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Pulsed Field Magnetization of Large MgB2 Bulk Fabricated by Reactive Liquid Mg Infiltration

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2012 Jpn. J. Appl. Phys. 51 103005(http://iopscience.iop.org/1347-4065/51/10R/103005)
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REGULAR PAPER

Japanese Journal of Applied Physics 51 (2012) 103005
http://dx.doi.org/10.1143/JJAP.51.103005

Pulsed Field Magnetization of Large MgB2 Bulk Fabricated by Reactive Liquid Mg Infiltration
Hiroyuki Fujishiro1 , Takuya Tamura1 , Takahiro Arayashiki1 , Mitsuru Oyama1 , Tomohisa Sasaki1 ,Tomoyuki Naito1 , Giovanni Giunchi2 , and Alessandro Figini Albisetti2
12Faculty of Engineering, Iwate University, Morioka 020-8551, JapanEDISON S.p.A., R&D Division, Foro Buonaparte 31, 20121 Milano, Italy

Received June 3, 2012; accepted August 10, 2012; published online October 3, 2012
Pulsed field magnetization (PFM) was performed for the first time on a large MgB2 bulk 50 mm diameter fabricated by a reactive liquid Mg
infiltration (Mg-RLI) method, and the time dependence of the local field BL C ðtÞ and the trapped field profiles were measured. The trapped field of
Bz ¼ 0:47 T and the total trapped flux of  ¼ 0:50 mWb were achieved at Ts ¼ 23 K and both values decreased with increasing temperature Ts .
The experimental results can be qualitatively reproduced by numerical simulation using electromagnetic and thermal fields for PFM. The flux
dynamics and the heat generation/propagation in the MgB2 bulk during PFM were in clear contrast with those in REBaCuO superconducting bulks
because of the large thermal conductivity, small specific heat, and narrow temperature margin against the transition temperature Tc .
# 2012 The Japan Society of Applied Physics

1. Introduction

The superconducting bulk magnet using an REBaCuO (RE:rare earth element or Y) bulk can be used for practicalapplications such as sputtering cathodes,1) magnetic separation,2) and drug delivery systems.3) The REBaCuO bulkswith 45–60 mm diameters are commercially available toproduce tesla-order quasi-permanent magnets, which arefabricated by a melt textured method. Although a large
single-domain bulk of over 100 mm in diameter is diﬃcult tofabricate, large bulks have recently been realized only by amultiseeding technique.4)
MgB2 bulk also has a promising potential as a quasipermanent magnet because the problem of weak links at thegrain boundaries can be ignored even in the polycrystalline
samples owing to their long coherence length, .5) The MgB2
bulk enables us to realize better and larger polycrystalline
bulk magnets below the transition temperature Tc . Several
groups have already reported a trapped ﬁeld on the MgB2
bulk by ﬁeld-cooled magnetization (FCM). A trapped ﬁeld
value of Bz ¼ 2:3 T was obtained at 6 K on the MgB2 bulk of
28 mm diameter and 11 mm thickness, which was sinteredunder a high pressure of 2 GPa.6) Yamamoto et al. reported
a 1.2 T MgB2 magnet (20 mm in diameter and 5 mm inthickness) magnetized by FCM at 17 K, and a 3 T-classmagnet, which consisted of doubly stacked MgB2 bulks.7)
One of the authors (G. Giunchi) has developed MgB2 bulks
by the reactive Mg liquid inﬁltration (Mg-RLI) technique,8)which is preferable to fabricate dense and large MgB2 bulk
disks and cylinders, where the maximum Bz value was about
1.3 T at 15 K by FCM on the Mg-RLI-MgB2 bulk of 55 mm
diameter and 15 mm thickness at the center hole of 6 mm.9)
Pulsed ﬁeld magnetization (PFM) is an another technique to magnetize bulk superconductors. However, for the
REBaCuO bulks, the trapped ﬁeld Bz achievable by PFM is
nonetheless lower than that achievable by FCM becauseof the large temperature rise caused by the dynamical motionof the magnetic ﬂux. Several approaches have been performed and succeeded in enhancing Bz using multipulse
techniques.10,11) We have experimentally examined the timeand spatial dependences of the temperature T ðt; xÞ, the local
ﬁeld Bz ðt; xÞ, and the trapped ﬁeld Bz on the surface of
cryocooled REBaCuO bulks during PFM for various startingE-mail address: fujishiro@iwate-u.ac.jp

