calorimetric method of ac loss measurement in a rotating magnetic field

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Calorimetric method of ac loss measurement in a rotating magnetic field P. K. Ghoshal, T. A. Coombs, and A. M. Campbell Citation: Review of Scientific Instruments 81, 074702 (2010); doi: 10.1063/1.3458003 View online: http://dx.doi.org/10.1063/1.3458003 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/81/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Influence of PreHeatTreatment Condition on Interstrand Contact Resistance in Nb3Sn Rutherford Cables by Calorimetric ACLoss Measurement AIP Conf. Proc. 824, 851 (2006); 10.1063/1.2192433 Measurements of Total AC Losses in HTS Short Sample Wires By Electric and Calorimetric Methods AIP Conf. Proc. 711, 805 (2004); 10.1063/1.1774645 Experimental setup for calorimetric alternating current loss measurements on high-temperature superconductor tapes in applied longitudinal magnetic fields carrying transport currents at variable temperatures Rev. Sci. Instrum. 75, 99 (2004); 10.1063/1.1633002 ac self-field loss measurement system Rev. Sci. Instrum. 70, 3087 (1999); 10.1063/1.1149872 Calorimetric apparatus for alternating current loss measurements on high-temperature superconductors Rev. Sci. Instrum. 69, 3320 (1998); 10.1063/1.1149096 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitationnew.aip.org/termsconditions. Downloaded to IP: 128.193.164.203 On: Mon, 22 Dec 2014 03:31:00

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Page 1: Calorimetric method of ac loss measurement in a rotating magnetic field

Calorimetric method of ac loss measurement in a rotating magnetic fieldP. K. Ghoshal, T. A. Coombs, and A. M. Campbell Citation: Review of Scientific Instruments 81, 074702 (2010); doi: 10.1063/1.3458003 View online: http://dx.doi.org/10.1063/1.3458003 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/81/7?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Influence of PreHeatTreatment Condition on Interstrand Contact Resistance in Nb3Sn Rutherford Cables byCalorimetric ACLoss Measurement AIP Conf. Proc. 824, 851 (2006); 10.1063/1.2192433 Measurements of Total AC Losses in HTS Short Sample Wires By Electric and Calorimetric Methods AIP Conf. Proc. 711, 805 (2004); 10.1063/1.1774645 Experimental setup for calorimetric alternating current loss measurements on high-temperature superconductortapes in applied longitudinal magnetic fields carrying transport currents at variable temperatures Rev. Sci. Instrum. 75, 99 (2004); 10.1063/1.1633002 ac self-field loss measurement system Rev. Sci. Instrum. 70, 3087 (1999); 10.1063/1.1149872 Calorimetric apparatus for alternating current loss measurements on high-temperature superconductors Rev. Sci. Instrum. 69, 3320 (1998); 10.1063/1.1149096

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Page 2: Calorimetric method of ac loss measurement in a rotating magnetic field

Calorimetric method of ac loss measurement in a rotating magnetic fieldP. K. Ghoshal,1 T. A. Coombs,2 and A. M. Campbell21Oxford Instruments NanoScience, Abingdon, Oxfordshire OX13 5QX, United Kingdom2Department of Engineering, Electrical Engineering, University of Cambridge,Cambridge CB3 0FA, United Kingdom

�Received 30 November 2009; accepted 5 June 2010; published online 15 July 2010�

A method is described for calorimetric ac-loss measurements of high-Tc superconductors �HTS� at80 K. It is based on a technique used at 4.2 K for conventional superconducting wires that allowsan easy loss measurement in parallel or perpendicular external field orientation. This paper focuseson ac loss measurement setup and calibration in a rotating magnetic field. This experimental setupis to demonstrate measuring loss using a temperature rise method under the influence of a rotatingmagnetic field. The slight temperature increase of the sample in an ac-field is used as a measure oflosses. The aim is to simulate the loss in rotating machines using HTS. This is a unique techniqueto measure total ac loss in HTS at power frequencies. The sample is mounted on to a cold fingerextended from a liquid nitrogen heat exchanger �HEX�. The thermal insulation between the HEXand sample is provided by a material of low thermal conductivity, and low eddy current heatingsample holder in vacuum vessel. A temperature sensor and noninductive heater have beenincorporated in the sample holder allowing a rapid sample change. The main part of the data isobtained in the calorimetric measurement is used for calibration. The focus is on the accuracy andcalibrations required to predict the actual ac losses in HTS. This setup has the advantage of beingable to measure the total ac loss under the influence of a continuous moving field as experienced byany rotating machines. © 2010 American Institute of Physics. �doi:10.1063/1.3458003�

I. INTRODUCTION

Superconductors generate thermal energy arising fromac loss as when exposed to a varying electromagnetic field.This thermal energy gives rise to a temperature gradientand/or change in the temperature of the sample. In experi-mental measurements, the change in sample temperature canbe used to calculate the total ac loss. This is an indirectcalorimetric method to measure ac loss using the temperaturerise method.

