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STEADYSTATE AND TIMEDEPENDENT BEHAVIOR OF FUSIONFISSION HYBRID SYSTEMS By WILLIAM G. VERNETSON A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Dedicated to Theresa without whom this work would have been impossible. ACKNOWLEDGMENTS The author would like to express his appreciation to his graduate committee for their assistance during the course of thi research. Special thanks are extended to Dr. H. D. Campbell, chairman of the author's super visory committee for providing guidance and encouragement throughout the course of this work. Dr. Campbell many helpful comments and suggestions have greatly aided the completion of this work Thanks are also extended to Dr. E. E Carroll, Dr. R . T. Schneider, and Dr. L. Bailey who have also served on the author's supervisory committee. Special thanks are extended to Dr. M. J. Ohanian for the research and teaching assistantship opportunities presented which enabled the author to pursue the doctorate. The author's studies at the University of Florida have been supported, in part, by a National Science Foundation Traineeship and also by a one year Fellowship from the University of Florida and this support is grate fully acknowledged. A large portion of the funds for the computer analysis were furnished by the Northeast Regional Data Center on the University of Florida campus through the College of Engineering. difficult to obtain Special thank This help, though at times meager and , is also acknowledged. are due to Dr. N. J. Diaz without whose efforts and Special thanks are also due to Dr. E. T. Dugan whose knowledge of computer analysis and nuclear reactor physics was of great assistance during much of thi work. In addition, thanks are extended to Mr Maya for his aid with some of the plasma calculations and their impli cations of helpful Thanks are also extended to Mr. B. G. Schnitzler for a number consultations. Finally, the author would like to extend his deepest appreciation to his wife whose support and encouragement made it possible to complete this work. TABLE OF CONTENTS ?agfi ACKNOWLEDGMENTS LIST OF TABLES. LIST OF FIGURES ABSTRACT. * a S S S S S S S S S S S S S S S~~~ ~~ ~~~~~ 0 5 55 0 S S S S S S CHAPTER INTRODUCTION Preliminary Concepts for FusionFi Review of Fusion Blanket Studies Critical Review of Hybrid Blanket Review of Controlled Thermonuclear Stability Analyses . Motivation for the Research. . Summary of the Research. . ssion Reactors Studies. Reactor Thermal * a a a a a * S S S S S S * S S S S S S S S S THE PLASMA MODEL Intro The P The L Trans Stabi duction to ointModel in ari 7PrH fer F lity the Plasma Plasma P1 a~ ma Mnorl Model unction Representation of Plasma Character Analysis of the Linearized Plasma Model. istic A HYBRID REACTOR ANALYTICAL MOD Development of the Hybrid Model Thp I inpAri pd Mvrid id Mndel . . . . 116 S S S S a S S S S 5 116 Incorporation of Feedback Effects into the Nonlinear and Linearized Hybrid Model Summ Transfer Function Representation of the Hy Stability Criteria for the Hybrid System HYBRID PLASMA OPERATIONAL CONSIDERATIONS . . Hybr ary. brid S . 1 31 id Model. 138 * 143 S . 147 * S S 5 5 5 1 60 * S S S S S S164. T ~ ~ ~ L l,, 4, .4.,~, 3 4. 2 .I4. II 4 rl *'2f,... r.. Irn Diie Uncontrolled Plasma Response to Perturbations. Predicted Stability Versus PointModel Response ShortTerm Plasma Transient Response . Plasma Response With Feedback. . HYBRID BLANKET ANALYSIS. .. . . introduction . lanket Calculations Using homogeneous Diffusion Th inetic Parameters transport Theory Calculati homogeneous Transport Th imeDependent Blanket Con or ec s * S S 181 .* S 196 .* S S 202 219 S258 25 Diffusion Theory . 26 3ry Calculations. . 30 ns. . 32 ory Calculations. . 34 iderations. . 34 CONCLUDING COMMENTS 356 Discussion and Conclusions . 356 Suggestions for Further Work . . 361 APPENDICES GLOBAL BLANKET ENERGY MULTIPLICATION HYBRID SYSTEM PHYSICAL CHARACTERISTIC BURNUP AND PLASMA SENSITIVITY CONSIDERATIONS FOR THE HYBRID S S S S S S S S 388 COMPUTER CODE DESCRIPTIONS REFERENCES. * 0 0 a a ..396 S S S S S S S S S S S S P S S S a S S S 41 1 BIOGRAPHICAL SKETCH S 0 5 S S S P 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4. 3 ec LIST OF TABLES Table Paae Fusion Reaction Parameters 1II , III Dependence of Tritium Breeding Ratios and Energy Deposition Rates for Lee' Summary Descriptions of ORN Blanket Designs . Fusion Blankets L Ootimistic an d Conservative ,IV Summary of teiner's Tritium Breeding Calculations Per Incident 14 MeV Neutron Neutron Economy of Lidsky's Hybrid Blanket. 1VI 1VII Lidsky' Lee' Hybrid Reactor Parameters. Neutron Balance in Infinite Met a S S 1VIII Subcritical Fast Fission Blanket Component tudied by Fast Fission Hybrid Neutron Economy Per 14 MeV Neutron Calculated by Lee . . Neutron Economy for ThoriumFueled Blankets Neutron Economy for UraniumFueled Blankets 1XII * S a * * S a a a Comparison of Best Natural UraniumFueled and Extrapo lated Thori umFueled Blankets . . Earl XIV y PNL Hybrid Neutron Balance. y PNL Hybrid Specifications PNL Hybrid Blanket Analysis 1XVI 'XVII Critical Temperatures for DT Fusion Reactors Predicted Blanket Global Response per 14 MeV Neutron. 1IX Table 4I 4II Page Selected Spectrum of Equilibrium Operating Conditions for the Hybrid Plasma With Constant Confinement. 173 Hybrid Plasma Equilibrium Operating Conditions for TEo = 1.7 sec to Meet Required Power Production. ... 175 4III 4IV 4V Equilibrium Plasma Conditions Selected for Transient Analysis With R = 2 and qPo = 1.41 x 1011 nts/cm3se c. Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a +5% Perturbation in the Temperature . Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Perturbation in the Temperature. . . 178 .187 . 188 4VI Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Step Increase in the SteadyState Source Feedrate. . . S . 0189 4VII 4VIII 4IX 4X 4XI 4XII 4XIII Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Step Decrease in the SteadyState Source Feedrate . . . . Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a +5% Perturbation in the Ion Density. . Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Perturbation in the Ion Density. Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Step Increase in the SteadyState Injection Energy . . Final Uncontrolled Hybrid Plasma Equilibrium Conditions Following a 5% Step Decrease in the SteadyState Injection Energy . . . . Summary of Predicted Stabilization Requirements for Instantaneous Temperature Feedback on the Feedrate Comparison of Confinement Time Effects on Plasma Temperature at 10 sec Following +5% Perturbation in Feedrate versus +5% Perturbation in Temperature for Six Hypothetical Hybrid Equilibrium States . .190 . 191 . 192 . 193 . 194 . 197 . .218 Boundaries for FourGroup Critical i ty Calculation. 511 . 263 BRT1 CellSmeared Thermal Constants for 1.35% Fnrih Ped FIP. 264 Table 5IV Flux Dep Lattices ress ion Factors for the 1.35% Enriched Average Cros Column. . Sections for 23U and 238U in th 5VI Space Point Placement for BRT1 Calculation Over Inner Half of th 5ViI Hybrid Blanket. Space Point Placement for BRT1 Calculation Over Outer Half of th Refl sector ssion Lattice and nto the Graphit VIII Summary of PHROG Calculations by Region Resonance Region Scattering Cross Nuclides. . . . Sections FourGroup, 13 Region Constants for 1 at 570K from BRT1 and PHROG . .35% for Blanke Enrichment 5XI PHROGGenerated Macroscopic Downscattering Cross tions for 1.35% Enrichment, 5700K, and 1 Regions. 5XII FourGroup, 13Region Constants for 1 .35% Enrichment at 9700K from BRT1 and PHROG 5XIII PHROGGenerated Macroscopic Downscattering Cross Sections for 1.35% Enrichment, 970K, and 5XIV Regions. Results of Diffusion Theory Criticality Calculations. Summary of Inhomogeneous CORA Calculations for Variations in Enrichment and Temperature . 5XVI Yield Fractions for Si Delayed Neutron Precursor Groups. 5XVII Delayed Neutron Energy Spectrum Yield Fractions for 4Group CORA Calculations . . . 5XVIII Blanket Kineti Parameters 5XIX 5XX Source Weighting Factors in Four Groups and Ten Regions Effectiveness of Uniform Volume Sources for Design Power Level Page Table 5XXIII Effective Moderator Scattering Cros Sections Per Absorber Atom. S S S S S S SS 5 327 5XXIV 5XXV XXVI Isotopi NITAWL Resonance Integra Values Obtained from SS SS S S S S S S S S SS S S 5 323 Hybrid Blanket Anal S4 Quadrature Constants. XSDRNPM 43Group Energy Boundaries 330 S S S S S S S S 333 5XXV II XSDRNPM Group and 11Group Energy Boundari . 335 XVIII 5XXI XSDRNPM 6Group Cross Section Energy Boundari XSDRNPM kef Results for a edition at the Vacuum Wall. * 337 ZeroFlux Boundary Con 337 5XXX Transmission Ratio for 14 MeV Neutrons Through the Hybrid Blanket S S S S S S S S S S S S S S 34l6 Hybrid Blanket Equivalent Unit Cell Geometry Fuel Column Spherical Micropartici B III . . 375 Design Parameters. 