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High-performance pulsed-field coils for applications in solid state research
PHYSICA
Physica B 184 (1993) 513-521 North-Holland
High-performance pulsed-field coils for applications in solid state research F r i t z H e r l a c h a, L u c V a n B o c k s t a l a'b, G u i d o H e r e m a n s a a n d L i a n g Li a aLaboratorium voor Lage Temperaturen en Hoge-Veldenfysika, Katholieke Universiteit Leuven, Belgium bNational High Magnetic Field Laboratory, Tallahassee, FI, USA New types of pulsed magnets with optimised fibre reinforcement are developed in order to obtain higher fields in the 70 tesla range, with a pulse duration of more than 10 ms and with a bore of 10-25 mm. Design elements are discussed with a view to material properties, optimisation of the reinforcement, and the electrical and thermal behaviour. The practical use of the coils in experiments is discussed. Several coils have been made and are in use for solid-state experiments at low temperatures down to the 3He temperature range.
1. Introduction High-field magnets are a standard research tool in solid state physics. In particular, there has b e e n mutual stimulation between semiconductor physics and the d e v e l o p m e n t of magnet technology. In addition to zero-field resistivity, the basic e x p e r i m e n t in a magnetic field is the measurem e n t of the Hall effect to determine the n u m b e r of carriers and the overall mobility. If different carrier types are present, m o r e information can be gained by combining this with magnetoresistance measurements. Q u a n t u m p h e n o m e n a such as the S h u b n i k o v - D e H a a s oscillations are useful to sort out different contributions such as the carrier density, effective mass and mobility of each carrier type which can be extracted from the different c o m p o n e n t s in the Fourier spect r u m and their t e m p e r a t u r e dependence. Electron or hole masses can be obtained from the m e a s u r e m e n t of the Landau level separation, either with radiation excitation (cyclotron resonance), p h o n o n excitation (magneto-phonon resonance) or activation studies. T h e spectroscopic region of interest for radiaCorrespondence to: F. Herlach, Laboratorium voor Lage Temperaturen en Hoge-Veldenfysika,K.U. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium.
tion excitation is the far infrared (10-100 meV), which is the region in which most of the excitation energies of impurities are located. The farinfrared laser is the natural counterpart of strong magnetic fields and has b e c o m e a standard research tool in high-field laboratories [1]. A t a recent E u r o p e a n workshop on the future of research with high magnetic fields up to 100 T, m u c h optimism was expressed regarding research opportunities in science and spinoff to technology [2]. Besides the traditional high-field research topics of semiconductors and magnetism, there are interesting proposals regarding superconductivity, organic conductors, chaos in atomic physics and the C o t t o n - M o u t o n effect in chemistry and biology. It was r e c o m m e n d e d to set up a large E u r o p e a n magnet laboratory for this purpose. 1.1. Natural scales for the magnetic field
Technically, the strength of the magnetic field B is best represented by the magnetic stress B2/2/.%. For solid state experiments there are other appropriate scales in relation to the relevance of magnetic effects. A typical measure for the effectiveness of the magnetic field in many experiments is the n u m b e r N c of cyclotron orbits a charged particle can complete before it is
0921-4526/93/$06.00 ~ 1993- Elsevier Science Publishers B.V. All rights reserved
514
F. Herlach et al. / High-performance pulsed-field coils
scattered: 2~N~
(1)
= ,.o -,-~.
Note that there is slight difference between the scattering time for phase coherence % and the m o m e n t u m scattering time re: for the latter, which is related to the resistivity, the scattering angle is important. The number N L of occupied Landau levels is a measure for the degree of quantisation of the motion perpendicular to the magnetic field. Using the model for the free electron gas and the degeneracy of the Landau levels D = eB/h, this is dependent on the carrier density n and the dimensionality of the system: in2dim.:
h NL=-ne
in 3 dim.:
NL = ~
1 B'
(2)
(2'rr2n) 2/3
(3)
.
These equations for the filling of the Landau levels are related to the magnetic length l = which is a universal quantity and gives the average distance between electrons when the last Landau level is completely filled. According to the type of experiment, other appropriate scales for the magnetic field are the cyclotron energy and the Zeeman level splitting. For the characterisation of intrinsic semiconductors, magnetic fields up to 15 tesla are usually sufficient. In cases of strong confinement, in mesoscopic devices, in devices with dirty materials or with strong doping or alloying, the relaxa-
tion time is so short that very strong magnetic fields are required to obtain clear results. In table 1, values of o)c~ and of the number of occupied Landau levels are listed for materials recently studied at our laboratory [3-7].
1.2. Field strength and pulse duration Generating high magnetic fields is basically a materials problem: for the confinement of the Lorentz forces (or magnetic stress) exceptional strength is required for the conductor as well as for additional reinforcement. A good estimate is given by the relation between the peak stress o-, and the field in a coil with free-standing windings where a is the ratio of the outer and inner diameter: B = ~
(4)
V~(1 - 1/c~)
(an error slipped into this well-known equation in ref. [8]). For magnetic fields above 30 tesla, the power level and the associated cooling of resistive magnets are problems which are easily overcome by switching to pulsed operation. Pulsed-field coils are designed to adiabatically warm up during the pulse and the pulse duration is limited by the temperature rise the magnet can withstand. Both short pulse duration and small bore represent an initial hurdle for researchers intending to experiment in pulsed magnetic fields. The bore size has a strong effect on the peak field that can be achieved. For example, according to eq. (4), similar coils with 6 0 m m outer
Table 1 Data on the charge carriers in different materials; the effectiveness of a magnetic field of 50 tesla is calculated in terms of w~- and on the n u m b e r of filled Landau levels [3-6]. Material
Sample
Type
Carrier type
Mobility lm-'/V s]
Carrier concentration
w~"
NL
GaAs/AIGaAs GaAs/GaInAs/GaAIAs n + G a A s wire Sco 3oEro.70As
G420 H2735 200 nm CP304
Scl143Er~l57As
CP123
2D 2D 40 nm 5.7 nm 5.7 nm 20 nm 20 nm
e e e e, p e• p
187 3.2 0.16 0.056 0.0379 0.0908 0.0767
3.48E + 15 m 2 1.65E + 16 m 2 3.30E + 16 m -2 !.57E + 26 m 3 2.06E + 26 m 3 1.12E + 26 m 3 2.86E + 26 m 3
9350 160 8 2.8 1.9 4.5 3.8
0.29 1.36 2.73 14 17 11 21
F. Herlach et al. / High-performance pulsed-field coils