Superconductors generate thermal energy arising fromac loss as when exposed to a varying electromagnetic field.This thermal energy gives rise to a temperature gradientand/or change in the temperature of the sample. In experi-mental measurements, the change in sample temperature canbe used to calculate the total ac loss. This is an indirectcalorimetric method to measure ac loss using the temperaturerise method.

Calorimetric measurements of ac losses are a widelyused technique for conventional low Tc superconductingwires at liquid helium temperature �4.2 K�.1–3 The calorimet-ric technique first used at liquid helium temperature involvedthe measurement of helium evaporation. Sensitivity of thismeasurement is poor and it has very long thermal time con-stants. With the development of low loss conductors the clas-sical boil off method was no longer useful. Several improve-ments were made by measuring the evaporation loss withinthe helium cryostat that increased the sensitivity to betterthan 1 mW, however long measuring times required.

For the calorimetric measurement at liquid nitrogen tem-

perature �77 K�, the evaporation method is restricted andsometimes cannot be used due to the larger latent heat ofliquid nitrogen resulting in much lower rates of evaporationper unit energy input compared to helium. The smaller ratiobetween the densities of liquid and gas at room temperaturelimits the sensitivity of measurement.

Another type of calorimetric measurement uses the tem-perature increase of the sample due to the ac-field as a mea-sure of losses where the sample is thermally insulated fromthe cooling bath.4,5 The sample is placed in a vacuum vesseland connected by a thermal resistance to the coolant �Fig. 1�achieving sensitivities of about 10−8 W �Ref. 6� at 4.2 K.The results from initial tests carried out on a copper sampleare compared with an analytical model7 available for the acloss in copper in order to gain confidence in the measure-ment technique for the power loss.

In this paper, the technique is adapted to a measurementof straight tapes at �80 K in order to characterize thehigh-Tc superconductors �HTS� conductor. The sensitivity ofthe method is reduced and thermal time constants are muchlonger if compared to 4.2 K. This is due to the properties ofmaterials such as the specific heat that is orders of magnitudehigher at this operating temperature.

This is a simple and straightforward technique, as longas the temperature and the temperature rises are measuredaccurately, for gross ac loss measurement.8 The apparatusrequired for temperature measurement is simple and has dis-tinct advantages for the measurement in ac magnetic fields.In this technique no transport current is applied to the super-

REVIEW OF SCIENTIFIC INSTRUMENTS 81, 074702 �2010�

0034-6748/2010/81�7�/074702/8/$30.00 © 2010 American Institute of Physics81, 074702-1

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Page 3: Calorimetric method of ac loss measurement in a rotating magnetic field

conducting tape. The arrangement is designed to mimic theconditions that will be seen by a superconducting tape lo-cated on the stator of a motor or generator.

As reported earlier by many researchers,9–12 if the mag-netic field is oriented perpendicularly to the tapes, the mea-sured ac loss is higher than the loss in a parallel magneticfield. The measured losses were compared to predictionsfrom the Bean critical state model and Brandt model.13 Thereare also many reported ac loss measurements4,6,14–20 carriedout at temperatures, 77 K and below where the external mag-netic field direction is changed between 0° and 90° and themeasured ac loss compared with available analytical lossmodels.

This technique has advantages and drawbacks in mea-surement. Any type of ac loss results in heat dissipation inthe superconductor. The dissipated heat is measured with thecalorimetric method, either by the amount of cryogen evapo-rated or by the temperature increase of the sample. This mea-sures the total ac loss in the sample, which is of most interestfor engineering applications. This experimental method isgood for complicated geometries, which are present in de-vices such as cables, transformers, motor, windings, etc.Once the calibration of the setup has been completed, theinterpretation of the results obtained is simple and straight-forward.

The drawbacks of this measurement technique are that itis very time consuming, needs a number of calibration setupcurves to be generated and the sample thermal stabilization isslower. The single tape and multiple tape assemblies need tobe characterized by thermally insulating them from the heatexchanger �HEX� �so that the temperature rise due to the heatgenerated due to magnetization is not removed too quicklyand can therefore be measured�. The main constraint of themeasurement is in the determination of the change of tem-perature �that is directly related to the measurable ac loss�because of the dependence of the temperature profile orchange of temperature along the length of the sample and thesample holder. Temperature rises or changes below 10 mKare normally difficult to measure accurately because of thethermal effects and electrical noise induced due to the exter-nal rotating magnetic field.

