Bromberg, L.

Cohn, D.R.

Schwartz, J.

Williams, J.E.

DSpace@MIT

DOE/ET-51013Performance Limits of High Field Tokamak Reactors*byJ. Schwartz,* L. Bromberg,D.R. Cohn and J.E.C. WilliamsAugust 15, 1988Plasma Fusion CenterMassachusetts Institute of TechnologyCambridge, Massachusetts 02139 USA*This work performed under D.O.E. Contract #DOE-ACO2-78ET-51013. Re-production, translation, publication, use and disposal, in whole or in part, by or forthe United States government is permitted.**This work performed under appointment to the Magnetic Fusion EnergyFellowship which is administered for the U.S. Department of Energy by Oak RidgeAssociated Universities.Submitted for Publication: Nuclear FusionPFC/JA-88-27ABSTRACTAn analysis has been performed to investigate the limits of high field com-mercial tokamak reactors. Variations of maximum mechanical stress, major radiusand performance parameter B 2a (where B is the magnetic field on axis and a isthe minor radius) were investigated to evaluate the potential impact of higherstrength structural materials and higher field superconductors. For fixed valuesof major radius and stress, tokamak parameters were chosen to optimize machineperformance. Increasing values of allowable stress correspond to decreasing capi-tal cost, and may be an effective approach to economical commercial fusion. Theprospects of using very high strength structural materials to provide sufficientlyhigh field for ohmic dominated heating to ignition in power reactors with majorradius - 6 meters are discussed.1I. IntroductionSignificant physics and engineering advantages may be obtained by operatingtokamak reactors at very high magnetic fields.1 High field operation could providecapability for high nr in relatively modest size plasmas, as well as strong ohmicheating. It could allow relatively low current operation, provide high wall loadingin DT plasmas with low 3 and compact size, and make possible advanced fueloperation with moderate values of 3. Super High Field Tokamak reactor designconcepts have been proposed to exploit these advantages.2 3' 4Although high field operation makes the toroidal field magnet design moredifficult, it could simplify the engineering of many other systems. Strong ohmicheating could greatly reduce or possibly eliminate startup auxiliary heating powerrequirements. Current drive requirements could be significantly reduced in twoways: (a) lower current requirements for sufficient nr due to high aspect ratio op-eration and, (b) more efficient current drive, such as improved lower hybrid currentdrive efficiency due to better accessibility." 5 Low 0 operation might also reducethe need to finely tune and shape the plasma, thus simplifying the plasma magnet-ics and reducing problems due to disruptions. Furthermore, if high field operationprovides adequate confinement for tritium-lean or advanced fuel operation6 , itcould substantially simplify the blanket design by reducing the required tritiumbreeding ratio.II. Limit AnalysisIt is natural to ask about the limits of this approach. To assess the point ofdiminishing returns of high field operation, a limit analysis has been performed.This analysis considers the impact on tokamak reactors of extrapolations of themaximum stress in structural materials and the maximum field at which a super-conductor can carry adequate current density. The maximum allowable stress has1been extrapolated to 1.5 GPa, and the maximum field with current to 39 T. Thelimits of extrapolation are based on the properties of existing laboratory materials- with extrapolation to improved performance and new fabrication techniques; andproduction on a larger scale and in more complicated geometries than is currentlypossible. Timescales for development are ten to twenty years assuming solid butnot 'crash program' support levels.With respect to the superconductor, Nb 3 Sn is capable of carrying sufficientlyhigh current density (J > 1x10 4 A/cm2 ) at B ~-- 0.75B, 2 , where Bc2 is the uppercritical field. 