diameter would generate 70 T in a 10 mm bore but only 56 T in a 20 mm bore. Many researchers still have the misconception that a large bore is needed for their experiments. As examples to the contrary, there are outstanding ShubnikovDe Haas experiments at liquid-helium temperatures using lock-in detection in a coil with a 10 mm bore and a pulse duration of 5 ms [9] and the installation of a helium-3 system in a 12 mm bore [10]. The effects of the pulse duration can be summarized as follows. The required bandwidth for signal detection is much larger than for DC fields; this is generally solved by using broadband amplifiers and recorders but at the sacrifice of increased noise. Recently, fast lock-in systems have been developed which give a substantial reduction of noise and other spurious signals [9]. Stray capacitance in electrical measurements becomes a problem when the sample resistance is high and undergoing strong variations: the RCnetwork induces phase lag and distorts the voltage signal. This distortion can be corrected by numerical deconvolution techniques which completely restore the original signal [11]. When the sample resistance is low, samples are heated by eddy currents. The improvement on the measurement using longer pulse duration At goes as X / ~ for the amplifier noise, and as At for the distortion by stray capacitance and eddy-current heating. According to our experience with measurements in pulsed magnetic fields, forsemiconducting samples most problems become manageable when the pulse duration is increased to the range 10-50 ms. With these effects in mind, the existing pulsedfield facilities can be placed in three categories, reflecting different magnet-design principles. Short pulses. Pulses shorter than 1 ms do not require high conductivity and thus can be generated using strong steel as conductor. The strongest steels available have a tensile strength of over 2 GPa and allow the generation of fields up to 60 tesla in a magnet with two concentric independent coils; a three-coil magnet generating 80 tesla is under development [12]. Standard pulses. A longer pulse duration in the range 5 - 5 0 m s requires the use of good
515
electrical conductors mainly based on strengthened copper. Precooling with liquid nitrogen becomes effective because of the larger resistance ratio. A field of 68 tesla has been achieved using a CuNb microcomposite wire [13] and 55 tesla with a copper wire jacketed with stainless steel [14,15]. Many materials gain strength at liquid-nitrogen temperature, notably stainless steel which can be up to 50% stronger. The coils are impregnated with epoxy resin by either wet winding or vacuum impregnation. An interesting variation is impregnation with ice which makes coils easy to manufacture ]16,17]. Long or quasi-stationary pulses. The pulse duration can be further increased if very large coils are used. With 50 kg of copper and 1.2 MJ of energy, 4 6 T pulses have been generated at Toulouse with a rise time of 80ms and an exponential decay with a time constant of 800 ms [18]. Similarly, pulses up to 62 tesla, but half as long have been obtained using copper wire reinforced with Nb filaments. A different type of pulsed magnet is in use at Amsterdam. Power is taken from the mains to energize a large coil of hard copper which can generate pulses up to 40 tesla with a flat top of 80ms [19]. At Amsterdam, Los Alamos and Princeton, facilities with 6 0 T long-pulse magnets are under development. Special magnets. For experiments at high-energy accelerators, water-cooled pulsed magnets with a high repetition rate have been built, e.g., a 20 tesla pulsed magnet with a 2 s repetition rate [201.
2. Present state-of-the-art
The use of high-strength conductors combined with external reinforcement is the most straightforward way to generate fields up to 70 tesla [13] but these materials require special manufacturing techniques and are not easily available. The alternative is a combination of a good conductor and a strong reinforcement. The technique of cowinding a stainless-steel ribbon with soft copper wire was used at Leuven to make coils which reached fields up to 45 tesla
F. Herlach et al. / High-performance pulsed-field coils
516
in a 17 m m bore using a 70 kJ capacitor bank [21]; these coils were wet-wound with a filled epoxy. Although the field was modest by modern standards, these coils had the advantage of a rapid cooldown.
2.1. Development o f fibre-reinforced coils The tensile strength of fibre composites with S-glass ( O w e n s - C o r n i n g ) was experimentally determined to be 2.6 GPa. By adjusting the thickness of different fibre layers, the reinforcement can be optimised to distribute the stress evenly throughout the coil [22]. Results obtained up to now are listed in table 2. A special winding machine was built to put layers of fibre rovings with precisely controlled thickness between the layers of a conductor [8]. A special series of coils with a 24 m m bore was developed for the pulsedfield facility of the U.S. National High Magnetic Field Laboratory. The bore size was chosen to a c c o m o d a t e a dilution refrigerator [23].
2.2. Features o f fibre-reinforced coils x_CARBONFIBRE Fig. 1. Schematic of the cross section of a glass-fibre-reinforced coil. Note the arrangement of the contacts which is a critical design element.
A cross section of our coil design is shown in fig. 1. Generally these coils have filling factors in the range from 45% to 65%; the heat capacity is therefore low and the pulse duration is kept in the range 10-20 ms to limit the t e m p e r a t u r e rise. The mechanical performance of the glass fibre coils is dominated by the low modulus of elasticity of the fibre composite, resulting in an elongation up to 5%. A b o v e a certain field level, the conductor will undergo plastic deformation,
reaching its ultimate strength, and resulting in a prestress against the restoring force of the fibre composite. Hence, the geometry of the coil will remain stable once this level is reached, as indicated by the inductance (see fig. 2). By contrast to coils without fibre reinforcement which show
Table 2 Properties of pulsed-field coils developed at the K.U. Leuven. /3 is the ratio of the axial length to the bore diameter. 'Bekaert' refers to a cable of ultra strong pearlitic steel wires around a copper core; 'Glidcop' is dispersion-hardened copper with 0.15% A1203.
Coil name M2 MeL8 MeL12 MeL19 [23] MeL25 [23] MeL27
Bore [ram]
a
17 20 17 24 24 12
3.03 3.92 4.41 4.15 4.06 6.73
fl
4.35 4.35 3.87 4.08 4.00 5.50
[T]
At [ms]
Energy [kJ]
Filling factor
Wire type
36 58 55 58 62 69
16 13 13 30 30 8
70 325 255 320 480 300
72 48 50 47 49 43
ETP-Cu ETP-Cu Bekaert ETP-Cu Glidcop ETP-Cu
Bma x
F. Herlach et al. / High-performance pulsed-field coils
517
inductance 105
i
T
M2
1 O4
102
..................................
t
HJI6
[]
MoL8
X
MeL25
....................
.
.
.
.
.
.
.
.
.
.
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.
.
.
.
! /
99 .............. i~: ::.
. .
.
.
.
.
:~-
-
" F "
......................
97[
.
..... / /
..............
.