temperatures Ts and applied ﬁelds Bex .12–14) To enhance Bz ,the reduction in temperature rise and the lowering of Ts areeﬀective because of the enhancement of the critical current
density Jc , similarly to the case for FCM. Considering theobtained experimental results, we proposed a new PFM
technique named the modiﬁed multipulse technique withstepwise cooling (MMPSC)15) and successfully realized thehighest ﬁeld trap of Bz ¼ 5:20 T on a GdBaCuO bulk of
45 mm diameter at 30 K,16) which is a record-high value
achieved by PFM to date. Recently, we have demonstrated
the numerical simulation of PFM for a cryocooled REBaCuO
bulk disk, where the results of the simulation reproduced
the experimental ones qualitatively.17–19) However, the PFM
procedure for the MgB2 bulk has not yet been reported.
In this study, we applied the PFM technique to a large
MgB2 bulk of 50 mm diameter for various applied ﬁelds
Bex and temperatures Ts . The PFM procedure for the MgB2
bulk is a ﬁrst and systematic approach to enhance Bz . The
numerical simulation for PFM was also performed for the
MgB2 bulk. Since the operation temperature of the MgB2
bulk is fairly lower than that of REBaCuO, the thermal
properties of the MgB2 bulk such as the speciﬁc heat and thethermal conductivity are quite diﬀerent. As a result, the PFM
performance is expected to be quite diﬀerent. We discuss thecharacteristics of PFM on the MgB2 bulk, compared withthose on the REBaCuO bulk.
2. Experimental Procedure

The MgB2 bulk disk used in this study was 50 mm indiameter and 16 mm in thickness, which was fabricated by
the Mg-RLI technique. The detailed fabrication process was
described elsewhere.8,9) Tc of the bulk was estimated to be
39 K using a small piece cut from a similar bulk fabricatedby the Mg-RLI method.20) The bulk was tightly mounted ina stainless steel (SUS316L) ring of 8 mm thickness using
a stycast 2850GT resin as a ﬁlling. Figure 1 shows theexperimental setup around the bulk and the magnetizing
pulse coil for PFM. The bulk was set on a soft iron yoke
cylinder of 40 mm diameter and 20 mm thickness and tightly
anchored onto the cold stage of a Giﬀord–McMahon (GM)cycle helium refrigerator. The initial temperature Ts of thebulk was set from 18 to 33 K. A magnetizing solenoid coil
(94 mm i.d., 153 mm o.d., and 67 mm height), which wasdipped in liquid nitrogen, was placed outside the vacuum
chamber. A magnetic pulse Bex with a rise time of 0.01 s

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H. Fujishiro et al.

Jpn. J. Appl. Phys. 51 (2012) 103005

Table I. Numerical values of parameters used in the simulation.

SymbolParameter

Value

Tc
Transition temperature in eq. (1)(MgB2 ) Mass density of MgB2 bulk

39 K
2:59  103 kg m3

(SUS)

7:93  103 kg m3

Mass density of SUS316L

C(MgB2 ) Speciﬁc heat of MgB2 bulk at 40 K

1:72  101 J kg1 K1C(SUS)

3:0  101 J kg1 K1Speciﬁc heat of SUS316L at 40 K

(MgB2 ) Thermal conductivity of MgB2 bulk at 40 K 80 W m1 K1Fig. 1. Experimental setup for PFM around the bulk and the magnetizing

coil.