7 A similar A-15 superconducting compound, Nb 3 (Al,Ge), has anupper critical field B, 2 - 52 T. A non-optimized Nb 3 (Al,Ge) tape has alreadycarried 1x10 4 A/cm 2 at 31 T,' and further increases in current density at higherfields can be expected. Furthermore, a B1 class superconductor, PbMo6 S 8 , hasan upper critical field B, 2 - 60 T.' This conductor is difficult to fabricate andprogress in its development has been relatively slow. If these low temperaturematerials can be developed to the level of present day Nb 3 Sn, it may not beunreasonable to extrapolate superconductor operation to 45 T. Furthermore, manyof the recently discovered perovskite high temperature superconductors have anupper critical field in excess of 100 T,10 and thus might be ultimately capable ofcreating effectively unlimited magnetic fields. To be used in practical magnets,however, these superconductors will have to overcome many obstacles, includingproblems associated with anisotropy and grain boundaries. For this analysis thefield limit resulting from Jc(H) is taken to be 39 T, based on Nb 3 (Al,Ge).Structural steels currently have ultimate tensile stresses in the neighborhoodof 1.8 - 2.0 GPa (e.g. Inconel 9XA, JBK-75, Fe-Mn alloys)." Nickel-Cobalt andNickel-Titanium maraging steels, however, have cryogenic strengths in the neigh-borhood of 2.5 - 3.3 GPa and Carbon, Silicon Carbide, Boron and polymer fibreshave strengths in the range of 3.5 to 4 GPa.12,13,14 In addition to high strength, the2utilization of these materials will require high fracture toughness and fabricabil-ity. Composite materials combining fibres with aluminum have already been suc-cessfully produced and are available commercially with ultimate tensile strengthgreater than 1.7 GPa.' Thus, one can imagine a composite comprised of a highstrength steel matrix and very high strength fibres to produce a material capableof operating with an allowable equivalent tensile stress greater than 2 GPa. How-ever, as there is no experimental database to demonstrate that these materialsare compatible as composites, a less aggressive extrapolation philosophy has beenemployed. Our approach is to assume the development of laboratory materials tousable, commercial products. On this basis, the materials described above providean allowable stress in the neighborhood of 1.5 GPa.III. Performance Parameter B 2aThe comparison of reactors requires a goodness parameter that quantifiesreactor performance. Using Neo-Alcator scaling for ohmically heated plasmas(TE - naR2 )' 6 , the ratio of ohmic power (PQ) to power losses (PLO,,) is found tobepo B 2 a-oa T 5(1)Phoss T 2where B is the toroidal magnetic field, a is the plasma minor radius and T is theplasma temperature. For pure ohmic heating,Ph-==1 -== T,, ~ (B2 a)i (2)PLosswhere Tq is the maximum temperature achievable with pure ohmic heating. Thus,TO scales with B 2a.Under certain circumstances, the confinement parameter n-r also scales withB 2a. The plasma density is constrained by the Greenwald limit" and f limit.The scaling for density isn ~ rJ ~ B/Rq. -+ nr ~ (B/Rq.)r (3)3n ~ B2 --+ nr - (OB2)-r (4)where 3 is the plasma beta. With Neo-Alcator confinement scaling, the Greenwaldlimited case becomesn7r ~ B 2 a/q,. (5)Since the maximum temperature from ohmic heating scales with B 2 a, high B 2atokamaks may require minimum auxiliary heating power. If the auxiliary power ismuch smaller than the ohmic heating power, neo-Alcator scaling may be the mostappropriate confinement scaling law. Alternatively, if Kaye-Goldston confinementscaling for auxiliary power heated plasmas is the used with alpha power substitutedfor input power, 2 one obtains nr - (B 2 a)0-6 . Thus B 2a could be an effectivemeasure of reactor performance for either confinement scaling.Moreover, if the density is Greenwald limited, it can be shown that the wallloading scales asP. oc B 2 a/R2 . (6)Although P, is also limited by first wall material