II. MEASUREMENT PRINCIPLE AND EXPERIMENTALSETUP

Figure 2 shows a schematic of the experimental arrange-ment. The magnet field �magnetic flux density� used for acloss measurement is comparable to that required within theair gap for most rotating machines. The present experimentalsetup is intended to simulate most of the conditions thatYBCO coated conductors would be exposed to while pro-ducing magnetic field and while sitting in a magnetic fieldthat is varying continuously at a rotational speed of 2100rpm. The schematic for the test rig is shown in Fig. 3. Thisconsists of a rotating dipole magnet assembly along with aliquid nitrogen cryostat. The rotating magnet is designed toproduce a magnetic flux density in the air gap of Bg�max�=0.35 T covering the range of flux densities normallyachievable within the air gap of present rotating machines.With the present experimental setup the field produced isrotated up to a speed to 2100 rpm �Table I�. This is intendedto simulate most of the conditions that the conductors will beexposed to while producing magnetic field and sitting in amagnetic field that is varying continuously.

Using Ampere’s law, the number of turns required ineach quadrant of the core is evaluated based on the conductorsize and power supply. N� I= �Bg� lg� / �2��0�, whereN=number of turns required, I=current in the coil requiredachieving the required ampere-turns, Bg=0.35 T at the cen-ter in the air gap, lg=15 mm �distance between the polepieces�, and N� I=9000 At �nominal� With currentI=1.0 A through the coil, the total number of turns requiredis 9000, hence 2250 turns in each quadrant.

The cryostat is a double walled �both inner and outer

Thermal resistance

Ohmic heater

Temperature sensor

Liquid Nitrogen or helium bath

Temperature sensor

Sample

Thermal binder to

hold sample

FIG. 1. Principle of calorimetric measurement.

Current source 100mA

Output voltage from Hall sensor

Pt100 wired RS232

Cryostat w ith thesample holder

Rotating MagnetAssembly rig to hold the

Cryostat within themagnet bore

(DC Servomotor)

PT-104Pico Logger

Power Supply to thecoil (rotating- magnet):

AGILENT/HP 6654A -60V / 9A DC Power

Supply 540W

Power Supply for theDC motor: 0 - 10A / 0-

32V DC Current source

OscilloscopeTektronix 2440

Power Supplyfor Hall sensor

FIG. 2. The schematic arrangement showing the experimental setup.

074702-2 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 4: Calorimetric method of ac loss measurement in a rotating magnetic field

vessel made of SS304� vacuum insulated cryostat to holdliquid nitrogen and a heat exchanger to cool the sampleholder using conduction cooling in the vacuum space. Thebase of the inner vessel is a copper HEX fitted with a cali-brated temperature Pt100 sensor. The thermal load from thesensor wiring to the sample is dumped by spiraling this alongthe inner vessel and copper heat exchanger, as shown in Fig.4. The top plate of the inner vacuum jacket holds the serviceand diagnostic ports.

The low eddy current sample holder is located within theouter vacuum container. The design of the holder is a com-promise between the thermal conduction and eddy currentheating along with electrical isolation. The holder is con-structed from copper wire mesh, cast in Stycast™ which is agood compromise for the purpose of the ac loss measure-ments using the temperature rise method. The holder is fixedto the copper heat exchanger and functions such as a con-ventional cold finger cooled by liquid nitrogen �Fig. 4�. Acalibrated Hall probe mounted on the sample holder face isused to measure and monitor the variation of magnet fluxdensity in the sample region while the magnet is rotated at2100 rpm. The temperature measurement at 77 K is per-formed with special Platinum-100 �Pt100� temperature sen-sors. The temperature measurement is carried out using a4-wire measurement technique. This sensor has a nominalresistance of 100 � at 273K with typical dimensions of1.9�2.3�1.0 mm3 and accuracy �10 mK at 77 K. An

Ohmic heater having a resistance of 11.05 � is made from aSWG42 insulated constantan wire, noninductively woundand laid longitudinally along the sample holder on a polyim-ide film tape with an overall film heater dimension of25 mm long�3 mm wide�0.5 mm thick. The primaryfunction of the heater is calibration for the temperature riseversus applied heat load. Upon mounting of sample, Ohmicheater, temperature sensor and the Hall sensor on to the HEXof the inner vessel tail section, the whole assembly is cov-ered with three loosely wrapped layers of multilayer insula-tion. A small amount of charcoal ��10 mg� contained in astainless steel mesh is attached to the inner vessel containerto act a sorption pump to improve the isolation vacuum.