/
1 O1
98-
' ji
. . . . . . . . . . . . . . . . . .
. .
. .
. .
. . . . . . . . . . . . . . . . . . . . . . .
. .
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
i............. ........
................................
.~. C ~
96;
-~
95,
-
94 0
10
........................
i
i
i
i
20
30
40
50
magnetic
field
60
70
(tesla)
Fig. 2. Irreversible inductance change of coils: M2 is a small copper coil, HJ16 is made of copper wire jacketed with stainless steel [14], MeLT is made with pearlitic steel cable, MeL25 is made with Glidcop wire [23] and MeL27 was the last coil of the 12 mm bore series which gave a peak field of 69 T.
asymptotic deformation behaviour, there is no indication of impending coil failure when training fibre-reinforced coils to reach the highest magnetic field. These coils are expected to be subject to fatigue because of the strong plastic deformation in each pulse. However, it was found that the first coil used regularly in experiments lasted for more than 300 pulses at a few tesla below the limiting field. This coil gave warnings in several pulses preceding the failure, consisting of spikes in the pick-up signal which is proportional to the field derivative. These indicate that the failure is due to breaking of the conductor resulting in arcing. The coil failure itself was not very vio-
lent, presumably because the composite material has still its full strength and can thus contain the effects related to the failure.
2.3. The design of glass fibre coils In order to determine optimized configurations for fibre-reinforced coils, a code was developed to calculate the stresses in the midplane of the coil [24]. The code calculates the radial distribution of the stress components (radial, axial and hoop stress, t~r, o-z and o-t) assuming the coil consists of a series of nested cylinders. The stresses are obtained starting from the Lorentz forces which are calculated from the radial dis-
F. Herlach et al. / High-performance pulsed-field coils
518
tribution of the field B and current density j or,
O ror r Or -
8
streu (GPa) a: at 55 tesla
(5)
B jr
com, pollaah - -
I~lg.
--
radial
....
The axial stress orz in the midplane is due to the sum of all axial forces in the layer and is calculated from the difference in vector potential between the midplane and the end of the layer. The distribution of the stresses throughout the coil depends strongly on the stress-strain (e i o-i), behaviour of the materials in the individual layers. Several types of material behaviour are presently considered: an elastic material where the strain is
, _l 0
I lO
I 20
I
30
I 40
e,-
3
T
(6)
'
FtnFInnn,
lanai.
.......
IIIIIHHHHP%"d I-I I--I HI-tHHH I
,
°
r r - - O r z ) 2 "~- ( 0 " z - - O - t ) 2 -~- ( 0 " t - - O r r ) 2
2
60
~.,.~.... i, --
(or' - p ) '
work-hardening where the elastic limit is increased isotropically to a v o n Mises stress
OrM =
I 80
slreu (GPa)
l+v
P +
q
radius (ram) b: at 67 teMa
1-2v E
axial
VMINs
(7) -I
at a plastic deformation ~p, where
0
i l0
i
i
i
i
2O
80
4O
50
60
radius (ram)
1-2u
l+u
e P+T 3 ~p(OrM) + 2
orM
Fig. 3. Stress components in coils with even (a) and optimised (b) distribution of the internal reinforcement.
(or'-u) (or' - p ) '
(8)
and, finally, anisotropic materials with
e,= ~ j=1,2,3
6,j+v,J(o)_p). Ej
(9)
In these equations, p is the average stress, E is the modulus of elasticity and v is the Poisson ratio. The stress components thus obtained are then used to estimate the onset of material failure. For most metals, the well-known von Mises stress OrM provides a good failure criterion. This criterion was used to optimise the reinforcement by distributing the stresses evenly throughout the coil; fig. 3 shows the stresses in an optimised coil (MeL9) and, for comparison, the stresses in a coil with equally spaced layers (fig. 3(b)).
A f t e r each coil test, the model was refined and the material properties used for the modeling were re-calibrated. Surprisingly, the axial behaviour of the conductor and composite material turned out to be an important factor determining the ultimate field. This is evident from the decrease in inductance shortly before coil failure which indicates axial elongation. It was determined that the friction between the layers of conductor and composite is strong enough such that their axial compression is nearly the same. This axial compression, which is applied in a direction perpendicular to the fibres, is found to w e a k e n the composite. In the later coils, additional reinforcement in the axial direction was added to the composite to reduce axial compression and expansion. This was done by inserting 'carpets' of fibres oriented in the axial direction, and by adding flanges with strong axial clamping.
519
F. Herlach et al. / High-performance pulsed-field coils
The presently gained knowledge of the material properties of the composite allowed accurate prediction of the failure field of recently tested large bore coils, while the results for coils in the 1 2 m m bore series still remain below expectations. Even with this restriction, extrapolating f r o m the 62 T in a 24 m m bore it is evident that fields in the 75 T range can be achieved in a 12 m m bore in the near future. The matching of the mechanical properties of the conductor and of the fibre composite is a general feature in the design of these coils. In the case of S-glass fibre, which reaches its full strength at elongations of the order 5%, the conductor has to withstand the same (repetitive) deformation, which requires a very high ductility of the conductor. The advantage to be gained by using stronger conductor replacing the soft copper will therefore depend mainly on the ductility and fatigue behaviour of this wire, or on the feasibility of using a stiffer fibre composite with similar strength (e.g. carbon). For matching a magnet coil to the capacitor b a n k , precise knowledge of the inductance is required. Inductance calculations for nonuniform current densities are not straightforward. These calculations are important as the inductance reflects the energy stored in the coil, and from simple discharge calculations the efficiency of a capacitor discharge can be estimated. Using the average radius of the conductor windings and a weighted average of the length [24] gives a good approximation which agrees with meastired values. The m e a s u r e m e n t of the coil impedance is the most practical way of monitoring a magnet: the
resistive part indicates the average t e m p e r a t u r e of the coil while the residual deformation can be monitored by the inductance which depends on the average radius and on the axial length of the coil. Inductance m e a s u r e m e n t s of a magnet should be done at the lowest possible frequency (typically 100 Hz which is close to the operating frequency of the coils) because of the skin effect in the wires which increases the resistance and lowers the inductance. In the actual field pulse, the transient skin effect produces nonnegligible effects, notably a sharp peak in the field derivative at the beginning.
