- Email: [email protected]
Guidelines for LTS magnet design based on transient stability
Cryogenics 46 (2006) 354–361 www.elsevier.com/locate/cryogenics
Guidelines for LTS magnet design based on transient stability Kazutaka Seo b
a,*
, Masao Morita
b
a National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan Mitsubishi Electric Corporation, 8-1-1 Tsukaguchi-honmachi, Amagasaki, Hyogo 661-8661, Japan
Received 13 December 2004; received in revised form 14 October 2005; accepted 22 November 2005
Abstract Stabilities of low critical temperature superconducting (LTS) magnets and their designs are studied and discussed. There are two contradictory necessities; those are low cost and high performance, in the other words, high magnetic field and large current density. Especially, the maximum magnetic fields of the latest high performance Nb3Sn magnets are around 20 T. Mentioned necessities result in the small stability margins. Needless to say, the superconducting magnet must produce its nominal field reliably. Therefore, maintaining adequate stability margin, the magnet design to draw out the high potential of the superconductor is required. The transient stability of the superconducting magnet is determined by the relationship between mechanical disturbance energy and stability margin. The minimum quench energy (MQE) is one of the index of stability margin and it is defined as the minimum energy to trigger quenching of a superconductor. MQE should be beyond any possible disturbance energy during the operation. It is difficult to identify the mechanical disturbance energy quantitatively. On the contrary, MQE had been evaluated precisely by means of our developed resistive carbon paste heater (CPH). At the same time, we can predict MQE by numerical simulations. Because the magnet comes to quench if the mechanical disturbance exceeds the MQE, the disturbance energies are suspected to be equivalent to MQEs during the magnet-training. When we achieved somewhat larger MQE, we may exclude numbers of training quenches. In this paper, we discuss the guidelines of LTS magnet design from the standpoint of MQE. We represent some case studies for various superconducting magnets and/or some different winding methods. 2005 Elsevier Ltd. All rights reserved. Keywords: Superconducting magnet; MQE; Stability; Magnet design
1. Introduction 1.1. Advantages of LTS coils and subjects to be solved Low Tc superconducting (LTS) magnets are widely installed due to following advantages. One is the lower cost of the LTS conductor than the latest HTS conductors. Another advantage is large n-value, which is necessary for persistent current magnets (e.g., MRI and NMR) to sustain stable persistent current. Small filament diameter is also advantage for the accurate magnetic field applications. We can predict the effective filament diameters and
*
Corresponding author. E-mail address: [email protected] (K. Seo).
0011-2275/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2005.11.020
the magnetizations of LTS conductors more accurately than HTS. At present, the superconducting magnet business market is MRI and NMR production basically. Because of these advantages, LTS magnets lead the superconducting business. Furthermore, the recent progresses of compact refrigerators promote the applications of LTS magnets. To obtain these advantages, we should design LTS magnets properly and avoid any training quench. Quench means the drastic transition from superconducting state to normal state. and it results in the huge liquid helium consumption and/or waste of the time. To prevent a magnet from quench, it is important to identifying the minimum quench energy (MQE) in the LTS magnet. Hence, MQE is defined as the minimum energy to make a superconductor quench [1–5].
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361
LTS coil is energized at liquid helium temperature (4.2 K). Heat capacities of materials become around 103 times smaller than room temperature (RT) and even minute thermal energy of disturbance introduces large temperature rise. On the contrary, current sharing temperature margins of LTS magnets are around 1–2 K. From this fact, we can estimate that MQE might be small amount. We do not have to discuss about MQE for HTS magnets which are generally operated at 20 K. The stabilization technique is preventing LTS magnet from quench and it is classified into two technologies. One is suppressing the initiation of normal transition, in the other word, mechanical disturbances. The other is improving the stability margin and making conductors hard to come to quench. In this paper, we discuss about the second issue intensively. 1.2. Mechanical disturbance As mentioned in following sections, MQEs in LTS magnets are evaluated as about several hundred microJoules. When the energies of mechanical disturbances, e.g., wire motions and/or epoxy cracks, exceed MQE, the magnet quenches. In the superconducting magnet, large electromagnetic force is induced during energization and it causes wire motions, cracks and debondings of molding epoxy resin. Here, we estimate the dissipated mechanical disturbance energies. The energy dissipation due to an epoxy crack is release of reserved elastic energy in it. If we assume elastic modulus (E) is 30 GPa and strain () is 5000 l, the elastic energy density is estimated as 1/2E2 = 400 lJ/mm3 and this energy is released after the breakage of epoxy resin. On the other hand, the energy due to wire motion is estimated as follows. We assume the friction factor is 0.2 and the wire, which is compressed with the stress of 10 MPa, slips 0.1 mm in transverse direction. The heat dissipation per 1 mm2 is calculated as 10 · 0.2 · 0.0001 = 200 lJ/mm2. The disturbance energy is roughly estimated to about 0.1–1 mJ. Superconducting magnets are forced quench with this small amount of energy. Such kind of disturbances happens not continuously but pulsively and the durations are reported several hundred
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microseconds [6]. These discrete disturbances are observed in acoustic emission (AE) signals and the differential voltage (VB) signals between balanced taps in coil tests [7]. It is difficult to observe the mechanical disturbances in the winding directly. However, lots of studies had been performed to comprehend the behavior of mechanical disturbances in the superconducting windings. The mechanical disturbances can be classified into two groups. One is the internal disturbance that occurs inside of the winding as mentioned above. The other is the external disturbance, which is caused by friction on the mandrel and/or coil-case or debondings from them. Recently, this sort of disturbance is solved by following technologies, those are (1) slipping mechanism of winding with thermal barrier on its inner surface, (2) mandrel-less coil [8] and (3) dummy winding. For the thermal barrier, this is not a special component but merely a ground insulation. When we design the slipping section on the out surface of ground insulation, it becomes a intrinsic thermal barrier to the superconducting winding. The number of quench due to external disturbances had been suppressed by the techniques based on these latest configuration recently. 2. MQE in LTS coil 2.1. MQE MQE is the index of transient stability. We explain MQE with quench behaviors of superconducting wire shown in Fig. 1. In Fig. 1(a), the tap voltage increased and varnished after 2 ms. This means the superconducting wire recovers superconducting state. On the contrary, in Fig. 1(b), it shows quenching. MQE is defied the minimum energy introducing quench. Therefore, the energy in Fig. 1(b) is almost MQE for this wire. When MQE is larger than the mechanical disturbance energy, the wire does not quench. In Fig. 1(b), normal state region is stagnating for 1 ms. The size of this normal state region is called minimum propagating zone (MPZ) [9]. When the normal region larger than MPZ is introduced, the wire quenches. Hence, MQE is the energy which introduces the normal zone comparable to MPZ.
