Blackfield, D.

Cheng, E.T.

Fisher, J.

Langton, W.

Montgomery, D.B.

Rapperport, E.J.

Tracey, J.E.

Wan, A.

Yang, T.F.

DSpace@MIT

CONCEPTUAL DESIGN OF BUNDLE DIVERTORSMassachusetts Institute of TechnologyT. F. Yang D. BlackfieldE. J. Rapperport A. WanJ. E. Tracey D. B. MontgomeryW. LangtonDraper LaboratoryJ. FisherGeneral AtomicE. T. C. ChengPFC/JA 80-32CONCEPTUAL DESIGN OF BUNDLE DIVERTORS*Massachusetts Institute of Technology1'. F. YangE. J. RapperportJ. E. TraceyW. Langton1). BlackfieldA. WanD. B. MontgomeryDraper LaboratoryJ. FisherGeneral AtomicE. T. C. Cheng* Work supported by DOE Cont.#DE-AC02-80ER-52057TABLE OF CONTENTS1. Introduction2. Magnetic Concept Development2.1 Magnetic Configuration2.2 a-Particle Confinement3. Structural Concept3.13.23.33.4General DescriptionMagnetic ForcesStructure ConceptConductor Considerations4. Nuclear Shielding Study5. SummaryAcknowledgementsReferencesI1. IntroductionIt has been discussed by many authors [1,2,3,4] that bundle divertors can be greatly improved by varyingthe coil configurations. The designs of a bundle divertor for reactors have been discussed in detail in references[1] and [2] and were found to be feasible. However, there were still many shortcomings which needed to beresolved. Two of the major shortcomings were: that the ripple is too large, which enhances the loss of energeticparticles; that the current required in the divertor coil is too large, and the divertor coils interfere with the TFcoils, making the maintenance difficult. To alleviate some of these problems a short T-shaped coil configurationhas been proposed by T. Yang [41 and a long T-shaped hybrid divertor has been proposed by H. Furth [5]. Thisdivertor configuration is illustrated by Figure 1. As has been discussed in the 1979 U.S. INTOR report and inreference [4], the horizontal conductor elements will increase the divertor field required to cancel the toroidalfield and will also enhance the radial component of the diverting flux lines. Such a divertor requires less currentand thus produces lower ripple. Another method of reducing the ripple is to use an "X"-shaped four-coilarrangement like a small tokamak, proposed by R. Dory and John Sheffield [2]. All these configurations havebeen examined in this report. It is found that four coil configuration gives the lowest ripple but the associatedengineering problems are quite difficult. A compromised physics and engineering solution can be obtainedfrom the two T-shaped coil configurations.2. Magnetic Concept2.1 Magnetic ConfigurationThe plasma parameters and TF coil number and size used in this study are listed in Table 1.2Table 1. Key parameters for INTOR and ETF used in this study.= INTOR ETFRo = 5.2 m 5.5 mBO = 4.8 T 5.5 Ta = 1.3 m 1.4 mR7 'F = 10.5 m 11.5 mTF# = 12 12*RTF, (outer radius)These parameters are chosen partly based on the INTOR and ETF spaee under consideration, and partlyfor computational convenience. They provide information and comparison for different sizes and field inten-sities and a flexible range when choosing final parameters. The coil configurations studied here are shown inFigure 2. The typical flux patterns for these coil configurations except (a) arc shown in Figure 3. The magneticconfiguration of coil type (a) is similar to Figure 3(c). Configuration 3(b) shows the T-shaped divertor withexpander coils. It shows that flux can be led to the outside of the TF coils and expanded which makes theparticle removal and thermal handling easier. The configuration 3(c) was considered to be desirable for lowerripple and energetic particle containment. The major disadvantage is that the magnetic intensity at the middleof the diverted flux loop, is 17 Tesla, i.e., the field becomes the strongest and the flux tightest at this point whereexpansion is needed most. The 17 Tesla field makes the expansion nearly impossible. An attempt has beenmade to expand the flux or reduce the field intensities by opening the outer legs as shown by configuration 