1 | OF I . . : * ORNL P 2492 L " . EE EEEFEEEE MICROCOPY RESOLUTION TEST CHART NATIONAL BUREAU OF STANDARDS - 1963 Line: ORNL-p. 2492 - Corf-660921-2 SEP 2 6 1966 The Large Volume, High Uniformity Magnets CFSTI PRICES . . HC. $ 7.0D, MN 30 at the Oak Ridge National Laboratory* 2 . W. F. Gauster Oak Ridge National Laboratory . .. .-.. MASTER ... .. E s t . SE Summary: Various magnet facilities at the Oak Ridge National Laboratory, each with continuous power ratings of up to 20 000 kW, generate large volume, high uniformity magnetic fields. The special computation methods which have been employed are discussed, | - - - - N 1 and the advantages and disadvantages of these water-cooled solenoids are compared with those of corresponding superconducting coil design. Les aimants à champs très homogènes et à grands volumes du Laboratoire National d'Oak Ridge ol Juft.* . . - Résumé: Le Laboratoire National d'Oak Ridge a construit divers aimants dont la puissance continue peut atteindre pour chacun : - 20 000 kW. Ils permettent des champs magnétiques très homogènes dans de grands volumes d'utilisation. Les nouvelles méthodes de calcul employées sont décrites et l'on compare les avantages et les inconvénients de ces bobines refroidies à l'eau avec ceux des bobines supraconductrices correspondentes. . *Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation. LEGAL NOTICE . - The report ms propered an account and Government sponored work, Matthar the United states, vor the Commission, vor any person acting and bell of the Comminaton: A. Makes may warranty or repunatation, expruded or implied, with repeat to the 2004- racy, completem., or wochelseas of the information contained in the maport, or that the wenn of my unformation, apparat, method, or proooos tecloud ban the report.wy not tattoo privately owned rights; or 2. Anna my Hamute, we repoot to throw al, or for damages related from the w of way tormation, appunto, methods or prooch dessound a p roport As wood in the wore, "porno moting a ball of the Comman" met my ployee or contractor of the Commiston, o ployho a woh contornotor, to the need that met euploywo of utructor of the Commission, of employee of much antincter peparu, downstmates, or provide acces to. Lay taformation pureun to Me employment of contract with the Comminaton, or No omployment with moda contractor. . . . . . . - IN NUCLEAR SCIENCE ABSTRACTS - - - - IN .. . . ... .. At the Oak Ridge National Laboratory several unique magnet facilities deserve special interest. These magnet systems are. designed for continuous operation, the windings are made of hollow, water-cooled copper conductors, and no ferromagnetic construction parts are used. The d.c. power ratings of these various coil systems are each between 3 500 ("B coil") and :: 20 000 kW (magnet system of "DCX-2"). (1) The multi-purpose "B-coils" Three coils ("Type B") have the following data() Inner diameter = 17 cm, outer diameter = 54 cm, length = 25 cm, rated current 9 760 A, rated power 3 400 kW. A "pancake" design with five parallel water paths has been used. The cooling water circulation rate is 22 l/sec. The conductors are completely . wrapped with Dacron-Fiberglas "stage B" polyester impregnated tape, and in addition a Mylar lish paper sandwich is inserted between all adjacent conductors. The individual pancakes are vacuum impregnated and baked, but they are not rigidly joined : together. The outer surface of the coils is covered with a strippable cocooning material in order to prevent the entrance of foreign particles, which might cause shorts. One magnet unit, consisting of one B coil, produces a field of 62.3 kgs at the coil center. At a distance of 5 cm .; from the center the field strength increases by 2.2% in the midplane and decreases by 4% on the axis. Another magnet unit is a co-axial set of two B coils with a gap between the coil. winding end planes of 1.5 cm. With 6 800 kW a field of 82.5 kgs is generated. The field homogeneity of this two-coil set is much better than that of a single coil: At a distance of 5 cm from the center the field strength decreases by 0.1% in the midplane and by 0.2% on the axis. The force between the two co-axial B coils is 230 000 kg. These two magnet units. . - - - . . - - - - - - - - ..-. .- Si . - 2- .. . .. . . ... . . - .. .. have been under severe operating condi+sane Por several years and have proved to be very reliable. (2) Power optimization of solenoids of nth order For certain experiments it was desirable to build a large volume, highest uniformity magnet unit. In order to achieve the greatest possible field strength with a power of 7 000 kW (produced by one of the available motor generator sets) a new computation method has been developed for designing power optimized solenoids of nth order. The power optimization .. of magnet coils without considering field homogeneity has been investigated carefully by many authors.