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Surface electrical losses of superconductors in low frequency fields
S u r f a c e E l e c t r i c a l Losses of S u p e r c o n d u c t o r s in Low F r e q u e n c y Fields T. A. Buchhold and P. J. Illolenda
Ge,ze,'alElectricCompany,
York
Schenectady, N e w
Received 28 June 1962
ACCORDING to the theory of superconductors, a.c. losses should only be significant for frequencies in and above the megacycle range. However, work done at the authors' laboratory, on superconducting niobium coils and on rotating spheres carried by superconducting bearings, revealed losses for frequencies as low as a few hundred cycles at field strengths considerably below the critical fields. Such losses appear to be associated with a slight field penetration (beyond the penetration depth) of the superconductor and flux-trapping, which may be caused by surface roughness, small voids close to the surface, or a filamentary structure of the materialJ Losses as low as 10 -8 W/cm 2 of surface area were measured for small cylindrical test specimens of niobium and lead. The method selected for the studies is based upon the calorimeter technique, which takes advantage of the small specific heat of metals at low temperatures and of the ability of the carbon resistance thermometer to measure temperature changes at liquid helium temperatures with accuracies better than one millidegree. A detailed theoretical treatment of the nature of these losses is in progress and will be published later.
strength is determined from the geometry and observations on the voltage induced in the 20 turn flux coil wound on the test chamber. Temperature changes are determined with an imbedded carbon resistance thermometer bonded to the sample by a small amount of epoxy resin. The opaque paper shield surrounding the device protects the specimen from incident radiant energy (nylon is transparent to infra-red radiation). Thermally isolated specimens of about 5 mm diameter and 25 mm length may be subjected to fields up to about 1,500 oersteds at frequencies to about 1,000 c/s, the limitation being set by breakdown of the superconducting field coil. The 1,000 f2 calibrated carbon resistance
//
\\
%
Hanganir
Copper heat sinks Upper indiumvacuum seal
Experimental
technique
To measure the power losses in superconductors subjected to low frequency external magnetic fields, portions of an existing test device were modified to the configuration shown schematically in Figure 1. The superconductor (such as niobium, lead, niobium-zirconium, etc.), prepared in rod form, rests on thin nylon disks within a test chamber which may be evacuated or filled with helium gas as a heat transfer medium. Longitudinal a.c., d.c., or superimposed fields are applied to the central portion of the thermally isolated specimens by the niobium field coil encircling the test chamber. The niobium centrepiece for this coil is designed with a rather large length-to-width ratio in order to achieve a high uniform flux density in the test region without subjecting the wire of the driving coil itself to the same field strengths. Assuming that the field is uniform in the test region and that the penetration into the superconducting specimen is small, the applied a.c. field 344
Copper cold trap Lower
Nylon test chamber
VQcuur
Carbon resistance thermometer
Niobium field shaper
Flux-meo coil Test sO(
Niobium field coil Inner dewar Black paper
Nylon su
shield
Nylon disks K3
Figure 1. Power loss measurement apparatus CRYOGENICS
- DECEMBER
1962
F o r higher losses the temperature rise, A0, which is about 50 mdeg, is too rapid for highly accurate determination of the temperature-time relations. Improvement of the measurement technique may make it possible to extend this calorimeter method to the 10 -4 W / c m 2 level. For higher losses, the use of direct electrical methods is preferable.