3(c)and by changing the coil shape as shown by Figure 3(d). The gain is insignificant. The radially outward transla-tional force in configuration 3(b) is approximately equal to 20 MN whereas it is nearly zero in configuration3(c). In the configuration 3(c) the interaction of the divertor with the TF coil is negligible. From an engineeringpoint of view it is nearly an independent structure, since minimal structure is required to hold the divertorassembly in place. As will be discussed in the mechanical section, the divertor can still be designed as a plug-in unit for case (b). Lacking an adequate method to expand the flux, or to remove the particle and heat load inthe very tight space in case (c) and (d), we will concentrate our effort in optimizing case (b). To determine theoptimized design parameters, the field ripple on axis and the divertor current are plotted in Figures 4, 5, 6 asfunctions of height, width and length, while the coil position and separatrix are fixed. Figure 7 plots the rippleand the position of the separatrix as function of current. The design point for INTOR is shown by the dot. The3choice was made based on many engineering and physics considerations. For physics consideration one wouldlike to'make the ripple as small as possible. The ripple reduces linearly as the width reduces and the lengthincreases. However, the current requirement increases in both cases. The ripple and current decrease with theheight and there is obviously no lower bound. Therefore, physical contraints have to be considered for makingthe selection of parameters.For the convenience of maintenance, the width of the divertor assembly was chosen to be smaller than thegap so that the whole assembly can be removed without interfering with the TF coils. The width and height arealso the minimum required to allow 30 cm of shielding on each side, 30 cm of plasma duct, 50 cm of conductorpack, and 10 cm of structure. The amount of shielding chosen is based on the life time of 1 MW-Year. Anythingless is considered dangerously optimistic.The magnetic field intensitites along a field line of the midplane for the two T-coil case are shown inFigure 8. The ripples calculated from these fields are plotted as a function of major radius and shown in Figure9. Figure 10 shows the ripple as a function of vertical distance z from the midplane for fixed radii. The ripplecurves can be approximated by an exponential functionE(z, R) = EI(R)e--/a,where a = 1.06 for this particular case and E(R) is the amplitude of the ripple given in Figure 10. Theexpanded ripple for T-coil with expander and for the four-coil type is also plotted in Figure 9. The ripple forthe T-coil with expander is only 0.4 on axis and becomes positive at a smaller radius and is generally betterthan the four-coil case. The implication of this kind of ripple distribution on the particle confinement has to bestudied. Preliminary calculations of an a-particle orbit and beam particles are given in the following section.2.2 a-Particle ConfinementThe a-particle orbits have been studied for four cases using the code FLOC developed by Fowler andRome [6]. In Case 1,the current is 7.2 MA and the divertor height-to-width ratio is 0.58; the orbit is shown inFigure 11, and the banana orbit is not confined. In Case 2, the current is 8.3 MA and the height-to-width ratio is0.5, but the coils are separated by 1.4 m. The banana orbit is again not confined as shown in Figure 11. In Cases3 and 4, the height-to-width ratio is 0.5 and the coils are separated by 1.2 m, and the divertor currents are 11.24MA-T and 6.72 MA-T respectively. In both cases the a-particles are confined as is shown in Figure 12. The timesequence of the banana shows that the banana steps toward the center of the machine. More study is requiredin order to draw a positive conclusion. However, the results indicate that the a-particle can be confined for sucha divertor system. The typical confined beam particle orbit is shown in Figure 