HTS Persistent Magnet for 30T ? Louie Vergara1 and Doan Nguyen2

1Electical Engineering Department, University of California, Santa Cruz CA 2NHMFL-PFF, Los Alamos National Laboratories, Los Alamos, NM

Motivation

Stacked Magnet Design and its Advantages

Finite Element Method

Jc (B) =0.7

1+Bm0.5 + 0.3e

−Bm3

"

#$

%

&'∗ Jc

Figure 5: Normalized Jc(B) of a standard YBCO tape measured in parallel and perpendicular

applied fields. Fitting curve is also plotted

Figure 4: Trapped field in a stacked magnet of 240 1.2-cm-wide tapes at t=20s (a) and t=300s (b). Magnet consists of 2 stacks placed with a 2 mm spacer. n-value = 20. Ba = 14 T

Normalized Magnetic Field

(a) (b) Figure 6: The decay rate of the trapped field simulated with several values of n (a)

and the decay rate measured at different temperatures (b) [1]

[1] A. Patel, K. Filar et. al.,“Trapped fields greater than 7 T in a 12mm square stack of commercial high-temperature superconducting tape Trapped fields greater than 7 T in a 12 mm square stack of commercial high-temperature superconducting tape,” vol. 102601, pp. 1–6, 2013. [2] a Xu, J. J. Jaroszynski, F. Kametani, Z. Chen, D. C. Larbalestier, Y. L. Viouchkov, Y. Chen, Y. Xie, and V. Selvamanickam, “Angular dependence of J c for YBCO coated conductors at low temperature and very high magnetic fields,” Superconductor Science and Technology, vol. 23, no. 1, p. 014003, Jan. 2010.

References REU program of NHMFL support Louie Vergara

Acknowledgements

Conclusion

How high field can be trapped with larger tapes of 4 and 10 cm widths?

(a) (b)

Figure 7: Trapped field and current profiles in stacks of 4-cm-wide (a and b) and 10-cm-wide (c and d) tapes. Simulation parameters are the same for both stacks:

Ba = 30T, n = 20 and t = 300s

Ultra-high field magnets are very important tools for research, furthermore the primary missions of NHMFL is to develop high-field efficient magnets for users. Field limit of low temperature superconducting magnets has been reached at 23.5T. With critical magnetic fields on the order of 70T or more, high temperature superconducting YBCO has shown potential at overcoming those high field limits. YBCO bulk magnets (YBCO “pucks”) have been investigated. However, the poor mechanical and thermal properties of the ceramic YBCO pucks limit their field strength due to cracking. YBCO tapes which have mechanical and thermal properties similar to steel have recently attracted a lot of interest for high-field magnets. However, the conventional coil technology faces other technological challenges. YBCO tapes are now available up to 500-m long, but its uniformity along the length is poor. Hence the performance of the entire coil is limited by the “weakest” tape spots. As a result of these challenges, the highest field achieved from a YBCO coil is now only about 9.8T at 4.2 K. So innovative designs for YBCO magnets are needed.

Stacked magnet design: Ø  Similar as YBCO “pucks”, YBCO films, after being “charged”, can posses a high

persistent current. Therefore, stack of these films with persistent current can trap high magnetic field (Figure 2)

Figure 1: Sketch for general structure of a YBCO tape [1].

Figure 2: Illustration of a permanent superconducting magnet fabricated by

stacking YBCO thin films

Figure 3: 1.2-cm cubical magnet as a stack of 240 thin YBCO tapes can trap 7T field

[1] using 14T magnetizing field

Ø  We used FEM to try reproducing the reported experimental data, and predict feasibility and requirements to create magnets of 30T level

Ø  Field cooling method is used to “charge” the magnet: Staked magnet in applied field and at room temperature => cooling the stack down to 4.2 K => ramping the field down to 0T => magnet is expected to trap magnetic field inside

Ø  FEM will calculate the trapped field in 300s after the applied field is turned off

Ø  2D FEM models implemented in COMSOL MultiPhysics were used (assume that magnet length >> magnet width)

Ø  Effect of “AC Loss” is neglected in FEM (very slow ramping rate of applied field is

assumed) Ø  Superconducting tapes are characterized by the power law: J = E0(J/Jc)n. In each

simulation, n is constant and engineering Jc (0T, 4.2 K) = 2400/0.012m*55µm (A/cm2)

Ø  Experimental data for Jc(B) in applied field up to 30T [2] was fitted by an equation. That equation was used for better accuracy.

Research Path

Ultra-high Field Permanent Superconducting Magnets Project # 20110347ER

Nguyen, Doan, N 4

Magnet samples used in experiments can be fabricated from YBCO tapes provided by our indus-trial partners. These magnets will be “charged” by different magnetizing processes using DC or pulse high field magnets at the NHMFL in Los Alamos or Tallahassee.

