Paper No. LWE-05

Measurement of Critical Current and Transient

Characteristics of a High-Temperature Superconductor

Tube Using a Pulsed Current Supply

DistributionR. W. WeeksR. B. PoeppelU. BalachandranR. A. ValentinAuthorsESA SectionET Division FileF. Y. FradinH. DruckerS. Lake

Y. S. Cha, D. J. Evans, and J. R.

Energy Technology DivisionArgonne National Laboratory

Argonne, Illinois 60439

%se submittedmanuscripthas bean created by theUniversity of Chicago as Operator of ArgonneNatlcnal Latsoretofy(7vgnmev underContmctNo.W-31-109.ENG-38 with ftre U.S. Department ofEnergy.The U.S. Governmentrelains for itself,andothersactingcm”* bsfvaff,a pef~up, n~exdusiveiIrrevcsable worldwide Ifcense fn said article torspmduce,preparederh’affvaworks.dk@rJfe -*to the publlc, end perform publlcfy end dkplayJmbtktv,byor on khalf of theGowsmmant.

Hull

Submitted to 1998 Applied Superconductivity Conference, September 13-18,1998, Palm Desert, CA.

*Work supported by the U.S. Department of Energy, Energy Efficiency andRenewable Energy, as part of a program to develop electric power technology,under Contract W-31-109-Eng-38.

——

DISCLAIMER

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——__ _______________ . . _.. -.——. . . .. . . . . . . --—- .... . . .._.._

DISCLAIMER

Portions of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.

\

4.

Measurement of Critical Current and Transient

Characteristics of a High-Temperature Superconductor

Tube Using a Puked Current Supply

Y. S. Cha, D. J. Evans, and J. R. Hull

Argonne National Laboratory

Argonne, Illinois 60439

Abstract

The transient response of a melt-cast-processed BSCCO-2212

superconductor tube is investigated by using a pulsed current source. It was

found that (1) the maximum induced current and the excitation current at

field penetration increase with the maximum excitation current, and (2) there

is a time delay between peak excitation current and peak magnetic field

inside the superconductor. These observations can be explained by the

concept of magnetic diffusion. The ac steady-state critical current of the

superconductor was found to depend on the magnitude of the current

increment. The critical current determined by using the pulsed current

system agrees fairly well with the ac steady-state critical current determined

by using relatively kwge current increment.

Introduction

Bulk high-temperature superconductors in the form of hollow cylinders

or rings have two potential practical applications. The first one is magnetic

2

shielding [1-6]. The

superconductor tube

magnetic field of the induced current in the cylindrical

cancels the externally applied field so that there is very

little field in the hole of the cylindrical tube provided that the applied field is

below the penetration field of the superconductor tube. The superconductor

tube can be used to shield both a DC and an AC applied field. Another

potential

inductive

inductive

application of high-temperature superconductor tubes is the

fault-current-limiter in the electric power industry [7-12]. The

fault-current-limiter consists mainly of an iron core inside a

superconductor tube and a copper coil wound on the outside of the

superconductor tube. The fault current limiter uses the shielding capability

of a superconductor tube to keep the inductance low under normal operating

conditions. Under fault conditions, the large current in the copper coil

exceeds the shielding capability of the superconductor tube and there is a

jump in inductance because the iron core is no longer shielded fi+omthe coil

by the superconductor tube.

In this paper, we describe the results of measuring induced critical

current and transient characteristics of a superconductor tube by using a

pulsed current supply. The main reason for using a pulsed current source is

that it provides an useful way of characterizing the superconductor. Pulsed

current test is particularly convenient for characterizing large bulk

superconductors or coils with high critical currents. Because the pulse

duration is small (in mini-seconds), relatively large current can be achieved

without using heavy cables or wires which are required for tests with

continuous current. We also measured the ac steady-state voltage/current

characteristics of the superconductor/coil assembly and the results are

compared to that of the pulsed current system.

-— —... .. ...-.. —-.. ...—— - —-- - -------- ... .. - . .... . -- ==?r—------ —— . . . .

II. Experimental Apparatus

A schematic diagram of the test setup and the test section is shown in

Fig. 1. The test setup is identical to that reported previously by Cha and

Askew [13] whereas the test section is different. The major differences are (1)

the superconductor tube used in the present experiments is much larger than

that used by Cha and Askew, and (2) the number of turns of the copper coil

used in the present experiments is much smaller than that used by Cha and

Askew. The test section is made of a copper coil and a cylindrical

superconductor tube. The copper coil has 80 turns and is made of 6.6 mm by

2.2 mm flat copper wire. The copper coil is approximately 150 mm long and

has an inside diameter almost identical to that of the superconductor tube.