A dc 0.15–0.4 kW Servomotor is used to rotate the mag-net core assembly via a belt drive and a direct current �dc�commutator. The dc servomotor is energized from a constantdc �current� source through a dc commutator that consistedof two conductors and was rated for 240 V ac/dc and to takea maximum current of 4 A. The dc commutator is rated up toa speed of 3600 rpm �under no-load condition� with a contactresistance�1.0 m�. A data logger PT-104 is used as aninterface between computer and temperature sensor to mea-sure and record the temperature with 24-bit resolution givinglinearity of 10 ppm and accuracy of 10 mK at 298 K.

A. Mounting of the heater and temperature sensoron the sample holder

The temperature profile within the sample holder is notexactly the same when comparing the temperature rise pro-duced in the sample due to heat from the Ohmic heater andwhen exposed to an ac field. For the test measurements theheater and the temperature sensor were glued using thermal-grease onto the same side of the sample holder. The Pt100sensor is temporarily fixed to the end of the sample/sampleholder away from the heat exchanger. During the sampleholder calibration, the heater and temperature sensor are bothattached to the surface of the sample holder and are in good

FIG. 3. Schematic diagram showing the test rig rotated up to a speed of 2100 rpm �35 Hz� and generate magnetic field of 0.35 T at the magnet center.

TABLE I. Brief summary of rotating magnet assembly.

Field at the center 0.35 T �maximum�Number of Poles 2Gap between pole pieces 15 mmField homogeneity overthe sample region

�3% ��10 mT at 0.35 T—over �6 mm diameter sphere

volume at Z=0 mm�Speed to rotation �rpm� 2100a �3600 at no-load speed�aAchieved at a field of 0.23 T.

074702-3 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 5: Calorimetric method of ac loss measurement in a rotating magnetic field

thermal contact with the sample holder surface. During thesample heat load versus temperature calibration, first, thesample is attached to the sample holder and subsequently thecalibration heater and the temperature sensor are mounted onthe top of the sample.

III. CONCEPT OF EXPERIMENTAL RIG

In this paper, we concentrate on a loss measurementtechnique at 77 K that is more difficult to perform than themeasurement at liquid helium temperature. The normal con-ventional method is to apply an external field to the samplethrough an external coil carrying ac at variable frequency.The technique discussed here is unique because it uses a dcmagnetic field rotating at variable speed to produce the de-sired varying field.

A. Calibration of the test rig

First the peak field is measured using a calibrated Hallgenerator-probe at room temperature ��295 K�. Subse-quently the coil current to field ratio and speed relationshipsis measured. The calibration enables to determine currentrequired achieving the required field over the sample holder,and dc current required for the motor to reach the specificspeed at different magnetic flux densities. With sample

mounted the stability and time constant is established forcool down and warm up. Depending on this time constant,the time for application of the rotating magnetic field is de-fined. Since the small temperature rise of the sample in anac-field is the measure of the losses, calibration is performedwith an Ohmic heater connected to the sample. With aknown heat applied, the temperature rise is recorded andtypical rise is shown in Fig. 5. In theory, there is no need tohave calibrated thermometers to measure the temperaturerise, but it is important to record the actual temperature undermeasurement conditions.

The criterion of �10 mK /min is used to define the ac-ceptable temperature stability during measurement. It is alsoobserved that 75% of the total temperature rise normallyhappens within the first minute after the heat is applied �Fig.5�. A typical sensitivity of 40 mK/mW is calculated on thesample holder from Fig. 5.

The calibration is needed every time the sample holderalone is changed and a set of measured temperature rises isobtained, as shown in Fig. 6, assuring that the relationshipbetween temperature increase and the heater power is linear.The relation between temperature rise and heat load due toac-field generated is usually determined before the measure-ment. Once this calibration is completed, the losses for dif-ferent field amplitudes and speeds �frequencies� can be mea-sured without intermediate calibration cycles. External heatload, Qh is represented as Qh=Cth�dT, where dT=temperature increase �milliKelvin�; Cth= thermal resistance

F i t t e d w i t h n o n - i n d u c t i v el o o p f o r He a t e r

Lo c a t i o n f o r t h e P t 10 0t e m p e r a t u r e s e n s o r

S a m p l e Ho l d e r w i t h P t - 10 0

S a m p l e h o l d e r l i n k t oH e a t E x c h a n g e r

FIG. 4. The inner vessel cold finger with the sample holder mounted alongwith the diagnostic wiring.