and a duration of 0.1 s was applied to the bulk by ﬂowing thepulsed current from a condenser bank. The time dependenceof the applied pulsed ﬁeld Bex ðtÞ was monitored from thecurrent IðtÞ ﬂowing in the shunt resister. The time evolutionsof the local ﬁeld BL C ðtÞ and the subsequent trapped ﬁeld
Bz at the center of the bulk surface were monitored inside thevacuum chamber by an axial-type Hall sensor (F W Bell,BHA 921), which touched the bulk surface, using a digital
oscilloscope. Two-dimensional trapped ﬁeld proﬁles of Bz(1 mm) were mapped at a distance of z ¼ 1 mm above thebulk surface, stepwise with a pitch of 1 mm by scanning
the same Hall sensor using an x–y stage controller. During
PFM, the time dependence of temperature T ðtÞ was measured at the side surface of the SUS316L ring using a Cernox
thermometer.
3. Model of Numerical Simulation for PFM

On the basis of the experimental setup around the MgB2
bulk for PFM, the framework of the numerical simulation
was constructed using the axi-symmetric coordinate. The
detailed procedure of the simulation was described elsewhere.17) The bulk was magnetized using a solenoid-type
coil and the sizes of the bulk and the coil were the same as
those of the experimental condition. Physical phenomenaduring PFM were described using electromagnetic andthermal ﬁelds, which were taken from ref. 21. The power-n
model (n ¼ 5) was supposed to describe the nonlinear E–J
characteristic in the superconducting bulk. The temperatureand magnetic ﬁeld dependences of the critical current
density Jc ðT ; BÞ are described as" 2 #3=2
T
B0
;
ð1Þ
Jc ðT ; BÞ ¼  1 
Tc
jBj þ B0
where Tc (¼ 39 K) is the critical temperature at B ¼ 0, andB0 (¼ 1:3 T) is constant. In eq. (1), the simulation was
performed for various  values. As a result, the  value of5  107 was best ﬁtted to reproduce the experimental results,
which corresponded to Jc (20 K, 0 T) of 3:2  107 Am2 .
This Jc value is two orders of magnitude smaller than that of
the MgB2 bulks fabricated by an in-situ method.6,22,23) Thisdiﬀerence may come from the deterioration of Jc caused

(SUS)

Thermal conductivity of SUS316L at 40 K

3 W m1 K1nn-value5

B0

Constant in eq. (1)Constant in eq. (1)

1.3 T
5  107 A m2



Rise time of the pulse in eq. (2)0.01 scont

Thermal conductivity of spacing plate

0.5 W m1 K1by the inhomogeneous Mg inﬁltration, as stated in a later
section. The time dependence of the applied pulsed ﬁeld
Bex ðtÞ with the rise time of  ¼ 0:01 s was approximated in
the following equation,tt
Bex ðtÞ ¼ Bex exp 1  :ð2ÞThe numerical parameters used in the simulation arepresented in Table I. The thermal conductivity  and thespeciﬁc heat C values of the MgB2 bulk were presumed to betemperature dependent, as referred from the literature.20,24)
For simplicity,  and C of the SUS316L ring and the massdensities  of MgB2 and the SUS316L ring were supposed tobe constant. We set the spacing plate with a thermal conductivity cont of 0.5 W m1 K1 between the bulk and thecold stage (and SUS316L ring), which imaginarily represents both the cooling power of the refrigerator and thethermal contact. Commercial software, Photo-Eddy, combined with Photo-Thermo (Photon Ltd.), was used foranalyses of the magnetic ﬁeld and temperature distribution
in the MgB2 bulk during PFM.
4. Experimental Results

Figure 2 depicts the trapped ﬁeld Bz at the center of the bulk
surface by PFM, as a function of applied pulsed ﬁeld Bex . At
Ts ¼ 18 K, the magnetic ﬂux intruded and was trapped at
the center of the bulk surface at Bex  1 T, the trapped ﬁeld
Bz takes a maximum at Bex ¼ 1:7 T and then decreased withincreasing Bex . At Ts  23 K, Bz showed a similar appliedﬁeld dependence, and the applied ﬁeld Bex 0 , at which
the magnetic ﬂux starts to be trapped at the bulk center,decreases with increasing Ts . The maximum Bz by PFM was
0.47 T at Ts ¼ 23 K in this study. These applied ﬁeld andtemperature dependences of Bz show similar characteristics
to those for REBaCuO bulks.14) However, note that the steep
Bex dependence of Bz is a peculiar characteristic of the
MgB2 bulk, compared with that for the REBaCuO bulk,
which results from the large thermal conductivity , small
speciﬁc heat C, and narrow temperature margin against thetransition temperature Tc in the MgB2 bulk at Ts . Detailed
discussion is performed in x5.
Figure 3 shows the time dependence of the applied ﬁeld
Bex ðtÞ and the local ﬁeld BL C ðtÞ at the center of the bulk
surface at Ts ¼ 23 K for various applied ﬁelds Bex . Eachcondition is indicated in Fig. 2, as the symbols of (a) to (d).