Fig. 1. Voltage traces during recovery and quench. NbTi superconducting wire is with 1.1 mm · 2.2 mm in cross-section and copper ratio: 1.0 [4].
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Superconducting wire has a stabilizer such as pure copper and its thermal diffusivity is very large. With conventional heating technique, it was difficult to introduce a small disturbance with short pulse durations comparing with thermal diffusion through the stabilizer. Fig. 2 shows the photograph of our carbon paste heater (CPH) is shown [4]. The thickness of resistive carbon layer is about 20 lm and the thermal diffusivity of the heater itself is small enough to demonstrate an actual mechanical disturbance. Utilizing this heater, we evaluated the MQE that showed good agreement with theoretical predictions. Fig. 3 shows the dependence of pulse width upon MQE. Due to the thermal diffusion, the quench energy is over estimated, when the pulse width is large. Utilizing conventional heating wire, quench energy is much more over estimated.
104 Heating wire (tpulse=1 ms) CPH (tpulse=200 µ s)
5T
103
MQE ( µ J)
356
7T
102 Open : 5 T Close : 7 T Our numerical simulation Dresner's formula
101 0
500
1000
Current (A)
Fig. 4. Transport current dependence on MQE. The NbTi wire is 2.2 mm · 1.1 mm in cross-section, Cu/SC ratio 1, RRR: 141 [4]. Dresner’s formula [1] shows good agreement with nonlinear numerical simulations. The closed marks show the data of 7 T and the open marks show 5 T, respectively.
Fig. 2. Photograph of the cross-sectional view of carbon paste heater (CPH) [4]. Thin resistive carbon paste layer realizes a test disturbance with short pulse length. Pulsive current flows from (+) terminal to the superconducting wire through carbon paste resistive layer and generates ohmic heat. Epoxy putty is the thermal insulation.
7 6
Constantan Heating Wire φ 0.1 mm Carbon Paste Heater A Carbon Paste Heater B (Pressed)
MQE (mJ)
5 4 3 2 1 Numerically Calculated
0
10-1
100
101
102
Pulse Width (ms) Fig. 3. The dependence of pulse width upon MQE. The wire is NbTi, 2.2 mm · 1.1 mm in cross-section and Cu/SC ratio: 1.0, RRR: 141 [4]. For CPH-B, the carbon layer was pressed mechanically to improve thermal contact.
Fig. 4 shows the dependence of transport current upon MQE. If the current becomes large, MQE degrades remarkably. Solid line represents the result of numerical simulations. Dashed line is obtained by Dresner’s formula mentioned later. The theoretical formula of MQE was reported by Dresner as Eq. (1) [1]. In this formula, the parameters are as follows: cC, volume specific heat of the wire; A, cross-section of the wire; ACu, cross-section of the stabilizer; k, equivalent thermal conductivity of the wire; Tc, critical temperature; TCS, current sharing temperature; Tb, bath temperature; q, equivalent resistivity of the wire; Iop, operation current; Ic, critical current and i, Iop/Ic. pffiffiffi 7=2 cCA k ðT c T b Þ3=2 1 I op =I c T CS pffiffiffiffiffiffiffiffiffiffiffiffi MQE ¼ p ð1Þ pffiffiffi I c =ACu q Tb I op =I c We considered temperature dependences of mentioned thermal properties. Those are obtained assuming the temperature as 0.5 · (TCS + Tb). Magnetic resistivity and Wiedemann–Franz law [10] which is the relationship between resistance and thermal conductivity are implemented. Eq. (1) is time independent. Therefore, this equation is applicable only to the case within a short pulse duration that can ignore the thermal diffusion effect along the wire. In fact, observed MQE shows remarkable pulse width dependence as shown in Fig. 3. In Fig. 4, our numerical results show good agreement with Dresner’s formula and the effectiveness of this formula is proved for the first time by our experiment. The thermal diffusivity of the heater itself had been the problem to be solved. Our CPH has several ten micrometers in thickness and can provide to estimate the actual mechani-
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 Table 1 Specifications of superconducting test coil Coil Inner diameter Outer diameter Height Material of mandrel
(mm) (mm) (mm)
Thickness of mandrel Turn number Magnetic field at I = 140 A
250 274 350 Stainless steel 10 10,350 4.2
(mm) (T)
Conductor Material Diameter Copper ratio Critical current at 5 T
NbTi 0.6 1.5 350
(mm) (A)
cal disturbances. We start to discuses about MQE in the superconducting magnet mainly using Dresner’s formula. 2.2. MQE in LTS test coil First, MQE in our test coil is discussed to comprehend the overview of stability of a superconducting coil. Table 1 shows the specification of our NbTi test magnet. Fig. 5 represents the calculated results of the degradation of MQE and TCS margin during energization. Comparing with TCS margin, MQE decreases drastically. When mechanical disturbance energy exceeds MQE, the
Strain (µ ε)
3000
magnet runs to quench. From this figure, magnet design based on MQE is more important than that based on TCS margin. Of course, it is still difficult to identify the mechanical disturbance energy triggering the quench. However, when we identify the MQE at the quench, the mechanical disturbance energy triggering that quench can be suspected, on the contrary. 2.3. Comparison between magnets Fig. 6 represents the calculated MQEs in various kinds of superconducting magnets. Transverse axis represents the current density of the wire. Here, for the accelerator, single-strand stability (SSS) is assumed. SSS is a phenomenon that the single strand quench in the Rutherford type cable determines the quench of the whole magnet. Based on this phenomenon, MQE of the single strand (not the cable) determines the quench behavior of the magnet. The trend of the larger magnets is smaller current densities and very stable (Fig. 6, upper-left). On the contrary, the small magnets have larger current densities and smaller MQEs (Fig. 6, lower-right). Small magnets are designed to accomplish the compactness and higher field. Of course, the electromagnetic force and the stored energy of the large magnet is quite large, therefore such magnet is designed based on cryo-stable principle [9]. 3. MQE and coil design parameters It is almost impossible to restrain the mechanical disturbance event into zero. However, fortunately, if MQE is
Hoop strain (mid-plane)
2000
357
1000 0 -1000
Axial strain (mid-plane)
-2000
IT ER LHD
103
MAGLEV Test Coil
(Out of range)
800
6
MRI High-B NMR
102
MQE (µ J)
5 600
µ 3
MQE ( µ J)
Tcs-Tb (K)
4 Tcs-Tb
400
Lab. Magnet
101
MQE
2
Accelerator
200
100
AE (Arb.)