The large cross-sectional area of the copper wire kept the resistance of the

copper coil fairly low and reduces the amount of heating during the test and

superconductor is minimally tiected by the resistive heating in the copper

coil. The material of the superconductor tube was bulk Bi2Sr2CaCu20x and

was made born a melt-cast process. The BSCCO tube is 190 mm long with a

wall thickness of 8.0 mm and an outside diameter of 70 mm. A Hall probe is

placed near the center of the tube to measure the magnetic field in the hole of

the tube. A Rogowski coil is employed to measure the induced current in the

superconductor tube. The response times of both the Hall probe and the

Rogowski coil are much smaller than the transient time of the present

experiments [13]. The copper coil is comected to a pulsed current source

which is shown schematically in Fig. la. It consists of several capacitors in

parallel and an array of field effect transistors (FETs). .The capacitors are

charged by a high-voltage DC current source (lIVDC). The FETs are driven

by a fknction generator and the gates of the FETs can open and close in less

than a mini-second which is much shorter than the transient time of the

4

current experiments. Currently, the pulser can be operated up to a voltage of

200Volts.

Experimental Results

Figures 2 to 5 shows the measured excitation current NI, the magnetic

field H near the center of the superconductor tube, and the induced current Is

as a finction of time for four different magnitude of M in ascending order.

Figures 2 and 3 are for relative small values of NI while Figs. 4 and 5 are for

relatively large values of NI. In other words, NI in Figs. 4 and 5 rises faster

and to a larger value than that in Figs. 2 and 3. Figures 2 to 5 show that the

peak value of NI is reached at approximately 4.5 ms independent of the value

of NI(max). The rise time of the excitation current (or applied field) is

therefore 4.5 ms which equals approximately the rise time of a 60-Hertz ac

sinusoidal current. Figure 2 shows that for relatively small value of NI(max),

the applied field did not penetrate the superconductor tube and the magnetic

field (H) inside the hole of the tube was very small and remained constant.

The induced current (Is) was in the opposite direction of the excitation

current (NI). Figure 3 shows that the magnetic field inside the hole of the

superconductor was constant initially and began to increase slightly after NI

reached its peak value and then remained fairly constant for a relatively long

period of time even though the excitation current was decreasing towards

zero. Field penetration of the thickness of the superconductor tube occurred

at 4.5 ms when both NI and Is reached its peak value and when H began to

increase slightly. The slight increase followed by the fairly constant value of

H after field penetration while NI was descending can be explained by the

concept of magnetic diffusion. Figure 4 shows similar result$when NI(max) is

increased, i.e., field penetration occurred at 4.5 ms when NI and Is reached

... . .—. ~— . ...— ---=...-.-. .-. ...... ------ --—- -, “---”

5

its peak value and H increased somewhat and remained fairly constant after

field penetration even though NI was decreasing. When NI(max) is increased

further as shown in Fig. 5, field penetration occurred at 3.0 ms slightly ahead

of the peak NI. After field penetration, H increased rapidly and reached its

maximum value at 12 ms. It can be clearly seen in Fig. 5 that peak H lags

peak NI. It should be mentioned that the induced current shown in Figs. 2 to

5 was always negative (relative to NI) initially and became positive near the

end (50 ms) to support a trapped field in the superconductor. Also, it should

be noted that the tests were conducted in increasing NI(max) without

warming up the superconductor tube between each test, therefore, there is

always a small trapped field inside the superconductor tube at the beginning

of each test [except for the first test at very small NI(max)]. This is why in

Figs. 2 to 5, H is always slightly positive at the beginning of the test.

Figure 6 shows the plots of maximum induced current Is(max) and the

excitation NI at field penetration NI* versus M(max). NI* is determined

&om the profiles of H and NI. Specifically, NI* is the value of NI at the point

of field penetration which corresponds to the point where H begins to increase

in Figs. 3 to 5. Both NI* and Is(max) increase monotonically with NI(max).

For relatively small NI(max), magnetic flux density did not penetrate the

tube and NI* does not exist. NI* can be measured only when NI(max) is

increased to some minimum value when the applied field penetrates the tube.