377 TemperatureIndependent FuelPinAveraged Nuclide Number Density Variation with Enrichment S. S 378 BIV Hybrid Blanket Shield Composition. a S S S* S S 5 330 Helium and Natural Lithium Number Density Variation with Temperature BVI S S S S S S S S S S S S S S 381 Effects of Vacuum Wall Radius on Blanket Power Requirements and Power Density S. 5 S S S S S 384 PointModel Comparison of Confinement Times and Related Plasma Parameters in UWMAKIII and the Hybrid Plasma S S S S S S 5 5 5 5 S S S S S S 5 5 390 Page LIST OF FIGURES Figure Page The essential components of a Tokamak fusion reactor Comparison of spatiallydependent heating rates for vacuum wall regions in two designs . Early PNL fusionfission hybrid configuration. . . ubcritical blanket Comparison of Lawson breakeven and plasma equilibrium regions Time variation of pointmodel plasma temperature and density for constant confinement and charged particle heating Typical Lawson breakeven curve for a 5050 DT plasma and 33% overall efficiency showing relative position of hybrid sys terns. . . . . Predicted variation of blanket fusion neutron energy multiplication with blanket effective neutron multi plication factor . . Transfer function formulation for a pointmodel fusioning plasma Block diagram for the pointmodel plasma system. Partiallyreduced block diagram for the pointmodel plasma system. . . . Alternate block diagram for the pointmodel plasma system. Partiallyreduced block diagram for the alternate point model plasma system formulation. . . . Reduced openloop block diagram for the pointmodel plasma Routh array for openloop point model fusioning plasma with burnuD a a a a a a a     Figure Page Variation of F(T) = nr with temperature . .* .* 105 Block diagram for the pointmodel plasma with temperature feedback to the feedrate. .a.*.. . 5 ** 110 Block diagram schematic for pointmodel blanket kineti retaining both source and reactivity perturbations . cs . 152 Block diagram of the hybrid reactor model inearized global fusionfi ssion Partiallyreduced hybrid block diagram with no artificial feedback. S S S S a S S S S S S S S S 5 156 Simplified reduced hybrid artificial feedback stem block diagram with no Closedloop block diagram for the linearized pointmodel plasma with temperature feedback to the feedrate. . . 159 Routh array for the cubic denominator for blanket effect in the overall hybrid transfer function . . . 161 Equilibrium curves for various equilibrium plasma conditions. S S S U S S S S U S U S S SS U 174 Mills steadystate curves including burnup for R  2. . 180 Illustration of the feedforward effectiveness of the feedrate and the injection energy on plasma conditions and transient behavior . Arbitrary equilibrium curve with a hypothetical source equilibrium S . 184 stable hybrid state at point A plus a possible equilibrium curve containing a perturbed unstable state at point B. Variation of plasma temperature following a step increase in the temperature of the six hypothetical hybrid equilib ri um states . . . Variation of plasma volumetric neutron production rate following a 5% step increase in the temperature of the six hypothetical hybrid equilibrium states. Variation of plasma temperature following a in the temperature of the si rlum step decrease hypothetical hybrid equilib states Variation of olasma volumetri neutron production rate S f f . 1541 200 o Figure Page Variation of the heating rate in the first wall region of the UMAKIII design. . Variation of plasma temperature following a step crease in the feedrates for the si hypothetical hybrid equilibrium states Variation of plasma volumetri following a neutron production rate step increase in the feedrates of the hypothetical hybrid equilibrium states . Variation of plasma temperature following a decrease in the feedrates for the si step hypothetical hybrid equilibrium states Variation of plasma volumetri following a neutron production rate step decrease in the feedrates for the six hypothetical hybrid equilibrium states Variation of plasma temperature following a incr ease in the feedrate of an equilibrium 5% step state at TE o sec with delayed shutoff times Variation of plasma volumetri following a equil ibrium times. neutron production rate step increase in the feedrate of an state at TEo o sec with delayed shutoff Variation of plasma temperature following a increase in the feedrate of an equilibrium 1.7 sec with delayed shutoff times . Variation of plasma volumetri following a 5% step state at TE o neutron production rate step increase in the feedrate of an equilibrium state at TEo ti mes =117 sec with delayed shutoff Variation of plasma temperature following a crease car (A' step in the feedrate of an equilibrium state at TE 444 rA/l c hnI nc Cki+nFF + 0 3 C L l I LI I UC I UJ cU .JU VI IULAJI U1111f Variation of plasma volumetri following a neutron production rate step increase in the feedrate of an equilibrium state at Tr sec with delayed shutoff ti umes U Variation of plasma temperature following a decrease in the feedrate of an equilibrium 1 5 npr with dplavpd hutnff timp 5% step state at TE 0 I I _ _ Figure 45. Variation of plasma temperature following a decrease in,' Ia step in the feedrate of an equilibrium state at TE 44h tin1 d l dr rk u4nC 4hI f i ace w e aye s uto f t mes Variation of plasma volumetric neutron production rate step decrease .in the feedrate of an equilibrium state at rE_  1.7 sec with delayed shutoff times. u Variation of plasma temperature following a decrease CcaC I,! 5% step in the feedrate of an equilibrium state at XE S+fh aHol n aId ckh nff +4mc o .J'..t.. III LoE At. I UJ C 4 311U LAJ I II.IIC Variation of plasma volumetric neutron production rate fol lowina a equilibri um times. step decrease in the feedrate of an state at rEo o sec with delayed shutoff Variation of plasma temperature with timperature feedback following a 5% 1 c rr nt r' step increase in the feedrate of the TE i t l d l di;/v/ h r' t4l rff f Ue o sec equ r um s ate p us e aye s u o o Variation of plasma temperature with temperature feedback following a 5 1.7 sec equil ih step increase in the feedrate of the TE v im cf+ nfine l aun chit+ntFf nC &R 0 P i uTi UL lui U3 U UU C 3IU3 IUV 4~IttI I 'U Variation of plasma temperature with temperature feedback following a 5% steo increase in the feedrate of the TE = 2.0 sec equilibrium state plus delayed shutoff of 6S . Variation of plasma temperature with temperature feedback following a 5 1.5 sec equil ib step decrease in the feedrate of the rt rium state olus delayed shutoff of 6S 0 Variation of plasma temperature with temperature feedback following a 5% 1 7 1 L step decrease in the feedrate of the rE 1.7 sec equilibrium state plus delayed shu f Variation of plasma temperature with temperature feedback following a 5% steo decrease in the feedrate of the TE ,1,,  .je o 2.0 sec equilibrium state plus delayed s f Variation of plasma temperature with temperature feedback following a 5% 1 , *4 1 1. step decrease in the temperature of the Eo *f a^ ***i r~* ^ ^'/  t~UL I et juI` I I u I .111 lLclLU Variation of plasma temperature with temperature feedback following a 5% 93 step increase in the temperature of the TEo 1 7 car annilibrium efate following a Page r J Figure Page Variation of plasma temperature with temperature feedback following a 5% fl fl ^ ^. 1 step increase in the temperature of the TEo 2.0 sec equilibrium state. Variation of plasma temperature with temperature feedback following a 5% r 1 L step decrease in the temperature of the TE U o c es e q u i l i b r i um s t a te. Variation of plasma temperature with temperature feedback following a 1.7 sec equ step decrease in the temperature of the TEo *o m uirbili s t a t e. Variation of plasma temperature with temperature feedback following a 2.0 sec equ 5% step decrease in the temperature of the TE bili r i u m s ta te. Variation of plasma volumetric neutron production rate with temperature feedback following a step increase in temperature of the TEo = 1.5 sec equilibrium state Variation of plasma volumetric neutron production rate with temperature feedback following a temperature of the XEo 0o = 1.7 step increase in sec equilibrium state Variation of plasma volumetric neutron production rate with temperature feedback following a temperature of the rEo step increase in = 2.0 sec equilibrium state Variation of plasma volumetric neutron production rate with temperature feedback following a step decrease in temperature of the TEo '.5 sec equilibrium state Variation of plasma volumetric neutron production rate with temperature feedback following a temperature of the TEo step decrease in = 1.7 sec equilibrium state Variation of plasma volumetric neutron production rate with temperature feedback following a step decrease in temperature of the TEo = 2.0 sec equilibrium state BRT1 thermal flux profiles across the equivalent unit cell for 1 .35% enrichment at 290K, 5700K, and 9700K. Typical paths for an unscattered neutron in an equivalent unit cell and an actual unit cell of a nuclear reactor BRT1 thermal flux profiles across the inner half of the hybrid blanket for 1.35% enrichment at 2900K, 570K, and 9700K with zeroflux vacuum wall boundary condition .  "1 L * Figure Page BRT1 thermal flux profiles across the outer half of the fission lattice out to 12 cm of graphite reflector for 1.35% enrichment and 2900K, 5700K, and 9700K . Thermal flux profiles from BRT1 calculations across the outer 18 cm of graphite reflector and 30 cm of shield for 2900K, 5700K, and 9700K. Fourgroup fundamental mode flux profiles from CORA for the 1.35% enrichment at 2900K with zerocurrent vacuum wall boundary condition. . . . . Fourgroup fundamental mode flux profiles from CORA for the 1.35% enrichment at 570K with zerocurrent vacuum wall boundary condition. . . Fourgroup fundamental mode flux profiles from CORA for the 1.35% enrichment at 9700K with zerocurrent vacuum wall boundary condition. . . . . Fourgroup fundamental mode flux profiles from CORA for the 1.35% enrichment at 9700K with zeroflux facuum wall boundary condition Variation of blanket effective neutron multiplication factor with temperature for the 1.35% enrichment using fourgroup diffusion theory. . . . Fourgroup flux profiles from inhomogeneous CORA run using group 1 surface source to generate 6500 MWth for 1.35% enrichment at 5700K. . . Fourgroup flux profiles from inhomogeneous CORA run using group 1 surface source to generate 6500 MWth for 1.35% enrichment at 9700K. . . . Fourgroup flux profiles from inhomogeneous CORA run using group 1 surface source to generate 6500 MWth for 1.50% enrichment at 570K. . . . . Fourgroup flux profiles from inhomogeneous CORA run using group 1 surface source to generate 6500 MWth for 1.50% enrichment at 9700K. . . . Blanket power density variation for 6500 MWth for enrichment at 5700K and 970K. . . .35% Blanket power density variation for 6500 MWth for 1.50 onrirhmpnnt at r700k ind Q700 Figure Paqe .,, . *.. Six group fundamental mode flux profile from XSDRNPM for 1.35% enrichment at 9000K with zeroflux vacuum wall boundary condition Sixgroup flux profiles for a 10' nts/cmLsec in group 1 t enrichment and 900K . surface source of 1.336 o generate 6500 MWth at 1 x .35% Fractional transmit on of 14 MeV neutrons through th hybrid blanket Power transient in th hybrid blanket following a 5 step increase in the neutron source for a forcedcritical sten Hybrid blanket power transient derived for a subcritical Conceptual Tokamak fusionfission hybrid reactor stem. Overall hybrid blanket slab geometry used in neutronics al culations Selected PNL hybrid blanket module geometry for Tokamak fusionfission hybrid. . . . Hybrid thermal fission lattice unit cell Geometri arrangement of the inner convertor with inner breeder and outer breeder. . . . . Reactivity and sensitivity variation with temperature for the DT fusion reaction. . . . . Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy STEADYSTATE AND TIMEDEPENDENT BEHAVIOR OF FUSIONFISSION HYBRID SYSTEMS By William G . Vernetson June 1979 Chairman: Huah D. Campbell Major Department: Nuclear Engineering Sciences study examined stability analysis of pointmodel systems repre sending pure fusioning plasmas as well as coupled fusionfission stems. The stability criteria for these systems were derived for constant plasma confinement conditions based on engineering perturbations of the system feedrate. The result of linearized pointmodel plasma stability anal ysis of the thermal instability were shown to be applicable to hybrid plasmas and to be attainable from considerations of engineeringrelated per turbations in the extrinsi plasma feedrate variabi A Tokamak fusionfi ssion hybrid design was ected for further, more specific analy sis. The modeled hybrid system in linearized form was found to be stable provided certain hybrid plasma temperature and con finement time limits are met. absolute stability is not suf However, for realistic installations, 'ficient; nor is it guaranteed by linearized anal ysis. Therefore, hybrid plasma behavior was examined under transient and overpower conditions. Timedependent analysis of a low reactivity hybrid plasma (8 keV with perturbations to pure fusion plasmas with high plasma reactivity. In addition , the predictions of plasma stability ranges were verified for various confinement times. transients following  The slowly developing hybrid plasma temperature or feedrate perturbations were found to be significant for the control of the powerproducing hybrid. Neutrons and their associated energy are multiplied in hybrid blank ets; therefore, the global equation in use to relate the blanket energy deposition per fusion neutron to the blanket effect multiplication factor was investigated. indicate the oloba neutron Results were obtained which approach supplies a poor estimate of blanket energy multiplication for a fusion neutron source and an even poorer estimate for fission energy neutrons. Although results showed the blanket energy deposition per fusion neutron to be some below pointmodel predictions, the selected blanket is still a significant multiplier, by a factor of 25 or more, of th neutron energy entering the blanket via fusion neutrons. The documenta tion of the reduced worth of fusion neutrons, entering the blanket through a convertor region, may be a significant factor in redesigning vacuum wall of hybrid reactors despite the advantages of reduced 14 MeV wall loadings. Diffusion theory and di screte ordinates transport theory anal ysis were both applied to establish the relative importance of the inner con vertor region for power generation. The results of the calculation were used to determine the source size transport required by volume equivalence with the Tokamak geometry to produce 6500 MWth in the blanket. The source value was used to establish the steadystate requirements on Tokamak hybrid plasma volume involved. In addition, the calculation was used to show that only about 6% of the 14 MeV fusion neutrons reach the thermal fission latti without a collision These transmission results indicate graphically why the blanket is less effective at energy multiplication than Finally, space expected from previous reports. time kinetics calculations were performed on the blanket to demonstrate the fast response of the blanket in keeping with its millisecond prompt neutron lifetimes and subcriticality Al though no timedependent feedback effects were examined, the speed of response of the system was determined for typical transients and some character istics for hybrid operational controllability were established. CHAPTER 1 INTRODUCTION Preliminary Concepts for FusionFission Reactors The fusionfission hybrid reactor concept is a combination of a subLawson fusion reactor and a subcritical ssion reactor in a single powerproducing system. Fiss ion reactors are "power rich" but "neutron poor," while anticipated DT fusion reactors will "neutron rich" but "power poor. these Hence, two systems to u the essential se excess fus hybrid feature the combination of ;ion neutrons to breed fissil fuel while simultaneous y sustaining and driving the sys ten for useful power er using fission energy multiplication of the fusion neutron source ~.ne rg: Limited studies , concentrating on blanket neutronics have been done on hybrid system in parallel with pure fusion blan t work how ever , no system dynamics or stability investigations have been reported for hybrids Some research effort ha been devoted to global stability anal of th plasma in pure fusion device present research extends such pure fusion timedependent studies into the area of hybrid systems. continued development of the hybrid in parallel with the fast breeder reactor is supported by the hybrid's potential a alternate and attainable energy and fuel producing concept. In fact, 2 Much research effort and capital investment have been committed to the realization of a mixed burnerbreeder nuclear reactor economy planned for the end of this century. This effort is justified by expected con tinued growth of energy needs sumption of fossil fuel within the past few deca des. and by a marked shift from direct con secondary consumption of electrical energy With the growth in nuclear generating capacity limited fissil fuel reserves have caused the thrust of research and deve opment in the nuclear industry to shift to the fast breeder reactor LHFBR) Even with the projected impact of the commercial LMFBR sometime after 1 siderabl 0, con additional enriching capacity and capital investment will be required for fueling burner reactors. Current emphasis on the safety and the environmental impact of nuclear generating faci liti as well as certain technological and political objection make it increasingly unlikely that high gain breeder reactors will make a significant rmpact prior to the mid1990 s or later. Even if the breeder i introduced sooner, the relatively lono doubling times under consideration (1 years or more may not be adequate for generation of sufficient additional fuel to support an reactor economy existing burner IWith so much effort and capital investment committed to the realization of the mixed burnerbreeder economy planned for the 1990's, the availability of an effective alternate concept to produce fissil fuel could be important. One candidate for producing fissile fuel is the controlled thermo nuclear reactor utilizing the DT cycl C1 e. Deuterium resources are virtu 7 fusion neutrons can be used to breed fissile material. By diverting neutrons from tritium production, the tritium supply can be maintained reasonable averted to fissi evel while fertile reactor fuel. materials (238U and Th) are con Unfortunately the realization of pure fusion power is too far removed and uncertain to be counted upon to pro duce fissil fuel in the near term. The alternative concept currently receiving renewed attention is the coupled fusionfission hybrid system combining a less than selfsustaining (energy) fusion reactor with a subcritical but power producing fission reactor. Although achievement of pure fusion power i not yet possible, recent advances indicate the plasma requirements for hybrids will be reached while the fission power component of the still increasing. electrical economy i 9 Then, as an alternative to the LMFBR for fi and power production, the hybrid can be very useful The hybrid concept has many potential advantages over the LMFBR for providing power and fissile fuel in the latter part of thi century. First, the hybrid reactor possesses great potential as a breeder of fissil be abl fuel. With its abundant supply of neutrons, the hybrid should to produce fissil material more rapidly than any of the current breeder reactor concepts to keep pace with power requirements. Second, the hybrid makes an alternative fuel cycle available for existing burner reactors. Reliance on the U239Pu fuel cycle with its weapons grade plutonium can be reduced in favor of the 233U fue cycle. Third , hybrid development allows early introduction of fusion 232Th_ 4 hybrid system, current advanced reactor technology would require only modest extensions to produce a hybrid system as a natural link in the development leading from pure fission to pure fusion power. Finally, the hybrid concept using from a safety standpoint subcritical blankets is attractive since it would diminish the need for critical nuclear reactors. 