(3) Likewise, the · problem of designing coil systems which produce very homoge- neous magnetic fields has been treated in great detail.'' Recently many special cases have beer calculated for coils with high field homogeneity but with due, regard also for power requirement and volume factor. Several of these solutions may approach closely the combined optimum of power and field homogeneity. However, to our knowledge, no systematic approach to the problem of a simultaneous optimization of power and field homogeneity has been made up to now. In ref. (2) this problem is solved for any prescribed shape of the coil cross section for three different types of distribution of the current density, J, namely, J is an un- known function of the coordinates z and r, J depends on z only, and n is an unknown function om z. There, the results are discussed in detail for solenoids with rectangular cross section and with specified volume factor. In the following only a short, simplified description of this new computation method will be presented.. Figure 1 shows two symmetrical current loops (Q and Q') each carrying a current I. The locations of these loops ------- --- -... . . .... aprenes Si . Y A W . are determined by the spherical co- ordinates R and a. AB is well-known, the axial field component at any point P (coordinates s and 0) 18 ... Fig. 1 . Here I Sinka. : Party (cosa) Pas (6cm ol (8.)** 0). . . - ......... .. .... . .. Fax are Legengre Polynomials. Now consider a symmetrical sole- noid with the cross section S and the current density J which is a symmetrical function of R and a: JIR, -.) = JIR, T-x) The axial field component at P produced by the solenoid is (3) with too ^24 P 28 (cosa Aza na pätti lica) ICR,«) d5 (4) Equation (4) contains the spherical coordinates R and a of the coil cross section points Q over which the integration is to be carried out. Introducing the cylindrical coordinates z and r of these points we obtain: (5) with Ammafra (2,) 3 (7,r) ds f243 pour la mismar ve Pierlot In Eq. (3) A. = 1. is the field at the coil center. The first nonzero coefficient Ax (K > 0) determines the field homogeneity near the center of the coil. A magnet coil or a co-axial coil . . . (7) arrangement is said to be of order 2n 11 A22=0 lek a no Aan to Therefore, a symmetrical solencid 18 in general of the second, the Helmholtz coil pair of the l'ourth, and Maxwell's coil arrangement of the sixth order. If p is the specific resistivity and a is the space factor . (conductor cross section divided by the total cross section area, including insulation and interspaces), the power is P: 41 Fr gads The power optimization calculations for solenoids of the 2nth order will be demonstrated by the example of a solenoia of the sixth order. Using Eqs. (5) to (8), Lagrange's method of undetermined multipliers yields 4r £ p Jedlo + juo (Ho. I to Juts)- - Me by to IAS - un bon ta I cl + min. (9) After differentiation with respect to J we obtain Jesten ( mofo + un fz +, un fy) (10) Successive multiplication by f, and integration leads to holde ds + me sy te ka d$ t,m te ft As - Ho (II) Using fą and 1%, respectively, instead of . We obtain two similar, but homogeneous equations which can be used to deter- mine Ho, Hz, and M2• Then, Eq. (10) yields J and the lowest possible value of the power is . r- - . . a. Figure 2 shows current".---- density distributions for power optimized solenoids second, fourth, sixth, and Fig. 2 . . eighth order. The current density J 18 a function of the axial coordinate z only. J' stands for a current density distribution of the type f(z)/r. Using the nomenclature &, and ag for the inner and outer radii, respectively, and 2b for the coil length, the examples shown are calculated for ß = 2 and a volume factor ins: (az-a i . 40 (13) mü, (3) 11 = constant and I ATI = constant contours; liela bomogeneity vs Fabry factor Families of surfaces of constant field strength magni- . tudes Il = constant are convenient for demonstrating how much a given magnet field deviates from the case of perfect. field homogeneity. For axisymmetric fields the intersection of these surfaces with a plane through the axis are called T = constant contours. Figure 3 shows such contours for power optimized solenoids of the second, fourth, sixth, and eighth order. The contours indicate deviations from the center field value H. by + 0.1%. Obviously, the field homo- geneity of power optimized solenoids of higher orders are much better than that of lower order.. PI - - -- -- - , . 7 . * * NUT. ww: AP -- - ; Fig. 3 On the other hand, better field homogeneity must be paid for by a lower Fabry factor G. As is well-known,'°) the field in the center of a coil is Ho a Great --- - - - - . . . . . - . 