Preliminary Studies In order to estimate the feasibility of this magnet technology, we initially developed a 2D FEM model implemented in COMSOL Multiphysics [20] to predict trapped field. Because the trapped field strongly depends on the current carrying capacity (critical current) of superconductors which is a function of applied magnetic field, the non-linear magnetic field dependence of criti-cal current density Jc must be considered in simulation models for better accuracy. The field de-pendent Jc can be obtained experimentally on short YBCO tapes. Figure 2 depicts field depend-ence of Jc on perpendicular applied field (B//c) and parallel applied field (B//ab) up to 31 T and at 4.2 K for a commercial YBCO tape [21]. As seen in the figure, Jc decreases much significantly in B//c than in B//ab. In simulations, we therefore only need to consider the effect of B//c on Jc. Jc(B//c) can be fitted well by: � � � �� �2/006.0exp5.02.0/5.05.0)//( 3.0 BBcBJ c ��� (see FIG. 2). Data for Jc(B//c) at LN temperature were provided by Dr. Maiorov (STC, LANL) and can be fitted by: � � )15.0/exp(4.012/16.0)//( 5.5 BBcBJ c ��� . These relations were used in simula-tions.

In the simulations, we used typical values for the dimensions and superconducting properties of available YBCO films: the thickness of YBCO layer is about 2 Pm and the total thickness of YBCO tape is 120 Pm, Jc of YBCO film is about 2 MA/cm2 at 77 K and 17 MA/cm2 at 4.2 K. We use time dependant FEM to simulate a field-cooling magnetization process. The initial con-dition was an applied magnetic field at ambient temperature. The model then simulates the stack being cooled in presence of a static applied field to a desire temperature (4.2 K or 77 K). At that temperature, the applied field is gradually swept down to zero. The trapped field inside the stack will represent for strength of the magnet.

Figure 3 plots profiles for trapped magnetic field in cross-section of a magnet fabricated by stacking a thousand of 10 cm wide YBCO tapes. So the width and the thickness of the magnet are 10 cm and 12 cm, respectively. As seen in FIG. 3(a), the stack can trap more than 4 T field at liquid nitrogen temperature using a 5 T applied field. At 4.2 K (FIG. 3(b)), a 20 T “charging” field can create a 20 T trapped field in a 4 cm wide space inside the magnet. This might allow a 1 cm diameter ‘bore’ for scientific experiments. The simulation shows that a field as high as 28 T

0

0.2

0.4

0.6

0.8

1

1.2

0 10 20 30 40

Applied field (T)

Nor

mal

ized

Jc;

Jc(

B)/

Jc(0

)

B//c

B//ab

Fitting curveFIG 2: Dependence of normalized Jc, (Jc(B)/Jc(0)) on perpendicular (B//c) and parallel (B//ab) applied fields up to 31 T and at 4.2 K

period measured, the flux creep rates are lower than for a typ-ical bulk, particularly at lower temperatures. The advantagesof using such a sample as a permanent magnet at low temper-atures are obvious given the more acceptable rates of fluxcreep. Given the lack of data for high trapped fields in stacksof superconducting tapes, it is clear that a more detailed,longer-duration study of flux creep is needed in future.

The field cooling results for the stack of tapes can becompared to a previous study on pulsed field magnetizationof a single stack containing 145 layers4 as shown in Fig. 4.In order to compare the trapped fields directly, the field cool-ing trapped fields obtained for the double 120 layer stackhave been scaled to give the expected field for a single 145layer stack measured at the same distance from the stacksurface (0.8 mm) as used the pulsed magnetization study.This scaling, which assumes uniform current densityand was achieved using a finite element model, is a goodapproximation. Such scaling cannot be used for the case of

pulsed field magnetization, which gives rise to complex cur-rent density distributions due to large heating effects duringa pulse. The tape layers used for both samples came from thesame tape length with most of the layers used in the pulsedmagnetization study re-used for the sample in the presentstudy. The comparison of the trapped fields gives an impor-tant insight into the limitations of the pulsed field method.Although the increase in trapped field with decreasing tem-perature using pulsed field magnetization is significantlyhigher than for a similar bulk sample,4 the differencebetween the trapped fields achieved by pulsed magnetizationand field cooling still increases with decreasing temperature.It is worth noting that, for the stack of tapes used in both thefield cooling and pulsed field studies, there may be anenhanced cooling effect due to the volume fraction of“empty space.” in the stacks (which would be filled with he-lium gas) and also due to the uneven sample sides (whichincreases the surface area for heat transfer; see Fig. 1(b)).These effects will be eliminated in future tests by making aself-supporting stack, with tape layers glued together andsample sides machined flat.