89.30

89.35

89.40

89.45

89.50

89.55

0 1 2 3 4 5 6

Time in minutes

Tem

pera

ture

inK

External heater input load of 4.42mW Heater OFF

Heater ON

FIG. 5. Temperature profile during sample holder calibration with a heatermounted on the sample holder.

Qh = 0.023 dTSH - 0.6421

0

5

10

15

20

25

30

35

40

45

0 200 400 600 800 1000 1200 1400 1600 1800 2000

dTSH - Temperature rise (mK)

Qh

-H

ea

tL

oa

d(h

ea

ter

po

we

r)m

W

Sample holder

Linear (Sample holder)

FIG. 6. The calibration curve between the temperature rise and fixed heatload applied to sample holder only �without samples� at 80 K.

074702-4 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 6: Calorimetric method of ac loss measurement in a rotating magnetic field

proportional constant. This calibration chart is used to evalu-ate the heat generated when exposed to the rotating magneticfield.

IV. CALIBRATION

The calibration for the heat load contribution from thesample holder alone could not be neglected. This tempera-ture rise within the sample holder is always subtracted formthe actual measured data when samples were attached in or-der to calculate the real temperature rise within the sample.The temperature rise within the sample holder is significantbecause there is a contribution from the copper heat-exchanger. A typical plot of temperature rise on the sampleholder is shown in Fig. 7. The fluctuations observed in Fig. 7are due to the susceptibility of the temperature sensor and itswiring to alternating magnetic field. This is not an issue be-cause we are measuring the peak temperature value that isobtained one the field is removed.

A. Estimation of ac loss from temperature rise

The calibration of the test rig is followed by ac loss ismeasurement. Once the calibration is completed for currentto field and current for motor drive at room temperature, acalibration curve is established for the temperature rise in thesample holder with an externally applied known heat load atthe operating temperature. This curve is used to work out the

heat load from the subsequent temperature rise measurement�Fig. 6�. A similar calibration curve for the copper sample inTable II with sample holder is established between heat ap-plied and temperature rise at operating temperature, asshown in Fig. 8 is represented as

Qh = 0.0134.dTCu − 0.3629, �1�

where Qh is the heat applied and dTCu is the temperature rise.Once the temperature rise versus the heat load is estab-

lished “copper calibration,” the temperature rise at varyingfields and frequencies are measured and fitted with a secondorder polynomial with an error fraction of 5%, as shown Fig.9. This temperature rise in the copper sample with varyingfrequency is transformed into ac loss in the copper samplewith Eq. �1�. The heat load due to ac loss are plotted withvarying field at fixed frequency along with the theoreticalmodel for the eddy current loss11 in Eq. �2� are plotted, asshown in Fig. 10. The power loss due to eddy currents incopper is given by

Qeddy =2

3Ba

2�2

n· f� t

2�2

��t � W � l� . f� , �2�

where Qeddy is the loss due to eddy current, Ba is the mag-netic field amplitude, n is the resistivity, f is the frequency,t is the thickness of the sample, W is the width of the sample,and l is the length of the sample.

89.0

89.5

90.0

90.5

91.0

91.5

92.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

Time in minutes

Te

mp

era

ture

ris

ein

K

AC Field

ON

dT

SH

FIG. 7. Sample holder temperature profile when exposed to a peak field of0.23 T and rotated at 1800 rpm �30 Hz� without any sample mounted.

TABLE II. Samples used in the measurement of ac losses and calibrating the test rig.

Property of the sampleCopper

�Cu�YBCO-123 coatedconductor sample 1

Manufacturer Commercial SuperPowerCritical current Ic0 in amperes ¯ 98Total thickness of the conductor in mm 0.2 0.055Width of the sample in mm 4.42 4.0Length of the sample in mm 26.5 30.0Copper stabilizer �thickness in mm� ¯ ¯

Hastelloy substrate �thickness in mm� ¯ 0.05YBCO-123 �coating thickness in mm� ¯ 0.001Silver at the top of YBCO-123 �coating thickness in mm� ¯ 0.002Silver resistivity �� m� at 77 K ¯ 2.9�10−9

Hastelloy resistivity �� m� at 77 K ¯ 100�10−8

Copper resistivity �� m� at 77K 6.81�10−9¯

Qh = 0.0134 dTCu- 0.3629

0

5

10

15

20

25

30

35

40

45

0 500 1000 1500 2000 2500 3000 3500

dTCu - Temperature rise (mK)

Qh

-H

eat

Lo

ad

(hea

ter

po

wer)

mW

4 mm Copper

Linear (4 mm Copper)

FIG. 8. The calibration curve between temperature rise and fixed heat loadin copper sample at 80 K.