10-5 ," (
E
.c.+o.c.o L
)'/ //
,"" , _
_ ./""
/
_
/
Results
g
?--
-
/
,/
,"
A.C. ~,,,r /
4
,"
/
/
I
/2
-
290 c/s /
/
The power losses per square ceniimetre of exposed surface determined for a 30.2 m m x 5.14 m m diameter sample cut from a 16 kg electron-beam-melted niobium ingot (better than 99.8 per cent purity) are shown in the log-log plot of Figure 2 as a function of field strength at frequencies of 70 and 290 c/s. Since the data follow approximately a straight line, the losses are of tile form :
I
I
.C. only I 70 c/s i
...(2)
P = oH" i 2
10-~00
4
A.C. field
: 6
~
8
1.000
(oersteds)
Figure 2. Power loss, u.c. only and a.c. with superimposedd.c. fiehls,
/or niobium
thermometer, using a constant 2 FA current and operated in a precision potentiometer circuit, provides sufficient sensitivity to determine temperature changes as small as 0.5 mdeg. in the vicinity of the helium bath temperature, which was selected as 4.0 ° K so that an electronic control could be used t o ' m a i n t a i n a constant reference temperature. A laboratory diffusion p u m p is used to provide a vacuum level within the test chamber which is sufficient to achieve thermal isolation equivalent to a thermal time constant, T, of about 6 min for the specimens. To obtain the specific power loss, P, the specimen is exposed for t sec to the a.c. field, H, and the temperature rise, A0, is determined by the carbon resistor. Then P-
Cp m ( A S ) At
(W/cm2)
...
(1)
where for both frequencies n is about 4.4. For various niobium samples, the field strength exponent, 17, has been found to vary from about 3.5 to about 5.0. Figure 2 clearly shows that losses covering several decades occur in superconductors, even at frequencies as low as 70 c/s and at fields considerably below the critical field strength. There are indications that these losses are not only dependent upon the bulk properties of the superconductor but that they are also very dependent upon such surface properties as smoothness, residual stresses, and minute quantities of entrapped gases. Studies to determine the relative importance of these parameters to the observed losses are now in progress. Figure 3 shows the dependence on frequency for two constant applied a.c. fields of H = 600 and H = 300 oersteds. The dependence is linear to beyond 1,500 c/s for the 300 oersted case, but the 600 oersted curve shows nonlinearity above 500 c/s. It is of importance in deterlnining
50xi0-(
SOOxI(Y8
600 oersteds
1=
E
4oo N
4c
where cp = superconducting specific heat m A A0 t
= = = =
(J/g.deg. K) t which are specimen mass (g) known exposed surface area (cm z) temperature rise (°K) 1 time of exposure to the external field I which are (sec) measured
o
300 oersteds
300 o
~ 2c
2oo ~. o
_q
~ 1(3
lOO 8.
u
Equation (1) may be used directly if the time, t, is small compared with the thermal time constant, T. However, small corrections depending on t i T are usually required. The apparatus described has been successfully used for loss measurements in the order of 10 - s to 10 -s W/cm 2. CRYOGENICS
• DECEMBER
1962
"0
& 200
400
600
1,000
800
Frequency
•
I
1,200
400
(c/s)
Figure 3. Power loss versus fi'equency and fieM strength for niobh~m
345
the nature of the losses to note that the slopes of these curves are finite and non-zero at the origin. If a differentiation is made between hysteresis losses (wherein the losses for constant field are proportional to frequency) and eddy current losses (wherein the losses are proportional to the second power of frequency) as is commonly done in consideration of magnetic materials such as iron, the superconductor losses appear to result from a hysteresis phenomenon. This result is surprising and indicates that any eddy current phenomena are of little importance at
~EE I0-6
---.
.
.
.
- - ~
.