4.10 The current concern over reactor safety and core meltdown could b essentially eliminated.11 Past hybrid ana studies of the hybrid concept have been restrictive. 1 yses Typical limited to steadystate evaluation of the technical characteristics of a concept with emphasis on the neutron economy of the conceptual blanket. 3,1214 Important features in such hybrid studies parallel ordinary fusion reactor blanket studies and include: Tritium conversion ratio and doubling time. Fissile breeding ratio and doubling time. Energy production and multiplication in the blanket Constraint on the fusion plasma due to neutronics. 5. Vacuum wall loading and neutron energy transport. The neutron economy and energy multiplication of the hybrid blanket have been of primary interest in these initial studio by fission events both are enhanced Little consideration has been given the fusioning plasma in these hybrid designs beyond setting plasma characteristics necessary to achieve the assumed blanket power performance. Basic fusion reactor blanket studies and hybrid blanket work to date are reviewed in the next section; the similarity of the two remarkable despite the increased importance of energy production in hybrid blankets. factor, keff, less than unity) as well blanket, no timedependent analysis as the heat generation rates in the has been considered; dynami behavior and associated safety of the hybrid fusionfission system have been ignored. The effects of perturbations on the coupled system have also been ignored. Some studies on safety and control analysis of pure fusion reactors have been reported.1 524 Mills' described the stability requirements on a state teadystate, (equilibrium point model, fusioning plasma, and found the steady plasma unstable against various parameter fluctua tions below a critical ion temperature. The effects of artificial feed back were simulated at lower temperatures to control this thermal instability and maintain equilibrium operation below the critical temperature. The work of Mill is a benchmark work in fusioning plasma global dynamics and control work on stability by Ohta et al 18 is one of the most complete thermal stability studi of point model thermonuclear plasmas. Stability criteria were established using linear analysis energy balance plasma equations. of coupled particle and The thermal instability was evaluated and suitable feedback control was implemented to allow stable operation below the critical plasma temperature set by the stability criteria. Stacey as well as Usher and Campbell23'24 have reported extensions of this work to more sophisticated plasma model Yamato et al 19,20 have have extended such stability studies to simpi comparable e i homogeneous plasmas with results. Since such timedependent analysis was neglected in previous hybrid of fusion energy blanket multiplication not previously considered. much larger hybrid blanket energy multiplication demands a coupled time dependent analysis establishment of specific safety and operating character ri stics for a coupled hybrid system is necessary for the con tinued development of the concept into a viable energy alternative. The effect of thermal instabilities in the fusioning plasma on the fissioning blanket are analyzed in this work to establish hybrid system interactions, deficiency in safety, and ea existing studies of control of hybrid This work systems eliminates a major so that a decision can be made on its pi ace in the power industry of this country in the last decades of this century. Review of Fusion Blanket Studies The Fusion Process Since hybrids depend on fusion neutrons to breed fissile fuel, at least two fusion reactions have potential for use in a hybrid reactor. These are the deuteriumtritium and the deuteriumdeuterium reactions which have the following balances: 2 3D+ D + ,T ~1 1 He (3.52) + n (14 He (3.52) + n (14.06) 2 0 e (0.82) + 2He (0.82) + n (2.45) (1 .01 + p (3.03) where the two DD branches have nearly equal probabilities at energies 2 3 D D 1 The properties of the DT fusion reaction are far superior to those of the DD reaction. For energies below 200 keV the DT reaction cross section with its broad resonance at 110 keV i nearly two orders of magnitude above the DD cross sections. The probabili for a fusion reaction occurring i characterized by the reactivity or rate coefficient, , which i an average of the product of the cross section for the fusion reaction in question and the relative speed , v, of the reactants. The reactivity can usually be approximated using a Maxwellian distribu tion of particle speeds. With a broad resonance around 65 keV the DT reaction rate coefficient i much greater than the DD reaction rate coefficient below 100 keV Finally , the energy released per fusion reaction, QF , is signifi cantly higher for DT fusion events. These comparative values are summarized in Tabl e I25 and indicate why near term fusion reactors and hence hybrids are limited to the DT fuel cycle. Table 1I Fusion Reaction Parameters o (barns) Reaction at 100 keV at 65 keV F ' 0.46 x 1016 x 1015 3.65 17.6 As noted in Eq 1), the 17.6 MeV per DT fusion reaction is divided 8 plasma, but the 14.06 MeV of neutron energy must be recovered in surround ing blanket regions. Fusion Reactor Blanket Studies Since only limited quantities of tritium occur in nature, sufficient tritium must be generated through nuclear reactions to refuel operating fusion devi ces. The 14.06 MeV fusion neutrons are used for this purpose in two lithium reactions: 6 Li + 3 1 n (slow) SHe + T3 + 4.8 MeV 2 1T 3Li + On (fast) 4He+?T+  2.82 where natural lithium has the composition: 7.56% 6Li and 92.44% The exothermic reaction has a thermi 2.9 b resonance at 0.25 MeV while reaction, with its threshold at the endo has a 450 mb resonance at 8 .0 MleV. For the usual toroidal fusion reactor using for the magnetic confinement, the position of thj superconducting coils blanket used for heat recovery and tritium generation is illustrated in Fig. 1. This con figuration conforms to the Tokamak designs most often considered for economic, powerproducing fusion machines. 2733 Refractory metals such as vanadium, molybdenum, and niobium are usually postulated as the vacuum and structural material due to the hiqh heat and stress load as well as the need for (n,2n) reactions to enhance tritium breeding raphi te 9 C, a) LI w Ad o o c C o Co  (3 0 I 0 4, a a E 0 C) a) LI E I 1, a) I. 10 tritium breeding are confined to the inner reflector/moderator regions of the overall blanket, the outer regions shield the low temperature superconducting magnets from the deposition of energy by high energy particle generated within the fusioning plasma and inner blanket region. A typical thickness for the total heat recovery and shielding regions of the blan about two (2) meters with actual heat recovery and tritium production confined to the first meter. Many early studies were conducted to evaluate tritium breeding and heat generation in idealized fusion blankets. These initial studies in dictated that adequate tritium generation was possible but with severe heat transfer requirements on the vacuum wall This problem was partly due to the fact that only the exothermic lithium reaction was known and used in the earliest studi Myers et a >11 used diffusion theory to examine homogeneous cylin drica blan ts of varying thicknes from 9 to 96 cm Material tested included a lithium berylliumfluoride natural lithium metal and 6Li metal. salt (LiF + BeF2) called "flibe," All but 6Li provided adequate tritium breeding ratios above 1.45; the value of only 0.976 for "L demonstrated the potential significance of 7Li breeding reactions. Impink and Homeyer also examined the effects of blanket composi tion on tritium breeding and on spatial heating rates , respectively Graphite was used the neutron moderator with molybdenum as the vacuum wall material because of its neutronic and refractory characteristic The flibe coolant and tritium generation medium was electromagnetic resistance to coolant circulation. ected to avoid For variations in 11 Since nuclear heating rate calculations showed extreme peaking near the first wall based on 14 MieV neutron energy flux of only MW/m on the vacuum wall, Homeyer concluded that cooling of the vacuum wall would be most severe heat removal problem in the blanket. blanket energy was calculated to be The recoverable 17.4 MeV oer entering 14MeV neutron. used multigroup transport calculations to analyze an infinite annular blanket and concluded that pure lithium is an attractive breeding material but requires a thicker blanket than one containing beryllium. Unfortunately beryllium is probably too expensive to justify its large volume usage in systems of the si of powerproducing fusion devi ces. Realistic blanket designs required more detailed neutron studies to consider structural and heat generation requirements as well as the tradeoff between tritium breeding and energy generation as shown in more S8,27,3843 recent, detailed calculations. ' used Monte Carlo theory to calculate neutronics results for a three zone spherical annular blanket with outer radii of 302 cm for a 100 cm radius plasma. Structural