3. Outlook to future developments 3.1. O p t i o n s f o r 1 M J
Most of the large capacitor banks available for pulsed-field work [12,18,25-28] are of the order 0 . 5 - 1 . 0 M J . Table 3 lists the options available for generating pulsed magnetic fields in coils with a 2 0 r a m bore at 1 MJ. The required tensile strength of the conductor material was calculated using a simple finite element method [24] assuming that there is no external reinforcement. The effect of an external reinforcement has been estimated by assuming a reduction of the load on the conductor by 20%. The figures in table 3 can be scaled with energy using the following scaling laws: [linear dimension] - [energy] 1/3 ,
(10)
[pulse duration] - [energy] 2/3 .
(11)
Table 3 Obtaining high magnetic fields with a capacitor bank of 1 MJ: requirements for conductivity and strength of the conductor showing the influence on the pulse duration. The filling factor for the conductor in the cross section of the coil was taken to be 90%. B [T]
a
50 60 70 80
8 7 6.2 5.8
fl
8 7 6.2 5.8
At [ms]
Cond. %IACS
RR
[K]
220 90 37 14
190 200 300 300
90 70 50 40
6 4 3 2
Tfina I
Tensile strength Without reinforcement
With reinforcement
0.71 GPa 1.10 GPa 1.56 GPa 2.08 GPa
0.57 GPa 0.88 GPa 1.24 GPa 1.66 GPa
520
F. Herlach et al. / High-performance pulsed-field coils
These numbers were obtained using conservative calculations and show that the required material properties (i.e. tensile strength and conductivity) are obtainable with present technology. Comparing these results to those presently achieved still leaves much room for improvement at the existing pulsed-field facilities.
3.2. Options for 100 T On the basis of recent developments, it is taken for granted that a nondestructive 100T field can be obtained before the end of this century. This will require very substantial efforts in the development of advanced conductor materials and coil construction techniques. As an alternative to the proposal of building a huge magnet with a gigawatt-gigajoule power supply, we would propose a gradual approach, beginning with a modular capacitor bank of up to 20 MJ to energize compact coils. With this bank, electrical and thermal limitations allow the generation of 100 T in a bore up to 30 mm for a total pulse duration up to 100 ms. The advantages are evident: a series of compact coils can be made and tested to destruction; duplicates of these coils are immediately available for experimentation, long before the ultimate goal of 100T is achieved. With reasonable effort, a number of measuring stations can be set up for coil testing and experiments. These coils will have cooling times of the order of one hour between high-field pulses. U n d e r the same roof and sharing part of the diagnostics instrumentation, an advanced installation with a very fast capacitor discharge into destructive single-turn coils [29] can be set up. With an optimized circuit, it appears feasible to obtain 2 0 0 T in a 1 0 m m bore and more than 300 T in a smaller bore. Requests for a fiat-top pulse shape of longer duration will require the installation of a very large magnet with controlled high power. It is suggested to use a modular power supply with solid state devices for direct control of power obtained from a suitable node in the electricity distribution grid (generators are less flexible and require much maintenance and power for idling).
As an intermediate stage, a long-pulse outer coil can then be combined with a capacitor-driven inner coil to obtain a longer pulse duration with the possibility of modulating the field. As a general recommendation, for any given experiment, the energy transferred to the magnet ought to be kept to a minimum. This will shorten the turnaround time and minimize damage in case of coil failure. No matter how well it is engineered, a 100 T coil will operate in a range close to its ultimate tensile strength. In addition, small irregularities may lead to instabilities in the 100 T region.
4. Experiments Experiments carried out at our facility are described in several papers in these proceedings. This includes measurements on quantum wires [3], heterojunctions with high carrier concentration [4], semimetals buried in GaAs [5], heterojunctions at low temperatures [6] and organic superconductors [7].
Acknowledgements L.V.B. is a senior research assistant of the Belgian science foundation (NFWO). Part of this work was sponsored by the E C ( S C I E N C E programme) and by the Belgian F K F O and NFWO.
References [1] M. von Ortenberg, Physica B 177 (1992) 446. [2] Proceedings of the Workshop "Science in 100 tesla", Leuven, 15-17 May 1992 (K.U. Leuven, 1992). [3] M. van der Burgt, A. Geim et al., Physica B 184 (1993) 369. [4] M. van der Burgt, A. Van Esch et al., Physica B 184 (1993) 211. [5] R. Bogaerts et al., Physica B 184 (1993) 232. [6] R. Nicholas et al., Physica B 184 (1993) 268. [7] J. Singleton et al., Physica B 184 (1993) 470. [8] G. Heremans, F. Herlach, L. Van Bockstal, J. Witters and I. Lefever, IEEE Trans. Magn. 28 (1992) 790. [9] M. von Ortenberg, Physica B 184 (1993) 432.
F. Herlach et al. / High-performance pulsed-field coils
[10] M. Springford, private communication. [11] M. van der Burgt, P. Thoen, F. Herlach, F.M. Peeters, J.J. Harris and C.T. Foxon, Physica B 177 (1992) 409. [12] A. Yamagishi and M. Date, Physica B 155 (1989) 91. [13] S. Foner, Appl. Phys. Lett. 49 (1986) 982. [14] H. Jones, private communication. [15] H. Jones, F. Herlach, J.A. Lee, H.M. Withworth, A.G. Day, D.J. Jeffrey, D. Dew-Hughes and J. Sherrat, IEEE Trans. Magn. 24 (1988) 1055. [16] M. Motokawa, H. Nojiri and Y. Tokunaga, Physica B 155 (1989) 96. [17] S. Takeyama, H. Ochimizu, S. Sasaki and N. Miura, Meas. Sci. Technol. 3 (1992) 662. [18] S. Askenazy, J. Marquez and D. Ricart, Physica B 155 (1989) 55. [19] R. Gersdorf, F.A. Muller and L.W. Roeland, Rev. Sci. Instr. 36 (1965) 1100.
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[20] M. Motokawa, H. Nojiri, J. Ishihara and K. Ohnishi, Physica B 155 (1989) 39. [21] F. Herlach, G. De Vos and J. Witters, J. Phys. C1 45 (1984) 915. [22] L. Van Bockstal, G. Heremans and F. Herlach, Meas. Sci. Technol. 2 (1991) 1159. [23] Presented at the 6th international conference "Megagauss Magnetic Field Generation and Related Topics", Albuquerque, New Mexico, November 8-11, 1992. [24] L. Van Bockstal, Physica B 177 (1992) 31. [25] H. Jones, Physica B 155 (1989) 65. [26] R.G. Clark, private communication. [27] L.J. Campbell, private communication. [28] F. Herlach, L. Van Bockstal, M. van der Burgt and G. Heremans, Physica B 155 (1989) 61. [29] K. Nakao, F. Herlach, T. Goto, S. Takeyama, T. Sakakibara and N. Miura, J. Phys. E 18 (1985) 1018.