13. The lower picture shows thevariation of angular momentum of which is time average is nearly conserved.3. Structural Concept of ETF Bundle DivertorA prime requirement of the structure is the necessity to provide easy demounting of the bundle divertorfrom between the TF coils for servicing requirements.Four "L"-shaped saddle magnet coils, each approximately 50 cm square in cross-section, 2.4 meters high,1.2 meters wide, and 1.2 meters long are arranged to form a bundle divertor for the INTOR. These coils maybe constructed of OFHC water-cooled copper conductors run at a current density of less than 6000 a/cm2 in theconductor. The substantial forces generated by these windings are delivered to their surrounding structure inthree dimensions. Hence, the structure conceived is made extremely stiff in all three dimensions.3.1 ForcesThe net horizontal plane forces delivered by the divertor coils to their containment structure is given inFigure 14. This figure shows an indicated net radial force of about 30 MN on the whole assembly.In addition to this net radial force, each pair of coils has substantial opposing forces in the perpendicularcircumferential direction, and also in the perpendicular axial direction (out of plane). These forces have beengiven preliminary examination as have the interactive forces on the adjacent four TF coils.53.2 Structure ConceptThe basic structure containing the bundle divertor coil forces consists of two thick 304L stainless steelplates (approximately 15 cm thick) top and bottom, with built-up box beams (keyed and/or welded) of 304Lstainless steel. A mid-plane section of a plan view is shown in Figure 15. The box beam sections shown inFigure 15 are schematic in nature, but they do have a geometry that keeps the bending stresses below 20,000psi, consistent with the ASTM Boiler and Pressure Vessel Code, Section VIII, Division 2.The four bundle divertor coils are envisioned as being sandwiched between the stainless steel platesmentioned above, with suitable intermediate tie-downs and strong-back cross-beams, to form a large, rigidmonolithic assembly which fits between two adjacent TF coils as shown in Figure 16. Keyed joints (demountable)will be made between the monolithic assembly at its edges, and mating plates attached to the two TF coils toSupport the approximately 16 million pound net racdial thrust of the divertor asssembly. The keyed joints aredesigned to allow remote removal of the keys and shim plates, which would then permit the radial movement ofthe entire monolithic divertor assembly outward from its operating position on rails, rollers, or other means.The stainless steel plates which remain with the TF coil assemblies will have low thermal conductivitycompressive links of G-10 in order to effect a satisfactory load link between the TF coils at liquid heliumtemperature and the divertor at ambient temperature. This compressive load link will have an intermediateliquid nitrogen cooled metallic intercept station to reduce the heat loss along the load path.3.3 Conductor ConsiderationWater-cooled copper conductors have been considered for use in theINTOR and ETF bundle divertor.Preliminary examination indicates that the 8.5 X 106 amp. turns required for each divertor coil can be achievedusing a conventional square O.D. conductor (2.3 cm on a side) with a round cooling hole (1.3 cm). For the 400turns per coil envisioned, the current in each conductor would be approximately 21,250 amperes at a currentdensity of about 5400 amps/cm2 in the conductor (3400 amps/cm2 average within the coil envelope).Half-turn (360 cm) cooling with a water flow velocity of 4.6 m/sec (approximately equal to 36.3 litres perminute per half turn) gives rise to a temperature increase of about 39"C to the cooling water at a pressuredifferential of about 0.79 Atm between inlet and outlet.6Alternatively, full-turn (7.2 m) cooling could be utilized with a water flow velocity of 9.2 m/sec (approximatelyequal to 72.3 litres per