- -; y
%,o /
l 10- - - Niobium ingot - / ~o --location numbery t;t~
2
Lead specimen ----4
I0 I00
2
4
A.C. field strength ~
6
8 000 (oersteds)
Figure 4. Power loss versas field strength at 290 c/s for lead and two niobium samples from same #~got
these low frequencies for the various samples tested. The losses are believed to depend strongly on the surface properties of the materials and are believed to arise from the alternate trapping and reversing of small amounts of flux during each cycle of the external field. During such reversals, small joule losses are produced. As a matter of interest, the power losses for superimposed a.c. and d.c. fields have been determined and are shown by the dotted lines in Figure 2. For these data, constant maximum fields of 925, 700, and 550 oersteds were maintained by adding appropriate d.c. currents to the a.c. exciting current of the field coil; the dotted curves show excellent agreement at their intersections with the solid curve based upon 290 c/s only. The data of Figure 2 are seen to be repeatable to within about 10 per cent. Re-examination of niobium specimens after periods of exposure to atmosphere as long as 6 weeks gave the same results. Pigure 4 shows a comparison between the power loss variation with 290 c/s fields for the above sample and for a similar sample cut from another location in the same niobium ingot. The specimen shows nearly the same 346
power exponent, n, for the field strength dependence, but the power losses are 15 times lower. A suitable explanation for this extreme difference is not yet available. F o r comparison, Figure 4 also shows the power loss data obtained on a zone-refined lead sample which was annealed and chemically polished. The field dependence exponent for this case is 2.6; but, for different samples, factors from 2.5 to 7-0 have been observed. Considering that lead is a soft superconductor, its relatively high loss is surprising. The losses for lead have been found to be less repeatable than for niobium over prolonged periods, and they are subject to considerable change with surface condition and penetration techniques. The level of power loss as well as the shape of the frequency dependence curves are affected by these conditions. Both positive and negative departures from the linear dependence on frequency have been observed, but the initial slopes of the frequency plots for lead also indicate that the losses arise from a hysteresis phenomenon. Another phenomenon found to affect the power losses in lead is shown by Figure 5, in which the losses determined at 4.0 ° K for a given a.c. test condition are plotted against the external d.c. field existing while a high purity lead sample was cooled to the 4.0°K test temperature. The decreased losses obtained when external fields, including the Earth's field, were cancelled are found to be most pronounced in the lower-power-loss lead specimens. This effect has not been observed in the niobium specimens for such small fields. However, care must be used to avoid any transients which exceed the critical field of the specimen or that of the field coil, because subsequent measurements will show considerably increased power losses.
140x10-8 E
~--Y~IO0 ~' 60 g.
-I
i
/
I
0 +I +2 +3 External magnetic field at transition temperature(Earth's fi~Id units)
Figure 5. Power loss at 450 oersteds, 290 c/s for high purity lead against external d.c. magnetic field durb~g cooling to 4"O°K (Helium bath temperature 4.02°K). Circled points are actual measurements; squares assume symmetry. External fields supplied by 75 cm diameter Helmholz coils
CRYOGENICS • DECEMBER 1962
Conclusions
A calorimeter method has been developed to measure extremely small surface losses for superconductors such as niobium and lead in the frequency range up to 1,000 c/s. It was found that these losses are observable for applied fields considerably below the critical fields and that they have the character of hysteresis losses. It is believed that in the future the field of loss measure-
EDITORIAL
ments of superconductors will give important hints toward the metallurgical preparation of materials which, at fields below the critical field of the bulk material, will exhibit a.c. losses which are more and more negligible in engineering designs. REFERENCE 1. MENDELSSOHN,K. Proc.
roy. Soc.
A152, 34 (1935)
NOTE
CRYOGENICS offers its congratulations to Academician Lev Davidovich Landau on being awarded the 1962 Nobel Prize for Physics. Academician Landau was born at Baku on 22 January 1908, studied in Leningrad, and worked in 1929 and 1930 with Niels Bohr in Copenhagen, visiting on that occasion England, Holland, and Switzerland. He then became Professor at Kharkov. Since 1937 he has been Director of the Theoretical Section of the Institute for Physical Problems of the U.S.S.R. Academy of Sciences and Professor at Moscow University. The Nohel Prize was awarded for Professor Landau's work on liquid helium and other researches on condensed Matter. Besides these, he is responsible for various other advances in low temperature physics, such as work on superconductivity, the extension of the de Haas-van Alphen effect, and antiferromagnetism. He is a Foreign Member of The Royal Society and the U.S. Academy of Sciences, and of the Dutch and Danish Academies of Sciences. We couple these congratulations with our best wishes for a speedy recovery from the grave injuries which he received in a motor accident earlier this year.