Physica B 184 (1993) 513-521 North-Holland
High-performance pulsed-field coils for applications in solid state research F r i t z H e r l a c h a, L u c V a n B o c k s t a l a'b, G u i d o H e r e m a n s a a n d L i a n g Li a aLaboratorium voor Lage Temperaturen en Hoge-Veldenfysika, Katholieke Universiteit Leuven, Belgium bNational High Magnetic Field Laboratory, Tallahassee, FI, USA New types of pulsed magnets with optimised fibre reinforcement are developed in order to obtain higher fields in the 70 tesla range, with a pulse duration of more than 10 ms and with a bore of 10-25 mm. Design elements are discussed with a view to material properties, optimisation of the reinforcement, and the electrical and thermal behaviour. The practical use of the coils in experiments is discussed. Several coils have been made and are in use for solid-state experiments at low temperatures down to the 3He temperature range.
1. Introduction High-field magnets are a standard research tool in solid state physics. In particular, there has b e e n mutual stimulation between semiconductor physics and the d e v e l o p m e n t of magnet technology. In addition to zero-field resistivity, the basic e x p e r i m e n t in a magnetic field is the measurem e n t of the Hall effect to determine the n u m b e r of carriers and the overall mobility. If different carrier types are present, m o r e information can be gained by combining this with magnetoresistance measurements. Q u a n t u m p h e n o m e n a such as the S h u b n i k o v - D e H a a s oscillations are useful to sort out different contributions such as the carrier density, effective mass and mobility of each carrier type which can be extracted from the different c o m p o n e n t s in the Fourier spect r u m and their t e m p e r a t u r e dependence. Electron or hole masses can be obtained from the m e a s u r e m e n t of the Landau level separation, either with radiation excitation (cyclotron resonance), p h o n o n excitation (magneto-phonon resonance) or activation studies. T h e spectroscopic region of interest for radiaCorrespondence to: F. Herlach, Laboratorium voor Lage Temperaturen en Hoge-Veldenfysika,K.U. Leuven, Celestijnenlaan 200 D, B-3001 Leuven, Belgium.
tion excitation is the far infrared (10-100 meV), which is the region in which most of the excitation energies of impurities are located. The farinfrared laser is the natural counterpart of strong magnetic fields and has b e c o m e a standard research tool in high-field laboratories [1]. A t a recent E u r o p e a n workshop on the future of research with high magnetic fields up to 100 T, m u c h optimism was expressed regarding research opportunities in science and spinoff to technology [2]. Besides the traditional high-field research topics of semiconductors and magnetism, there are interesting proposals regarding superconductivity, organic conductors, chaos in atomic physics and the C o t t o n - M o u t o n effect in chemistry and biology. It was r e c o m m e n d e d to set up a large E u r o p e a n magnet laboratory for this purpose. 1.1. Natural scales for the magnetic field
Technically, the strength of the magnetic field B is best represented by the magnetic stress B2/2/.%. For solid state experiments there are other appropriate scales in relation to the relevance of magnetic effects. A typical measure for the effectiveness of the magnetic field in many experiments is the n u m b e r N c of cyclotron orbits a charged particle can complete before it is
0921-4526/93/$06.00 ~ 1993- Elsevier Science Publishers B.V. All rights reserved
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F. Herlach et al. / High-performance pulsed-field coils
scattered: 2~N~
(1)
= ,.o -,-~.
Note that there is slight difference between the scattering time for phase coherence % and the m o m e n t u m scattering time re: for the latter, which is related to the resistivity, the scattering angle is important. The number N L of occupied Landau levels is a measure for the degree of quantisation of the motion perpendicular to the magnetic field. Using the model for the free electron gas and the degeneracy of the Landau levels D = eB/h, this is dependent on the carrier density n and the dimensionality of the system: in2dim.:
h NL=-ne
in 3 dim.:
NL = ~
1 B'
(2)
(2'rr2n) 2/3
(3)
.
These equations for the filling of the Landau levels are related to the magnetic length l = which is a universal quantity and gives the average distance between electrons when the last Landau level is completely filled. According to the type of experiment, other appropriate scales for the magnetic field are the cyclotron energy and the Zeeman level splitting. For the characterisation of intrinsic semiconductors, magnetic fields up to 15 tesla are usually sufficient. In cases of strong confinement, in mesoscopic devices, in devices with dirty materials or with strong doping or alloying, the relaxa-
tion time is so short that very strong magnetic fields are required to obtain clear results. In table 1, values of o)c~ and of the number of occupied Landau levels are listed for materials recently studied at our laboratory [3-7].
1.2. Field strength and pulse duration Generating high magnetic fields is basically a materials problem: for the confinement of the Lorentz forces (or magnetic stress) exceptional strength is required for the conductor as well as for additional reinforcement. A good estimate is given by the relation between the peak stress o-, and the field in a coil with free-standing windings where a is the ratio of the outer and inner diameter: B = ~
(4)
V~(1 - 1/c~)
(an error slipped into this well-known equation in ref. [8]). For magnetic fields above 30 tesla, the power level and the associated cooling of resistive magnets are problems which are easily overcome by switching to pulsed operation. Pulsed-field coils are designed to adiabatically warm up during the pulse and the pulse duration is limited by the temperature rise the magnet can withstand. Both short pulse duration and small bore represent an initial hurdle for researchers intending to experiment in pulsed magnetic fields. The bore size has a strong effect on the peak field that can be achieved. For example, according to eq. (4), similar coils with 6 0 m m outer
Table 1 Data on the charge carriers in different materials; the effectiveness of a magnetic field of 50 tesla is calculated in terms of w~- and on the n u m b e r of filled Landau levels [3-6]. Material
Sample
Type
Carrier type
Mobility lm-'/V s]
Carrier concentration
w~"
NL
GaAs/AIGaAs GaAs/GaInAs/GaAIAs n + G a A s wire Sco 3oEro.70As
G420 H2735 200 nm CP304
Scl143Er~l57As
CP123
2D 2D 40 nm 5.7 nm 5.7 nm 20 nm 20 nm
e e e e, p e• p
187 3.2 0.16 0.056 0.0379 0.0908 0.0767
3.48E + 15 m 2 1.65E + 16 m 2 3.30E + 16 m -2 !.57E + 26 m 3 2.06E + 26 m 3 1.12E + 26 m 3 2.86E + 26 m 3
9350 160 8 2.8 1.9 4.5 3.8
0.29 1.36 2.73 14 17 11 21
F. Herlach et al. / High-performance pulsed-field coils