properties, B 2 a again plays animportant role.IV. Parametric StudiesParametric analysis was performed to determine the effects of increased reac-tor size and allowed stress level on the performance parameter B 2 a. The assumedinput parameters which are constant for all parametrics can be seen in Table 1.A plasma - TF coil distance of 1.4 m will allow tritium breeding and sufficientreduction of the neutron flux into the magnet for at least 30 years of magnet oper-ation. Owing to very large forces in the TF coil, the current density in the TF coil,JTF, is less than that in the ohmic heating coil, JOH. The maximum field in theohmic heating coil, BOH, could be increased to the limit value of ~ 39 T, howeversubstantial reductions in the required area would not be obtained. The inductive4capability indicates the number of seconds the OH coil is capable of driving theplasma without other forms of current drive. For a combination of allowed stresslevel and major radius, the field strength, minor radius and aspect ratio are chosensuch that the reactor performance B 2 a is maximized.Figure 1 plots B 2 a vs. major radius at the limit stress a = 1.5 GPa. Thisstress represents the average equivalent stress in the TF coil structural material.This shows the smallest major radius that may ever achieve a given level of reactorperformance. For example, if it is found that B 2a= 250 T 2m provides ohmicignition, then a major radius of ~ 6 m is required to achieve this goal.' 8Figure 2 shows the toroidal magnetic field strength at the coil (B,) and atthe plasma (B0 ) as a function of major radius for a = 1.5 GPa. The superconduc-tor must be able to carry adequate current density at B, for the correspondingreactor in Figure 1 to be built. If it were ever desirable to build the largest ma-chine indicated, R. = 10 m, Pthermal,blanket =10 GWth (at maximum density,see Figure 3), the required field at the coil is 31 T. This is achievable today inthe laboratory with Nb 3 (AI,Ge), 8 and could thus preclude the need for the lessdeveloped PbMo6 S8 and the high temperature perovskites (although there may beother advantages to operating superconducting magnets at higher temperature).Furthermore, for a reactor of more reasonable size (R,=6.0 m, Ptherma,blanket=2.3 GWth), the required field at the coil for optimum B 2a is 27 T; the strengthof structural materials and not the properties of the superconductor limit the field.Figure 3 shows wall loading and fusion power for combined f and Greenwaldlimits. The transition from 0 limited operation to Greenwald limited operationoccurs at R0 - 6 m. The Greenwald limit was taken to ben(102 0 m- 3 ) ~ 0.75nB,/R0 (7)5where K is the plasma elongation, while the 3 limit wasfl(%) ~- 3I/aB,, (8)where I is the plasma current in MA. The wall loading limit due to first wallmaterial properties may be the dominating limit for R, greater than about 3 m.Figure 4 shows reactor performance (B 2 a) and Figure 5 shows the maximumblanket thermal power and the maximum neutron wall loading as a function ofallowable stress level for a tokamak with R, = 6 m. The maximum power iscalculated based on operating the density at the lesser of the Greenwald and flimits. If the maximum wall loading is greater than the maximum allowed bythe first wall material, then both the wall loading and the blanket thermal powermust be scaled down. The flattening of the power and wall loading curves atabout a- = 1.8 GPa in Figure 5 corresponds to the transition from 3 limiteddensity operation to Greenwald limited operation. If the Greenwald density limitincreases, the transition will occur at a higher stress level and higher fusion powerdensities might become obtainable. The power limits associated with economicfirst wall operation must also be obeyed.As material properties improve with experience and time, the 'EquivalentTensile Stress' axis in Figures 4 and 5 could be equivalently considered as a timedependence. Since these figures are