MultiPhysics Analysis of Trapped Field in Multi-Layer YBCO Plates

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Dwain McBride
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1 Exerpt from the Proeedings of the COMSOL Conferene 9 Boston MultiPhysis Analysis of Trapped Field in Multi-Layer YBCO Plates Philippe. Masson Advaned Magnet Lab *7 Main Street, Bldg. #4, Palm Bay, Fl-95, pmasson@magnetlab.om Abstrat: superondutors have the unique apability of trapping magneti flux. This feature has the potential to enable and improve several appliations inluding high power density rotating mahines. Current material used as trapped flux magnets (TFM) is single domain YBCO that present numerous limitations in terms of performane, stability and size. One way to overome the limitations is to use thin layers of YBCO deposited on disks and stak them. Multi-layer trapped flux magnets were suessfully modeled and analyzed using COMSOL MultiPhysis through oupled eletromagneti and thermal transient simulations. Simulations allow for a better understanding of how the urrent redistributes during thermal disturbanes and validate the potential of the tehnology. Keywords: trapped flux magnets, superondutors, YBCO, non-linear problem. Introdution Trapped Flux Magnets (TFM) are very attrative for appliation to power devies. The major limitation of flux trapping apabilities of bulk YBCO stems from mehanial problems. Indeed, Lorenz fores an beome very important when stored magneti energy inreases. As most of the stress is applied loally on pinning enters in the material, a failure usually results in destrution of the material struture. In order to improve flux trapping apability in TFMs, mehanial reinforement an be done using epoxy impregnated fiber glass loth and a reord of 7 T trapped at 9 K was ahieved. However, due to the erami nature of YBCO, it remains struturally weak and an very likely fail if eletro-thermal instabilities our. We have studied the feasibility of TFMs based on multi-layer onfigurations that ould be ahieved by staking disks made of oated ondutors. The multi-layer onfiguration would bring a muh better stress distribution and should lead to more stable flux trapping. Even though paking fator remains an issue for staked oated ondutors, it is expeted that YBCO an be deposited advantageously in multiple layer onfiguration speifially developed for this speifi appliation. The paper presents a FEA eletromagneti-thermal analysis of flux trapping in YBCO multi-layers plates using COMSOL MultiPhysis.. Flux trapping in superondutors Beause of their unique properties, superondutors an trap magneti flux and at as permanent magnets. The phenomenon an be explained by the ritial state model in whih urrent density an only be ± or. Sine magnetization of superondutors is hystereti in nature, the magneti state of the material depends of the temperature and external field history.. Flux trapping methods Several methods to trap magneti flux in a superondutor an be used. Their effetiveness and pratiality differ from one method to another. Field ooling Field ooling onsists of a ool down of the superondutor under applied field. This method is very effetive but requires a large magnet generating at least the value of flux density desired in the superondutor. Zero field ooling If zero-field ooling is performed, the superonduting material will first reat by shielding flux variation and will expel magneti flux from its volume. The method then requires full saturation in urrent and neessitates large magnets providing at twie the value of flux density desired in the superondutor. Pulsed magnetization Pulse magnetization is idential in priniple to zero field ooling, however, beause the flux variation is very fast, the superondutor an enter a flux flow regime and generate losses

2 dereasing the magnitude of the ritial urrent density. Additionally, the method rrequire equiress energy storage for pul pulse se generation generation. Flux pumping Reently flux pumping tehniques have been developed requiring a omplex omplex to set up up,, ontrollable temperature and magneti gate material material.. This method represents a very promising alternative as no large field soure is needed. Field ooling is the most eff effetive etive way to trap magneti flux in a superonduting material. After a field ooling, a superonduting plate behaves like a permanent soure of magneti field. Its major differenes with permanent magnets are: a muh larger magnetization operation at onstant flux instead of onstant magnetization (trapped flux magnets annot be defluxed ) Table : F Field ield ooling of a superonduting plate Step Step Step Bext = Bmax Bext = Bmax Bext = T > T T < T T < T. Appliations of TFMs Trapped flux magnets enable the development of several superonduting devies requiring onstant magneti flux or large values of magneti flux density. Magneti bearings Some appliations, suh as flywheels or high speed eletrial mahines, require fritionless bearings. TFMs an be advantageously used as they an provide very large fores and do not require ative ontrol. Indeed, sine the magneti flux intrinsially re remains mains onstant, any variation is automatially ompensated by indued persistent urrents. Rotating mahines High speifi power rotating mahine require large exitation field that an be produed by TFMs []. []. The major hallenge is to magnetize the super superondutor ondutor without adding weight or volume to the mahine. An example of suh mahine is shown in figure []. ]. The mahine takes advantage of the flux trapping apability of superonduting plates to reate, shape and onentrate magneti flux leading to a very high power density. Figure.. Illustration llustration of Bean s model 4. Properties of YBCO The most widely used material in TFMs is YBCO. YBCO is a erami that beome beomes superonduting below 9 K and exhibits very high urrent density in single domain blo bloks. ks. A flux density of 7 T has been trapped in a small YBCO plate at 9 K [[].. While bulk YBCO is a very attrative option, it presents severe limitations: Brittle material that an develop raks Stress applied by the Lorentz fores on pinning enters a ann lead to mehanial failure Size limited to a few entimeters with homogeneous properties Cannot annot be bent Figure. Single ingle grain YBCO ylinder ylinder ( Superondutors exhibit a highly non non-linear linear eletrial ondutivity as shown in figure and equation ().

