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Physics Procedia 58 (2014) 286 – 289

26th International Symposium on Superconductivity, ISS 2013

Trapped field and flux dynamics in MgB2 superconducting bulks
magnetized by pulsed field
H. Fujishiroa *, T. Naitoa, T. Ujiiea, A. Figini Albisettib, G. Giunchic
aDepartment Materials Science and Engineering, Iwate University, Morioka 020-8551, Japanb
EDISON S.p.A., R&D Division, Foro Buonaparte 31, 20121 Milano, Italy
cMaterials Science Consultant, via Teodosio 8, 20131 Milano, Italy

Abstract
Pulsed field magnetization (PFM) was performed at Ts=14 K for the MgB2 bulk of 55 mm diameter fabricated by a reactiveliquid Mg infiltration (Mg-RLI) method. The time dependence of the local field BLC(t) and temperature change T(t) and thetrapped field profiles were measured. The numerical simulation of the flux dynamics and heat propagation in the bulk was alsoperformed. The experimental results can be qualitatively explained by the model analyses. We discuss about the characteristic
differences of the flux dynamics and heat propagation during PFM between MgB2 and REBaCuO bulks.
© 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license©
2014 The Authors. Published by Elsevier B.V.
(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Selectionandpeer-review
underofresponsibilityof the ISS2013 Program Committee.
Peer-review
underresponsibility
the ISS 2013 ProgramCommittee
Keywords: MgB2 bulk; pulsed field magnetization; trapped field; numerical simulation

1. Introduction
MgB2 bulk magnet has attractive features such as low cost, light-weight, and weak-link-free homogeneous current
flow, which are a clear contrast with REBaCuO superconducting bulk magnets (RE=rare earth element). Tomagnetize the REBaCuO bulks, a field-cooled magnetization (FCM) is used usually. A pulsed field magnetization(PFM) has been recently investigated because of an inexpensive and mobile experimental set-up with no need of asuperconducting magnet. However, the trapped field Bz achievable by PFM is nonetheless lower than that achievable
by FCM because of a large temperature rise caused by the dynamical motion of the magnetic flux. We haveinvestigated the PFM procedure experimentally and numerically for the REBaCuO bulks to enhance the trappedfield [1]. On the other hand, for MgB2 bulks, the results of the trapped field by FCM have been mainly reported; the* Corresponding author. Tel.: +81-19-621-6363; fax: +81-19-621-6363.
E-mail address: fujishiro@iwate-u.ac.jp

1875-3892 © 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/3.0/).
Peer-review under responsibility of the ISS 2013 Program Committee
doi:10.1016/j.phpro.2014.09.054

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maximum trapped field was 2.25 T at 15 K on the single MgB2 bulk [2] and 3.14 T at 17.4 K in the bulk pair [3]. We
have performed the PFM procedure for the MgB2 bulks fabricated by various methods [4, 5], where the maximum
trapped field was as low as 0.71 T at 16 K for the bulk fabricated by a capsule method [4].
To enhance the trapped field on the MgB2 bulk by PFM, we must consider the inherent nature of the MgB2 bulk.
That is, the thermal properties such as thermal conductivity N(T) and specific heat C(T) and the magnetic fielddependence of the critical current density Jc(B) are fairly different from those of REBaCuO bulk at operating
temperature. In this study, we performed the PFM experiments for the MgB2 bulk fabricated by a reactive liquid Mg
infiltration (Mg-RLI) [6], which can realize a large and homogeneous MgB2 bulk. A numerical simulation was also
performed considering the flux dynamics and heat conduction in the bulk. The magnetic flux intrusion and flux
trapping during PFM are discussed, compared with those for the REBaCuO bulk.
2. Experimental procedure
The MgB2 bulk disk of 55 mm in diameter and 15 mm in thickness was prepared, which was fabricated by the MgRLI technique [6]. The superconducting transition temperature Tc and the trapped field Bz at 20 K by FCM were,respectively, confirmed to be 38 K and 1.40 T. Figure 1 shows the experimental setup for PFM around the bulk andthe magnetizing pulse coil. The bulk, mounted in stainless steel (SUS316L) rings of 8 mm thickness, was tightly
anchored onto the cold stage of a Gifford–McMahon (GM) cycle helium refrigerator. The initial temperature Ts ofthe bulk was set to 14 K. A magnetizing solenoid coil (94 mm i.d., 153 mm o.d., and 50 mm height), which wasdipped in liquid nitrogen, was placed outside the vacuum chamber. A magnetic pulse Bex(t) with a rise time of 0.013
s and a duration time of 0.15 s was applied to the bulk by flowing the pulsed current from a condenser bank. Thetime evolutions of the local field BLC(t) and the subsequent trapped field Bz at the center of the bulk surface (z=0mm) were monitored by Hall sensors (F W Bell, BHA 921) using a digital oscilloscope. Two-dimensional trappedfield profiles of Bz (z=1 mm) were mapped at a distance of 1 mm above the bulk surface.
3. Modeling and numerical simulation
Based on the experimental setup shown in Fig. 1, the framework of the numerical simulation was constructed.
Physical phenomena during PFM were described using electromagnetic and thermal equations. The details of thesimulation are described elsewhere [7]. The power-n model (n=100) was supposed to describe the nonlinear E-J
characteristic in the bulk. The magnetic field dependence of the critical current density Jc(B) for the Mg-RLI bulk
was fitted using the equation of Jc(B)=Jc0exp[-(B/B0)1.5] (B0=1.25) based on the previous report [8], where Jc0 (=2.2 x109 A/m2 at 14 K) is the critical current density under zero field. The temperature dependences of the specific heatC(T) and the thermal conductivity N(T) for the present MgB2 bulk [9, 10] and SUS ring were also introduced in thenumerical simulation.
4. Results and discussion
4.1. Experimental results
Figure 2 shows the trapped field Bz at the center of the bulk surface, as a function of the applied pulsed field Bex.
Bz increases for Bex>1 T, takes a maximum at Bex=1.79 T and then decreases with increasing Bex. The maximum Bz
was 0.41 T. The Bz vs Bex curve and the maximum Bz are typical for PFM of MgB2 bulks [5, 6].
Figures 3(a) and 3(b) present the trapped field profiles Bz(z=1 mm) on the bulk for Bex=1.17 T and 1.79 T andFigure 3(c) shows the cross sections of the Bz profiles along x=0 mm. For Bex=1.17 T, the magnetic flux was trapped
only at the bulk periphery, which comes from the strong inner shielding current. For Bex=1.79 T, the magnetic flux
intrudes into the center and the trapped field profile is nearly the conical one. The conical Bz profile maintains for
Bex>1.97 T with the decrease in the maximum value. Figure 4 shows the time evolution of the applied field Bex(t)and local field BLC(t) at the center of the bulk surface for typical applied field. For each Bex, BLC(t) starts to increase
for t=0.005 s with a time delay, takes a maximum at 0.02 s, and then decreases to a final value due to the flux flow.