for fixed size (- fixed capital investment), theincreasing fusion power corresponds to decreasing COE. Figure 6 shows the fieldstrength at the TF coil required for these reactors (R0 = 6 m). It is interestingto note that full utilization of currently producible Nb 3 (Al,Ge) requires an equiv-alent tensile stress in the neighborhood of 3 GPa. From the perspective of thisanalysis, the development of high field superconductors leads the development ofhigh strength structural materials.Figure 7 offers an alternative perspective. This figure plots the required stress6level as a function of major radius to obtain a fixed level of performance. Aperformance level of B 2a= 250 T 2m was selected as a point for which ohmicignition, 1 8 or at least ohmic dominated ignition,1 might be obtainable. Theupper curve assumes that the stabilizer material (usually copper) supports a stressof 300 MPa (as assumed in Figures 1-6). The lower curve shows the impact of ahigh strength stabilizing material, such as CuNb or Al-SiC. This curve assumesa stabilizer stress level of 800 MPa. Thus the combination of high strength, lowresistivity materials for magnet stabilization and protection and very high strengthstructural materials may allow a reduction in the size of the tokamak.This is further seen in Figure 8. As the allowed stress level increases fromabout 640 MPa to 1500 MPa, the required plasma volume is reduced by a factorof 3. If the allowed stress level in the structure can be increased from 1.5 to 2GPa, and the stress in the stabilizer increased from 300 to 800 MPa, then themajor radius of the tokamak can be decreased from 6 m to 5.5 m, thus providinga substantial cost savings. As the major radius decreases further, the rate ofincrease of the required stress level eventually becomes infinite. Figure 7 can beequivalently thought of as a plot of time vs. cost. If the allowed stress intensityincreases with time, then the required capital cost of the reactor could decrease.V. ConclusionsObtaining very high magnetic field strength (B 01 i > 18 T) in a superconduct-ing tokamak will require development of both superconductor and structural ma-terials. Presently, sufficient current density at high field in Nb 3 Al and Nb 3 (AI,Ge)is only obtainable when the superconductor is in a tape form. Tape superconduc-tors are inherently unstable in the presence of a magnetic field normal to the faceof the tape. Thus, dynamic stabilization is required and the allowed width of thesuperconductor may be limited. Furthermore, unconditional cryostability would7appear not to be possible for these compact, high field magnets. Further inves-tigation into the stability of Nb 3 Al and Nb 3 (Al,Ge) tapes is required. If Nb 3Alor Nb 3 (Al,Ge) could be developed to carry high current density at high magneticfield in a multifilamentary form, some of these restrictions would be removed. Fur-thermore, optimization of Nb 3 Al and Nb 3 (Al,Ge) processing, including improvedflux pinning to increase J, at higher magnetic fields in Nb 3 Al and consistent pro-duction of very long lengths with quality assurance may lead to the commercialavailability of a superconductor capable of performing at over 30 T.The development of stronger structural materials, capable of supporting al-lowable stresses near the ultimate stress of currently available materials will greatlyenhance the prospects for very high field tokamaks and thus possibly fusion powerdevelopment as a whole. Obtaining materials capable of supporting stresses be-yond the capabilities of currently available advanced steels is likely to require thedevelopment of fibrous composites and/or maraging steels. Presently developmen-tal laboratory materials should be capable of eventual utilization in toroidal fieldmagnets with stresses around 1.5 GPa. Candidate fibre materials are carbon, sil-icon carbide, boron and poly-(p-phenylene benzobisthiazole). Furthermore, thedevelopment of CuNb microcomposite or Al-SiC to a bulk form (i.e. strips) mayalso improve overall reactor performance.In general, increased attention to high strength materials and advanced su-perconductors may provide a significantly accelerated path for the development offusion power systems.Acknowledgement The authors wish to thank Professor R. Conn for usefuldiscussions about very high field operation.8References(1) D.R. Cohn and L. Bromberg, Journal of Fusion Energy, 5(3), p. 161,1986.