The discrepancy between field cooling and pulse mag-netization results (Fig. 4) exceeds a factor of two at the low-est temperatures due to unavoidable heat generation inpulsed magnetization. There should also exist a discrepancyfor total trapped flux but this is expected to be slightlysmaller given the broader field profiles which tend to betrapped using pulsed magnetization compared to field cool-ing. Although the fields trapped by field cooling represent alimit which can never be reached at low temperatures bypulsed magnetization, for many applications it is worth sacri-ficing this full potential given the practicality and lower costof pulsed field magnetization.18

Trapped fields over 7 T were achieved using the fieldcooling method of magnetization in a 12 mm square stack ofsuperconducting (RE)BCO tape, with an approximately lin-ear dependence of trapped field on temperature, and highthermal stability below !30 K compared to bulk (RE)BCO.6.3 T was achieved at 20 K, which is noteworthy given thepopular choice of using 20 K as a balance between coolingcost and Jc performance. SuperPower tape was used with arated Ic of 240 A (77 K and self-field) corresponding to 200A cm"1 (A per cm width). Assuming approximately linearscaling of trapped field with critical current, much highertrapped fields should be possible using higher performancetape. 12 mm wide, 460 A tape is currently available fromSuperPower and should, therefore, be able to trap approxi-mately 14 T, with even higher fields expected for researchsamples. These include 600 A/cm for long 600 m lengths(Fujikura)19 and greater than 1000 A/cm for shorter samples(THEVA),20 at 77 K. The picture looks even more positivewhen considering the opportunity to scale up. 12 mm is a rel-atively small size for a bulk when trapping field, but stacksof tapes should be able to compete with bulks on size giventhat some manufacturers produce 40 mm wide tape prior toslitting,5 with future plans to produce 100 mm widths.Assuming simple geometric scaling, a 40 mm square stackwith the same Ic per cm width as the tape used in this studyshould in theory trap approximately 24 T. Although thisvalue seems optimistic and may be limited by flux jumps, it

FIG. 3. Flux creep measurements for trapped field for different temperaturesin the first 5 min after magnetization. B0 is the trapped field 10 s after mag-netization. The creep rate appears strongly dependent on temperature.

FIG. 4. Comparison of pulsed magnetization results for a single stack of 145tapes4 and prediction for field cooling of the same stack. The prediction isbased on geometric scaling of trapped field for 120 layer double stackreported in this paper and assumes the current density would be the same forboth stacks.

102601-4 Patel et al. Appl. Phys. Lett. 102, 102601 (2013)

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(c) (d)

Ø  Stack of 4-cm wide tapes can trap only 15T in 30T applied field

Ø  Stack of 10-cm wide tapes can trap 30 T in 30T applied field

Ø  Strong induced critical currents at the sides of the tape in applied field (low field region)

Ø  So 30T persistent

field is possible with this stacked magnet design, if the 10-cm wide tape is available

Advantages of the design: Ø  Does not require conductor with long piece-length Ø  Current carrying capacity in the design is self-optimized in the response to the

change of charging field, therefore they would always have full capacity performance Ø  YBCO films in a stack are essentially “parallel connected”, so quenching is not a big

issue as for coils

Result and discussion Ø  Time-frame definition: t = 0s is when Ba is reached 0T (completely turned off).

Ø  Simulations clearly show the decay of trapped field

Ø  Decay is faster for the tape with lower n-value Ø  Measured decay rate [1] at all temperatures is slower than that obtained with

tapes having n-value = 20. Further refinement of simulation is needed

Ø  2-D FEM simulations can be used to predict trapped field and its decay for a new magnet design using YBCO tapes: Stacked magnet

Ø  Calculated trapped field is lower than measured data reported in [1]. 3D models may be needed for better accuracy

Ø  30T persistent field is possible with this stacked magnet design, if the 10-cm wide tape is available

than strictly needed to saturate the sample (as is often thecase), then the magnetic stresses can be significantly higherthan given by Eq. (1). The 550 MPa limit for the Hastelloysubstrate corresponds to a maximum trapped field of 42.8 T,which suggests that there is no real mechanical limit to trap-ping high fields in a stack of tapes, as other factors wouldprevent ever reaching such a high value.

The tensile strength of bulks is often quoted as beinghigher than 30 MPa but these values are typically for small testsamples (!3 mm). However, the fracture strength ("30 MPa)defined for larger samples is limited by micro-cracks and the

weakest part of the whole bulk. Although reinforced YBCOsamples can survive the magnetic pressures of high trappedfield, the external reinforcement in the form of a steel ring orcomposite fiber adds complexity and increases the samplediameter. Even then, they can fracture during magnetization orsubsequently, during demagnetization.13 Stacks of YBCO tapeare not expected to fracture like this due to the Hastelloy sub-strate and its volume fraction.