diameter would generate 70 T in a 10 mm bore but only 56 T in a 20 mm bore. Many researchers still have the misconception that a large bore is needed for their experiments. As examples to the contrary, there are outstanding ShubnikovDe Haas experiments at liquid-helium temperatures using lock-in detection in a coil with a 10 mm bore and a pulse duration of 5 ms [9] and the installation of a helium-3 system in a 12 mm bore [10]. The effects of the pulse duration can be summarized as follows. The required bandwidth for signal detection is much larger than for DC fields; this is generally solved by using broadband amplifiers and recorders but at the sacrifice of increased noise. Recently, fast lock-in systems have been developed which give a substantial reduction of noise and other spurious signals [9]. Stray capacitance in electrical measurements becomes a problem when the sample resistance is high and undergoing strong variations: the RCnetwork induces phase lag and distorts the voltage signal. This distortion can be corrected by numerical deconvolution techniques which completely restore the original signal [11]. When the sample resistance is low, samples are heated by eddy currents. The improvement on the measurement using longer pulse duration At goes as X / ~ for the amplifier noise, and as At for the distortion by stray capacitance and eddy-current heating. According to our experience with measurements in pulsed magnetic fields, forsemiconducting samples most problems become manageable when the pulse duration is increased to the range 10-50 ms. With these effects in mind, the existing pulsedfield facilities can be placed in three categories, reflecting different magnet-design principles. Short pulses. Pulses shorter than 1 ms do not require high conductivity and thus can be generated using strong steel as conductor. The strongest steels available have a tensile strength of over 2 GPa and allow the generation of fields up to 60 tesla in a magnet with two concentric independent coils; a three-coil magnet generating 80 tesla is under development [12]. Standard pulses. A longer pulse duration in the range 5 - 5 0 m s requires the use of good
515
electrical conductors mainly based on strengthened copper. Precooling with liquid nitrogen becomes effective because of the larger resistance ratio. A field of 68 tesla has been achieved using a CuNb microcomposite wire [13] and 55 tesla with a copper wire jacketed with stainless steel [14,15]. Many materials gain strength at liquid-nitrogen temperature, notably stainless steel which can be up to 50% stronger. The coils are impregnated with epoxy resin by either wet winding or vacuum impregnation. An interesting variation is impregnation with ice which makes coils easy to manufacture ]16,17]. Long or quasi-stationary pulses. The pulse duration can be further increased if very large coils are used. With 50 kg of copper and 1.2 MJ of energy, 4 6 T pulses have been generated at Toulouse with a rise time of 80ms and an exponential decay with a time constant of 800 ms [18]. Similarly, pulses up to 62 tesla, but half as long have been obtained using copper wire reinforced with Nb filaments. A different type of pulsed magnet is in use at Amsterdam. Power is taken from the mains to energize a large coil of hard copper which can generate pulses up to 40 tesla with a flat top of 80ms [19]. At Amsterdam, Los Alamos and Princeton, facilities with 6 0 T long-pulse magnets are under development. Special magnets. For experiments at high-energy accelerators, water-cooled pulsed magnets with a high repetition rate have been built, e.g., a 20 tesla pulsed magnet with a 2 s repetition rate [201.
2. Present state-of-the-art
The use of high-strength conductors combined with external reinforcement is the most straightforward way to generate fields up to 70 tesla [13] but these materials require special manufacturing techniques and are not easily available. The alternative is a combination of a good conductor and a strong reinforcement. The technique of cowinding a stainless-steel ribbon with soft copper wire was used at Leuven to make coils which reached fields up to 45 tesla
F. Herlach et al. / High-performance pulsed-field coils
516
in a 17 m m bore using a 70 kJ capacitor bank [21]; these coils were wet-wound with a filled epoxy. Although the field was modest by modern standards, these coils had the advantage of a rapid cooldown.
2.1. Development o f fibre-reinforced coils The tensile strength of fibre composites with S-glass ( O w e n s - C o r n i n g ) was experimentally determined to be 2.6 GPa. By adjusting the thickness of different fibre layers, the reinforcement can be optimised to distribute the stress evenly throughout the coil [22]. Results obtained up to now are listed in table 2. A special winding machine was built to put layers of fibre rovings with precisely controlled thickness between the layers of a conductor [8]. A special series of coils with a 24 m m bore was developed for the pulsedfield facility of the U.S. National High Magnetic Field Laboratory. The bore size was chosen to a c c o m o d a t e a dilution refrigerator [23].
2.2. Features o f fibre-reinforced coils x_CARBONFIBRE Fig. 1. Schematic of the cross section of a glass-fibre-reinforced coil. Note the arrangement of the contacts which is a critical design element.
A cross section of our coil design is shown in fig. 1. Generally these coils have filling factors in the range from 45% to 65%; the heat capacity is therefore low and the pulse duration is kept in the range 10-20 ms to limit the t e m p e r a t u r e rise. The mechanical performance of the glass fibre coils is dominated by the low modulus of elasticity of the fibre composite, resulting in an elongation up to 5%. A b o v e a certain field level, the conductor will undergo plastic deformation,
reaching its ultimate strength, and resulting in a prestress against the restoring force of the fibre composite. Hence, the geometry of the coil will remain stable once this level is reached, as indicated by the inductance (see fig. 2). By contrast to coils without fibre reinforcement which show
Table 2 Properties of pulsed-field coils developed at the K.U. Leuven. /3 is the ratio of the axial length to the bore diameter. 'Bekaert' refers to a cable of ultra strong pearlitic steel wires around a copper core; 'Glidcop' is dispersion-hardened copper with 0.15% A1203.
Coil name M2 MeL8 MeL12 MeL19 [23] MeL25 [23] MeL27
Bore [ram]
a
17 20 17 24 24 12
3.03 3.92 4.41 4.15 4.06 6.73
fl
4.35 4.35 3.87 4.08 4.00 5.50
[T]
At [ms]
Energy [kJ]
Filling factor
Wire type
36 58 55 58 62 69
16 13 13 30 30 8
70 325 255 320 480 300
72 48 50 47 49 43
ETP-Cu ETP-Cu Bekaert ETP-Cu Glidcop ETP-Cu
Bma x
F. Herlach et al. / High-performance pulsed-field coils
517
inductance 105
i
T
M2
1 O4
102
..................................
t
HJI6
[]
MoL8
X
MeL25
....................
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
! /
99 .............. i~: ::.
. .
.
.
.
.
:~-
-
" F "
......................
97[
.
..... / /
..............
.
/
1 O1
98-
' ji
. . . . . . . . . . . . . . . . . .