1
0
200
400
Current density 0
0
0
50
100
150
Current (A) Fig. 5. Degradation of MQE and TCS margin during energization. Strains are obtained by the experiment. MQE is calculated from Dresner’s formula. Comparing with TCS margin, MQE decreases drastically. Strains, in the other word, stresses are proportional to square of the current. Mechanical disturbances occur during energization. If this energy exceeds MQE, the magnet quenches. In this figure, instead of mechanical disturbances, typical AE signals are shown for descriptive purposes.
600
800
(A/mm2
Cond)
Fig. 6. MQE vs. current density of the conductor. Closed circles indicate MRI magnets [11,12], open circles: MAGLEV test coil [13], closed rectangles: accelerators [14,15], open rectangles and upside-down triangle: laboratory magnets (rectangles correspond to multi-sectional 15 T magnet discussed later [16]), open triangle: high field NMR (most inner section) [17] and closed triangles: test magnet represented in Table 1. One of the closed triangles corresponds to the initial quench and the other is the achieved maximum current density. Only current densities are represented for ITER and LHD helical coil [18] and their quench energies are much larger than others.
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always larger than any possible mechanical disturbances, the magnet does not quench. The effort to suppress the coil deformation in order to decrease mechanical disturbance had been performed a lot. Here, we discuss how to increase and/or optimize MQE during magnet design. There are lots of parameters of the wire, such as superconducting materials, dimensions, copper ratio, sensitivities of stabilizers and so on. Winding configuration also have some parameters, those are cooling conditions, steel bind reinforcement etc. For instance, for the medium size magnet, choosing stabilization philosophy is annoying issue. We should select the relevant stability theory from cryo-stable and transient stability based on MQE. We discuss about the influence of stabilizer, cooling channel, reinforcement and conductor dimension upon MQE sequentially. 3.1. Stabilizer and MQE If we increase copper stabilizer, the volume of superconducting material decreases and critical current also decreases. On the contrary, without any copper, superconducting material has poor thermal conductivity and it results in small MQE. It had been reported that there is an optimum copper ratio for certain superconducting wire [3]. The optimum copper ratio can be derived conveniently from Dresner’s formula. The resistance of stabilizer is also important. Instead of the resistivity of the metal at cryogenic temperature, residual resistivity ratio (RRR) is represented in the specification table of the superconducting wire. RRR is the ratio of resistances at 273 and 4.2 K. Wiedemann–Franz law [10] denotes that resistivity is inversely proportional to thermal conductivity. Applying this relation to Dresner’s formula, MQE is proportional to RRR. We must take into account of the magnetic resistivity of copper under the high magnetic field applications because it increases under the high field. In case of Nb3Sn wire, sometimes diffusion barrier is broken and stabilizer is contaminated. It results in higher resistance and degrades MQE. Internal reinforcement is popular for the high field applications, but it causes the decrease of the volume of pure copper stabilizer. The Cu alloy with high strength also has large resistivity. In general, persistent current switches are wound with CuNi matrix wires, therefore MQE in PCS is miserably small. 3.2. Cooling channel and MQE Fig. 7 shows the transport current dependence upon MQE. The sample has LHe cooling channels; the pitch length is 35 mm and width is 23 mm. Experimental results had been only obtained at 7 T. Comparing with adiabatic condition, MQEs are almost identical. This means that there is no merit of pool boiling LHe cooling on the stability. Numerical results also represent similar tendency. MQEs at 3 T are calculated for both LHe cooled and adiabatic models. Around 750 A, MQE is improved by
Fig. 7. Influence of LHe cooling channel on MQE. The wire dimensions are 1.3 mm · 2.6 mm and Cu ratio: 1.5. The pitch length and the width of the LHe cooling channel are 35 and 23 mm, respectively. The solid lines show the numerically calculated results for the wire with cooling channel and dashed lines for adiabatic case. When the transport current is large, MQEs are identical between adiabatic and LHe cooling conditions. The wire dimension becomes small when the cooling channel is located. Thicker wire can be adopted in the case of adiabatic design, when the cross-section of the winding and number of turn are identical. Assuming the gap of cooling channel 0.4 mm, the wire dimensions are is (2.6 + 0.4) · (1.3 + 0.4)/(2.6 · 1.3) = 1.51 times larger than the wire with cooling channel. In this case, MQE becomes large as shown with thick dashed line which is larger than the case with cooling channels.
LHe cooling. Here, we tried to do some correction on this data. Cooling channels decrease the conductor fraction in the winding. If the spacer with 0.4 mm in thickness is assumed, the conductor size becomes 1/1.5 smaller than the original. In the other word, the packed wound wire can be enlarged up to 1.5 times larger than cooled wire, and the current density becomes 1/1.5. Also the cross-section of windings becomes 1.5 times larger. According to these discussions, the data can be redrawn with thick dashed line in Fig. 7. The magnet design should be performed after considering these effects. Whether we adopt a cooling channel or not must be determined after identifying these MQE curves as represented in Fig. 7. 3.3. Reinforcement and MQE (multi-sectional 15 T magnet) MQEs in the 15 T multi-sectional magnet [16], which was developed and installed at Tohoku University, are calculated. Table 2 shows the specifications of the magnet. Using these parameters, the influence of reinforcement on MQE is discussed too. Fig. 8 shows the distribution of the calculated MQE in the cross-sections of the windings. The smallest MQEs in coil-1, coil-3 and coil-5 are almost identical, therefore the design is assumed to be almost reasonable. These sections are designed to be comparable stabilities. The quantity of MQE is several ten microJoules and it is as small as that of typical accelerator magnet as shown in Fig. 6.
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Table 2 Specifications of multi-sectional 15 T superconducting magnet [16] Coil Coil number Inner diameter (mm) Outer diameter (mm) Coil height (mm) Maximum field (T) Number of turn Operating current (A)
1 74 110 229 15.3 3562 90
2 124 160 229 13.8 3564 90
3 175 207 280 12.4 3872 157
4 226 278 280 9.9 6292 157
5 306 395 366 6.3 16,512 157
Conductor Material Diameter (mm) Critical current (A)
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
NbTi 1.0 820 at 5 T, 4.2 K
Fig. 8. The distribution of magnetic field and MQE in the 15 T multi-sectional magnet. MQEs in the winding cross-section distribute remarkably. Here, horizontal axis is a log scale.