CRYOGENICS
• DECEMBER
1962
347
Ge,ze,'alElectricCompany,
York
Schenectady, N e w
Received 28 June 1962
ACCORDING to the theory of superconductors, a.c. losses should only be significant for frequencies in and above the megacycle range. However, work done at the authors' laboratory, on superconducting niobium coils and on rotating spheres carried by superconducting bearings, revealed losses for frequencies as low as a few hundred cycles at field strengths considerably below the critical fields. Such losses appear to be associated with a slight field penetration (beyond the penetration depth) of the superconductor and flux-trapping, which may be caused by surface roughness, small voids close to the surface, or a filamentary structure of the materialJ Losses as low as 10 -8 W/cm 2 of surface area were measured for small cylindrical test specimens of niobium and lead. The method selected for the studies is based upon the calorimeter technique, which takes advantage of the small specific heat of metals at low temperatures and of the ability of the carbon resistance thermometer to measure temperature changes at liquid helium temperatures with accuracies better than one millidegree. A detailed theoretical treatment of the nature of these losses is in progress and will be published later.
strength is determined from the geometry and observations on the voltage induced in the 20 turn flux coil wound on the test chamber. Temperature changes are determined with an imbedded carbon resistance thermometer bonded to the sample by a small amount of epoxy resin. The opaque paper shield surrounding the device protects the specimen from incident radiant energy (nylon is transparent to infra-red radiation). Thermally isolated specimens of about 5 mm diameter and 25 mm length may be subjected to fields up to about 1,500 oersteds at frequencies to about 1,000 c/s, the limitation being set by breakdown of the superconducting field coil. The 1,000 f2 calibrated carbon resistance
//
\\
%
Hanganir
Copper heat sinks Upper indiumvacuum seal
Experimental
technique
To measure the power losses in superconductors subjected to low frequency external magnetic fields, portions of an existing test device were modified to the configuration shown schematically in Figure 1. The superconductor (such as niobium, lead, niobium-zirconium, etc.), prepared in rod form, rests on thin nylon disks within a test chamber which may be evacuated or filled with helium gas as a heat transfer medium. Longitudinal a.c., d.c., or superimposed fields are applied to the central portion of the thermally isolated specimens by the niobium field coil encircling the test chamber. The niobium centrepiece for this coil is designed with a rather large length-to-width ratio in order to achieve a high uniform flux density in the test region without subjecting the wire of the driving coil itself to the same field strengths. Assuming that the field is uniform in the test region and that the penetration into the superconducting specimen is small, the applied a.c. field 344
Copper cold trap Lower
Nylon test chamber
VQcuur
Carbon resistance thermometer
Niobium field shaper
Flux-meo coil Test sO(
Niobium field coil Inner dewar Black paper
Nylon su
shield
Nylon disks K3
Figure 1. Power loss measurement apparatus CRYOGENICS
- DECEMBER
1962
F o r higher losses the temperature rise, A0, which is about 50 mdeg, is too rapid for highly accurate determination of the temperature-time relations. Improvement of the measurement technique may make it possible to extend this calorimeter method to the 10 -4 W / c m 2 level. For higher losses, the use of direct electrical methods is preferable.