9* 0.179 . For a coil with uniform current density and rectangular wind- ing cross section, the dimensionless Fabry factor G has a maximum value of 0.179, if a = 3.09 and B = 1.88. We define a relative Fabry factor . G (15) Its values for the power optimized solenoids discussed above . of second, fourth, sixth, and eighth order are 1.073, 0.962, 0.913, 0.883, respectively. For an actually built power optimized solenoid of eighth order, the so-called "C coil," the H] = constant contours for positive and negative field deviations of 1, 0.1, and 0.01% are shown in Fig. 4. Within a sphere of 10 cm radius . the field strength magnitude Fig. 4 varies less than 0.01% from its value H. at the center of the coil. The graph on the right side of the same fig. . ure shows contours of the "total vector error" |#-# . They are much simpler than the H = constant contours and for some purposes they may be more significant. - - -- - - --- .. .. C. 8 . . . . . 1. (4) The high homogeneity "C-coil" As mentioned in section (2), at the Oak Ridge National Laboratory a new power optimization method has been developed in order to design the large volume, high uniformity magnet (8) facility called "C-coil" which is a solenoid of eighth order.'? The coil weight was first fixed by cost considerations at : approximately 3 000 kg. This corresponds to a volume factor V ~ 100. The optimization procedure was performed with various B values and showed that a flat optimum for the Fabry factor G occurred at B ñ 3. The inside working diameter was calculated to be 32 cm. For the optimization procedure it was initially assumed that the coil is divided into 60 "pancakes" of equal axial thickness, each having a constant current density J. Thus, tubular conductors with 30 different radial heights would be necessary. However, many "effective" conductor sizes can be obtained by winding together conductors of a fixed axial width but with different radial heights. Since coils of large diameter require several parallel water. paths for sufficient cooling, the above "mixing" can easily be done. In this way many different current densities can be achieved with only a few different conductor sizes. A detail study showed that instead of 60 only 19 pancakes, made with four different conductor sizes, yield almost the . . optimum theoretical data. That can be achieved by "mixing," by using four "triple pancakes" (cooling water enters in the midplane and leaves in two side planes) and by arranging trin- ming shunts (for relatively small currents) across two pan- . cakes (the remaining little imperfections can be noticed on : the slight distortions of the contours in Fig. 4): . . : Based on a careful heat transfer calculation it is ex- pected that with 6 700 kW a field of 62 kGs can be safely achieved. Power tests and precision field strength measure- . ments are presently being done. ("D coils")(9) Another large-volume coil assembly in the magnet labora- -- . .. .. , . .. .. --ev. 1. - is. current density, a common vertical axis, and a variable gap in between. The usable inner diameter is about 33 cm for the aiding case, but because of the necessity of a mechanical support sleeve, only 28 cm for the "cusp" arrangement (coils producing fields in opposite directions). Each coil is 32.3 cm: long. The power consumption of the coil pair is 6 400 kW.. Helmholtz position is achie red with a center-to-center . spacing, 's, of 37.5 cm, and the center field H, is 61.7 kgs. With s = 36.1 cm, H = 63.4 kGs and an oblate zone of high field homogeneity results which can be advantageously used for certain planned experiments. The maximum center field strength of 67.9 kGs (which corresponds to a Fabry factor of almost 0.179) is achieved with zero gap (s = 32.3 cm); however, in this case the field homogeneity is appreciably reduced. In cusp operation the maximm field gradient occurs. with 8 = 37.8 cm. At the "Maxwell position," s = 59.2 cm, Fig. 5 the field gradient magnitude around the coil center changes very little (Fig. 5). The gradient is only 68% of that . obtained with s = 37.8 cm, but is 92% of the possible maximum . .. . Bi. 10 . . .. : :. . which can be achieved by means of any fourth-order coil pair. The axial field has a maximum at 39.9 kGs at z =. 31.5 cm.' . When the coils are operaced with their fields aiding, the magnetic force tends to pull the coils together and this force can be withstood by a flat Micarts.plate between the coils. At zero gap the total force is 430 000 kg, but the average pressure is well within the compressive strength of Micarta. Because of the very high repulsive forces in cusp operation, besides very strong bolts & center sleeve has been foreseen (Fig. 6). Seventy-six strain gauges are provided for measuring the mechanical forces acting on the · Fig. 6 various parts of the coil assembly.. : (6) Conventional vs superconducting coins The present state of designing stabilized superconducting coils is 80 advanced that the technological difficulties in manufacturing large - volume superconducting solenoids l'or 50 to 80 kGs are approxi- mately the same as those for building the corresponding conventional magnet coils. Despite good experience with water- cooled, large volume magnets in several laboratories, we would not dare to say that all technological problems concerning conventional magnet coils have been perfectly solved. . At the Oak Ridge National Laboratory around 30 000 kW d.c. power is available (mostly from magnetic mass separation facilities built during World War II), and electric energy is very cheap. Therefore, at this place investment and operation costs are in favor of conventional magnet coils. . . . . . c. . R RA . → . . ? 