Frings, P.H.

Louis, J-M.

International Migration, Integration and Social Cohesion online publications

UvA-DARE is a service provided by the library of the University of Amsterdam (https://dare.uva.nl)UvA-DARE (Digital Academic Repository)Beyond 60 T; a fruitful staircase to long-pulse 100 T fieldsLouis, J-M.; Frings, P.H.Publication date1995Published inPhysica B-Condensed MatterLink to publicationCitation for published version (APA):Louis, J-M., & Frings, P. H. (1995). Beyond 60 T; a fruitful staircase to long-pulse 100 T fields.Physica B-Condensed Matter, 201, 69-72.General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s)and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an opencontent license (like Creative Commons).Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, pleaselet the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the materialinaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letterto: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. Youwill be contacted as soon as possible.Download date:10 Mar 2023mlgl  ELSEVIER Physica B 211 (1995) 69 72 i Beyond 60T; a fruitful staircase to long-pulse 100 T fields J.-M. Louis*, P.H. Frings, R. Gersdorf Van der Waals-Zeeman Laboratory, University of Amsterdam, Valckenierstraat 65, NL-I 018 XE Amsterdam, The Netherlands Abstract The design study for a power-limited semicontinuous 100 T magnet carried out in Amsterdam is presented i It appears that such a magnet, wound from existing wire material, would become very large and expensive. Several designs are given for smaller magnet coil systems, where the stresses and thermal loads will be the same as in the larger 100l T magnet, producing, for example, 85 T during 1 ms in a 2 cm bore. 1. Introduction Since 1969 the High Field Facility of the University of Amsterdam has a semicontinuous 40 T, 100 ms coil in operation [1]. The installation will be upgraded in the next few years with a new 60 T, 100 ms coil. Besides that, our Institute is also involved in a European Network for the study of the feasibility of even higher fields in the 100 T region. The final aim of this study was the design of a magnet capable of producing 100 T during a constant period of the order of 1 s. Preliminary calculations of the heat and stress limited current densities in a more realistic magnet system capable of producing 100 T in an inner bore of 2.5 cm for 100 ms were performed. It turned out that it is possible to build such a magnet with existing materials; however, for the present state of the art in uitrastrong wires technology, a 100 T, 100 ms magnet would require a power of 1 GW and would have a diameter of several meters. As a pilot study for this 100 T magnet, we restricted ourselves to a scaled down magnet in terms of power, time, size, and energy but kept the same thermal and mechanical loads, resulting in 85 T during 1 ms in an * Corresponding author. inner bore of 2 cm. Such a 85 T magnet would require realistic power, energy and dimensions, allo~ving us to test its detailed behaviour, in connection with ~aovel cons- truction techniques. Furthermore, a small 85 T magnet even with a short constant field plateau gives !he possibi- lity for physicists to perform useful measurements once it has been built and tested. The use of exact scaling laws allows us to stale up this magnet to a 85 T, approximately 50 ms coil w!th an inner bore of about 15 cm [1]. The next step woul d then be to design an insert to be placed in this magnet] capable of producing 15 T during 50 ms in an inner bore of 2.5 cm. The calculations ~1 to we have performed showe this be possible with the same material characteristics. We have considered different materials eithgr available today, or in the next future. The first category is given by the homogeneous wires, such as coppe~-beryllium (CuBe) or copper-silver (CuAg), which have ~i large yield strength and a rather large electrical conductivity. The second category is given by the so-caUed '!composite" wires, which consist of pure copper with a large electrical conductivity reinforced by stainless steel with very large yield strength. The main electrical and mechanical prop- erties of the wires are summarised in Table il. For  the composite wires, two different sil~'uations can be considered, namely adiabatic or isothermal. In the adiabatic situation the heat created by the current flow in 0921-4526/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0921-4526(941}00946-5  70 J.M. Louis et al. /Physica B 211 (1995) 69 72 Table 1 Relevant physical properties of wire materials Yield strength p ~ @RT Po (MPa) (%IACS) (p.Q cm) CuBe 1400 ~ 20 ~ 6.0 CuAg 910 83 0.353 Hardened Cu 360 100 0.06 Composite 2 × ac~ + (1 - 2) x as.s. Cu (frac. 2) ac~ = 100 100 x 2 (%IACS) Steel (frac. 1 - 2) as.s. = 2000 See Ref. [2] the copper remains there. Larger current densities can be used in the isothermal case, where the heat is, during the pulse, redistributed among the copper and the stainless steel [2]. ,2oot, ' ' ' 1 8 5  T ,  I m s ,  i n n e r  r a d i u s  1 c m  o i l  # 0  " ~  ' 0 0  ~ C o i l  #1  - - -  H e a t  l i m i t e d  ~ 1 1 1 \  - -  S t r e s s  l i m i t e d  i ii co,, 400 " ~ ~ .  ~ - ~ ~ ~ ~ ~ ~ - - 0 10 2 0  30  4 0  R a d i u s  ( e r a )  50  Fig. 1. Stress and heat limited current densities throughout the 85 T coil. The rectangles represent the division of the coil in subcoils with adapted current densities. 2. The scaled down magnet In the following we will consider the design of the 85 T, 1 ms, magnet with an inner bore of 2 cm. The magnet will consist of three sections of concentric coils. Two different, extreme situations can be considered if the total coil system is energised from a power limited supply. In the innermost coils, where the needed power is almost negligible, the important point is to reduce the outer diameter, so that the power in the outer coils will be strongly reduced by the decrease of the overall radius of the outer system. This imposes the use of very strong wire, which makes the use of high current densities pos- sible. The opposite situation is obtained for the outer- most part. There we are clearly in the power limited case. The strength of the wire is not so important. As far as the total pulse time and the demanded power in the outer system are concerned the use of a wire with an electrical resistivity as low as possible has to be considered. In the intermediate part, we have to find a delicate balance between strong material (reduction of the size) and better conducting material (minimisation of the power). The calculations are based on the formulae de- scribing the mechanical behaviour of coils [1] and opti- misation of the magnets is based on paper [3]. 2.1. Stress and heat limitations The two important limitations for the calculation of the allowable current densities in the coils are the heat and stress limitations. The heat limited current density J~ea, can be approximated from the resistive and thermal properties of the wire using Eq. (1), where AT is the maximum allowable temperature rise, e.g. 250 K. C .... is the averaged specific heat of the wire, Pv is its averaged resistivity, and Ate is the duration of the constant field [3]: Jh~,<~ C~,~ ,AT .  ~[ p,vAtc (1) The stress limited current density.~t .... is roughly given by Eq. (2), where Bz(r) is the axial field throughout the coil [3]: J~t .... <~ 1.1"rB/r  ~')o t (2) Assuming these two equations, we have plotted in Fig. l the heat and stress limited current densities for a 85 T, 1 ms coil. We used the mechanical and electrical proper- ties of the CuBe alloy. It turns out that the inner coils are stress limited rather than heat limited; this is due to the short pulse duration. An ideal optimisation would be to adapt continuously the current density and the strength throughout the coil. Since we cannot do this, we have divided the magnet in different parts where the current density is kept constant. This division in subcoils shown in Fig. 1 will be used later on. The energising of the magnet system is done by a vary- ing number of rectifiers with different voltage and current capacities. Coils # 0 to # 4 are energised via rectifier # 1, coils # 5 and # 6 by rectifier # 2, and coils # 7 and # 8 by rectifier # 3. The initial temperature is always liquid nitrogen temperature. J.M. Louis et al./Physica B 211 (1995) 69-72 71 2.2. Design using homogeneous wires In the inner part of a 85 T magnet system where the highest stresses exist, a very strong wire material is used. Our first choice was the copper beryllium. The resulting inner part is capable of producing an additional field of about 55 T at a background field of 30 T, with an outer radius of 23.5 cm. The background field is produced in an outer part of the system wound of CuAg, which allows to gain on the power, where the strength of the wire is less important. The overall radius of this magnet system is around 48 cm. The total power we calculated for this entire system is about 525 MW, the total pulse time is about 2.8 s and the stored energy 210 MJ. 2.3. Design using composite wires In this part, a design for the 85 T magnet, using realis- tic or existing material is given. We present first the results we got for the almost realistic situation of an "adiabatic" wire formed of a copper wire externally rein- forced with stainless steel. The final inner part is capable