. .
. .
. .
. . . . . . . . . . . . . . . . . . . . . . .
. .
. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
i............. ........
................................
.~. C ~
96;
-~
95,
-
94 0
10
........................
i
i
i
i
20
30
40
50
magnetic
field
60
70
(tesla)
Fig. 2. Irreversible inductance change of coils: M2 is a small copper coil, HJ16 is made of copper wire jacketed with stainless steel [14], MeLT is made with pearlitic steel cable, MeL25 is made with Glidcop wire [23] and MeL27 was the last coil of the 12 mm bore series which gave a peak field of 69 T.
asymptotic deformation behaviour, there is no indication of impending coil failure when training fibre-reinforced coils to reach the highest magnetic field. These coils are expected to be subject to fatigue because of the strong plastic deformation in each pulse. However, it was found that the first coil used regularly in experiments lasted for more than 300 pulses at a few tesla below the limiting field. This coil gave warnings in several pulses preceding the failure, consisting of spikes in the pick-up signal which is proportional to the field derivative. These indicate that the failure is due to breaking of the conductor resulting in arcing. The coil failure itself was not very vio-
lent, presumably because the composite material has still its full strength and can thus contain the effects related to the failure.
2.3. The design of glass fibre coils In order to determine optimized configurations for fibre-reinforced coils, a code was developed to calculate the stresses in the midplane of the coil [24]. The code calculates the radial distribution of the stress components (radial, axial and hoop stress, t~r, o-z and o-t) assuming the coil consists of a series of nested cylinders. The stresses are obtained starting from the Lorentz forces which are calculated from the radial dis-
F. Herlach et al. / High-performance pulsed-field coils
518
tribution of the field B and current density j or,
O ror r Or -
8
streu (GPa) a: at 55 tesla
(5)
B jr
com, pollaah - -
I~lg.
--
radial
....
The axial stress orz in the midplane is due to the sum of all axial forces in the layer and is calculated from the difference in vector potential between the midplane and the end of the layer. The distribution of the stresses throughout the coil depends strongly on the stress-strain (e i o-i), behaviour of the materials in the individual layers. Several types of material behaviour are presently considered: an elastic material where the strain is
, _l 0
I lO
I 20
I
30
I 40
e,-
3
T
(6)
'
FtnFInnn,
lanai.
.......
IIIIIHHHHP%"d I-I I--I HI-tHHH I
,
°
r r - - O r z ) 2 "~- ( 0 " z - - O - t ) 2 -~- ( 0 " t - - O r r ) 2
2
60
~.,.~.... i, --
(or' - p ) '
work-hardening where the elastic limit is increased isotropically to a v o n Mises stress
OrM =
I 80
slreu (GPa)
l+v
P +
q
radius (ram) b: at 67 teMa
1-2v E
axial
VMINs
(7) -I
at a plastic deformation ~p, where
0
i l0
i
i
i
i
2O
80
4O
50
60
radius (ram)
1-2u
l+u
e P+T 3 ~p(OrM) + 2
orM
Fig. 3. Stress components in coils with even (a) and optimised (b) distribution of the internal reinforcement.
(or'-u) (or' - p ) '
(8)
and, finally, anisotropic materials with
e,= ~ j=1,2,3
6,j+v,J(o)_p). Ej
(9)
In these equations, p is the average stress, E is the modulus of elasticity and v is the Poisson ratio. The stress components thus obtained are then used to estimate the onset of material failure. For most metals, the well-known von Mises stress OrM provides a good failure criterion. This criterion was used to optimise the reinforcement by distributing the stresses evenly throughout the coil; fig. 3 shows the stresses in an optimised coil (MeL9) and, for comparison, the stresses in a coil with equally spaced layers (fig. 3(b)).
A f t e r each coil test, the model was refined and the material properties used for the modeling were re-calibrated. Surprisingly, the axial behaviour of the conductor and composite material turned out to be an important factor determining the ultimate field. This is evident from the decrease in inductance shortly before coil failure which indicates axial elongation. It was determined that the friction between the layers of conductor and composite is strong enough such that their axial compression is nearly the same. This axial compression, which is applied in a direction perpendicular to the fibres, is found to w e a k e n the composite. In the later coils, additional reinforcement in the axial direction was added to the composite to reduce axial compression and expansion. This was done by inserting 'carpets' of fibres oriented in the axial direction, and by adding flanges with strong axial clamping.
519
F. Herlach et al. / High-performance pulsed-field coils
The presently gained knowledge of the material properties of the composite allowed accurate prediction of the failure field of recently tested large bore coils, while the results for coils in the 1 2 m m bore series still remain below expectations. Even with this restriction, extrapolating f r o m the 62 T in a 24 m m bore it is evident that fields in the 75 T range can be achieved in a 12 m m bore in the near future. The matching of the mechanical properties of the conductor and of the fibre composite is a general feature in the design of these coils. In the case of S-glass fibre, which reaches its full strength at elongations of the order 5%, the conductor has to withstand the same (repetitive) deformation, which requires a very high ductility of the conductor. The advantage to be gained by using stronger conductor replacing the soft copper will therefore depend mainly on the ductility and fatigue behaviour of this wire, or on the feasibility of using a stiffer fibre composite with similar strength (e.g. carbon). For matching a magnet coil to the capacitor b a n k , precise knowledge of the inductance is required. Inductance calculations for nonuniform current densities are not straightforward. These calculations are important as the inductance reflects the energy stored in the coil, and from simple discharge calculations the efficiency of a capacitor discharge can be estimated. Using the average radius of the conductor windings and a weighted average of the length [24] gives a good approximation which agrees with meastired values. The m e a s u r e m e n t of the coil impedance is the most practical way of monitoring a magnet: the
resistive part indicates the average t e m p e r a t u r e of the coil while the residual deformation can be monitored by the inductance which depends on the average radius and on the axial length of the coil. Inductance m e a s u r e m e n t s of a magnet should be done at the lowest possible frequency (typically 100 Hz which is close to the operating frequency of the coils) because of the skin effect in the wires which increases the resistance and lowers the inductance. In the actual field pulse, the transient skin effect produces nonnegligible effects, notably a sharp peak in the field derivative at the beginning.
3. Outlook to future developments 3.1. O p t i o n s f o r 1 M J
Most of the large capacitor banks available for pulsed-field work [12,18,25-28] are of the order 0 . 5 - 1 . 0 M J . Table 3 lists the options available for generating pulsed magnetic fields in coils with a 2 0 r a m bore at 1 MJ. The required tensile strength of the conductor material was calculated using a simple finite element method [24] assuming that there is no external reinforcement. The effect of an external reinforcement has been estimated by assuming a reduction of the load on the conductor by 20%. The figures in table 3 can be scaled with energy using the following scaling laws: [linear dimension] - [energy] 1/3 ,
(10)
[pulse duration] - [energy] 2/3 .
