Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1978 A toroidal fusion reactor design based on the reversed-field pinch Randy Lee Hagenson Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Nuclear Engineering Commons, and the Oil, Gas, and Energy Commons Recommended Citation Hagenson, Randy Lee, "A toroidal fusion reactor design based on the reversed-field pinch " (1978). Retrospective Theses and Dissertations. 6455. https://lib.dr.iastate.edu/rtd/6455 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. 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University Microfilms International 300 North Zeeb Road Ann Arbor. Michigan 48106 USA St. John's Road, Tyler's Green High Wycombe. Bucks. England HP10 8HR f8l3228 HAGE^SON, ?A\uY LEE A TOROIDAL FuslO'^ WEACTO- SAsEC 0^ THE REVERSED-FIELD 10*6 STATE UMVtScITY, F^.D., 1978 Liniversi^ Microfilms InfiSmcltionaJ SOON ZEEB ROAD, ARBOR, MI AEIOO A toroidal fusion reactor design based on the reversed-field pinch by Randy Lee Hagenson A Dissertation Submitted to the Graduate Faculty in Partial Fulfillmait of The Requirements for the Degree of DOCTCR OF PHILOSOPHY Department: Chemical Engineering and Nuclear Engineering Major: Nuclear Engineering Approved: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. For the Major Departmait Signature was redacted for privacy. rafuate College Icwa State University Ames, Icwa 1978 ii TABLE OF OCMTENTS Page ABSTRACT vii I. INTRODUCTION 1 A. Summary of the Reversed-Field Pinch Concept 1 B- Reactor Ccnsideraticns 5 C. Objectives 9 II. LITERATURE REVIEW 10 A. Theory 10 B. Experiments 17 C. Reactor Studies 21 III. DESCRIPTION OF ENERGY BALANCE 24 A. General Model 24 B. Plasma and Magnetic Field Models 26 C. Plasma Energy Balance 30 D. Magnetic Energy Storage and Joule Losses 34 E. Calculational Procedure 37 IV. RESULTS 39 A. Reactor Startup Phase 39 B. Thermonuclear Burn Cycles 41 C. Plasma Quench 49 D. Operating Point(s) Determination 51 iii Page V- FINAL SYSTEM DESIŒ 61 A. General Reactor Description 61 B. Consideration of Major 67 System Cairponents VI. SUMMARY AND ŒNCLUSICMS 83 VII. TOPICS FOR FURTHER STUDY 87 VIII. LITERATURE CITED 88 IX. ACKNOWLEDGMENTS 95 X. APPE3Œ)IX 96 iv LIST OF TABLES Page Table 1. Summary of reversed-field pinch parameters 18 Table 2. Dimensions used in RFPR energy-balance study 44 Table 3. Summary of typical RFER parameters 57 Table 4. Haropolar specifications 82 V LIST OF FIGURES Page Fig. I. In the toroidal system R is taken as the major radius and 2 r as the minor radius. The minor axis of the torus is denoted by z, and the angle about z is given by 0. Fig. 2. Field profiles of various fusion ooncepts. 3 Fig. 3. Cross-sectional drawing of the envisioned RFPR. 8 Fig. 4. Sanple MHD stable pressure and field profiles for a 13 linear pinch shewing the effect of increasing the pressure on the location of the conducting wall for stability (13). Fig. 5. Conplete RFPR energy balance used in conjunction with a 25 time-dependent RFP plasma model to evaluate a range of reactor operating points. Refer to text for notation. Fig. 6. Canparison of assumed poloidal % and toroidal B 28 fields and actual MHD stable field profiles (13). ^ Fig. 7. Generalized pressure-volume diagram for the RFPR. 42 Magnetic field pressures, plasma pressure p, and the plasma direct-oonversion work for high-beta plasma expansion against a magnetic f^ld are shewn for the assumed sharp-boundary plasma model. Fig. 8. Lines of constant Q for various first-wall radii r and 46 maximum average toroidal current densities j (solid curves) where a 50%-50% D-T fuel mixture is used. The dotted-dashed curves are lines of constant first-wall ((0.3 mm)Al20g/(2 im)Nb-lZr) surface tenperature rise ATw(k). Fig. 9. Dependence of the engineering Q-value Q_ on the initial 48 plasma tritium fraction f^ for 90% burnup of the available tritium in the plaana. Fig. 10. Lines of constant for various first-wall radi^ r and 50 maximum average toroidal current densities j^ (solid curves) where a 90%-10% D-T fuel mixture is used. The dotted-dashed curves are lines of constant first-wall ((0.3 mm)Al203,/(5 ram)Nfc»-lZr) surface tenperature rise AT^(k). vi Page Fig. 11. Time-dependence of plasma and energy quantities for the 53 50%-50% D-T operating point sunmarized in Table 3. Fig, 12. Time-dependence of plasma and energy quantities for the 54 90%-10% D-T operating point summarized in Table 3. Fig. 13. Depaidence of on the magnetic energy transfer/ 55 storage efficiency for both cases investigated. Fig. 14. Time-dependence of various plasna parameters and daninant 56 powers for a tokamak-like RFPR star tip. Fig. 15. Plan and elevation view of 750 J®?e (net) RFPR. 62 Fig. 16. Schematic diagram of the primary-coolant circuit 63 illustrating the major lithium flow paths. Fig. 17. ISOTietric view of 2-m-long RFPR reactor modules (vacuum 65 vessel, blanket, toroidal field coil) and associated poloidal field coil assembly and iron-core pieces. Fig. 18. Time dependence of the blanket temperature distribution 69 for the 50%-50% D-T burn cycle summarized in Table 3. Fig. 19. Time dependence of lithium coolant flow in the RFPR 71 blanket for the 50%-50% D-T fuel mixture case. Fig. 20. Dependence of first-wall tenperature and stress during 73 the ignition, burn, quench, and plasma cooling periods as­ sociated with the 50%-50% D-T bum cycle given in Table 3. Fig. 21. Dependence of first-wall temperature and stress during 74 the ignition, burn, quench, and plasma cooling periods as­ sociated with the 90%-10% D-T burn cycle given in Table 3. Fig. 22. Schanatic diagram of hcnopolar-generator driven circuit 76 for both TFC and PFC systems. The voltage V~4-5 kV, the rise time i^^ioQ ms, and "îg^l-ô s. vii ABSTRACT The toroidal reversed-field pinch (RFP) achieves gross equilibrium and stability with a ccxnbination of high shear and wall stabilization, rather than the inposition of tokamak-like q-constraints. Consequently, confinemoit is provided primarily by poloidal magnetic fields, poloidal betas as large as — 0.58 are obtainable, the high ohmic-heating (toroidal) current densities premise a sole means of heating a D-T plasma to ignitiai, and the plasma aspect ratio is not limited by stability/equilibrium constraints. A reactor-like plasma model has been developed in order to quantify and to assess the general features of a power system based ipcn RFP confinement. An "operating point" has been generated cn the basis of this plasma model and a relatively detailed engineering energy balance. These results are used to generate a conceptual engineering model of the reversed-field pinch reactor (RFPR) which includes a general description of a 750 Mfe power plant and the preliminary consideration of vacuui^/fueling, first wall, blanket, magnet coils, iron core, and the energy storage/transfer system. 1 I. INTBODUCTim A. Summary of the Reversed-Field Pinch Concept The desire for power production frcxn fusion reactions has lead to the pursuit of many plasma confinement schemes. The present experimen­ tal goal of containing a reacting plasma for a sufficient time to achieve a net energy output has been difficult to attain. Even when plasma jiiysics problems are overcone, the economics of the reactor system may be unfavorable and render a particular concept useless.