103005-2# 2012 The Japan Society of Applied Physics

H. Fujishiro et al.

Jpn. J. Appl. Phys. 51 (2012) 103005
0.5

Bex=0.99Tz

Trapped field B (r =0) (T)(b)

Bex=1.06T

B

18K
23K
28K
33K

0.4
0.3
(c)
(d)

0.2
(a)

0.1
0

0

2

1
B

ex

(a)

(b) A

Bex=1.36T

Bex=1.69T

(c)

(d)

B

3

(T)

Fig. 2. (Color online) Trapped ﬁeld Bz at the center of the MgB2 bulk
surface by PFM for each starting temperature Ts , as a function of applied
pulsed ﬁeld Bex .

Fig. 4. (Color online) Trapped ﬁeld proﬁles Bz (1 mm) on the surface ofthe MgB2 bulk at Ts ¼ 23 K for various applied ﬁelds Bex .

Total trapped flux Φ (mWb)

0.8
18K
23K
28K
33K

0.6

0.4

0.2

0

0

2

1
B

ex

3

(T)

Fig. 5. (Color online) Total trapped ﬂux  just above 1 mm from the bulk
surface for each starting temperature Ts , as a function of applied pulsed ﬁeld
Bex .
Fig. 3. (Color online) Time dependence of the applied ﬁeld Bex ðtÞ and the
local ﬁeld BL C ðtÞ at the center of the bulk surface at Ts ¼ 23 K for(a) Bex ¼ 0:99 T, (b) 1.06 T, (c) 1.36 T, and (d) 1.69 T.

All the BL C ðtÞ were noisy because of insuﬃcient electricalshielding. For each condition, BL C ðtÞ starts to increase fort  0:01 s with a time delay, takes a maximum at 0.02 s, andthen decreases to a ﬁnal value due to the ﬂux ﬂow. It should
be noted that, for Bex ¼ 1:36 T as shown in Fig. 3(c), theabrupt BL C ðtÞ drop was observed at t ¼ 0:08 s because of theﬂux jump.
Figure 4 presents the trapped ﬁeld proﬁles Bz (1 mm)on the surface of the MgB2 bulk at Ts ¼ 23 K for various
applied ﬁelds Bex . For a lower applied ﬁeld of Bex ¼ 0:99 T
shown in Fig. 4(a), a small amount of magnetic ﬂux was
mainly trapped at the coordinates of ð10; 10Þ. For Bex ¼
1:06 T shown in Fig. 4(b), where the trapped ﬁeld shows amaximum at Ts ¼ 23 K as shown in Fig. 2, the magnetic ﬂux
was trapped mainly on the oblique line (region A) together
with several spots around the periphery. For Bex ¼ 1:36 T
shown in Fig. 4(c), the magnetic ﬂux was trapped mainly
around the bulk periphery, and for Bex ¼ 1:69 T shown in