Critical Current

Figure 6 shows that both the induced current and the excitation current

at field penetration increase monotonically with NI(max). This indicates that

there is no single (constant) value of NI* or Is(max) that can be assigned as

.

6

the critical current of the superconductor tube for the transient tests

described here. However, one of our objectives is to determine the ac steady-

state critical current of the superconductor tube by using the pulsed current

supply. The induced current Is(max) at the point where NI* first appears in

Fig. 6 may correspond to the ac steady-state critical current. This is also the

maximum induced current Is in Fig. 3 where M(ma) is increased enough so

that the magnetic flux just penetrated the tube. From Fig. 6, we found that

1~6,820 A. The critical current determined this way is the peak value.

Therefore, IC(RMS)=4,823 A. To compare this critical current with the ac

steady-state critical current, we have measured the current/voltage

characteristics of the same coilhube assembly with an ac source at 60 Hz and

the results are shown in Fig. 7. Inside the superconductor tube, there is a

steel bar which forms an open core. These tests were conducted by

monotonically increasing the current through the copper at intervals. The

solid circles are the data for tests with relatively small increments of current

while the open circles are the data for relatively Iarge increments in current.

Before field penetration, the voltage rises linearly with current in Fig. 7. At

the point of field penetration the inductance of the coil jumps and it begins to

limit the current. This is shown as a rise in voltage and sharp decrease in

current in Fig. 7. Tests with small AI indicates that IC(RMS) is

approximately 7,000 A while tests with large AI give IC(RMS)4,000 A. Thus,

the ‘critical current measured by using the pulsed current supply

[IC(RMS)=4,823 Al is closer to the ac steady-state Ic with large AI than that

with small AI.

_.. -- ..-4.—.

_.— .—. ..—

7

Magnetic Difftwion

Under the magnetoquasistatic assumption, Maxwell equations can be

reduced to a magnetic difision equation [14]. For the present system with

cylindrical geometry, it can be shown that the following magnetic difision

equation applies

~[Dm(r ~B/&)]/i3r / r = ~Bfit, (1)

where the magnetic M?bsion coefficient Dm is

Dm = f)/f..@ (2)

and p is resistivity, ~ is permeability of free space, B is magnetic flux density

in the axial direction, r is the radial coordinate, and t is time. The magnetic

diffusion coefficient Dm is inside the derivative because the resistivity of the

superconductor is not uniform during the transient. This is the result of non-

uniform current distribution during the transient. The characteristic

diffusion time z is

T = a2/Dm

where a is the characteristic dimension of

2

the system. In the present

experiments, a is the thickness of the superconductor tube and equal to 8.0

mm. Magnetic diffusion arises because the characteristic diffusion time is

equal or larger than the characteristic time (the rise time) of the pulsed

system. As pointed out by Cha and Askew [13], the characteristic difision

time of the BSCCO-2212 tube is on the order of several hundred milli-

seconds, The rise time of the current pulse is only 4.5 ms. Therefore,

(3)

———-. — — —.. —. . ,— -— -. ——..

8

magnetic diffusion is important for the present experiments. Physically, this

means that NI is rising faster than the time required for the magnetic flux to

reach its steady-state value (Bean’s critical state model) and one must solve

the magnetic diffusion equation to obtain the correct magnetic flux density

distribution inside the superconductor tube during the transient. The reason

that H continues to increase while NI is decreasing, as shown in Figs. 3 to 5,

is the result of magnetic difision. Steady-state flux distribution does not

have time to develop and flux continues to diffise from the interior of the

superconductor towards both inner and outer surfaces of the superconductor

tube. The flux density at the inner radius continues to increase for sometime

while the applied field at the outer radius has already begun to descend.

Results similar to those shown in Fig. 6 were reported and explained (in

terms of magnetic difftmion) by Cha and Askew [13].

It should be emphasized that the flux creep/flux flow resistivity of the

BSCCO-2212 tube can change over several orders of magnitude during a

transient where the induced current changes born 500 to 2,000 A/cm2 [13].

This large variation in p will have significant impact on the characteristic

diffusion time and must be accounted for in the analysis. Work is in progress

in solving the non-linear diffusion equation (1) and the results will be

reported in the future.