For high field NMRs and MRI magnets with large bores, coils need to be reinforced by steel bind. Adapting the steel bind, the fraction of superconductor decreases and current density increases. Another reinforcement method is using internal reinforced wire, which contains copper alloy in itself. The copper alloy has larger resistance than pure copper stabilizer and MQE must be decreased.
We analyzed the influence of internal reinforced wires and binds on the coil-1 and the coil-3 of the 15 T magnets. For the reinforced wire, half of copper stabilizer is assumed to be replaced with copper alloy from the original model. For the steel bind, 20% of winding cross-section is occupied by the steel bind and the size of the conductor is assumed to be reduced to 80% from the original.
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K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 100 1st Section (B=13.5 T)
3rd Section (B=12.4 T)
MQE (µ J)
80 60
Original Internal reinforced (ACu×0.5)
Orginal
40 20
Internal reinforced (ACu×0.5) Bind (A×0.8)
Bind (A×0.8)
0
We have discussed about the influence of parameters of superconducting conductors and windings on MQEs. Here, mechanical disturbance energy is still difficult to be identified; therefore magnet design should be performed based on the experiences, those are databases shown in Fig. 6. This kind of databases must be established at individual superconducting magnet manufacturers to decrease the number of premature quench.
Conductor Size
Fig. 9. Influence of steel bind and internal reinforcement on MQE. MQEs are calculated from Dresner’s formula. Original indicates MQE of the 15 T multi-sectional magnet.
The calculated results are represented in Fig. 9. MQE is very sensitive to the current density, and steel bind results in remarkable decrease of MQE. In the case of the reinforcement, the external reinforcement is better than internal one. The reason is that the external reinforcement with resistive alloy, e.g., CuNb, stainless steel and so on, plays a role of thermal barrier to improve MQE [19]. 3.4. LHe free magnet (nominal current and MQE) In the case of LHe free magnets, the small operating current is required. The small operating current permits utilizing small power leads, power supplies and PCSs. Especially, the small heat load can be achieved with thin power leads. However, it is trivial that the small size wire results in poor MQE. In the case of the identical current density in the winding, MQE is proportional to the conductor size. We assumed that the thermal diffusivity of the stabilizer is large and the cross-sectional temperature distribution is uniform in spite of the larger cross-section. Fig. 10 represents the calculated results of MQEs. MQE is inversely proportional to the size of the conductor. Thick conductor brings following advantages too, those are small inductance and easy to be wound without conductor breakages. The small inductance brings benefit on quench protection.
Fig. 10. MQE vs. wire size derived from Dresner’s formula. NbTi superconducting wire is with 1.1 mm · 2.2 mm of cross-section and copper ratio: 1.0. Magnetic field and current are 5 T and 500 A, respectively, in the default case.
4. Conclusion The stability of the superconducting magnet is discussed applying MQE theory. To select the proper wire parameters and winding constitutions are important to achieve good stability. Mechanical disturbance energy still remains to be identified precisely. However, based on the past database, we can choose the proper design of a magnet for a certain usage from the view point of MQE. Acknowledgement The authors would like to thank Prof. K. Watanabe of Tohoku University to offer us the specifications of the 15 T multi-sectional magnet. References [1] Dresner L. Quench energies of potted magnets. IEEE Trans Magn 1985;21:392–5. [2] Schmidt C. The induction of a propagating normal zone (quench) in a superconductor by local energy release. Cryogenics 1978;18:605–10. [3] Amemiya A, Tsukamoto O. Influence of disturbance characteristics and copper to superconductor ratio on stability. Adv Cryogen Eng A 1992;37:323–9. [4] Seo K, Morita M. Minimum quench energy measurement for superconducting wires. IEEE Trans Magn 1996;32:3089–93. [5] Wilson M, Iwasa Y. Stability of superconductors against localized disturbances of limited magnitude. Cryogenics 1978:17–25. [6] Maeda H, Iwasa Y. Heat generation from epoxy cracks and bond failure. Cryogenics 1982;22:473–6. [7] Tsukamoto O, Iwasa Y. Epoxy cracking in the epoxy-impregnated superconducting winding: non-uniform dissipation of stress energy in a wire-epoxy matrix model. IEEE Trans Magn 1984:377–9. [8] Urata M, Maeda H, Aoki N, Uchiyama G. Compact 17 T epoxyimpregnated magnet without bore tube. Cryogenics 1991;31:570–4. [9] Wilson M. Superconducting magnets. Oxford: Oxford University Press; 1983. [10] Iwasa Y. Case studies of superconducting magnets: design and operational issues. New York: Plenum Press; 1994. p. 139. [11] Davies F, Elliott R, Hawksworth D. A 2-Tesla active shield magnet for whole body imaging and spectroscopy. IEEE Trans Magn 1991; 27:1677–80. [12] Yanaguchi M. Application of superconducting technologies—magnetic resonance imaging. J Plasma Phys Fusion Res 1994;70:1168–74. [13] Tsuchiyama H, Terai M, Yoshida H, et al. Heat load characteristics of new superconducting magnet for Yamanashi test line. J Cryogen Soc Jpn 1994;29:530–6. [14] Devred A et al. About the mechanics of SSC dipole magnet prototype. In: API conference proceeding series. The physics of particle accelerators; 1992. [15] Nakamoto T et al. Design of superconducting combined function magnets for the 50 GeV proton beam line for the J-PARC neutrino experiment. IEEE Trans Appl Supercond 2004;14:616–9.
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 [16] Mikami Y, Sakuraba J, Watazawa K, Watanabe K, Awaji S. Development of a 15 T cryocooled superconducting magnet. J Cryogen Soc Jpn 1999;34:200–2005. [17] Kiyoshi T et al. Operation of a 930-MHz high-resolution NMR magnet at TML. Presented at ASC 2004, Jacksonville, FL, USA; 2004.
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[18] Lee P. Engineering superconductivity. New York: Wiley-Interscience; 2001, ISBN 0-471-41116-7. [19] Seo K, Morita M, Yamamoto S. Stability of synthetic enameled superconducting wires. In: Proceedings of ICMC/ICEC in Kokura, Japan; 1997.