10-5 ," (
E
.c.+o.c.o L
)'/ //
,"" , _
_ ./""
/
_
/
Results
g
?--
-
/
,/
,"
A.C. ~,,,r /
4
,"
/
/
I
/2
-
290 c/s /
/
The power losses per square ceniimetre of exposed surface determined for a 30.2 m m x 5.14 m m diameter sample cut from a 16 kg electron-beam-melted niobium ingot (better than 99.8 per cent purity) are shown in the log-log plot of Figure 2 as a function of field strength at frequencies of 70 and 290 c/s. Since the data follow approximately a straight line, the losses are of tile form :
I
I
.C. only I 70 c/s i
...(2)
P = oH" i 2
10-~00
4
A.C. field
: 6
~
8
1.000
(oersteds)
Figure 2. Power loss, u.c. only and a.c. with superimposedd.c. fiehls,
/or niobium
thermometer, using a constant 2 FA current and operated in a precision potentiometer circuit, provides sufficient sensitivity to determine temperature changes as small as 0.5 mdeg. in the vicinity of the helium bath temperature, which was selected as 4.0 ° K so that an electronic control could be used t o ' m a i n t a i n a constant reference temperature. A laboratory diffusion p u m p is used to provide a vacuum level within the test chamber which is sufficient to achieve thermal isolation equivalent to a thermal time constant, T, of about 6 min for the specimens. To obtain the specific power loss, P, the specimen is exposed for t sec to the a.c. field, H, and the temperature rise, A0, is determined by the carbon resistor. Then P-
Cp m ( A S ) At
(W/cm2)
...
(1)
where for both frequencies n is about 4.4. For various niobium samples, the field strength exponent, 17, has been found to vary from about 3.5 to about 5.0. Figure 2 clearly shows that losses covering several decades occur in superconductors, even at frequencies as low as 70 c/s and at fields considerably below the critical field strength. There are indications that these losses are not only dependent upon the bulk properties of the superconductor but that they are also very dependent upon such surface properties as smoothness, residual stresses, and minute quantities of entrapped gases. Studies to determine the relative importance of these parameters to the observed losses are now in progress. Figure 3 shows the dependence on frequency for two constant applied a.c. fields of H = 600 and H = 300 oersteds. The dependence is linear to beyond 1,500 c/s for the 300 oersted case, but the 600 oersted curve shows nonlinearity above 500 c/s. It is of importance in deterlnining
50xi0-(
SOOxI(Y8
600 oersteds
1=
E
4oo N
4c
where cp = superconducting specific heat m A A0 t
= = = =
(J/g.deg. K) t which are specimen mass (g) known exposed surface area (cm z) temperature rise (°K) 1 time of exposure to the external field I which are (sec) measured
o
300 oersteds
300 o
~ 2c
2oo ~. o
_q
~ 1(3
lOO 8.
u
Equation (1) may be used directly if the time, t, is small compared with the thermal time constant, T. However, small corrections depending on t i T are usually required. The apparatus described has been successfully used for loss measurements in the order of 10 - s to 10 -s W/cm 2. CRYOGENICS
• DECEMBER
1962
"0
& 200
400
600
1,000
800
Frequency
•
I
1,200
400
(c/s)
Figure 3. Power loss versus fi'equency and fieM strength for niobh~m
345
the nature of the losses to note that the slopes of these curves are finite and non-zero at the origin. If a differentiation is made between hysteresis losses (wherein the losses for constant field are proportional to frequency) and eddy current losses (wherein the losses are proportional to the second power of frequency) as is commonly done in consideration of magnetic materials such as iron, the superconductor losses appear to result from a hysteresis phenomenon. This result is surprising and indicates that any eddy current phenomena are of little importance at
~EE I0-6
---.
.
.
.
- - ~
.