The magnet used for field cooling the samples was a15 T Oxford Instruments superconducting magnet. The fieldcooling procedure involved ramping the field of the magnetup to the desired applied field whilst holding the sampleat 100 K to ensure it is non-superconducting ((RE)BCOTc" 92 K), cooling the sample down to the desired fieldcooling temperature whilst holding the applied field constant,and finally ramping the applied field down slowly to zero,leaving a trapped field in the sample. The sample was in asealed insert filled with helium gas. The insert was cooleddirectly with liquid helium so that the sample was cooled viathe helium gas. The temperature of the sample was con-trolled using a heater mounted close to the sample. A centralcryogenic Hall probe (type Arepoc LHP-MP) was used tomeasure the trapped field, with another Toshiba Hall probeused to determine whether the sample was saturated or notby measuring off-centre trapped field.

The results for the field trapped in the double stack oftapes for different field cooling temperatures are shown inFig. 2. The graph shows clearly the significant increase infield that can be trapped if field cooling below 77.4 K. Thelower off-center field shows that the sample was saturated.No damage was observed in any of the tape layers afterthe tests. The ramp rates used for the applied field werehigher for higher temperatures (0.5 T min#1 for 77.4 K and0.34 T min#1 for 60 K) and lower when approaching 4.2 K(0.15 T min#1 for 20 K and 13 K, with the rate reduced to0.07 T min#1 for the last 1 T of the 13 K ramp). The lowerramp rates required for the 20 K and 13 K temperature stagesmeant that the field cooling took approximately 1 h giventhat the applied field was 8.5 T in both cases. The trappedfield for 4.2 K was not strictly achieved using field cooling.To begin with, a zero field cooling test was performed with ahigh ramp rate (0.25 T min#1) to separately test how fluxpenetrated the sample. Interestingly, the high ramp ratecaused flux to penetrate in a series of sudden global fluxjumps. As a result of this instability, at the maximum 14 Tapplied, the central field in the sample was 10.7 T and there-fore the stack was saturated. This behavior shows that eventhough a stack of tapes may be more thermally stable at lowtemperatures, even this type of sample will suffer from

FIG. 1. (a) Schematic of the double (RE)BCO tape stack used for the fieldcooling experiment. (b) 120 of the square tape layers compressed to form atape stack. (c) Components of the 12 mm wide SuperPower superconductingtape from which 12 mm lengths were cut.

TABLE I. Parameters and volume fraction for each compressed 120 layer

stack of tapes used in the experiment.

Parameter

120 layer (RE)

BCO tape stack

Sample height (mm) 6.9

Density (kg m#3) 8380

(RE)BCO volume fraction 1.7%

Hastelloy volume fraction 87.0%

Silver volume fraction 5.2%

Stacking space fraction 6.1%

TABLE II. Properties of Hastelloy C-276 substrate, silver over-layer and bulk YBCO at cryogenic temperatures. A range of values is given for 10–77.4 Kwhere there is a known temperature dependence.

Parameter Hastelloy Silver over-layer Bulk YBCO

Density (kg m#3) 88907 10 490 59003

Thermal conductivity (W m#1 K#1) 3–7.57 "500–15008–10 6–20 ab-plane, 1–4 c-axis11

Heat capacity (J kg#1 K#1) 2–2007 2–1558 "1–20011

Tensile strength (MPa) 670–760 (yield)12 "60 (yield)8 "30 (fracture)3

102601-2 Patel et al. Appl. Phys. Lett. 102, 102601 (2013)

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Ø Recently, magnets of highest energy density were experimentally demonstrated with a stack of 1.2-cm square YBCO tapes (Figure 3) . This tiny magnet can trap 7T at 4.2 K [1]

Ø  Figure 4 plots profiles for trapped field in cross-section of a magnet fabricated by stacking 240 1.2-cm-wide YBCO tapes

Ø  The trapped field inside the stack represents the strength of the magnet

Ø  Maximum trapped field inside the stacks is about 6T, and 5.7T in the spacer (spacer is 2-mm separation between each stack)

Ø  With n = 20, field properties at 20s and 300s are nearly identical => very slow decay rate of trapped field

Ø  Calculated trapped field is lower than 7 T reported experimentally, but our 2-D simulation neglected the current at the ends of the tapes => 2D FEM models underestimate the trapped field

Ø  3-D simulations may be needed for better accuracy

Ø  The results of each verified model will be used to guide the magnet design for the next stage

(b) YBCO Stack

(a)