic field calculation with FEM  𝝁𝟎𝑯𝐦𝐚𝐱 = 𝟑. 𝟕 𝐓 (𝝁𝟎𝑯⊥𝐦𝐚𝐱 = 𝟏. 𝟗 𝐓)𝑰𝐞 𝐦𝐢𝐧~𝟕𝟎𝟎 𝐀 𝟐𝟎 𝐊 (4 mm-w)1.2-2.2 T(50 K)0.2-1.2 T(20 K)Change in magnetic field strength along the central axisTimeAC fieldAC fieldAntiphaseTime① ② ③ ④① ②③ ④Waveform of one cycle①: Mag. (1.5 s)②: C to H Flow (3.5 s)③: Demag. (1.5 s)④: H to C Flow (3.5 s)Upper AMRLower AMR163. Design and AC Loss on SC Magnet© NIMS All Rights Reserved. 17AC Loss calculation methodHysteresis loss density [W/m2] based on Brandt and Indenbom[3]𝒑𝐡 = 𝝁𝟎𝒘𝑱𝐞𝑯⊥𝐦𝒈𝑯⊥𝐦𝑯𝐜𝒇, 𝒈 𝒙 = Τ𝟐 𝒙 𝐥𝐧 𝐜𝐨𝐬𝐡 𝒙 − 𝐭𝐚𝐧𝐡 𝒙,𝑯𝐜 = Τ𝑱𝒄𝒅 𝝅H calculated by FEM was used.Assumptions about Variables of REBCO𝑱𝐞 = 𝝀𝑱𝐜 (𝝀: Occupancy rate), 𝑯⊥𝐦(𝒓, 𝒛) = Τ𝑯⊥𝐦𝐚𝐱 −𝑯⊥𝐦𝐢𝐧 𝟐,𝒘 = 𝟒/𝒏 mm (𝒏: Number of divisions), 𝒅 = 𝟏. 𝟓 um, 𝑱𝒄 = 𝐜𝐨𝐧𝐬𝐭.= 𝟓 × 𝟏𝟎𝟏𝟎 A/m2 Critical length: 𝒍𝑷𝑪~𝟐𝟐𝝆𝒘𝑱𝒄𝝁𝟎 ሶ𝑯~𝟐𝟐∙𝝆∙ Τ𝟒 𝒏×𝟏𝟎−𝟑∙𝟓×𝟏𝟎𝟏𝟎𝟏~𝟒 × 𝟏𝟎𝟒𝝆𝒏𝐦-> Assume that coupling loss 𝒑𝐜 is negligible3. Design and AC Loss on SC Magnet[3] E H Brandt et al Phys. Rev. B 48 (1993)12893[4] Superpower-inc. HPTape c axis direction(Vertical ⊥ direction)REBCO Superconducting Tape[4]© NIMS All Rights Reserved. 18Integration of AC loss density𝑬𝐭𝐨𝐭𝐚𝐥 Τ𝐉 𝐜𝐲𝐜𝐥𝐞 = 𝑬𝐡𝐲𝐬𝐭𝐞𝐫𝐞𝐬𝐢𝐬 + 𝑬𝐜𝐨𝐮𝐩𝐥𝐢𝐧𝐠 = 𝑷𝐭𝐨𝐭𝐚𝐥 𝑾 ∙ 𝒇= ׬ 𝒑𝐡 + 𝒑𝒄 𝒅𝑽 ׮= 𝒑𝐡 + 𝒑𝒄 𝒓𝒅𝒓𝒅𝜽𝒅𝒛3. Design and AC Loss on SC MagnetAC Loss of Magnet with 4 mm-w tapes𝑬𝐭𝐨𝐭𝐚𝐥 = 𝟏. 𝟎 × 𝟏𝟎𝟒 Τ𝐉 𝐜𝐲𝐜𝐥𝐞𝑷𝐭𝐨𝐭𝐚𝐥 = 𝟏. 𝟎 × 𝟏𝟎𝟑𝑾High hysteresis loss due to wide widthLosses occur only in AC magnets subject to strong magnetic field fluctuationsB⊥m=μ0(H ⊥max-H ⊥min) [T]© NIMS All Rights Reserved. 19AC Loss of Magnet with 4/100 mm-w tapes𝑬𝐭𝐨𝐭𝐚𝐥 = 𝟏. 𝟎 × 𝟏𝟎𝟐 Τ𝐉 𝐜𝐲𝐜𝐥𝐞𝑷𝐭𝐨𝐭𝐚𝐥 = 𝟏𝟎𝐖AC loss is reduced to 1/100 of the original value.It is small enough compared to the refrigeration capacityand is acceptable as heat generation.Striation can avoid AC loss problems.3. Design and AC Loss on SC Magnet© NIMS All Rights Reserved.Outline1. What are “Magnetic Refrigeration” and “AMR”2. Concept of Stationary Metamagnetic AMR System3. Design and AC Loss on Superconducting Magnet4. Scalability of Stationary Metamagnetic AMR System20© NIMS All Rights Reserved.3. Scalability of Stationary Meta-AMR System21Scalability of 200 W Class Meta-AMRAssuming that the product of magnetic material volume and frequency is proportional to the capacity,𝒇𝟏 ∙ 𝝅𝒓𝟏𝟐𝒍𝟏 = 𝒇𝟐 ∙ 𝝅𝒓𝟐𝟐𝒍𝟐, 𝒓: radius, 𝒍: lengthAssuming Τ𝒓𝟏 𝒍𝟏 = Τ𝒓𝟐 𝒍𝟐,           Τ𝒓𝟐 𝒓𝟏 = Τ𝒍𝟐 𝒍𝟏 = Τ𝟏𝟑 Τ𝒇𝟐 𝒇𝟏 = ൗΤ𝟏 𝟑 𝒇𝟐 Τ𝟏 𝟑 𝒇𝟏Frequency [Hz]𝒇Dimension ofmagnetic material∝ Τ𝟏𝟑𝒇0.1 