11 OH A great advantage of superconducting coils is that the regulation of small power sources in much more convenient than that of power supplies for thousands of k. Further- more, the operation of surerconducting coils in persistent mode yie.lds Ideally constant magnetic fields without the necessity of high precision regulation devices. On the other hand the possibility of achieving large rates which are at any rate limited by the inductance of large volume magnets, might be even more curtalled by the permissible rate of . current change of superconducting coils. In the design of solenoids for extremely high field homogeneity, it might be necessary to consider the remanent fields of superconducting coils. Initial difficulties in building dewar vessels which are able to withstand the extreme ly high mechanical forces of large coil systems seem to be overcome. Finally, concerning the accessibility of the magnetic field volume of interest, superconducting coils are more advantageous if the experiments for which the magnetic fields are provided are to be performed at liquid gas tempera- tures... References od (1) R. L. Brown and J. N. Luton, Oak Ridge National . Laboratory, ORNL-3315, 74 (April 1962). ... (2). W. F. Gauster and M. W. Garrett, ORNL-3652, 105-112 . (April 1964). (3) C. Fabry, L'Eclairage Electrique 17 (43), 133-41 (1898) and J. Phys. 2, 129-34 (1910); J. D. Cockcroft, Proc. Roy. Soc. (London) 227A, 317-43 (1928); F. Bitter, Rev. Sci. Inatr. 1, 479-87 (1936); 8, 318-19 (1937); 2, 373-81 (1939); W. F. Gauster, Trans. Am. Inst. Elec. Engr., Pt. I: Commun. and Electron. 79, 822-28 (1961); F. Gaume, pp. 27-38 in Proc. Intern. Conf. High Magnetic Fields, Cambridge, Mass., Nov. 1-4, 1961, ed. by H. Kolm et al., MIT Press and Wiley, New York, 1962. (4) M. W. Garrett, J. Appl. Phys. 22(9), 1091 (September 1951). From references cited there, the following ate of special interest: J. C. Maxwell, Treatise on Electricity and Magnetism, vol. II, sec. .715, Clarendon Press; Oxford, 1873; L. W. McKeehan, Rev. Sci. Instr. 1, 150 (1936); A. E. Shaw, Phys. Rev. 54, 193 (1938); M. Ference, A. E. Shaw, and R. J. Stephenson, Rev. Sci. Instr. 11, 57 (1940); and A. Sauter and F. Sauter, Zeit. Physik 122, 120 (1944). F. Gaume, loc. cit.; M. W. Garrett, Production of Strong Magnetic Fields and Gradients with Homogeneity of the 6th to 20th Order with Thick Cylindrical Coils (to be.. published). An extensive list of special cases calculated by M. W. Garrett is contained in D. B. Montgomery and J. Terrell, National Magnet Laboratory, MIT, AFOSR-1525 (1961). .- .- - - . - - - - - - . . an . .! " IS References (continued). (6) Ch. Fabry, L'Eclairage Electrique 17 (43), 133-141 (1898). (7) J. N. Luton, ORNL-3908, 216-118 (October 1965). (8) J. N. Luton and C. E. Parker, ORNL-3760, 80-87 (October 1964). (9) See ref. (7), pages 118-124. - - (11) W. F. Gauster et al., World Power Conf., Lausanne, .: Switzerland, Rep. 56, 1954–1972 (1964). - - - - - - -- -- - - - - --' . - -- - - - . . - - -- - - - .- - .. ..- .. . - . - -.- 4- - .. . .... ...... .... . ..... List of Figures (1) Magnetic field of a symmetrical solenoid. . (2) Current density distributions J = J(z) and J' = f(z) /r .. of power optimized solenoids of second, fourth, sixth, and eighth order. v = 40; B = 2.0. (3) 1l = constant contours for power optimized solenoids. : Solid lines indicate second and fourth, broken lines sixth and eighth order solenoids. Field deviations + 0.1%. Left picture for solenoids of second and el-ghth, right picture for fourth and sixth order. (4) 18 = constant (left), and AH = constant (right) contours. (5) la grad i = constant contours o.the D coil pair. (6) D coil pair assembly.. - - - : : .. 1 3 .- - - ORNL-DWG 64-5195 Figure I. . ------- ORNL-DWG 64-4609 R 1.0 MT Q2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 10 Figure 2. OWNL-OWO 64-626OR . اه ل 1. 00 Figure 3.. One-owo ni-mw S-in (COMPUTATIONAL INNER RADIUS) 2009 clin) ခုအခါ Figure 4. - . . . - - - ZA . . - a ''WW. . . . . ... * i m intito 1. . 4 . : : 16 . N 0 . - 2 4 . ce Rn 11. " . . > 77 * P . 174 ON . . 1 * The - . . .. - MUR -N Y Shir - -0 * TW " . . . . , ** . 1 09 # S . . 2 * # . 26 . 2 L . Figure 6. f . . & . . I . . . AL " .. * : : . . W* 7 . ti .: . E 1 + . . . C . FN . . . . mometer . . . ' . . . 1 . 1.1., : 1 ....... .................... T ORNL-DWG 66-622 R 0.5% (40) ?' Figure 5. 2 0.1% OO ("u!) d - - END DATE FILMED 10/25 /66 22 .