- -; y
%,o /
l 10- - - Niobium ingot - / ~o --location numbery t;t~
2
Lead specimen ----4
I0 I00
2
4
A.C. field strength ~
6
8 000 (oersteds)
Figure 4. Power loss versas field strength at 290 c/s for lead and two niobium samples from same #~got
these low frequencies for the various samples tested. The losses are believed to depend strongly on the surface properties of the materials and are believed to arise from the alternate trapping and reversing of small amounts of flux during each cycle of the external field. During such reversals, small joule losses are produced. As a matter of interest, the power losses for superimposed a.c. and d.c. fields have been determined and are shown by the dotted lines in Figure 2. For these data, constant maximum fields of 925, 700, and 550 oersteds were maintained by adding appropriate d.c. currents to the a.c. exciting current of the field coil; the dotted curves show excellent agreement at their intersections with the solid curve based upon 290 c/s only. The data of Figure 2 are seen to be repeatable to within about 10 per cent. Re-examination of niobium specimens after periods of exposure to atmosphere as long as 6 weeks gave the same results. Pigure 4 shows a comparison between the power loss variation with 290 c/s fields for the above sample and for a similar sample cut from another location in the same niobium ingot. The specimen shows nearly the same 346
power exponent, n, for the field strength dependence, but the power losses are 15 times lower. A suitable explanation for this extreme difference is not yet available. F o r comparison, Figure 4 also shows the power loss data obtained on a zone-refined lead sample which was annealed and chemically polished. The field dependence exponent for this case is 2.6; but, for different samples, factors from 2.5 to 7-0 have been observed. Considering that lead is a soft superconductor, its relatively high loss is surprising. The losses for lead have been found to be less repeatable than for niobium over prolonged periods, and they are subject to considerable change with surface condition and penetration techniques. The level of power loss as well as the shape of the frequency dependence curves are affected by these conditions. Both positive and negative departures from the linear dependence on frequency have been observed, but the initial slopes of the frequency plots for lead also indicate that the losses arise from a hysteresis phenomenon. Another phenomenon found to affect the power losses in lead is shown by Figure 5, in which the losses determined at 4.0 ° K for a given a.c. test condition are plotted against the external d.c. field existing while a high purity lead sample was cooled to the 4.0°K test temperature. The decreased losses obtained when external fields, including the Earth's field, were cancelled are found to be most pronounced in the lower-power-loss lead specimens. This effect has not been observed in the niobium specimens for such small fields. However, care must be used to avoid any transients which exceed the critical field of the specimen or that of the field coil, because subsequent measurements will show considerably increased power losses.
140x10-8 E
~--Y~IO0 ~' 60 g.
-I
i
/
I
0 +I +2 +3 External magnetic field at transition temperature(Earth's fi~Id units)
Figure 5. Power loss at 450 oersteds, 290 c/s for high purity lead against external d.c. magnetic field durb~g cooling to 4"O°K (Helium bath temperature 4.02°K). Circled points are actual measurements; squares assume symmetry. External fields supplied by 75 cm diameter Helmholz coils
CRYOGENICS • DECEMBER 1962
Conclusions
A calorimeter method has been developed to measure extremely small surface losses for superconductors such as niobium and lead in the frequency range up to 1,000 c/s. It was found that these losses are observable for applied fields considerably below the critical fields and that they have the character of hysteresis losses. It is believed that in the future the field of loss measure-
EDITORIAL
ments of superconductors will give important hints toward the metallurgical preparation of materials which, at fields below the critical field of the bulk material, will exhibit a.c. losses which are more and more negligible in engineering designs. REFERENCE 1. MENDELSSOHN,K. Proc.
roy. Soc.
A152, 34 (1935)
NOTE
CRYOGENICS offers its congratulations to Academician Lev Davidovich Landau on being awarded the 1962 Nobel Prize for Physics. Academician Landau was born at Baku on 22 January 1908, studied in Leningrad, and worked in 1929 and 1930 with Niels Bohr in Copenhagen, visiting on that occasion England, Holland, and Switzerland. He then became Professor at Kharkov. Since 1937 he has been Director of the Theoretical Section of the Institute for Physical Problems of the U.S.S.R. Academy of Sciences and Professor at Moscow University. The Nohel Prize was awarded for Professor Landau's work on liquid helium and other researches on condensed Matter. Besides these, he is responsible for various other advances in low temperature physics, such as work on superconductivity, the extension of the de Haas-van Alphen effect, and antiferromagnetism. He is a Foreign Member of The Royal Society and the U.S. Academy of Sciences, and of the Dutch and Danish Academies of Sciences. We couple these congratulations with our best wishes for a speedy recovery from the grave injuries which he received in a motor accident earlier this year.
CRYOGENICS
• DECEMBER
1962
347