𝝓𝟖𝟎 × 𝟑𝟎𝟎𝐦𝐦0.5 𝝓𝟒𝟕 × 𝟏𝟕𝟓𝐦𝐦1 𝝓𝟑𝟕 × 𝟏𝟑𝟗𝐦𝐦If the frequency can be increased, the magnetic material can be made smaller. If the magnetic material is made smaller, the magnet can also be made smaller.0.1 Hz Design(×1) 0.5 Hz Design (×0.58) 1 Hz Design (×0.46)© NIMS All Rights Reserved.3. Scalability of Stationary Meta-AMR System22Scalability calculation of 200 W Class Meta-AMRFrequency [Hz]𝒇MagnetWeight [a.u.]∝ Τ𝟏 𝒇AC loss∝ 𝒇 × Τ𝟏 𝒇 = 𝟏(independent of 𝒇)AC OperatingCurrent [A]∝ 𝟑 𝒇AC Voltage[V]∝ Τ𝟏 𝟑 𝒇𝟔× 𝟑 𝒇 × 𝒇= Τ𝟏 𝟑 𝒇AC Input Power* [W]∝ 𝟑 𝒇 × Τ𝟏 𝟑 𝒇 = 𝟏(independent of 𝒇)0.1 1 10 W (100 J/cycle)100(2.5×104 A/cm2)76 7.6 k0.5 1/5 10 W (20 J/cycle)171(4.3×104 A/cm2)44 7.6 k1 1/10 10 W (10 J/cycle)215(5.4 A/cm2)35 7.6 kAC loss does not change even if frequency is changed.Smaller (High freq.) design has advantage in system weight and AC voltage.Smaller design requires high current (density).-> Even smaller design seems to be feasible.*If regeneration is used, the net input power will be smaller.© NIMS All Rights Reserved.ConclusionWe propose “Meta-AMR,” a stationary AMR system that replaces conventional ferromagnetic refrigerants with metamagnetic materials.Using metamagnetic Ho, we achieved a magnetic entropy change comparable to HoAl₂ driven by a 5 T field change, while reducing the required field swing to 1 T.With a DC offset field, Ho provides more than 0.1 J/cc·K of ΔSₘ over a broad 20–50 K range.Two REBCO SC magnets were designed to generate suitable fields for a 200 W-class Meta-AMR.The estimated AC loss is about 10 W, within an acceptable heat budget.Further AC-loss reduction will require improved filamentarization of REBCO tapes.Higher-frequency operation could further downsize the system, though optimized power-supply design and magnetic-energy recovery schemes remain key issues.23Appendix© NIMS All Rights Reserved.Benchmark gas refrigeratorCreare TB Refrigerator (Hydrogen)Refrigeration capacity: 150W @ 20K, Mass: 660 kg, Power: 9 kWCreare TB Refrigerator (Oxygen)Refrigeration capacity: 350W @ 90K, Mass: 140 kg, Power: 2.8 kWCreare TB Refrigerator for HST (20 years ago)Refrigeration capacity: 7W @ 70K, Mass: 18.5 kg (2.64 kg/W), Power: 350 W (50 W/W) 表紙 スライド 0 本文 スライド 1 スライド 2 スライド 3 スライド 4 スライド 5 スライド 6 スライド 7 スライド 8 スライド 9 スライド 10 スライド 11 スライド 12 スライド 13 スライド 14 スライド 15 スライド 16 スライド 17 スライド 18 スライド 19 スライド 20 スライド 21 スライド 22 スライド 23 スライド 24 スライド 25