E E (V/m) E ( B, T ) n( B, T ) = () Figure. E(I) harateristi of superondutors The ritial urrent density of YBCO is depending on the temperature and on the applied magneti flux density.

3 E E (V/m) E ( B, T ) n( B, T ) = () Figure. E(I) harateristi of superondutors The ritial urrent density of YBCO is depending on the temperature and on the applied magneti flux density. It an be parameterized as follows: 5.E-4 4.5E-4 4.E-4.5E-4.E-4.5E-4.E-4.5E-4.E-4 5.E-5.E B, T ) (,) e T B T 9 T ( (4) = B The parameters ( T, K), T and T b an be obtained experimentally. Current flows in the a-b plane of the material and urrent density in the - axis of the material is negligible. 5. Multilayer onfiguration YBCO an be deposited in thin films and turned into tapes. YBCO is the basis for seond generation ondutors or oated ondutors and an be deposited on large areas. Up to entimeter wide ribbons are urrently manufatured and ut into 4 mm wide tapes to make ondutors. Disks oated with YBCO film an be manufatured and staked to form ylinders. The eletrial properties would then be strongly anisotropi as urrent is allowed to flow only in parallel planes (a-b planes) and no urrent is flowing between layers. YBCO is deposited on substrate and the filling fator of a stak is a lot less than 5 %. However, urrent density in YBCO films or thin layers is orders of magnitude larger than in large blok and therefore ompensate for the low filling fator. Suh a onfiguration brings numerous advantages: Material an be bent Intrinsially mehanially reinfored I (A) Improved flux pinning Larger systems an be built Figure. YBCO ondutor from Amerian Superondutor In. [4] Commerially available wide ondutors an be used, however, the stabilization layers neessary for stable ondutor operation are not requires in TFM and a higher filling fator an be ahieved with a dediated onfiguration. 6. Problem definition 6. Geometry The system is modeled in D with axial symmetry, whih is a valid approximation for the system of interest sine YBCO an be deposited uniformly. The geometry implemented in COMSOL is shown in figure 4. YBCO Figure 4. Geometry implemented in Comsol The system is modeled with homogeneous YBCO layers.5 mm thik and separated by. mm layers of resin insulation. 6. Material properties YBCO TFM Epoxy resin Field oil Heater Axis YBCO exhibits non-linear eletrial and thermal properties. In COMSOL, ondutors are modeled with their eletrial ondutivity, based

4 on equation (), the ondutivity of YBCO an be expressed as follows. σ[ S / m] = E T T B + B E E n (5) 6. Mesh, Soures and boundary onditions The mesh, represented in figure 7, is omposed of about 8, elements leading to a system with over, degrees of freedom. The mesh is kept oarse in the surrounding air and in the field oil. Where T is the ritial temperature, is the value of the ritial urrent density at K and T, E is the eletrial field magnitude defining, B and n are determined experimentally. The eletrial field E is a parameter of the eletrial ondutivity whih would pose a problem in most FEA pakage but COMSOL allows for this dependene to be modeled. Speifi heat and thermal ondutivity of YBCO are plotted as a funtion of temperature in figure 5. Cp (/(kg.k) Thermal properties of YBCO k (W/(m.K) Cp YBCO K YBCO Figure 7. Mesh in the multi-layer omponent The thermal simulation only onsiders the YBCO, resin and heater. A heat exhange ondition is set on the resin simulating ooling. The heat pulse applied to the heater is shown in figure Temperature (K) Figure 5. Thermal properties of YBCO Resin G resin is used to hold the YBCO layers together. Its thermal properties are shown in figure 6. Cp (/(kg.k) Thermal properties of resin Temperature (K) Figure 6. Thermal properties of G resin k (W/(m.K) Cp resine k resine Figure 8. Heat pulse. The field oil generates a flux density on the TFM whih is ramping down linearly from 5 T to T. 7. Simulation sequene Sine field ooling requires full field penetration before the YBCO beomes superonduting, the initial ondition orresponding to this state needs to be omputed first. When a superondutor is ooled down under field, part of the magneti flux is expelled from its volume; if the applied field is below H, whih is of a few mt, then the

material is diamagneti (Meissner effet), if the applied field is greater than H, then the material is in the mixed state and normal zones are developed allowing quanta of flux to go through the

Initial state (steady state): maximum external field applied, T=85 K. Transient analysis part : external field ramped down, no external heat soure.