effects were simulated by homogeneous volume fractions of niobium chosen for its refractory, fabricating, and welding characteristic exce llent results were obtained for a structureless lithium blanket. simulated by making Zone in Zones More realistic blankets were (1 cm) all niobium and diluting the lithium and 4 with increasing volume fractions of niobium structure. Lee's results are summarized in Table 1II where the increase in energy generation per fusion event i due to Nb(n,y) reactions Since enrichment was found to be ineffective and only 5 to 6% niobium is 12 Electromagnetic resistance to lithium flow may excessive near the vacuum wall where high coolant velocity are needed. Induced currents in the lithium act to retard lithium flow across magnetic field lines; but such resistance great reduced in the outer blanket regions where heating rates and hence flow rates are reduced. Tabl 1 Il Dependence of Tritium Breeding Ratios and Energy Deposition Rates for Lee' Fusion Blank Nb (Volume Per Cent) QB (MeV) 1 .38 1.16 1.00 19.60 20.20 20.50 Steiner8'39 analyzed the neutronic behavior of two designs based on the ORNL standard blanket configuration containing niobium structure, coolant, and graphite reflector. optimistic (D These two blankets reflected an esign 1) and a conservative (Design 2) outlook on the problem cooling the vacuum wall Design 1 contained lithium throughout the blanket Design assumed that flibe must be used to cool th vacuum wall with lithium elsewhere. Steiner rejected flibe coolant throughout the blanket since it produced an inadequate = 0.95) tritium breeding ratio. Neutron activation problems were also first revealed by Steiner. Niobium was selected over molybdenum as the vacuum wall and struc 13 lower sputtering ratio despite molybdenum's demonstrated superiority for tritium breeding. reflector in both designs. Summa with typical Graphite was employed as the moderator/ ry descriptions of these two blankets niobium structure are presented in Table 1III to indicate blanket model Table 1I'' Summary Descriptions of ORNL Optimistic (1) and Conservative (2) Blanket Designs Region Number Description of Region Thickness by Region Volume Composition by Region Design 1 Design Coolant 94% Li 94% Flibe Structure 6% Nb Second wall Coolant 94% Li 94% Li 60.0 Structure 6% Nb Moderator reflector 30.0 Gra white Graphite Coolant 94% Li 94% Li Structure 6% Nb The basic 100 cm Design 1 blanket with first wall at 200 cm radius 2A' n n + O rl a c *h n c+anA hl n n\ a* mn^al 3a +ka MIa tI rn nar r c Zncc in c F as well 44 National Laboratory (ORNL) in June 1971. This blanket has been frequently used to check neutronics calculations. Transport theorywas applied in slab geometry to obtain the tritium breeding results listed in Tab 1IV where the breeding ratio of 1.35 in Design is some 10% above the 1 value for Design Slab geometry is adequa to th large plasma radii meters) for steadystate fusion reactors. 33,45 Tabl e 1IV Summary of Steiner's Tritium Breeding Calculations per Incident 14 MeV Neutron Design T/n Neutron Leakage 0.023 0.020 If hypothesized low levels of tritium holdup 46,47 are realized, then breeding rati only slightly above unity .01) will be sufficient for seven year doubling times. Therefore, Steiner s relatively low 1 breeding ratio i sufficient to obtain the one month doubling time to establish initial tritium inventories. Steiner' results for spatially dependent, nuclearheating rates were based on a standard first wall energy transport of 10 MW/mn due to the 14 MeV neutron flux Extreme peaking of nuclearheating rates was I,,,, :, 1,, ,, S n 4: n 4 J f n,,:,, 1 15  DESIGN 1 (STEINER) DESIGN (STEINER) 170 160  150  140 1 30  1 20 1101 90 80 70 60 50 40 30 FIRST WALL SECOND WALL COOLANT & STRUCTURE   Distance from Vacuum iWal (cm Figure Comparison of spatiallydependent heating rates for vacuum wall * 200  16 heating rate peak at the vacuum wall will be 510% more extreme than in dicated These extreme heating rates (power densities) near the first wall along with the excess ve fusion neutron wall loading represent a major technological problem for all Tokamak fusion power reactors.30,33,47 Steiner' work supported previous work indicating that blankets employ ing lithium the only coolant are superior to those employing flibe since: Design 1 has a 10 higher tritium breeding ratio. Design since has a 50 lower heat load in the niobium vacuum walls high gamma cross section of flibe has been removed. Neutron irradiation effects within the vacuum wall are essen tially the same in both designs along with rates nea excess ive heating r the first wall. Blow et al.40 used Monte Carlo calculations in cylindrical geometry with first wall at 150 cm to examine Steiner's two basic 100 cm thick blanket model with varying ( 28%) niobium structural content. Good breeding rati cl usive 1.151.54) were reported for all use of flibe cases except the coolant in the entire blanket where T/n = 1.027. Blow reported additional good breeding results (T/n = 1.58) for blankets of Design where niobium was replaced with molybdenum. Examination of molybdenum was justified because the Mo) has the neutronic characteristic characteristics alloy TZM (0 of pure molybdenum but welding similar to niobium. A modular blanket design using heat pipes has been proposed by Werner et al in which neutron behavior was examined in a 100 cm thick cylindrical annulus with 200 cm inside diameter. n relocating the "standard" vacuum wall of a thermonuclear reactor beyond the neutron moderatina. enerovconvertina blanket (at 320 cm). the entire moderator 17 to eliminate the neutronic losses and structural buckling problems of previous designs. The interlocking modular blanket units incorporated heat pipes which remove radiant energy from the inner module surface and flatten the power distribution in the blanket by moving excess energy outward to power deficient zones WJerner's blanket model contained beryllium for neutron multiolica tion , lithium for tritium breeding, sodium for energy generation niobium for structural strength. The 100 cm moderator section of the blanket was divided into two zones Zone 1 contained Li and wh i e Zone contained varying volume percentages of Be, Na, and Li Both zones contained % 20% volume for heat pipe voids. Zone 1 was used to buffer the energy density in the fluid so that all nuclear and radiant heating energy could be removed by convective heattransfer through the heat pi densiti Thi resulting in power flattening and increased average power tradeoff between tritium breeding and energy multiplication through use of beryllium or tions in a 90 cm thick Zone neutron up to odium was examined for varying volume frac Increased energy generation per fusion .0 MeV for beryllium and 26.05 MeV for sodium was obtained but with a reduction in the tritium breeding ratio. Unless maximum energy is very important, Werner recommended maintenance of tritium breeding probably because of beryllium costs and sodium activation. Struve and Tsoulfanidi used Monte Carlo methods to calculate tritium breeding ratios and heating rates for two proposed blanket designs 18 The two blanket configurations included a basic Steinertype the vacuum wall surrounds the plasma and a Wernertype where the where vacuum wall surrounds the blanket. To avoi the problem of coolant flow, Struve proposed a heat transfer fluid such as helium which would be un affected by magnetic field lines and transparent to neutron It was simulated by volume void in the lithium. Breeding ratios above were obtained and agreed areas onably well with previous blanket studio using niobium structure. 8,40,42 The use of helium as a fusion blanket coolant has been investigated by Hopkins and Mlelesed'Hosoital and others at Genera patiall Atomic Company.31 dependent nuclearheating rates for the two blankets showed high vacuum wall heating and agreed with previous results. Steiner's generally higher calculated heating rates were caused by niobium blanket structure. These detailed neutronic studies of fusion blankets indicate ample tritium breeding possible in realistic blankets. The inability to breed tritium is not a problem in fusion designs The real problems in clude providing adequate heat removal for the first wall and protecting and designing the vacuum wall to withstand the required 15 MeV neutron fluxes. These fusion reactor blanket scoping studies have formed the basis for a number of design studies for Tokamak fusion power reactors of either full commercial scale or demonstration size 2832 various oure fusion Tokamak blankets use either flibe, natural lithium as coolant and flibe, natural lithium, or or hel ium ome lithiumbearing medium 19 of flibe. All blankets are on the order of 100 cm thick and some 2025 MeV are deposited in the blanket per 14 MeV neutron entering the blanket with extreme peaking of heating rates near the first wall are not expected then to be The blankets significantly energy multiplying. In genera the tendency i toward more compact fusioning plasmas with an associated reduction in the first wall neutron flux to well below 10 NiH~/r of 14 lMeV neutron energy transport. 2833 The basis for such reduc tions is the extreme technological problems of designing a first wall which will function for at least two years or more. If such cannot be accomplished, then fusion power plants that are viable in other respects are likely to be too limited in outage maintenance time to compete economically with other electrical power sources. 