Fig. 4(d), the magnetic ﬂux escaped and was re-distributed
owing to the temperature rise. These results indicate that
region A has a lower Jc and region B, as shown in Fig. 4(b),has a relatively higher Jc . Because, from the analogy in the
REBaCuO bulks during PFM, the magnetic ﬂux was trappedmainly around the growth sector region (GSR) with a lower
Jc for the lower magnetic pulse application, then the trapped
ﬂux region was inclined at 45 to the growth sector boundary(GSB) with a higher Jc for the higher magnetic ﬁeld. If
the Jc is ideally homogeneous in the bulk, the trapped ﬁeld
proﬁle should show a concave proﬁle for a lower Bex and aconvex proﬁle for a higher Bex , according to the Beanmodel. These results shown in Fig. 4 suggest that the present
MgB2 bulk fabricated by the Mg-RLI method was inhomogeneous for the Jc distribution, which may result from theinhomogeneous inﬁltration of the Mg liquid.
Figure 5 shows the total trapped ﬂux  on the surface ofthe MgB2 bulk at Ts ¼ 23 K for various applied ﬁelds Bex ,which was calculated by integrating the magnetic ﬂux
density Bz (1 mm) over the region where it was positive. All
the –Bex curves take a maximum and then decrease withincreasing Bex . The maximum  value increases and the Bex

103005-3# 2012 The Japan Society of Applied Physics

H. Fujishiro et al.

Jpn. J. Appl. Phys. 51 (2012) 103005
0.5

0.5

18K
23K
28K
33K

0.4
Bz (r =0) (T)Total trapped flux Φ (mWb)(a) simulation

0.3
0.2
0.1
0

0

2

1
B

ex

z

B (T)

1

2

0.2

(a) simulation

BL (r =0) (T)

0
30

40

B =0.9T

1

0.1

20

3

Fig. 7. (Color online) Results of the simulation of applied ﬁeld
dependence of the total magnetic ﬂux  for various Ts .

0.8T
0.9T
1.0T
1.1T
1.2T
1.3T
1.4T
1.5T

0.3

10

0.1

Bex (T)

s

0

0.2

(T)

(b) T =23K (simulation)

-0.1

18K
23K
28K
33K

0.3

0
0

3

0.5
0.4

simulation
0.4

ex

1.1T
1.4T
reduced B (t )T =23K
s

ex

0.5

50

pulse

r (mm)
0Fig. 6. (Color online) Results of the simulation of the (a) trapped ﬁeld Bz

at the center of the bulk surface as a function of the applied ﬁeld Bex forvarious Ts and (b) cross-sections of the trapped ﬁeld Bz ðrÞ at Ts ¼ 23 K forvarious Bex .

40(b) simulations

T (r =0) (K)35

value, at which  takes a maximum, shifts to a higher value
with decreasing Ts .
5. Results of Numerical Simulation and Discussion

We present the results of the numerical simulation for a
MgB2 bulk during PFM. Figure 6(a) depicts the results ofthe simulation of the trapped ﬁeld Bz (r ¼ 0) at the centerof the bulk surface as a function of the applied ﬁeld Bex forvarious starting temperatures Ts . In all the cases, Bz (r ¼ 0)
starts to increase concomitantly with increasing Bex , becomesmaximum, and then decreases with a further increase in Bex .
The critical applied ﬁeld Bex 0 , at which the magnetic ﬂux
starts to trap at the bulk center, decreases concomitantlywith increasing Ts . The results of the simulation reproduce
qualitatively the experimental ones shown in Fig. 2.
Figure 6(b) presents cross sections of the trapped ﬁeld
proﬁle Bz ðrÞ at Ts ¼ 23 K for various Bex . The positions of
r ¼ 0 and 25 mm are, respectively, the center and the edgeof the bulk surface. The Bz ðrÞ proﬁle changes from concave
for a lower Bex to convex for a higher Bex and then the Bz(r ¼ 0) value decreases with a further increase in Bex . Thesebehaviours are apparent for each Ts , but are not always
strictly consistent with the experimental ones, as shown in
Fig. 4, where region A was estimated to have a low Jc . In
this study, the numerical simulation was performed under
the ideal condition, in which the Jc value was homogeneousin the bulk. However, the results of the numerical simulation
roughly reproduced the experimental ones.

T =23K

B =0.9T
ex
1.1T
1.4T

30

25

20 -4
10

10

-3

-2

10
10
Time (s)

-1

10

0

10

1

Fig. 8. (Color online) Results of the simulation of time dependence of(a) the local ﬁeld BL C ðtÞ and (b) the temperature T ðtÞ at the center of thebulk surface at 23 K for a typical applied ﬁeld Bex .