minute per turn) with the same 39*C temperature rise inlet to outlet and a pressuredifferential of about 5.5 Atm inlet to outlet.Each front coil, therefore, requires approximately 70 MW of electric power for its operation and about28,766 litres of water per minute to remove this power. The power requirement for half height coil and current6.72 MA-T would be approximately 33 MW.4. Nuclear Shielding StudyA one-dimensional ANISN calculation has been done to estimate the shielding thickness needed for thenormal conduction operation. The one-dimensional shield model is shown in Figure 17. The dose rate on theinsulation material (epoxy-base material such as G-10) as a function of shield thickness for three shield materialcombinations, 10% H20 (B) + 50% W, 30% H20 (B)+ 70% W and 50% H2 0 (B)+ 50% W have been obtained.The results show that the 10% H20 (B)+ 90% W shield is the best material combination. The neutron flux,nuclear heating and dose rate are plotted in Figures 18, 19, and 20, as functions of thickness for the best case.The dosage on the insulator can be expressed asD~x)= Do~e0. 140081--3.3333 x 10-4t2D(z) =  io~*e-where D(o) = 2.5 x 10'" Gray/year at MW/M 2 wall loading and t is the shield thickness with unit measureof cm. The lifetime of the insulation for three thicknesses for the dose limits of 107 and 109 Grays are listed inTable 2. Since there is 10 cm structure and 30 cm shielding, it is fair to say that the divertor can operate for 1MW-Yr/m 2 . If the duty factor is 50%, the divertor lifetime would be one year for 2 MW/M 2 wall loading. Sincethe divertor can be designed as a plug-in unit, a one-year replacement schedule should be very reasonable.7Table 2. Magnet Lifetime (MW-YR/nm2) for Dose Limits of 107 and 10) Grays.Shield Thickness Insulation Dose Limitscm 107 Gray 109 Gray (MIT test)[7]30 cm 0.004 0.440 cm 0.02 250 cm 0.1 1060 cm ~ 1 1005. Summary and DiscussionThe coil dimensions, current and power consumption are listed in Table 3.Table 3. Dimensions and Currents for Selected Bundle Divertor for INTORheight = 1.40 m I = 6.72 MA-turnslength = 1.20 m 12 = 4.8 MA-turnsR, = 7.3 m- coil cross-section = 50 x 50 cmR 2 = 10.2 m Averagej = 2.6 ka/cm2= 0.56 ka/cm2/TeslaThe current required for ETF is 8.3 MA-T and R, = 7.6 m. This divertor is feasible from an engineering andphysics standpoint; the power consumption and lifetime arc reasonable, and the replacement is easy. The mostsignificant achievement of this concept is the drastic reduction in size and outboard forces. This fact can bedemonstrated by the comparison of INTOR and ETF with a similar reactor design DTHR() as is shown inFigure 21. DTHR uses conventional two coil divertor whose size is more than double that of INTOR and ETF.Further optimism and detailed study of particle confinement are in progress.8References1. T. F. Yang et al, 8th Symposium, IEEE, San Francisco (1979).2. John Sheffield, R. A. Dory, "The Ripple Bundle Divertor for Tokamaks", ORNL-TM6220 (March, 1978)and U. S. INTOR Report (1979).3. A. D. Sanderson, P. E. Stott, "A Bundle Divertor for Fusion Reactor", CLM-P530, Culliam Laboratory,Abingdon, Oxfordale, England (1978).4. T. F. Yang, U. S. INTOR Report (1979) and Westinghouse Report (1980) "Bundle Divertor Magneticsfor ISX-B, ETF and Reactors" pro. of the U. S./Japan Workshop on Divertors, 1st Wall Materials andImpurity Control, JAERI-M8971 Japan, (March, 1980) P. 165.5. H. Furth, C. Ludescher, U. S. INTOR Report (1979).6. R. Fowler and J. Rome, FLOC code.9Conductors( _________r -NullFraceFig. 1 Schematic of a T-shaped bundle divertor coil.3,8''0(a)(b)(c)(d)Figure 2 Divertor Coil Configurations3.9(b)+3.0- +1.08.0X( c)+10 \I II-1.0 Al-.-'-3. 0rI I y6.0 8.0X(c)04,0 6.0(d)117.3/10.0 4.0 6.0Figure 3 Magnetic Flux Configurations for thecoil type (b), (c), (d) and (e) inFigure 2. 3.10U-1.0-3.04.0 8.0XC0,-wD4.0 8.0 -X10.0I1.50 14.01.4013.01.30-. 