Guidelines for LTS magnet design based on transient stability Kazutaka Seo b
a,*
, Masao Morita
b
a National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, Gifu 509-5292, Japan Mitsubishi Electric Corporation, 8-1-1 Tsukaguchi-honmachi, Amagasaki, Hyogo 661-8661, Japan
Received 13 December 2004; received in revised form 14 October 2005; accepted 22 November 2005
Abstract Stabilities of low critical temperature superconducting (LTS) magnets and their designs are studied and discussed. There are two contradictory necessities; those are low cost and high performance, in the other words, high magnetic field and large current density. Especially, the maximum magnetic fields of the latest high performance Nb3Sn magnets are around 20 T. Mentioned necessities result in the small stability margins. Needless to say, the superconducting magnet must produce its nominal field reliably. Therefore, maintaining adequate stability margin, the magnet design to draw out the high potential of the superconductor is required. The transient stability of the superconducting magnet is determined by the relationship between mechanical disturbance energy and stability margin. The minimum quench energy (MQE) is one of the index of stability margin and it is defined as the minimum energy to trigger quenching of a superconductor. MQE should be beyond any possible disturbance energy during the operation. It is difficult to identify the mechanical disturbance energy quantitatively. On the contrary, MQE had been evaluated precisely by means of our developed resistive carbon paste heater (CPH). At the same time, we can predict MQE by numerical simulations. Because the magnet comes to quench if the mechanical disturbance exceeds the MQE, the disturbance energies are suspected to be equivalent to MQEs during the magnet-training. When we achieved somewhat larger MQE, we may exclude numbers of training quenches. In this paper, we discuss the guidelines of LTS magnet design from the standpoint of MQE. We represent some case studies for various superconducting magnets and/or some different winding methods. 2005 Elsevier Ltd. All rights reserved. Keywords: Superconducting magnet; MQE; Stability; Magnet design
1. Introduction 1.1. Advantages of LTS coils and subjects to be solved Low Tc superconducting (LTS) magnets are widely installed due to following advantages. One is the lower cost of the LTS conductor than the latest HTS conductors. Another advantage is large n-value, which is necessary for persistent current magnets (e.g., MRI and NMR) to sustain stable persistent current. Small filament diameter is also advantage for the accurate magnetic field applications. We can predict the effective filament diameters and
*
Corresponding author. E-mail address: [email protected] (K. Seo).
0011-2275/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2005.11.020
the magnetizations of LTS conductors more accurately than HTS. At present, the superconducting magnet business market is MRI and NMR production basically. Because of these advantages, LTS magnets lead the superconducting business. Furthermore, the recent progresses of compact refrigerators promote the applications of LTS magnets. To obtain these advantages, we should design LTS magnets properly and avoid any training quench. Quench means the drastic transition from superconducting state to normal state. and it results in the huge liquid helium consumption and/or waste of the time. To prevent a magnet from quench, it is important to identifying the minimum quench energy (MQE) in the LTS magnet. Hence, MQE is defined as the minimum energy to make a superconductor quench [1–5].
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361
LTS coil is energized at liquid helium temperature (4.2 K). Heat capacities of materials become around 103 times smaller than room temperature (RT) and even minute thermal energy of disturbance introduces large temperature rise. On the contrary, current sharing temperature margins of LTS magnets are around 1–2 K. From this fact, we can estimate that MQE might be small amount. We do not have to discuss about MQE for HTS magnets which are generally operated at 20 K. The stabilization technique is preventing LTS magnet from quench and it is classified into two technologies. One is suppressing the initiation of normal transition, in the other word, mechanical disturbances. The other is improving the stability margin and making conductors hard to come to quench. In this paper, we discuss about the second issue intensively. 1.2. Mechanical disturbance As mentioned in following sections, MQEs in LTS magnets are evaluated as about several hundred microJoules. When the energies of mechanical disturbances, e.g., wire motions and/or epoxy cracks, exceed MQE, the magnet quenches. In the superconducting magnet, large electromagnetic force is induced during energization and it causes wire motions, cracks and debondings of molding epoxy resin. Here, we estimate the dissipated mechanical disturbance energies. The energy dissipation due to an epoxy crack is release of reserved elastic energy in it. If we assume elastic modulus (E) is 30 GPa and strain () is 5000 l, the elastic energy density is estimated as 1/2E2 = 400 lJ/mm3 and this energy is released after the breakage of epoxy resin. On the other hand, the energy due to wire motion is estimated as follows. We assume the friction factor is 0.2 and the wire, which is compressed with the stress of 10 MPa, slips 0.1 mm in transverse direction. The heat dissipation per 1 mm2 is calculated as 10 · 0.2 · 0.0001 = 200 lJ/mm2. The disturbance energy is roughly estimated to about 0.1–1 mJ. Superconducting magnets are forced quench with this small amount of energy. Such kind of disturbances happens not continuously but pulsively and the durations are reported several hundred
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microseconds [6]. These discrete disturbances are observed in acoustic emission (AE) signals and the differential voltage (VB) signals between balanced taps in coil tests [7]. It is difficult to observe the mechanical disturbances in the winding directly. However, lots of studies had been performed to comprehend the behavior of mechanical disturbances in the superconducting windings. The mechanical disturbances can be classified into two groups. One is the internal disturbance that occurs inside of the winding as mentioned above. The other is the external disturbance, which is caused by friction on the mandrel and/or coil-case or debondings from them. Recently, this sort of disturbance is solved by following technologies, those are (1) slipping mechanism of winding with thermal barrier on its inner surface, (2) mandrel-less coil [8] and (3) dummy winding. For the thermal barrier, this is not a special component but merely a ground insulation. When we design the slipping section on the out surface of ground insulation, it becomes a intrinsic thermal barrier to the superconducting winding. The number of quench due to external disturbances had been suppressed by the techniques based on these latest configuration recently. 2. MQE in LTS coil 2.1. MQE MQE is the index of transient stability. We explain MQE with quench behaviors of superconducting wire shown in Fig. 1. In Fig. 1(a), the tap voltage increased and varnished after 2 ms. This means the superconducting wire recovers superconducting state. On the contrary, in Fig. 1(b), it shows quenching. MQE is defied the minimum energy introducing quench. Therefore, the energy in Fig. 1(b) is almost MQE for this wire. When MQE is larger than the mechanical disturbance energy, the wire does not quench. In Fig. 1(b), normal state region is stagnating for 1 ms. The size of this normal state region is called minimum propagating zone (MPZ) [9]. When the normal region larger than MPZ is introduced, the wire quenches. Hence, MQE is the energy which introduces the normal zone comparable to MPZ.