(11)
Table 3 Obtaining high magnetic fields with a capacitor bank of 1 MJ: requirements for conductivity and strength of the conductor showing the influence on the pulse duration. The filling factor for the conductor in the cross section of the coil was taken to be 90%. B [T]
a
50 60 70 80
8 7 6.2 5.8
fl
8 7 6.2 5.8
At [ms]
Cond. %IACS
RR
[K]
220 90 37 14
190 200 300 300
90 70 50 40
6 4 3 2
Tfina I
Tensile strength Without reinforcement
With reinforcement
0.71 GPa 1.10 GPa 1.56 GPa 2.08 GPa
0.57 GPa 0.88 GPa 1.24 GPa 1.66 GPa
520
F. Herlach et al. / High-performance pulsed-field coils
These numbers were obtained using conservative calculations and show that the required material properties (i.e. tensile strength and conductivity) are obtainable with present technology. Comparing these results to those presently achieved still leaves much room for improvement at the existing pulsed-field facilities.
3.2. Options for 100 T On the basis of recent developments, it is taken for granted that a nondestructive 100T field can be obtained before the end of this century. This will require very substantial efforts in the development of advanced conductor materials and coil construction techniques. As an alternative to the proposal of building a huge magnet with a gigawatt-gigajoule power supply, we would propose a gradual approach, beginning with a modular capacitor bank of up to 20 MJ to energize compact coils. With this bank, electrical and thermal limitations allow the generation of 100 T in a bore up to 30 mm for a total pulse duration up to 100 ms. The advantages are evident: a series of compact coils can be made and tested to destruction; duplicates of these coils are immediately available for experimentation, long before the ultimate goal of 100T is achieved. With reasonable effort, a number of measuring stations can be set up for coil testing and experiments. These coils will have cooling times of the order of one hour between high-field pulses. U n d e r the same roof and sharing part of the diagnostics instrumentation, an advanced installation with a very fast capacitor discharge into destructive single-turn coils [29] can be set up. With an optimized circuit, it appears feasible to obtain 2 0 0 T in a 1 0 m m bore and more than 300 T in a smaller bore. Requests for a fiat-top pulse shape of longer duration will require the installation of a very large magnet with controlled high power. It is suggested to use a modular power supply with solid state devices for direct control of power obtained from a suitable node in the electricity distribution grid (generators are less flexible and require much maintenance and power for idling).
As an intermediate stage, a long-pulse outer coil can then be combined with a capacitor-driven inner coil to obtain a longer pulse duration with the possibility of modulating the field. As a general recommendation, for any given experiment, the energy transferred to the magnet ought to be kept to a minimum. This will shorten the turnaround time and minimize damage in case of coil failure. No matter how well it is engineered, a 100 T coil will operate in a range close to its ultimate tensile strength. In addition, small irregularities may lead to instabilities in the 100 T region.
4. Experiments Experiments carried out at our facility are described in several papers in these proceedings. This includes measurements on quantum wires [3], heterojunctions with high carrier concentration [4], semimetals buried in GaAs [5], heterojunctions at low temperatures [6] and organic superconductors [7].
Acknowledgements L.V.B. is a senior research assistant of the Belgian science foundation (NFWO). Part of this work was sponsored by the E C ( S C I E N C E programme) and by the Belgian F K F O and NFWO.
References [1] M. von Ortenberg, Physica B 177 (1992) 446. [2] Proceedings of the Workshop "Science in 100 tesla", Leuven, 15-17 May 1992 (K.U. Leuven, 1992). [3] M. van der Burgt, A. Geim et al., Physica B 184 (1993) 369. [4] M. van der Burgt, A. Van Esch et al., Physica B 184 (1993) 211. [5] R. Bogaerts et al., Physica B 184 (1993) 232. [6] R. Nicholas et al., Physica B 184 (1993) 268. [7] J. Singleton et al., Physica B 184 (1993) 470. [8] G. Heremans, F. Herlach, L. Van Bockstal, J. Witters and I. Lefever, IEEE Trans. Magn. 28 (1992) 790. [9] M. von Ortenberg, Physica B 184 (1993) 432.
F. Herlach et al. / High-performance pulsed-field coils
[10] M. Springford, private communication. [11] M. van der Burgt, P. Thoen, F. Herlach, F.M. Peeters, J.J. Harris and C.T. Foxon, Physica B 177 (1992) 409. [12] A. Yamagishi and M. Date, Physica B 155 (1989) 91. [13] S. Foner, Appl. Phys. Lett. 49 (1986) 982. [14] H. Jones, private communication. [15] H. Jones, F. Herlach, J.A. Lee, H.M. Withworth, A.G. Day, D.J. Jeffrey, D. Dew-Hughes and J. Sherrat, IEEE Trans. Magn. 24 (1988) 1055. [16] M. Motokawa, H. Nojiri and Y. Tokunaga, Physica B 155 (1989) 96. [17] S. Takeyama, H. Ochimizu, S. Sasaki and N. Miura, Meas. Sci. Technol. 3 (1992) 662. [18] S. Askenazy, J. Marquez and D. Ricart, Physica B 155 (1989) 55. [19] R. Gersdorf, F.A. Muller and L.W. Roeland, Rev. Sci. Instr. 36 (1965) 1100.
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[20] M. Motokawa, H. Nojiri, J. Ishihara and K. Ohnishi, Physica B 155 (1989) 39. [21] F. Herlach, G. De Vos and J. Witters, J. Phys. C1 45 (1984) 915. [22] L. Van Bockstal, G. Heremans and F. Herlach, Meas. Sci. Technol. 2 (1991) 1159. [23] Presented at the 6th international conference "Megagauss Magnetic Field Generation and Related Topics", Albuquerque, New Mexico, November 8-11, 1992. [24] L. Van Bockstal, Physica B 177 (1992) 31. [25] H. Jones, Physica B 155 (1989) 65. [26] R.G. Clark, private communication. [27] L.J. Campbell, private communication. [28] F. Herlach, L. Van Bockstal, M. van der Burgt and G. Heremans, Physica B 155 (1989) 61. [29] K. Nakao, F. Herlach, T. Goto, S. Takeyama, T. Sakakibara and N. Miura, J. Phys. E 18 (1985) 1018.