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Fig. 1. Experimental PFM setup around the bulk and appliedmagnetizing coil.

Fig. 2. Trapped field Bz (z=0mm) at Ts=14 K on the bulk as a function of
the pulsed field Bex The result of the simulation is also shown.

Fig. 3. Trapped field profiles at z=1 mm above the bulk surface for (a) Bex=1.17 Tand (b) 1.79 T. (c) Cross sections of the trapped field profiles at z= 1 mm.

Fig. 4. Time evolution of the applied field Bex(t) andlocal field BLC(t) for (a) Bex=1.54 T and (b) 1.79 T.

4.2. Results of numerical simulation and discussion
The result of the simulation for the trapped field Bz at the centre of the bulk surface as a function of applied
pulsed field was shown in Fig. 2. The Bz vs Bex behaviour reproduces the experimental one qualitatively. The
difference of the maximum Bz value may come from the difference of Jc0 and/or Jc(B) characteristics. Figure 5
shows the results of the simulation of the cross sections of the trapped field profile Bz for typical Bex values. The
profile changes from concave to convex (or flat) with increasing Bex and then the maximum Bz decreases, which
reproduces the experimental results qualitatively as shown in Fig. 3.
Figure 6 presents the results of the simulation of the time dependence of the local field BLC(t) at r=0, 10 and 20mm for Bex =1.5 T and 1.8 T. The magnetic flux intrudes from the bulk periphery and BLC at the bulk centre (r=0mm) starts to rise with a slight time delay. The similar time delay can be observed in the experiments shown in Fig.
4, but in the simulation, the time delay is larger, compared with the experiments.
Finally, we discuss about the difference the flux dynamics during PFM between MgB2 and REBaCuO bulk. First,we must comment on the specific heat C per unit volume and thermal conductivity N for both bulk systems. At thetypical operating temperature, for example, Ts=14 K for MgB2 and Ts=40 K for REBaCuO, the specific heat per unit
volume of MgB2 is 2 x 10-4 J/cm3K [9], which is three-orders of magnitude smaller than that for GdBaCuO at 40 K.
In addition, the thermal conductivity of MgB2 is 40 W/mK at 14 K [10], which is about three times larger, comparedwith that of the GdBaCuO bulk at 40 K. The difference of these thermal properties between two systems may
seriously influence on the flux dynamics and heat propagation. Second, Jc(B) characteristics are quite different; theJc(B) characteristics of the REBaCuO bulk show the well-known peak effect and the irreversibility field Birr was

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Fig. 5. Cross sections of the trapped field profile Bz for typicalBex values. (simulation)

Fig. 6. Time dependence of the local field BLC(t) at r=0, 10 and 20 mm
for Bex=1.5 T and 1.8 T at 14 K. (simulation)

Fig. 7. Time dependence of the local field BLC and temperature T (a) for the MgB2 bulk after applying the pulsed field of 1.8 T at 14 K and (b) for
the GdBaCuO bulk after applying the pulsed field of 6.0 T at 40 K [8]. (simulation)enhanced. On the other hand, Jc(B) of MgB2 monotonically decreases with increasing applied field. The temperature
margin between Ts and Tc for the MgB2 is smaller than that for the REBaCuO, which may also affect the stability.
Figure 7(a) shows the results of the simulation of the time dependence of the local field BLC and temperature T
after applying the pulsed field of 1.8 T at 14 K. For comparison, the similar results of the simulation were also
shown in Fig. 7(b), where the pulsed field of 6 T was applied for the GdBaCuO bulk at 40 K [7]. It should benoticed that the flux creep terminates in 0.1 s and the temperature rise recovered within 10 s for the MgB2 system,
mainly because of small C(T), large N(T) and poor Jc(B) characteristics. On the other hand, for the GdBaCuO system,
the flux creep continues and terminates in about 10 s because the temperature rise recovered in about 100 s.
In summary, time dependence of the local field BLC(t) and temperature change T(t) and the trapped field profilesof the MgB2 bulk during PFM can be qualitatively explained by the model analyses. The flux dynamics and heatgeneration in the MgB2 bulk are clear contrast with those in the ReBaCuO bulks.
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