074702-5 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 7: Calorimetric method of ac loss measurement in a rotating magnetic field

In order to establish the accuracy of this measurementmethod, the measured data is then compared with the losscalculated for the eddy current. The values clearly follow therelationship

Qmeas = Fconver · Qeddy, �3�

where Qmeas is the loss as measured and Fconver is the linearconstant factor of �5.2 �in this case�.

Figure 10 is in good agreement between the measuredand calculated losses obtained with the factor, Fconver for cop-per giving confidence in the measurement method to reason-able accuracy after correction �within 10%�. This factorFconver is attributed to quasiadiabatic nature of the setup, po-sition of the temperature sensor with respect to the heatsource, temperature gradient along the sample, and mountingof the sample onto the sample holder.

Similarly the loss for sample 1 is also obtained and pre-sented in the form of plots for temperature rise along withthe calibration curves. The temperature rise in sample 1 inTable II for total ac loss is measured when exposed to vary-ing rotational speed at a fixed magnetic flux density in Fig.11. First, the loss measurement in sample 1 is completed andsubsequently sample 1 is heated to eliminate the HTS sectionof the coated conductor and defined as neutralized sample inorder to characterize the substrate of coated conductor andused for the loss measurement. A set of curves shown in Fig.

12 are also obtained for the temperature rise due to total acloss for the applied magnetic field at varying frequencies forthe sample 1-neutralized. Further calibration curve as shownin Fig. 13 is established with sample 1-neutralized mountedon the sample holder with an applied known heat load at theoperating temperature that is used to work out the heat loadfrom the subsequent temperature rise measurement.

The temperature rise in the HTS only is calculated bysubtracting the temperature rise in sample 1-neutralized fromthe temperature rise in sample 1. Table III shows sample 1temperature rise with frequency at 0.1 T. This temperaturerise is then transformed into ac loss in the sample 1 using Eq.�4� obtained form Fig. 13

Qh_Sample = 0.0203dTSample + 0.3982, �4�

where Qh_Sample is the heat load in sample and dTSample is thesample temperature rise.

B. A loss calculation with at 0.10 T is shown below

The temperature rise in the HTS is calculated asdTSample=T1−T2, where T1 and T2 are the temperature rise insample 1 and sample 1-neutralized from Table III and con-verted into a heat load contribution using Eq. �4�. WithdTSample=471 mK at 20 Hz and 0.10 T, the sample HTS heatload Qh_Sample=9.96 mW is obtained and followed by calcu-lating the actual losses in HTS. A brief summary of the tem-

dT = 2.0323 f2

+ 2.2343 f + 68.138

dT = 1.2501 f2

- 0.5259 f + 31.894

dT = 0.376 f2

+ 1.3037 f + 57.404

dT = 0.2733 f2

- 3.9964 f + 75.85

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35 40

f -Frequency (Hz)

dT

-T

em

pera

ture

ris

e(m

K)

Temp rise_0.23T

Temp rise_0.17T

Temp rise_0.10T

Temp rise_0.07T

Poly. (Temp rise_0.23T)

Poly. (Temp rise_0.17T)

Poly. (Temp rise_0.10T)

Poly. (Temp rise_0.07T)

FIG. 9. Variation in temperature rise against frequency with Bmax variedfrom 0.07 to 0.23 T in copper sample.

0

5

10

15

20

25

30

0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25

Magnetic Field (T)

Lo

ss

inm

W

Model 10hz Measured 10hz

Model 15hz Measured 15Hz

Model 20Hz Measured 20hz

Model 25hz Measured 25Hz

Model 30hz Measured 30hz

FIG. 10. ac loss in copper sample to establish the loss measurement tech-nique at 80 K

0

500

1000

1500

2000

2500

0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25

Applied magnetic field (T)

dT

-T

em

pe

ratu

reri

se

(mK

)

Temp rise 30Hz Temp rise 25Hz

Temp rise 20Hz Temp rise 15Hz

Temp rise 10Hz Poly. (Temp rise 30Hz)

Poly. (Temp rise 25Hz) Poly. (Temp rise 20Hz)

Poly. (Temp rise 15Hz) Poly. (Temp rise 10Hz)

FIG. 11. Temperature rise due to total ac loss in sample 1 when exposed torotating magnetic field at 84 K.