of producing 55 T in an inner bore of 2 cm for 1 ms. The total power needed by this system is around 125 MW and the outer radius is 23.5 cm. The inner coils have been designed in order to be heat and stress limited everywhere. This subsystem requires an outer part producing 30 T. The outer part can be designed using composite wire with a lower fraction of stainless steel, since the stresses are lower. The stainless steel fractions have been recal- culated afterwards to match the stresses. This design requires the least power among all. The total power is about 290 MW, the total pulse time is 4.2 s, and the total stored energy is around 180 MJ. Since the power is the more expensive part of such a project, this design has been power optimised. Fig. 2 shows the typical field profile of the 85 T pulse. The first two designs concerned existing materials. We will now consider the case of "isothermal" composite wires to show that further developments in ultrastrong conducting wires technology are of great importance. This aspect is developed in the related paper "strength versus conductivity" [2]. 2.4. "Isothermal" composite wire We have calculated a magnet capable of producing 85 T for 1 ms using a hypothetical "isothermal" com- posite material. Experiments performed on this new ma- terial may be successful in the next future and provide us with a very strong and conducting wire. We have con- m aJ .o 100 80 60 40  20 0 I 9v  ' I ' b 7O 2.35 2 3 6  T i m e  ( s e c )  I i I i 2 3 7  / , t 1 2 3 T i m e  ( s e c )  Fig. 2. Field profile of the "adiabatic" composite coil. sidered a wire where it is possible to adapt t~ae relative fractions of materials, and performed the calc~alations in both power and size minimised ways, since these are the two different ways of optimising magnets. On~ can try to decrease the total needed power or the overall radius of the magnet using higher current densities. The actual volume would become lower than the optimum volume (giving the lowest power) and the needed po~ver would strongly increase. The size optimised design is an extreme cas~ where the dimensions of the system are as small as possit~le, in order to show that we can design very compact magnet systems with this wire technology. The power and energy for this system are 400 MW and 34 M J, respectively. The opposite extreme situation can also be reached, where we concentrate more on the minimisation of the power, and less on the magnet size.i We have designed a 85 T coil on the basis of a power of the order of 150 MW. The size and pulse duratilon of such a low power magnet is increased compared io the pre- vious one, 3. A 100 T sys tem Finally, as an example for a complete 100 T system, we present the results of calculations we have performed on a scaled-up 85 T magnet provided with an insert creating the additional 15 T (see Table 2). The starting 85 T mag- net was the so-called "size minimised isothermal com- posite" magnet since its dimensions are relatively small. 72 J.M. Louis et aL /Physica B 211 (1995) 69-72 Table 2 Summary of the important features for the considered 85 T, 1 ms and 100 T, 60 ms magnets (see text) Design Outer radius Power # i, Power #2, Power #3, Total power Energy Pulse (cm) Field Field Field (MW) (M J) duration (s) CuBe/CuAg 48 129 MW, 30 T 214 MW, 27 T 182 MW, 28 T 525 208 2.9 Adiabatic composite 55 70 MW, 33 T 57 MW, 23 T 161 MW, 29 T 290 180 4.2 Isothermal composite 47.3 52 MW, 35 T 66 MW, 32 T 31 MW, 18 T 150 100 7.0 power minimised Isothermal composite 20 115 MW, 38 T 281 MW, 47 T - -  396 34 0.32 size minimised 100 T (large power) 100 14 MW, 15 T 567 MW, 38 T 1343 MW, 47 T 1925 2500 8.0 100 T (low power) 236.5 18 MW, 15 T 302 MW, 35 T 239 + 179 MW, 738 6390 170 32 + 18 T We used a scaling factor of 5, giving a total power of around 2000 MW, and a total pulse durat ion of about  8 s for an outer  diameter of 2 m. If we start from the "power minimised" magnet, the resulting system is somewhat larger (5 m in diameter) and has a strongly reduced power of about  0.75 GW, the total pulse durat ion is, however, dramatically increased. References [1] R. Gersdorf, F.A. Muller and L.W. Roeland, Rev. Sci. Instrum. 36 (1965) 1100. [2] P.H. Frings and L. van Bockstal, Physica B 2l l  (1995) 73. [3] R. Gersdorf and P.H. Frings, Optimisation of coils for semi-continuous magnetic fields, Physica B, to be pub- lished. 

English

Beyond 60 T; a fruitful staircase to long-pulse 100 T fields

https://pure.uva.nl/ws/files/2973330/1424_14052y.pdf

Beyond 60 T; a fruitful staircase to long-pulse 100 T fields

Abstract

Similar works

Full text

Available Versions

International Migration, Integration and Social Cohesion online publications