Figure 7 shows the results of the simulation of the appliedﬁeld dependence of the total magnetic ﬂux  for various Ts .
All the –Bex curves take a maximum and then decrease
with increasing Bex . The maximum  value increases andthe Bex P value, at which  takes a maximum, shifts to ahigher value with decreasing Ts . The Bex P value for each Ts
is slightly lower than Bex , at which BT C takes a maximum.
These behaviours are qualitatively consistent with the experimental ones, as shown in Fig. 5.
Figures 8(a) and 8(b) show, respectively, the timedependences of the local ﬁelds BL C ðtÞ and the temperatures
T ðtÞ at the center of the bulk surface at Ts ¼ 23 K for a typicalapplied ﬁeld Bex . The time dependence of the reduced magnetic pulse Bex ðtÞ is also shown. In Fig. 8(a), the local ﬁeld

103005-4# 2012 The Japan Society of Applied Physics

H. Fujishiro et al.

Jpn. J. Appl. Phys. 51 (2012) 103005

BL C ðtÞ starts to increase rapidly with a time lag for Bex ¼ 1:1
and 1.4 T and then decreases. In Fig. 8(b), the temperature
T ðtÞ at the bulk center starts to rise rapidly and then decreases. The temperature starts to rise at t ¼ 0:01 s, at which
Bex ðtÞ takes a maximum. T ðtÞ takes a maximum at t ¼
0:07{0:1 s, which becomes shorter with increasing Bex . For
Bex ¼ 1:4 T, a steep decrease in BL C ðtÞ results from theapproach of the temperature to Tc ¼ 39 K. In this case, thetemperature at the bulk periphery exceeded Tc and most of
the trapped ﬂux escaped from the bulk. The results of thesimulation of the MgB2 bulk were in clear contrast with thosefor REBaCuO bulks;17) the applied ﬁeld dependence of thetrapped ﬁeld was broad and the temperature T ðtÞ takes amaximum at 7 s. The diﬀerences come from the large thermal
conductivity, small speciﬁc heat, and narrow temperature
margin against the transition temperature Tc in the MgB2
bulk. It is possible to add the secondary phases in the bulk to
reduce the thermal conductivity and to enhance the speciﬁcheat. As a result, the temperature rise decreases during PFM
and the trapped ﬁeld will increase. The use of numericalsimulation can optimize the operating parameters for PFM
to enhance the trapped ﬁeld.17) MgB2 bulk magnets are
expected to be applicable in magnetically levitated trains andso on using liquid H2 or cryocooler cooling.
6. Conclusions

Acknowledgment

This work is supported in part by a Grant-in-Aid for
Scientiﬁc Research (No. 23560002) from the Ministryof Education, Culture, Sports, Science and Technology,
Japan.

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Pulsed ﬁeld magnetization (PFM) was performed for the ﬁrst
time for a large MgB2 bulk of 50 mm diameter fabricatedby a reactive liquid Mg inﬁltration (Mg-RLI) method, andthe trapped ﬁeld properties were measured. Important resultsof experiment and simulation and conclusions obtained inthis study are summarized as follows.
(1) The maximum trapped ﬁeld of Bz ¼ 0:47 T was
realized at the center of the bulk surface and the total
trapped ﬂux  ¼ 0:5 mWb was achieved at Ts ¼ 23 K. Bothvalues decreased with increasing temperature Ts .
(2) The experimental results can be roughly reproducedby numerical simulation using electromagnetic and thermalﬁelds, although inhomogeneous Jc distribution exists in thepresent MgB2 bulk fabricated by the Mg-RLI method fromthe trapped ﬁeld proﬁles by PFM.
(3) The ﬂux dynamics and the heat generation/propagation of the MgB2 bulk during PFM were in clear contrast
with those for REBaCuO bulks because of the large thermal
conductivity, small speciﬁc heat, and narrow temperature
margin against the transition temperature Tc in the MgB2
bulk. In the future, using liquid H2 , high-strength MgB2 bulk
magnets are expected for practical applications.

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