0

200

400

600

800

1000

1200

1400

1600

0.05 0.07 0.09 0.11 0.13 0.15 0.17 0.19 0.21 0.23 0.25

Applied magnetic field (T)

dT

-T

em

pera

ture

ris

e(m

K)

Temp rise 10Hz Temp rise 15Hz

Temp rise 20Hz Temp rise 25Hz

Temp rise 30Hz Poly. (Temp rise 30Hz)

Poly. (Temp rise 25Hz) Poly. (Temp rise 20Hz)

Poly. (Temp rise 15Hz) Poly. (Temp rise 10Hz)

FIG. 12. Temperature rise due to total ac loss in sample 1 neutralized whenexposed to rotating magnetic field at 84 K.

074702-6 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 8: Calorimetric method of ac loss measurement in a rotating magnetic field

perature rise measured in the sample when exposed to a ro-tating magnetic flux density of 0.1 T at an operatingtemperature of 84 K is tabulated below in Table III.

The actual measured ac loss �Qh-meas� is given by

Qh-meas = FCorrection � Qh_Sample, �5�

where FCorrection the correction factor that is introduced be-cause of the variation in operating temperature and heat re-moval. This factor is represented as FCorrection=TF ·HF; whereTF temperature factor and HF the heat sink coefficient.

Temperature factor, TF is given by TF

= �Toper-temp /TLN2�2= �84 /77�2=1.19, where Toper-temp the op-erating temperature and with TLN2 liquid nitrogen boilingtemperature. The heat sink coefficient �HF� is calculatedfrom the ratio of the slopes with sample in the sample holderand without sample in the sample holder. This is been pre-sented in Fig. 13 for sample 1-neutralized and sample holderonly as Qh=0.0203dT+0.3982 and Qh=0.0216dT+0.3626,respectively, with Qh the fixed known heat load applied dur-ing calibration and dT the temperature rise measured. HF iscalculated from above as HF= �0.0216 /0.0203�2=1.13. Thus,FCorrection=TF ·HF=1.19�1.13=1.35

In order to find the ac loss due to the HTS only, we areevaluating the differential temperature rise between thesample 1 and sample 1-neutralized. Therefore, Fconver is notapplicable to the metallic section in this situation because thetemperature rise is subtracted in order to get the contributionof HTS alone. Table III represents the effect on the HTSalone once the temperature rise in the metallic components iseliminated.

With Eq. �5�, the actual loss at 0.1 T with varying fre-quency is shown in Table IV. Measured ac loss �Qh-meas� iscompared with the analytical model13 is given by

Qh-ana = BaIc�B�W�X � Y� �6�

and

fh�Ba,Ic� =BaW�

�0Ic�B�, �7�

where Qh-ana is the analytical model for ac loss,

X = � 2

fh�Ba,Ic�ln cosh�fh�Ba,Ic��� − tanh�fh�Ba,Ic��, Y = f · l ,

Ba is the applied magnetic field, Ic�B� is the critical currentof the sample at the incident field Ba, W is the width of thesample, f is the frequency, and l is the length of the sample.

V. AC LOSS RESULTS

The ac loss obtained is a result of rotating magnetic fielddue to the flux penetration that periodically becomes incidentto the broad face of the sample in every quarter of the timeperiod. The loss measured in HTS at 84 K for the sample 1 iscompared with the analytical model13 as a function of ampli-tude of magnetic flux density and frequency is shown in Fig.14. The loss is in good agreement between the analyticalmodel �solid symbols� and the measurement �open symbols�within 10% at low magnetic field and about 15% at higherfield.

TABLE III. Sample 1 temperature rise with frequency at 0.1 T.

Freq�Hz�

Sample 1temp rise in

mK T1

Sample1-neutralized HTS

temp rise inmK T2

Temp rise withinthe HTS in mKdTSample=T1−T2

10 277 19 25815 425 64 36120 596 125 47125 791 208 58330 1009 307 702

Qh = 0.0203 dT + 0.3982

Qh = 0.0216 dT + 0.3626

0

2

4

6

8

10

12

14

16

18

20

0 100 200 300 400 500 600 700 800 900 1000

dT - Temperature rise (mK)

Qh

-H

eat

Lo

ad

(he

ate

rp

ow

er)

mW

Sample#1 Neutralised

Sample holder only

Linear (Sample#1 Neutralised)

Linear (Sample holder only)

FIG. 13. The calibration curve obtained to establish temperature rise in �a�the sample holder only with open symbols and �b� sample holder with thesample 1-neutralized with solid symbols against a fixed heat load.

TABLE IV. Heat load worked out due to temperature rise.