The discussion so far has been limited to the case of constant

temperature in the superconductor tube. This assumption is valid provided

that dissipation and heat generation in the superconductor is small. As far

as NI(max) is relatively small, which is probably true for the present tests,

temperature variation in the superconductor can be neglected. However, in

practical applications where the fault current limiter is exposed to much

larger NI(max), heating (particularly near the outer radius of the

_., .—. —.. ---

9

superconductor tube) can be significant and equation (1) cannot be decoupled

from the heat transfer equations.

Summary and Conclusions

The transient response of a melt-cast-processed BSCCO-2212

superconductor tube is investigated by using a pulsed current source and a

copper coil wound externally to the tube. The induced current in the

superconductor tube is measured by a Rogowski coil. The penetration field is

measured by a Hall probe inside the hole of the tube. Experimental results

show (Fig. 6) that the maximum induced current Is(max) is not constant and

increases with maximum excitation current NI(max). Another experimental

observation is that there is a time delay between peak excitation current NI

and peak magnetic field H inside the hole of the superconductor tube (Fig. 5).

Both observations can be explained by magnetic difision in a conductor with

small but finite (flux-creep) resistivity. Magnetic difision arises because the

characteristic difision time for magnetic flux density is larger than the

characteristic time (the rise time) of the pulsed system. Consequently, there

is not enough time for the magnetic flux density to reach its steady-state

value (Bean’s critical state model) during the transient.

A critical current for the superconductor tube can be determined by

using the pulsed current system. This critical current is the induced current

in the superconductor tube at the point of field penetration when NI(max) is

increased just enough to penetrate the superconductor tube (Fig. 3). The

critical current determined this way is IC(RMS)=4,823 A. For comparison to

ac steady-state critical current, we also measured the voltage/current

characteristics of the superconductor tube. It was found that the ac steady-

—— ._.. ..== —m. . .,, ------- . . —.-.-3=-?=+=----====-=------ ---- ‘-~—. ‘ — - ‘“-

10

state critical current depends on the magnitude of AI used in the experiments

(Fig. 7). For relatively large AI, the ac steady-state critical current was

IC(RMS)S4,000 A which is in fair agreement with that measured by the

pulsed current system.

Acknowledgments

This work has been supported by the U.S. Department of Energy, Energy

Efficiency and Renewable Energy, as part of a program to develop electric

power technology, under Contract W-31-109-Eng-38.

References

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and S. Yasuhara, Cryogenics 37,381 (1997).

2. V. Plechacek, J. Hejtmanek, and V. Sims, IEEE Trans. on Applied

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Zimmer, Appl. Phys. Lett. 70,7,898 (1997).

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X. Fu, Cryogenics 36,989 (1996).

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Physics C 225,361 (1994).

. ..- ..---”=,.,-, —— ~=,r-..”,. . ~,. ,, ,,. ,, , . . . . * . . . &-n————— —.—.——7%....

11

(5.

7.

8.

9.

10.

11.

12.

i3.

14.

B. W. lticketts, K.-H. Muller, and R. Driverj Physics C 183, 17 (1991).

V. Meerovich, V. Sokolovsky, G. Jung, and S. Goren, IEEE Trans. on

Applied Superconductivity, 5,2,1044 (1995).

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Superconductivity, 5,2,1067 (1995).

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Obradors, and S. Pinol, IEEE Trans. on Applied Superconductive@, 5,2,

1071 (1995).

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T. P. Orlando and K. A. Delin, Foundations

Superconductivity, Chapter 2, Addison-Wesley, 1991.

of Applied

— -——. .

12

Figure Captions

Fig. 1 Schematic diagrams of the experimental apparatus and the test

section.

Fig. 2 Variations of the excitation current NI, the magnetic field H,

and the induced current Is in the

NI(max)=5,696 A.

superconductor tube with

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Variations of the

and the induced

NI(max)=7,317 A.

Variations of the

and the induced

NI(max)=9,522 A.

Variations of the

excitation current NI, the magnetic field H,

current Is in the superconductor tube with

excitation current NI, the magnetic field H,

current Is in the superconductor tube with

excitation current NI, the magnetic field H,

and the induced current Is in the superconductor

NI(max)=15,342 A.

tube with

Variations of the excitation current at field penetration NI* and

maximum induced current Is(max) with M(max).

Voltage (AW/Current (NI) characteristics

superconductor/coil assembly for ac steady-state tests

with small and large AI.

of the

conducted

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