Fig. 1. Voltage traces during recovery and quench. NbTi superconducting wire is with 1.1 mm · 2.2 mm in cross-section and copper ratio: 1.0 [4].
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Superconducting wire has a stabilizer such as pure copper and its thermal diffusivity is very large. With conventional heating technique, it was difficult to introduce a small disturbance with short pulse durations comparing with thermal diffusion through the stabilizer. Fig. 2 shows the photograph of our carbon paste heater (CPH) is shown [4]. The thickness of resistive carbon layer is about 20 lm and the thermal diffusivity of the heater itself is small enough to demonstrate an actual mechanical disturbance. Utilizing this heater, we evaluated the MQE that showed good agreement with theoretical predictions. Fig. 3 shows the dependence of pulse width upon MQE. Due to the thermal diffusion, the quench energy is over estimated, when the pulse width is large. Utilizing conventional heating wire, quench energy is much more over estimated.
104 Heating wire (tpulse=1 ms) CPH (tpulse=200 µ s)
5T
103
MQE ( µ J)
356
7T
102 Open : 5 T Close : 7 T Our numerical simulation Dresner's formula
101 0
500
1000
Current (A)
Fig. 4. Transport current dependence on MQE. The NbTi wire is 2.2 mm · 1.1 mm in cross-section, Cu/SC ratio 1, RRR: 141 [4]. Dresner’s formula [1] shows good agreement with nonlinear numerical simulations. The closed marks show the data of 7 T and the open marks show 5 T, respectively.
Fig. 2. Photograph of the cross-sectional view of carbon paste heater (CPH) [4]. Thin resistive carbon paste layer realizes a test disturbance with short pulse length. Pulsive current flows from (+) terminal to the superconducting wire through carbon paste resistive layer and generates ohmic heat. Epoxy putty is the thermal insulation.
7 6
Constantan Heating Wire φ 0.1 mm Carbon Paste Heater A Carbon Paste Heater B (Pressed)
MQE (mJ)
5 4 3 2 1 Numerically Calculated
0
10-1
100
101
102
Pulse Width (ms) Fig. 3. The dependence of pulse width upon MQE. The wire is NbTi, 2.2 mm · 1.1 mm in cross-section and Cu/SC ratio: 1.0, RRR: 141 [4]. For CPH-B, the carbon layer was pressed mechanically to improve thermal contact.
Fig. 4 shows the dependence of transport current upon MQE. If the current becomes large, MQE degrades remarkably. Solid line represents the result of numerical simulations. Dashed line is obtained by Dresner’s formula mentioned later. The theoretical formula of MQE was reported by Dresner as Eq. (1) [1]. In this formula, the parameters are as follows: cC, volume specific heat of the wire; A, cross-section of the wire; ACu, cross-section of the stabilizer; k, equivalent thermal conductivity of the wire; Tc, critical temperature; TCS, current sharing temperature; Tb, bath temperature; q, equivalent resistivity of the wire; Iop, operation current; Ic, critical current and i, Iop/Ic. pffiffiffi 7=2 cCA k ðT c T b Þ3=2 1 I op =I c T CS pffiffiffiffiffiffiffiffiffiffiffiffi MQE ¼ p ð1Þ pffiffiffi I c =ACu q Tb I op =I c We considered temperature dependences of mentioned thermal properties. Those are obtained assuming the temperature as 0.5 · (TCS + Tb). Magnetic resistivity and Wiedemann–Franz law [10] which is the relationship between resistance and thermal conductivity are implemented. Eq. (1) is time independent. Therefore, this equation is applicable only to the case within a short pulse duration that can ignore the thermal diffusion effect along the wire. In fact, observed MQE shows remarkable pulse width dependence as shown in Fig. 3. In Fig. 4, our numerical results show good agreement with Dresner’s formula and the effectiveness of this formula is proved for the first time by our experiment. The thermal diffusivity of the heater itself had been the problem to be solved. Our CPH has several ten micrometers in thickness and can provide to estimate the actual mechani-
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 Table 1 Specifications of superconducting test coil Coil Inner diameter Outer diameter Height Material of mandrel
(mm) (mm) (mm)
Thickness of mandrel Turn number Magnetic field at I = 140 A
250 274 350 Stainless steel 10 10,350 4.2
(mm) (T)
Conductor Material Diameter Copper ratio Critical current at 5 T
NbTi 0.6 1.5 350
(mm) (A)
cal disturbances. We start to discuses about MQE in the superconducting magnet mainly using Dresner’s formula. 2.2. MQE in LTS test coil First, MQE in our test coil is discussed to comprehend the overview of stability of a superconducting coil. Table 1 shows the specification of our NbTi test magnet. Fig. 5 represents the calculated results of the degradation of MQE and TCS margin during energization. Comparing with TCS margin, MQE decreases drastically. When mechanical disturbance energy exceeds MQE, the
Strain (µ ε)
3000
magnet runs to quench. From this figure, magnet design based on MQE is more important than that based on TCS margin. Of course, it is still difficult to identify the mechanical disturbance energy triggering the quench. However, when we identify the MQE at the quench, the mechanical disturbance energy triggering that quench can be suspected, on the contrary. 2.3. Comparison between magnets Fig. 6 represents the calculated MQEs in various kinds of superconducting magnets. Transverse axis represents the current density of the wire. Here, for the accelerator, single-strand stability (SSS) is assumed. SSS is a phenomenon that the single strand quench in the Rutherford type cable determines the quench of the whole magnet. Based on this phenomenon, MQE of the single strand (not the cable) determines the quench behavior of the magnet. The trend of the larger magnets is smaller current densities and very stable (Fig. 6, upper-left). On the contrary, the small magnets have larger current densities and smaller MQEs (Fig. 6, lower-right). Small magnets are designed to accomplish the compactness and higher field. Of course, the electromagnetic force and the stored energy of the large magnet is quite large, therefore such magnet is designed based on cryo-stable principle [9]. 3. MQE and coil design parameters It is almost impossible to restrain the mechanical disturbance event into zero. However, fortunately, if MQE is
Hoop strain (mid-plane)
2000
357
1000 0 -1000
Axial strain (mid-plane)
-2000
IT ER LHD
103
MAGLEV Test Coil
(Out of range)
800
6
MRI High-B NMR
102
MQE (µ J)
5 600
µ 3
MQE ( µ J)
Tcs-Tb (K)
4 Tcs-Tb
400
Lab. Magnet
101
MQE
2
Accelerator
200
100
AE (Arb.)