12.01.20RippleC 1.10 11.001.00/ 10.0Current.90DesignPoint9.0.80.70 8.01.4 1.6 1.8 2.0 2.2 2.4Height (m)Figure 4 Both ripple and current increase with height.3.11Rip.1 1 I I I2.6 2.8Width (m)Ripple and current as functions of width(Ripple increases while current decreases with width)3.121.50 4-1.401.30 +1.20o 1.10W)x1.00 .4.Designpoint.90 4-.80.70/2.4Figure 53.2-8.5.8.07.57.0-6.504-- 6.0.5.5.04.5Currentple0.85 9.50.80 Ripple 9.00.75 8.5Currentf00.70 8.00.65 7.50.60 7.01.0 1.1 1.20 1.3 1.4 1.5Length (m)Figure 6 Ripple and current as functions of length3.131.00 4I I7.0 8.0 9.0 10.0 11.0Divertor Current (MA-T)Figure 7 Ripple and radius of separatrix as function of current.3.141.10RippleRadius ofseparatrixDesignpoint.90 4.80 1.70.60- 6.60- 6.55.- 6.50.-Hca~-6.45 w06.406.3512.0--.dxpetf5bfl .frame: 31.117A6AI6.51AM6a."zigIM3Err bauM O:arMu 0a r-c .srt 18:40:sa asZb/alFIELD MRN1UDE RLONI FLUX LI R3 TI RWUL 9I I -11'- - ' ~ -* £ IU i. - -U - UUUNU Ui ISFigure 8 Field Intensities along the FieldLine for Configuration 3C.3.15w 0to0 0 - eI .1 . . . . IImcm1+E r=omx ca)wzIw-L.z-/INY Co0* - 00I I0 N3.16.-00C-,)I-e . ,* 0.9-ICo 0£000x4-£0000..... 1..e 0i4I I*-iw-Lo .o0W 0*NN3.17dxplotssivframe: SGUIDING CENTER ORBIT.-I.0 3.0 0R (m)c- W0.0 keYA - ..IV - 72MG. M0 - o.o8+o- S.24 T*|S.D,- 7Me. M- 3.5Ap- 3. 3 301- D.20o- 0.47a9M(a)-3.0 3.0 3.0GUIDING CENTER ORBIT*0~~~~~**/ ~*r -*~\* . / ,qs>~(I I I~ * I *~ I I I I I.I.0 S 0JI~.f.jlI j *~~i0~ ~. \ \'0to. \'.1' i~ */.i...'0 * .--*~I I. 3.0 C:AR (a)- W3500.0 ke0- 0. s - cos- S.24 t.7. I~oy ,- 79. M-3.4i4. - 330S- n~an- 0.47xFigure 11 Unconfined a-particle orbits.3.18R - 8.70 nz - O.fl gToo VLawj0.3 23.0R - 6.70 r* -- M. Mz - 0.00 aaI,a§so0NarCI.9(b)Top VLov.20.1 23.0iRIRGUIDING CENTER OR8[TaI.,a-qN* (* ~kflI . /i..: j~d *T.4S...-.,aI.0 50 60 ..P.fin)0 - :3500.0 k1- 4.0Ere - 9600. mB - 0.06480- 5.24 TI A- S.70-90.00- 0.00 i-x~. I I Ia9~4 Ej4]ci-5GUIDING CENTR ORBETr --I**1iR (a)- 3500.0 keYN - 40Io- ao0. M0 - 0.08 .80 - S.24 *r[p - 78e. kMIS - 3.6S- 3.250- .20- 0.47R - 6.70 a* -0.,z - 0. 00 nlop YLQwSa>4- H-aa0~~ V.O '3.0 L.0 3.0 30.1 10oxConfined a-particle orbits3.19.3ey I,, - 7898. kA Rq - 3.6 , 0Bp - 3 .50- 0.50 --0.47Top VLew*-/i.IaaNa(~~) jaaNa*55~~IIFigure 12-GUIDING CENTER ORBITN094.0 5.0 6.0R (mlE0 - 150.0 keM - 2.01RC - 8000. kF- 0.0068o - 5.50 Ta.------0In00. I7.0 8.0v I - 4900. kAqS - 4.3O, - 0.532e - 0.50y - 0.74Top VLew--- - - -- - - ---------10.0 -5.0 0.0 5.0 10.0x -, A. 00-amo 0.0 2.0 4.0 8.0 8.0 10.0 12.0 ti.0 18.0 L8.0 20.0 22.0 24.02 .0TIME (SEC)Figure 13 Typical confined beam particle3.20R - 6.50 m0 -- 90.00z - 0.~00 ma *..:.,/a , ,as, * *a.a,...,..' *. a a.a,.a~ *,a - - a tt~a* a aa a,a *,a *gaaaa a.I *:I,~~it at,.* a. at.... *4,t *aa a a~. a.a a. a, a a/a. aaaaat. aa a.a~ a ~aa a a aa a a a aa *a a ~ *'a' a~ta a a aa a aL5.028.09 0I3.6MN3.6 MN4.9 MNr - 30 M NZZM3OM22MN-7.6MN- m8.93.6Figure 14 Preliminary summatibundle divertor coi3,6on of forces acting on energizedls of INTOR. 3.21V0-om-LJ3.22I 00*1-4-0LI.CCCCooIIz0i--LLL -JuJ- :D >I--cc00Xzw uoz - 0> C)cr 0z0--0C,-)Uw3.23ONE- DIMENSIONAL SHIELD MODELPLASMAANDVACUUM00+2cmTUNGSTENBORATEDWATERxMAGNET40cmFigure 17 One-dimensional shield model3.2410 2710-0.0 0.2 0.4 0.6 0.8Figure 18SHIELD THICKNESS (m)flux as function shield thickness3.25NEUTRON FLUXATDEPTH INTO MA-KN0.wS.IO510 24102310-I010-GNETI I1.0to.NeutronI100710-TINGAGNET0.2 0.4SHIELDNuclear heating0.6 0.8THICKNESS (m)as function of shield thickness3.26NUCLEAR HEAATDEPTH INTO M~-SCJS I-z-21O-110-0.0Figure 191.0I . I-.]i 2iIOi10'010 10.2 0.4 0.6-K50%W< 50% (B) H2 0-.70% 130 090 % w10% (B) H20-NI 10.8Figure 20 DoseSHIELD THICKNESS (m)rate as function of qhild thirknoetc 3.27w%(B) H2010108I~j-wC,,0010710*100.0 1.0I Ij07PS-SMIRROR COILTF COIL DEWARDIVERTOR COILDEWAR- 40'FLUX BUNDLE4-MIRROR COILDEWARCOILFigure 21 Comparison of two circular coil divertorsand two T-shaped coil divertors3.28-. 4

Conceptual design of bundle divertors

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Conceptual design of bundle divertors

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