5 material is diamagneti (Meissner effet), if the applied field is greater than H, then the material is in the mixed state and normal zones are developed allowing quanta of flux to go through the material. In the ase presented, the material is in the mixed state and the resulting partial diamagnetism whih is typially of a few perents is negleted. The simulation sequene is the following:. Initial state (steady state): maximum external field applied, T=85 K. Transient analysis part : external field ramped down, no external heat soure. Transient analysis part : no applied field, apply pulse of heat Table : urrent penetration in the TFM 8. Simulation Results One the flux is trapped, the TFM is exited with a heat pulse. This thermal disturbane an lead to a derease of the trapped flux or a omplete demagnetization of the material. A ritial value for the heat pulse leading to non-stable behavior an be determined. This relates to the minimum quenh energy (MQE) for quenh studies whih is the minimum amount of energy leading to instability of the material. The two ases are desribed in this setion. 8. Current penetration As predited by the ritial state model, the urrent indued by a dereasing magneti flux penetrates from the side in the material. Sine all the layers are magnetially oupled, the stak behaves as a single blok of YBCO. The magnitude of the urrent density strongly depends on the applied flux density leading to a lower urrent value in the entral part of the TFM. In table : - The applied field ramp-down starts, urrent penetrates in the superondutor - As the field keeps dereasing, urrent penetration inreases, urrent density is already lowered in the enter of the TFM - All the field is generated by the TFM The urrent an penetrate until the material is fully saturated for larger applied field values. 8. Stable behavior A heat pulse of 8 is applied to the TFM one the field oil is ompletely ramped down. As shown in following table, the urrent in the layers loser to the heater heat up, thus beoming dissipative. The heat exhange is high enough to maintain the top layers in the superonduting state; the trapped flux is nearly unhanged. Indeed, when the urrent in the bottom layer is dissipated, the assoiated flux variation is ompensated by a redistribution of the urrent in the top layers; the urrent penetrates deeper in the material. In table : - Current starts penetrating in the material - Magneti flux is trapped - Heat pulse is generated dereasing urrent magnitude in the lower layers 4- After urrent redistributes to keep flux variation to a minimum

Table : stable behavior Color represents urrent density and lines the flux lines. field oil. The end of the simulation shows the field trapped in the superondutor. Figure 9.

Any hange of flux reates an eletrial field as predited by Faraday s law of indution. The simultaneous presene of eletrial field and urrent density reates losses.

6 Table : stable behavior Color represents urrent density and lines the flux lines. field oil. The end of the simulation shows the field trapped in the superondutor. Figure 9. flux distribution on top of the TFM During flux trapping, magneti flux is hanging in the area where urrent is flowing. Any hange of flux reates an eletrial field as predited by Faraday s law of indution. The simultaneous presene of eletrial field and urrent density reates losses. Suh losses an be alulated by integrating E over the volume of superondutor. The instantaneous power, shown in figure, peaks at.5 mw and leads to a. m of dissipated energy in the material, whih in this ase is negligible. However, for faster flux variation, these losses an beome signifiant. 4 Figure. Heat dissipated in the superondutor 8. Unstable behavior Figure 9 shows the flux distribution on the top of the TFM during the first s. The initial distribution is the uniform field generated by the In some ases, an avalanhe phenomenon an our destroying the magnetization of the material. This an happen for large energy deposition suh as heat pulse and/or weak

7 ooling. In the presented simulation, the heat pulse was inreased by % leading to instability. The following table shows the simulation results. Table 4: unstable behavior Color represents urrent density and lines the flux lines. Figure. Flux distribution the enter top of the TFM Figure. Heat dissipated in the superondutor 9. Conlusion In table 4: - No external field. The flux is trapped and the heat pulse starts - Current redistributes and penetrates deeper in the material - An avalanhe phenomenon dissipates all the stored energy 4The magnitude of the flux density at the enter top of the TFM is shown in figure. The entire trapped field disappears at the beginning of the pulse, evidene of the instability. Figure shows the energy dissipated in the superondutor. A peak of.5 W appears at the beginning of the pulse releasing the stored energy. Multi-layer trapped flux magnets present a very interesting alternative to bulk bloks of erami YBCO. A model was developed to investigate their stability against thermal disturbanes. Modeling superonduting material is not trivial beause of the strong non-linearity of the eletrial ondutivity. COMSOL allows for a better understanding of the behavior of trapped flux magnet through suessful oupled eletromagneti and thermal simulations.. Referenes. P. Masson et Al., Design of HTS Axial Flux Motor for Airraft Propulsion, IEEE Trans. Appl. Superon., 7,, pp 5-56, (7). P. Masson et Al., High Power Density Superonduting Motor For All-Eletri Airraft Propulsion, Trans. Appl. Superon.,5,, 69, (5). Tomita et Al., High-temperature superondutor bulk magnets that an trap magneti fields of over 7 Tesla at 9 K, Nature, 4, 57-5, () 4.

Effect of magnetization process on levitation force between a superconducting. disk and a permanent magnet

Effect of magnetization process on levitation force between a superconducting. disk and a permanent magnet Effet of magnetization proess on levitation fore between a superonduting disk and a permanent magnet L. Liu, Y. Hou, C.Y. He, Z.X. Gao Department of Physis, State Key Laboratory for Artifiial Mirostruture