33,49 Critical Review of Hybrid Blanket Studies Overview of Hybrid Blanket Studies Fusion blanket designs attempt to maximize energy generation while maintaining the tritium breeding ratio. The inclusion of fissionable materials in the blanket is an obvious possibility for achieving signifi cant power and neutron multiplication. Such a hybrid blanket must still meet the basic fusion blanket requirements of adequate tritium breeding, heat transfer, and magnet shielding as well as produce energy multipli cation and/or fissile material As with pure fusion systems, previous evaluations of hybrid concepts have been based primarily on the cal culated neutronic behavior of the conceptual blanket as reflected in the 20 Fusion plasma characteristics. Neutron first wall loading. The tritium breeding ratio must be sufficient to refuel operating hybrid systems and fuel new on As for pure fusion systems, adequate values are in the range T/n  1.1 and are relatively y easy obtain. Simultaneously, a hybrid may also be required to produce or even breed significant amounts of fissile fuel ,3,6 Energy deposition in the blanket per fusion event i a very important hybrid criterion. Usually DT fusion systems assume a blanket energy deposition, QB neutron and th of about 20 MeV per fusion to account for the 14.1 MeV MeV per 6)3T reaction. Li(n, a) T reaction. Fusion blanket studies show thi position energy deposition is relatively insensitive to design or com with calculated values per fusion neutron ranging from a maximum of 26 MeV for Werner's41 best design down to 18. MeV evaluated by Leonard for the ORNL standard design. Although fusion blankets are limited in their energy multiplication capabil iti this is not the case for hybrids which are evaluated for significantly increased blanket energy deposition per fusion event through fission energy multiplication. Interest in subsystem interactions and dynamics studies of such a coupled hybrid system is certainly justi fied when the potential for energy generation through energy multiplication in the subcritical blanket i considered. The third area of technical assessment of hybrids involve fusion plasma characteristics required to achieve the assumed blanket Th' ic fnr nm a ic cc cm n cmn+t da c irol ma in fho hin.nL'ot onnn nv/ nn rf:n mi ~ n r a 21 to reach overall breakeven in energy production or scientific breakeven. The breakeven nTvalue varies inversely with the total energy generated per fusion event. Therefore , the potential value of a hybrid system is characterized by its ability to relax the Lawson condition through effec fission increase of energy released per fusion event. Finally , the required transport of neutron energy through the fi vacuum wall an important figure of merit. Previous projections of 10 MW/m impose stringent material problems so more recent designs attempt to achi eve val 1 loadings in the range 0.25 to MW/m 1,3,13 hybrid relaxation of first wall pure fusion oadings is a technical advantage over systems Such potential for breeding fissile fuel with fission energy multi plication of the fusion neutron source strength to sustain and drive the coupled stem h been examined by many researchers. Early concepts were summarized adequately by Leonard and have little more than historical significance.1 Lontai Attenuator Model The first detailed calculations on the neutron economy of hybrid blankets were performed by Lontai in 1965.10 He assumed a steadystate, DT clyindrical plasma with a 5.0 MW/m energy transport of 14 MeV neutrons but performed the neutron balance calculations for an infinite slab source geometry. Lontai's results were based on blanket configura tions using flibe coolant channelled in a graphite matri Neutron iI * 22 ratios Such a scope of study and results reported set the stage for most of the hybrid studi Lontai which followed. s best results were reported for a blanket concept consisting of a cm molybdenum vacuum wall , 1.5 cm coolant (flibe) region, and 49 cm attenuator region containing 21 graphite by volume with 70 salt bearing uranium (LiF  BeF2  UF4) natural lithium case had insufficient tritium breeding. Adequate tritium breeding was calculated only by using lithium salt enriched to 50% Li and varying composition. The fi ssion energy multiplication increased by nearly a factor of two over nonfissile blankets with better heat transfer characteristics. Similar calculations for 90% enriched 6Li resulted in much lower fissile fuel production with no increase in energy multiplication. Plasma requirements are not relaxed much by such small amounts of fission energy deposition; however, Lontai opti mistically labeled th 6Li attenuator practical because of possible reduced plant Lontai' capital costs hybrid feasibility study currently has little more than historical significance because of inherent deficiencies: Faiure to consider values of plutonium production. Failure to consider cost of maintaining high 6Li enrichment. Failure to consider U present in depleted uranium. Use of obsolete computer Lidsky codes and poor cross section data. Symbiosis Concept A novel approach to the fusionfission hybrid concept was proposed * .a I *tJ b j. S 23 feature of this symbioti tritium and fissile nuclei device such scheme was a fusion system breeding sufficient to fuel itself and a powerproducing fission as an MSCR. A cylindrical m radius torus of DT plasma was used in the symbiosi The basi duplex blanket configuration contained a thorium bearing blanket fl i be salt composed of LiF :SeF2: ThF4 in the ratio 71:0O 2:27 and lithium depleted in Th neutron properties of pure molybdenum with ts large Mo(n,2n) cross section, were utilized in the TZM structural alloy Since Lidsky' s fusion reactor was designed for , not power production, a graphi moderating region was used to prevent thorium fission products from poisoning the blanket during opera tion. only p055 ibie at initial operation until fissile 233 is U ls produced which impli which Lidsky ignored. frequent refueling and possible cost penalties Lidsky used SN transport theory to evaluate the neutron this economy of th hybrid blanket configuration as well as variations in the base design are results for shown i n Tabi ,V. Since simultaneous production of fissile nuclei and tritium be attainable system can be over a range of production ratios optimi found to each component of the for power or fuel production to utilize the strong points of both fusion reactors (neutron rich) and fission reactors (power rich). The reactors in the symbiosi were coupled by the production of fuel for th ssion reactor by the fusion reactors Lidsky6 also analyzed equations for the time dependence of the fuel inventori of the two rPacrtnrR in thp fuiinnnficinn 24 Tabi Neutron Economy of Lidsky' s Hybrid Blanket Events per 14neV Source Neutron Calcul ated Range Tritium production Thori u Total captu covers 1.126 0.325 1.451 0.050.50 2 1.40 Lidsky results demonstrated that the fuel doubling time of such a balanced hybrid system determined entirely by the neutronrich fusion reactor component. Lidsky power production analysis indicated further that the net power production in such a dual system i determined pri marily by the fission reactor component since the fusion power reactor is onl y a small perturbation on the net power r of real systems. Thus each symbiosis can theoretically be optimized for its respective primary purpose of fuel or power production. T important point to remember with respect to hybrid reactor Lidsky his i system design. selected a CTRMSCR power plant with 1500 MWe output and a 10 year doubling time for symbiosis study MSCR was rated at 4450 14JMWth with a fuel conversion ratio of 0.96 operating on the cle. Lidsky calculated a 10 year fissile doubling time with a tritium linear fuel doubling time of 0.113 years. For a 40% thermodynanmi efficiency the fusion reactor would be a net consumer of the overall MWe while stem was calculated to be able to provide 1690 fWe net subsystem in 233U_23~Th 25 Required plasma characteristics were encouraging since the vacuum wall loading due to 14 IMeV neutrons was only 1.00 MW/m well below that necessary to assure technological feasibility in pure fusion plants In addition, there was no energy multiplication in the fusion reactor blanket of the symbiotic scheme; this assumption was clearly not accurate as soon as some fissile fuel breeding has occurred. Plasma parameters are near Lawson conditions as indicated by the hybrid parameters summary in Table 1VI and the fact that only MWth was required to support the fuelproducing fusion system. Table 1VI Lidsky Hybrid Reactor Parameters = 1014 ions/cm = 0.625 sec 0 keV Wall loading 233 U production =1 MIW/r = 1.1 kg/day The symbiosis has a number of advantages. simplify First, this scheme construction of power plants capable of breeding and processing all requisite fuel in situ. Second , the lessening of fuel cost constraints makes the modifications of existing reactors possible to avoid thermal pollution. Finally, by developing this concept, the 26 In addition to the symbiotic hybrid concept and the usual power producing hybrid concept, Lidsky has also formalized consideration of a third hybrid concept called the augean concept. concept involves using the hybrid blanket to burn the actinide waste from fission reactors. augean concept is of little interest for dynamic consideration. Lee's Fast Fission Hybrid Concept eliminated Lidsky' separate fusion and fission reactors in favor of the socalled subcritical fast fission blanket. Monte Carlo Transport theory was used to perform neutron balance calculations in infinite media of pure thorium, pure the breeding potential of hybrid blan 1VII