1
0
200
400
Current density 0
0
0
50
100
150
Current (A) Fig. 5. Degradation of MQE and TCS margin during energization. Strains are obtained by the experiment. MQE is calculated from Dresner’s formula. Comparing with TCS margin, MQE decreases drastically. Strains, in the other word, stresses are proportional to square of the current. Mechanical disturbances occur during energization. If this energy exceeds MQE, the magnet quenches. In this figure, instead of mechanical disturbances, typical AE signals are shown for descriptive purposes.
600
800
(A/mm2
Cond)
Fig. 6. MQE vs. current density of the conductor. Closed circles indicate MRI magnets [11,12], open circles: MAGLEV test coil [13], closed rectangles: accelerators [14,15], open rectangles and upside-down triangle: laboratory magnets (rectangles correspond to multi-sectional 15 T magnet discussed later [16]), open triangle: high field NMR (most inner section) [17] and closed triangles: test magnet represented in Table 1. One of the closed triangles corresponds to the initial quench and the other is the achieved maximum current density. Only current densities are represented for ITER and LHD helical coil [18] and their quench energies are much larger than others.
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always larger than any possible mechanical disturbances, the magnet does not quench. The effort to suppress the coil deformation in order to decrease mechanical disturbance had been performed a lot. Here, we discuss how to increase and/or optimize MQE during magnet design. There are lots of parameters of the wire, such as superconducting materials, dimensions, copper ratio, sensitivities of stabilizers and so on. Winding configuration also have some parameters, those are cooling conditions, steel bind reinforcement etc. For instance, for the medium size magnet, choosing stabilization philosophy is annoying issue. We should select the relevant stability theory from cryo-stable and transient stability based on MQE. We discuss about the influence of stabilizer, cooling channel, reinforcement and conductor dimension upon MQE sequentially. 3.1. Stabilizer and MQE If we increase copper stabilizer, the volume of superconducting material decreases and critical current also decreases. On the contrary, without any copper, superconducting material has poor thermal conductivity and it results in small MQE. It had been reported that there is an optimum copper ratio for certain superconducting wire [3]. The optimum copper ratio can be derived conveniently from Dresner’s formula. The resistance of stabilizer is also important. Instead of the resistivity of the metal at cryogenic temperature, residual resistivity ratio (RRR) is represented in the specification table of the superconducting wire. RRR is the ratio of resistances at 273 and 4.2 K. Wiedemann–Franz law [10] denotes that resistivity is inversely proportional to thermal conductivity. Applying this relation to Dresner’s formula, MQE is proportional to RRR. We must take into account of the magnetic resistivity of copper under the high magnetic field applications because it increases under the high field. In case of Nb3Sn wire, sometimes diffusion barrier is broken and stabilizer is contaminated. It results in higher resistance and degrades MQE. Internal reinforcement is popular for the high field applications, but it causes the decrease of the volume of pure copper stabilizer. The Cu alloy with high strength also has large resistivity. In general, persistent current switches are wound with CuNi matrix wires, therefore MQE in PCS is miserably small. 3.2. Cooling channel and MQE Fig. 7 shows the transport current dependence upon MQE. The sample has LHe cooling channels; the pitch length is 35 mm and width is 23 mm. Experimental results had been only obtained at 7 T. Comparing with adiabatic condition, MQEs are almost identical. This means that there is no merit of pool boiling LHe cooling on the stability. Numerical results also represent similar tendency. MQEs at 3 T are calculated for both LHe cooled and adiabatic models. Around 750 A, MQE is improved by
Fig. 7. Influence of LHe cooling channel on MQE. The wire dimensions are 1.3 mm · 2.6 mm and Cu ratio: 1.5. The pitch length and the width of the LHe cooling channel are 35 and 23 mm, respectively. The solid lines show the numerically calculated results for the wire with cooling channel and dashed lines for adiabatic case. When the transport current is large, MQEs are identical between adiabatic and LHe cooling conditions. The wire dimension becomes small when the cooling channel is located. Thicker wire can be adopted in the case of adiabatic design, when the cross-section of the winding and number of turn are identical. Assuming the gap of cooling channel 0.4 mm, the wire dimensions are is (2.6 + 0.4) · (1.3 + 0.4)/(2.6 · 1.3) = 1.51 times larger than the wire with cooling channel. In this case, MQE becomes large as shown with thick dashed line which is larger than the case with cooling channels.
LHe cooling. Here, we tried to do some correction on this data. Cooling channels decrease the conductor fraction in the winding. If the spacer with 0.4 mm in thickness is assumed, the conductor size becomes 1/1.5 smaller than the original. In the other word, the packed wound wire can be enlarged up to 1.5 times larger than cooled wire, and the current density becomes 1/1.5. Also the cross-section of windings becomes 1.5 times larger. According to these discussions, the data can be redrawn with thick dashed line in Fig. 7. The magnet design should be performed after considering these effects. Whether we adopt a cooling channel or not must be determined after identifying these MQE curves as represented in Fig. 7. 3.3. Reinforcement and MQE (multi-sectional 15 T magnet) MQEs in the 15 T multi-sectional magnet [16], which was developed and installed at Tohoku University, are calculated. Table 2 shows the specifications of the magnet. Using these parameters, the influence of reinforcement on MQE is discussed too. Fig. 8 shows the distribution of the calculated MQE in the cross-sections of the windings. The smallest MQEs in coil-1, coil-3 and coil-5 are almost identical, therefore the design is assumed to be almost reasonable. These sections are designed to be comparable stabilities. The quantity of MQE is several ten microJoules and it is as small as that of typical accelerator magnet as shown in Fig. 6.
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Table 2 Specifications of multi-sectional 15 T superconducting magnet [16] Coil Coil number Inner diameter (mm) Outer diameter (mm) Coil height (mm) Maximum field (T) Number of turn Operating current (A)
1 74 110 229 15.3 3562 90
2 124 160 229 13.8 3564 90
3 175 207 280 12.4 3872 157
4 226 278 280 9.9 6292 157
5 306 395 366 6.3 16,512 157
Conductor Material Diameter (mm) Critical current (A)
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
Nb3Sn 1.0 320 at 10 T, 4.2 K
NbTi 1.0 820 at 5 T, 4.2 K
Fig. 8. The distribution of magnetic field and MQE in the 15 T multi-sectional magnet. MQEs in the winding cross-section distribute remarkably. Here, horizontal axis is a log scale.