Frequency�Hz� 10 15 20 25 30

dTSample �mK� 258 361 471 583 702Qh_Sample �mW� 5.63 7.72 9.96 12.23 14.65Qh_meas �mW� 7.60 10.42 13.5 16.51 19.80

0

5

10

15

20

25

30

0.050 0.075 0.100 0.125 0.150 0.175 0.200 0.225 0.250

Applied magnetic field (T)

AC

los

s(m

W)

Measured AC loss in HTS_15Hz Measured AC loss in HTS_20Hz

Measured AC loss in HTS_25Hz Measured AC loss in HTS_30Hz

Brandt fit_30Hz Brandt fit_25Hz

Brandt fit_20Hz Brandt fit_15Hz

FIG. 14. Total ac loss in sample 1 HTS YBCO-123 coated conductor.

074702-7 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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Page 9: Calorimetric method of ac loss measurement in a rotating magnetic field

VI. CONCLUSION

The aim is to build a device which allows an easy andprecise loss measurement of superconducting high-Tc tapesin an external rotating magnetic field. Such an experimentalsetup for a calorimetric measurement technique should in-clude measurements that always address the problems ofproper calibration. This is expected to vary with everysample holder, sample mount and the location of temperaturesensor on the sample and/or sample holder. It is thereforeimportant to establish Fconver, which is unique for every ex-perimental setup and sample holder before the start of anymeasurements.

Measurements at �80 K for a rotating field were carriedout with all necessary temperature sensors and the calibrationheater potted within the sample holder. The sample mountingis easy where the sample is placed onto the rectangularsample holder face. For the calorimetric measurement thesample holder material is a compromise between the thermalconduction and eddy current heating and fixed to the copperheat exchanger that functions such as a conventional coldfinger cooled by liquid nitrogen.

This is a reasonably fast and sensitive method comparedto that of the boil-off method and could be easily extendedfor any transport current. This measurement technique is themeasure of temperature rise and is independent of the phaseangle of the transport current and incident magnet field. acloss data obtained in terms of the temperature rise in the HTSdo not require any preconceived model on magnetic fluxpenetration into the superconductor.

ACKNOWLEDGMENTS

The author would like to thank Mr. Neil Houghton andMr. Alistair Ross at Cambridge University design office andworkshop in building the measurement rig, SuperPower forproviding the sample and Oxford instruments for the supportin preparation of the experimental setup and facilitating thework. This work was supported by Oxford InstrumentsNanoScience, Abingdon �U.K.�.

1 M. N. Wilson, Superconducting Magnets �Clarendon, Oxford, 1983�.2 K. Kuroda, Cryogenics 26, 566 �1986�.3 J. A. Eikelboom, Cryogenics 31, 363 �1991�.4 S. P. Ashworth and M. Suenaga, Cryogenics 41, 77 �2001�.5 C. Schmidt, Cryogenics 41, 393 �2001�.6 C. Schmidt and E. Specht, Rev. Sci. Instrum. 61, 988 �1990�.7 K. V. Namjoshi and P. P. Biringer, IEEE Trans. Magn. 24, 2181 �1988�.8 P. K. Ghoshal, T. A. Coombs, R. Fair, and A. M. Campbell, IEEE Trans.Appl. Supercond. 17, 3199 �2007�.

9 J. Ogawa, M. Ciszek, and O. Tsukamoto, IEEE Trans. Appl. Supercond.13, 1735 �2003�.

10 M. Iwakuma, Y. Fukuda, M. Fukui, K. Kajikawa, and K. Funaki, PhysicaC 392–396, 1096 �2003�.

11 N. Amemiya, T. Nishioka, Z. Jiang, and K. Yasuda, Supercond. Sci. Tech-nol. 17, 485 �2004�.

12 D. N. Nguyen, P. V. P. S. S. Sastry, G. M. Zhang, D. C. Knoll, and J.Schwartz, IEEE Trans. Appl. Supercond. 15, 2831 �2005�.

13 E. H. Brandt, Phys. Rev. 54, 4246 �1996�.14 E. H. Brandt and M. Indenbom, Phys. Rev. B 48, 12893 �1993�.15 A. M. Campbell, IEEE Trans. Appl. Supercond. 5, 682 �1995�.16 S. P. Ashworth and M. Suenaga, Physica C 313, 175 �1999�.17 Z. Jiang and N. Amemiya, Supercond. Sci. Technol. 17, 295 �2004�.18 D. N. Nguyen, P. V. P. S. S. Sastry, D. C. Knoll, and J. Schwartz, Super-

cond. Sci. Technol. 19, 1010 �2006�.19 M. D. Sumption, S. Kawabata, and E. W. Collings, Physica C 466, 29

�2007�.20 C. Schmidt, Physica C 468, 978 �2008�.

074702-8 Ghoshal, Coombs, and Campbell Rev. Sci. Instrum. 81, 074702 �2010�

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