are in good agreement with expe Weal 238U, and natural uranium to verify kets. The results shown in Table measurements done by 51 et al Table 1VII Lee's Neutron Balance in Infinite Media Blanket QB (MeV) Breeding Reactions per 14MeV Neutron Thorium 2.7 [232Th(n,y)] 4.4 [23U(n,y)] 5.0 [238U(n,y)] Natural Uranium 27 sperhical annulus having an inner radius of 200 cm and an outer radius of 300 cm with composition as listed in Table 1VIII. For constant blanket qeometry and material volume fractions, the following optimum results were obtained for depleted lithium (4% Li) and depleted uranium (0.04% U) per 14 MeV neutron: = 103 MeV = 0.986; U(n,y) reactions  1. Because of the 1.68 239Pu breeding reactions per DT fusion event, Lee chose Pu as the fissile fuel. Tabl Subcritical Fast Fi e 1VIII on Blanket Components Studied by Lee Element Volume Fraction Zone 1 (30 cm thick) 0.95 0.05 Zone cm thick) Nb Heavy Element 0.30 0.05 0.65 Lee also studied the neutronics effects of changes in the thickness of Zone 1 and material volume fractions in Zone for the composition shown in Table 1VIII results were reported for the following heavy element material variations: Depleted uranium versus U content. Metallic and oxide mixtures of plutonium and uranium versus 239p 28 Best energy generation with sufficient breeding was reported for the metallic uranium blanket with 4% plutonium. poisoned with case fission products are summarized in Table and one IX. Tabl e 1IX Fast Fission Hybrid Neutron Economy per 14 MeV Neutron Calculated by Lee Plutonium Tritium Conversion B Material Production Ratio (MeV) eff 4% PuU 1.38 3.14 431 0.84 4% PuU + 8% FP 1.18 3.03 306 The usefulness of a hybrid concept is contingent upon a short ssile fuel doubling time . Lee estimated a very high 14 MeV neutron wall loading of 12. MW/m to obtain a year plutonium doubling time for the Leonard la FP blanket but reports no fusion plasma characteristics. ter claimed that the 306 MeV blanket energy release per fusion neutron n Lee's 8% FP model would lead to a threefourths reduction of the usual Lawson breakeven condition. However, current engineering con siderations indicate that such first wall power loadings will almost certainly make fusion power unrealistic due to the need for frequent first wal Since hi times over nonfissil replacement results indicated energy production increases of 10 to 20 blankets with simultaneous adequate tritium and 29 advantage over other concepts except as a fuel producer. Considerabi additional research has been reported on blankets and hybrid systems using the fast fission concept. All have emphasized fuel production versus power production and have worked with reduced first wall neutron loadings of 15 MW/m advantages of using fusion neutrons for fast fission as well as breeding fuel in situ are probably only applicable in the true symbiotic conceptS where the hybrid is not a system energy producer but a fuel producer, since blan fission. multiplication Hence, th lowered for low enrichments with fast fast fission hybrid is of little interest in this current study. Texas Fast Fission Hybrid Parish and Draoer presented extensive hybrid neutronics results for their no del which was also a fast fission design. They investigated the potential of 14 MleV fusion neutrons to fission fertile material (232 Th and U) while maintaining adequate fusion blanket performance. Parish and Draper based the a tive abundance of such fertile attractiveness of this concept on the rela fuels and the elimination of dependence on breeding fissil fuel for hybrid usage. The large fission energy multiplications obtained in other studi 1,3 were not paralleled in thi hybrid; however, the potential of both thorium and natural uraniumfueled fast fission blankets to produce both fission power and fissile material was demonstrated. .. /L .. . 30 various calculational methods. To verify methods of analysis Parish and Draper calculated the neutronic and photonic characteristic standard fusion blanket model using ENDF/BIII cross of the section data in the ANISN5 code for a P3S4 transport approximation. The resultant standard blanket neutron economy compared wel with Steiner s latest results on the same standard.59 Good agreement was obtained for breeding 1.445 versus T/n = 1.452) and (n,2n) reactions as well as neutron leakage despite Steiner's use of preENDF/BIII cross section data hybrid was one of the first hybrid studies to account for (n,3n s Texas reactions which become very important in such poorly multiplying blankets. Since high energy neutrons are needed to fission fertile fuels fission material regions in this concept were placed as as possibi to the vacuum walls. offset by (n,2n) and Low energy neutron absorption was only n,3n partially reactions. The volume fractions of fuel, clad niobium) and coolant (lithium) in the model tively were maintained constant at 0.45, 0.15, and 0.40, , to approximate fuel regions n a LMFBR respec The tritium breeding fissil region breeding, fission power, and spatial heat deposition by were presented in the T blanket exas study for various blanket fuel thick nesses. blank The results of these calculations for two thoriumfueled and four uraniumfueled blankets are presented in Tabi and 1XI. The calculation of spatial heat deposition rates in the standard and fertile fueled blankets in this work emphasized the problems with ow mul tipli cation hybrid blankets. 31 Table 1X Neutron Economy for ThoriumFueled Blankets Thorium Fue Reactions/Fusion Event Region Thickness 2Th(n,f) 232Th(n,) Th(n, ) 6 cm .3012 .0310 .1326 13 cm 1.0964 .0472 .3118 Table U "LXI Neutron Economy for UraniumFueled Blankets Natural Uranium Reactions/Fusion Event Region Thickness U(n,f) 235U(n,f) Total Fission 238U(ny) 10 cm 1.3252 .133 .0133 .1463 .2487 1.2694 20 cm 1.0865 .0161 .0259 .2024 .2096 .3818 .5320 0.9614 .1986 .0315 .2301 .6654 For the large 10 MW/m first wall neutron loading limit, the two thoriumfueled blankets showed peak power densities of 200 W/cm 3 For the 1 wall of 20 cm natural uranium case ranged from 510 to 364 W/cm to 146 W/cm , the power density between the niobium the related thorium case had a ranqe Fuel was eliminated in the 3 cm region between 1 L~.......ll 11 1 32 density, Parish and Draper have claimed these hybrid blanket power den siti are acceptable. This is doubtful because of the ow power den siti at blanket positions removed from the vacuum wall and the resultant unit cost of electrical and fusion power produced. The superiority of natural uranium to thorium as a fast fission hybrid blanket fuel because of its larger fast fission cros illustrated in Parish presented in Tabl section is s comparison of the best case for each fuel II. Table 1XII Comparison of Best Natural UraniumFueled and Extrapolated ThoriumFueled Blankets Uranium Thorium Tritium Breeding Ratio Fusion Blanket Energy Multiplication Fissile Nuclei Produced per Fusion Event Peak Power Density at Nb First Wall 1.09 , 20 '"" 3 409 W/cm3 1.15 0.5 0.31 S200 W/cm However, the low return of the fissioning blanket renders this concept uneconomical versus other concepts relying on better fissile blankets. Increasing fuel costs could make this concept more attractive at some future date but others seem more appropriate. Light Water Hybrid Reactors The feasibility of fusionfission hybrid reactors based on breeding 33 Princeton Plasma Physics Laboratory.60 Emphasi was placed on fuel self sufficient (FSS) hybrid power reactors fueled with natural uranium. Light Water Hybrid Reactors (LWHR) considered included FSSLWHR' Other fueled with spent fuel from Light Water Reactors (LWR's), and LWHR's to sup plement LWR's by providing a tandem LWRLWHR power economy that would be fuel selfsufficient similar to Lidsky symbiotic concept Nuclear power economies based on any of these LWHRs were found to be free from the need for uranium enrichment and for the separation of plutonium. They offer a high utilization of uranium resources (including depleted uranium) and have no doublingtime limitations. study investigated the property atti of subcritical thermal for hybrid applications and concluded that light water is the best moderator for FSS hybrid reactors for power generation. latti Several geometries and compositions of particular promise for LWHR'swere identified with thicknesses up to 250 cm. The performance of several conceptual LWHR blankets was investigated and optimal blanket designs were identified for natural uraniumfueled lattices. The effect of blanket conversion efficiency and the feasibility of separating the functions of tritium breeding and of power generation to different blankets were investigated. Optimal ironwater shields for LWHR were also determined. The evolution of the blanket properties with burnup was evaluated along with fuel management schemes. The feasibility of using the lithium system of the blanket to control the blanket power amplitude and was also investigated shape A parametric study of the energy balance of LWHR 34 with critical systems and delineated the advantages of such hybrids in alleviating nuclear technology problems relating to resource utilization, prol iferation and safety issues. In general , this study reported the same types of information as previous studio but for a different blanket design. PNLThermal Fission Hybrid Pacific Northwest Laboratories (PNL)1'61 initially studied a hybrid fusion reactor utilizing a subcritical thermal fission latti around the usual cylindrical DT plasma The four distinct regions of the hybrid blanket configuration are illustrated in Fig. cm thick neutron convertor region