(2) D.R. Cohn, Journal of Fusion Energy, 6(3), p. 281, 1987.(3) D.R. Cohn, L. Bromberg, R. Potok and D.L. Jassby, Fusion Technology,20, p. 159, 1986.(4) J. Schwartz, D.R. Cohn, L. Bromberg and J.E.C. Williams, Proceedings of the1 2th Symposium on Fusion Engineering, Volume 2, p. 870, 1987.(5) S.Y. Yuen, J.H. Schultz, D. Kaplan and D.R. Cohn, Massachusetts Insti-tute of Technology Plasma Fusion Center, RR-79-22, November, 1979.(6) J.H. Schultz, L. Bromberg and D.R. Cohn, Nuclear Fusion,20(6), p. 703,1980.(7) S. Pourrahimi, C.L.H. Thieme and S. Foner, Proceedings of the AppliedSuperconductivity Conference, Baltimore, Md., October, 1986.(8) K. Togano and K. Tachikawa, Adv. Cryo. Engr. 34, p. 451, 1988.(9) R. Fliikiger, Journal de Physique, C1-365, 1984.(10) T. Orlando, K. Delin, S. Foner, L.H. Greene, G.W. Hull, W.R. McKin-non, E.J. McNiff, Jr. and J.M. Tarascon, Phys. Rev. B, 35, p. 7249, 1987.(11) J. Martin, R.G. Ballinger, M.M. Morra, M.O. Hoenig and M.M. Steeves,Adv. Cryo. Engr. 34, p. 149, 1988.9(12) D.L. Corn, Presented at the Cryogenic Engineering Conference, BoulderCo., June, 1966.(13) S.R. Allen, R.J. Farris and E.L. Thomas, J. Mat. Sci., 20, p. 4583, 1985.(14) T. Hamada, T. Nishida, Y. Sajiki and M. Matsumoto, J. Mat. Res., 2(6),p. 850, 1987.(15) M.E. Buck, Mat. Engr. and Des., VIII(5), 1987.(16) R.R. Parker, M. Greenwald, S.C. Luckhardt, E.S. Marmar, M. Porkolaband S.M. Wolfe, Nuclear Fusion, 25, p. 1127, 1985.(17) M. Greenwald, J. Terry, S. Wolfe, S. Ejima, M. Bell, S. Kaye and G.H.Neilson, Submitted for Publication, Nuclear Fusion.(18) I.H. Hutchinson, Journal of Fusion Energy, 6(3), p. 257, 1987.10Table 1Input Parameters for ParametricsK 1.8Plasma-TF coil distance (m) 1.4q* 4BOH (T) 32JOH (MA/rm2 ) 30JTF (MA/rM2) 20Ostabilizer (MPa) 300Inductive Capability (s) 300Blanket Power Multiplication 1.2I = 5a 2 KBplasmaRoq*,.ax = O.O3 Ip/aBlasma11900-800-700-600-500-400-300-200-10004.0REACTOR PEFORMANCEEQUIVALENT TENSILE STRESS =1.5 GPa00101.1I5*.o.6.0.7.0I8.0.9.0MAJOR RADIUS (m)2250 Tm 2---BaFIGURE INEHvOptimum FieldEquivalent Tensile~14.0i5.0i6.0i7.0Stress= 1.5GPaIao.9.0 10.0B plasmaajor Radius (m)--- B coilFIGURE 232p *Now www-000,0 000 0000 0030 -28-26-24-22-20-18-I6-014-0)II0-BLANKET POWER AND NEUTRON WALL LOADINGEQUIVALENT TENSILE STRESS = 1. 5 GPaMAXIMUM DENSITY40 5.0 6.0 7.0 8.0 9.0 -10.0MAJOR RADIUS (m)- -NEUTRON WALL LOADING --- BLANKET THERMAL POWERFIGURE 3-c*0-*(94-a):50~in0987654-/---d-40- ~e-0,oI.C-50~IReactorMajor*Perfor manceRadius= 6 Meters360320280240200I-160-120 F500Equivalent-- 250TensileTanStress (MPa)--- B2aFIGURE 4E~I.0.////1000 1500 2000 2500 3000---Blanket Thermal Power AndNeutron-Wall LoadingMajor RadiusMaximum-0CLN0. 1500= 6 MetersDensity2000 2500Equivalent Tensile Stress (MPa)-- Neutron Wall Loading--- Blanket Thermal Pow erFIGURE7.654-1000WOO-I -C)500 30005Optimum FieldMajor Radius= 6 MetersI-1000 1500Equivalent Tensile Stress (MPa)-B plasma --- B coilFIGURE 6--000 0- 00 -10ai)C:CP3230-28-26-2422120181614-12-10.5 2000 2500 3000ISTRESS VS. MAJORib = 250 Tnci.J(9zw1-zw5.5-54.5-43.5-3-2.52-1.5-5 6RADIUSI I U U U6.4 6.8 7.2MAJOR RADIUS (m)- STABILIZER STRESS=300 MPa--- STABILIZER STRESS= 800 MPaFIGURE 75.2I U.2 7.6-PLASMA VOLUME VS. STRESS2 2600 Ba 250 Tm5oo0w400-300-~200O-1004 I I I0.5 1.5 2.5 3.5 45 5.5EQUIVALENT TENSILE STRESS (GPa)FIGURE 8

Performance limits of high field tokamak reactors

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Performance limits of high field tokamak reactors

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