For high field NMRs and MRI magnets with large bores, coils need to be reinforced by steel bind. Adapting the steel bind, the fraction of superconductor decreases and current density increases. Another reinforcement method is using internal reinforced wire, which contains copper alloy in itself. The copper alloy has larger resistance than pure copper stabilizer and MQE must be decreased.
We analyzed the influence of internal reinforced wires and binds on the coil-1 and the coil-3 of the 15 T magnets. For the reinforced wire, half of copper stabilizer is assumed to be replaced with copper alloy from the original model. For the steel bind, 20% of winding cross-section is occupied by the steel bind and the size of the conductor is assumed to be reduced to 80% from the original.
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K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 100 1st Section (B=13.5 T)
3rd Section (B=12.4 T)
MQE (µ J)
80 60
Original Internal reinforced (ACu×0.5)
Orginal
40 20
Internal reinforced (ACu×0.5) Bind (A×0.8)
Bind (A×0.8)
0
We have discussed about the influence of parameters of superconducting conductors and windings on MQEs. Here, mechanical disturbance energy is still difficult to be identified; therefore magnet design should be performed based on the experiences, those are databases shown in Fig. 6. This kind of databases must be established at individual superconducting magnet manufacturers to decrease the number of premature quench.
Conductor Size
Fig. 9. Influence of steel bind and internal reinforcement on MQE. MQEs are calculated from Dresner’s formula. Original indicates MQE of the 15 T multi-sectional magnet.
The calculated results are represented in Fig. 9. MQE is very sensitive to the current density, and steel bind results in remarkable decrease of MQE. In the case of the reinforcement, the external reinforcement is better than internal one. The reason is that the external reinforcement with resistive alloy, e.g., CuNb, stainless steel and so on, plays a role of thermal barrier to improve MQE [19]. 3.4. LHe free magnet (nominal current and MQE) In the case of LHe free magnets, the small operating current is required. The small operating current permits utilizing small power leads, power supplies and PCSs. Especially, the small heat load can be achieved with thin power leads. However, it is trivial that the small size wire results in poor MQE. In the case of the identical current density in the winding, MQE is proportional to the conductor size. We assumed that the thermal diffusivity of the stabilizer is large and the cross-sectional temperature distribution is uniform in spite of the larger cross-section. Fig. 10 represents the calculated results of MQEs. MQE is inversely proportional to the size of the conductor. Thick conductor brings following advantages too, those are small inductance and easy to be wound without conductor breakages. The small inductance brings benefit on quench protection.
Fig. 10. MQE vs. wire size derived from Dresner’s formula. NbTi superconducting wire is with 1.1 mm · 2.2 mm of cross-section and copper ratio: 1.0. Magnetic field and current are 5 T and 500 A, respectively, in the default case.
4. Conclusion The stability of the superconducting magnet is discussed applying MQE theory. To select the proper wire parameters and winding constitutions are important to achieve good stability. Mechanical disturbance energy still remains to be identified precisely. However, based on the past database, we can choose the proper design of a magnet for a certain usage from the view point of MQE. Acknowledgement The authors would like to thank Prof. K. Watanabe of Tohoku University to offer us the specifications of the 15 T multi-sectional magnet. References [1] Dresner L. Quench energies of potted magnets. IEEE Trans Magn 1985;21:392–5. [2] Schmidt C. The induction of a propagating normal zone (quench) in a superconductor by local energy release. Cryogenics 1978;18:605–10. [3] Amemiya A, Tsukamoto O. Influence of disturbance characteristics and copper to superconductor ratio on stability. Adv Cryogen Eng A 1992;37:323–9. [4] Seo K, Morita M. Minimum quench energy measurement for superconducting wires. IEEE Trans Magn 1996;32:3089–93. [5] Wilson M, Iwasa Y. Stability of superconductors against localized disturbances of limited magnitude. Cryogenics 1978:17–25. [6] Maeda H, Iwasa Y. Heat generation from epoxy cracks and bond failure. Cryogenics 1982;22:473–6. [7] Tsukamoto O, Iwasa Y. Epoxy cracking in the epoxy-impregnated superconducting winding: non-uniform dissipation of stress energy in a wire-epoxy matrix model. IEEE Trans Magn 1984:377–9. [8] Urata M, Maeda H, Aoki N, Uchiyama G. Compact 17 T epoxyimpregnated magnet without bore tube. Cryogenics 1991;31:570–4. [9] Wilson M. Superconducting magnets. Oxford: Oxford University Press; 1983. [10] Iwasa Y. Case studies of superconducting magnets: design and operational issues. New York: Plenum Press; 1994. p. 139. [11] Davies F, Elliott R, Hawksworth D. A 2-Tesla active shield magnet for whole body imaging and spectroscopy. IEEE Trans Magn 1991; 27:1677–80. [12] Yanaguchi M. Application of superconducting technologies—magnetic resonance imaging. J Plasma Phys Fusion Res 1994;70:1168–74. [13] Tsuchiyama H, Terai M, Yoshida H, et al. Heat load characteristics of new superconducting magnet for Yamanashi test line. J Cryogen Soc Jpn 1994;29:530–6. [14] Devred A et al. About the mechanics of SSC dipole magnet prototype. In: API conference proceeding series. The physics of particle accelerators; 1992. [15] Nakamoto T et al. Design of superconducting combined function magnets for the 50 GeV proton beam line for the J-PARC neutrino experiment. IEEE Trans Appl Supercond 2004;14:616–9.
K. Seo, M. Morita / Cryogenics 46 (2006) 354–361 [16] Mikami Y, Sakuraba J, Watazawa K, Watanabe K, Awaji S. Development of a 15 T cryocooled superconducting magnet. J Cryogen Soc Jpn 1999;34:200–2005. [17] Kiyoshi T et al. Operation of a 930-MHz high-resolution NMR magnet at TML. Presented at ASC 2004, Jacksonville, FL, USA; 2004.
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[18] Lee P. Engineering superconductivity. New York: Wiley-Interscience; 2001, ISBN 0-471-41116-7. [19] Seo K, Morita M, Yamamoto S. Stability of synthetic enameled superconducting wires. In: Proceedings of ICMC/ICEC in Kokura, Japan; 1997.