was filled with niobiumclad pins of both depleted uranium carbide and natural lithium. Niobium structure walls are used along with helium coolant. The 150 cm thick thermal fission lattice, consisting of a graphitemoderated, natural uraniumfueled, heliumcooled matrix, was designed for fi ssion power generation. The last 50 cm of blanket thickness are filled with graphite reflector and natural lithium absorber , respectively The ENDF/B III cross section data were used in the HRG362 RevisedThermos (BRT1)63 and Battelle cross section codes to obtain fast and thermal broad group data trained using a P , respectively The final neutron balance results ob transport calculation in ANISN58 are summarized in column of Table 1 XII I. Neutronic effects from slight enrichment of the uranium in the fi ssion lattice are also shown in the neutron balances I~~ 5 II tt r I 35 S' 4 A 4 ~C~L~ll*ll~: t I~ ,& 36 Table 1XIII Early PNL Hybrid Neutron Balance Events per Source 14MeV Neutron 235 U Atom Percent Enrichment 0.7196 0.80 0.90 Tritium Production 0.956 0.019 1.188 0.019 1.763 0.020 Total Tritium Production 0.975 1.207 .783 Fissions 0.234 1.936 U Captures 1.121 0.251 .776 0.988 .292 4.863 0.853 U Absorptions Estimated kff eff 0.84 0.884 0.928 1050 Based on their composite behavior with fi enrichment, an enrichment was predicted 0.77 atom ) for which both the tritium and fissile conversion ratios could be optimized to excee d unity. The cal culated energy deposition in the blanket for the best case was calculated to be about 500 MeV per pl ication of about significantly 0.7 source neutron corresponding to an energy multi This PNL optimum hybrid is attract nce enriched uranium can be produced than the higher 37 reactor capabilities which is very low. This power density was used to determine the plasma and blanket specifications shown in Table IXIV where the plasma requirements are substantially less than for a nonmultiplying blanket and the vacuum wall loading i Tabl very low. e 1XIV Early PNL Hybrid Specifications Blanket Plasma Specific power Thermal power Vacuum wall loading keV) 0.75 W/cm3 20 MW/m 0.05 MW/m2 nT (steady tate) (sec/cm3) x 1013 x 1013 Since a nonnegligible fraction of the thermal energy produced in the blanket must be used to sustain such a plasma, the need for investigation of controls i tion i justified, especially since the fission energy multiplica predicted to be so high. This preliminary PNL hybrid design was faced with drawbacks such as large (2 m thick blanket) and low power density 0.75 W/cm3). However, it was favored with low wall loading and plasma conditions re duced to S1/6 Lawson Criterion value. Since the hybrid objective energy multiplication with adequate breeding of tritium and fissile fuel are attainable, the PNL concept appeared to be a promising competitor for the LMFBR program. Much additional work has been performed including 38 studies have identified and delineated the merits of the heliumcooled, thermal fission hybrid fueled with natural or slightly enriched uranium moderated with graphite, and cooled with helium. In addition, the optimal use of lithium for breeding has been delineated. This PNL concept of a fusionfission system has been developed to a considerable degree as reported by many studio 6467 The most complete results on blanket parameters were reported by the combined efforts of Lawrence Livermore Laboratory and Pacific Northwest Laboratories. Although thi hybrid blanket design was intended for use in the spherical geometry of Livermore' mirror (YinYang) fusion reactor concept, the basic blanket geometry is very similar to that shown in Fig. modul Blanket of varying composition were analyzed using a fuel pin lattice geometry similar to that used in HighTemperature GasCooled Reactors. Results reported for th hybrid blanket analysis are included in Table 1XV showing seven (7) different cases analyzed, all of approximately 200 cm thickness. The inner convertor region was closest to the plasma and contained helium coolant and stainl steel structure as well as depleted uranium to enhance neutron multiplication. The inner thin breeder contained lithium for fast neutron tritium breeder while the thicker outer lithium breeder contained lithium for thermal neutron breeding of tritium. The reflector, where used was composed of graphite and the thermal fission latti was composed of hexagonal unit cell slightly enriched (as noted) fuel pins in a heliumcooled graphite matrix. The fuel pin geometry and cell pitch were optimized using transport calculations. 39 Tabi 1XV PNL Hybrid Blanket Analysis Tritium Fissile Blanket Case Blanket Breeding Breeding Fusion Energy Arrangement Ratio Ratio Multiplication 1 8.5 cm convertor 1.5 cm breeder 150 cm lattice (1.0%)* 0.766 1.59 18.9 20 cm reflector 15 cm breeder 2 10 cm convertorbreeder mix 150 cm lattice (1.0%) 0.725 1.57 19.8 20 cm reflector 15 cm breeder 3 10 cm convertorbreeder mix 180 cm lattice (1.0 %) 0.365 1.62 25.2 10 cm breeder 4 8.5 cm convertor 1.5 cm breeder 0.737 1.55 20.0 180 cm lattice 10 cm breeder 5 8.5 cm convertor 1.5 cm breeder 1e 0.893 1.22 31.8 180 cm lattice (1.25%) 10 cm breeder 6 8.5 cm convertor 1.5 cm breeder 15cbed 41.26 0.984 59.6 180 cm lattice (1.50%) 10 cm breeder 7 8.5 cm converter 1.5 cm breeder n 00 1. 11 39 .8 180 cm lattice (1.35%) 10 cm breeder 40 unity In addition, the energy multiplication of the fusion power was found to be very large for thi best case (MB = 39.8). This energy multiplication was claimed to be related to the effec neutron multiplication of the blanket and the neutrons produced per fission in the blanket by the following global parameter equation: 200 MeV 1) 14 MeV eff  kff eff where 200 and 14 represent the energy deposited due to fission reactions and fusion neutrons, respectively, v is the number of neutrons released per fission and tion factor. keff i usual blanket effective neutron multiplica this equation related global parameters and since 4 MeV source i introduced inhomogeneously, the current work was partially directed at determining if this equation might be inadequate despite its frequent use in describing and analyzing results from cal culations performed on hybrid blankets. Review of Controlled Thermonuclear Reactor Thermal Stability Ana yses Fusioning Plasma Operational Criteria The first determinations of operational criteria for thermonuclear reactors were performed using global or pointmodel reactor parameters. Rigorous descriptions of comply plasma dynamics with attendant spatial variations were usually beyond the scope of such criteria development. The first attempt to soecifv fusion reactor operational criteria 41 uniform temperature, T, and confined for a time, r, after which cooling was allowed. Conduction losses were entirely neglected. This initial work established values of temperature and the product of ion density and confinement time, nr, for a zeropower but nuclear system. A system energy balance was u selfsustaining thermo sed in which the energy to heat the plasma, E and the energy to overcome bremsstrahlung radiation losses energy , Eg, were upplied supplied to produce fusion reaction energy as well as the fusion reaction energy, was assumed to be recoverable and converted to useful output energy at some efficiency, n. The minima condition for breakeven is simply defined as follows: [EF + E + Ep]n EB + Ep where n is the overall system energy conversion efficiency For a DT fusion system as described above, the socalled Lawson Criterion for breakeven becomes simply: ( )p(l  p)QF where = fuel ion density (ions/cm3 ) = plasma temperature (keV) = reactivity of DT plasma (cm 3/sec n = overall system energy conversion efficiency = proportionality constant for bremsstrahlung radiation = tritium fraction of ion density r.. ./i.. \  bT1/2 42 The Lawson Criterion for the pure DT fuel cycle is represented by a series of parametri spectrum of curves in Fig. curves in the efficiency as shown in the lower Points on such parametric curves represent minimum nr and T values for breakeven fusion energy production no net fusion energy i produced. If the energy per fusion event can be aug mented by fission reactions in the hybrid blanket, then the requirements on the plasma can be significantly relaxed. Cyclotron or impurity radiation losses are not considered in Lawson type anal yses. No stability i considered since the conditions quoted from such analyses refer to minimum requirements for overall breakeven. Another early study of the reactor energy balance was done by Jensen et al Again the DT reaction was of primary concern though subsidiary fusion reactions were also treated. Jensen reported on the effects of finite energy transfer rates and found selfsustaining reactors were possible over an increased parameter range, although all ion speci were treated at a uniform temperature. The major shortcoming of Jensen energy balances was its failure to consider particle confine ment times of diffusion losses. Additional energy balance considerations were reported by Woods. Horton and Kammash have also considered energy balances and operating conditions for the DT fusion cycle. since alpha particles are a significant plasma heating mechanism, energy and particle conservation equations were introduced for the alphas created in DT fusion reactions. Both bremsstrahlung and synchrotron radiation 1 losses were treated along with the effects of cold and energetic fuel injection. This work was 43 temperature and density, some of which were applied in the later stability work of Mill 1517 and Ohta et al A similar but more realistic condition than the Lawson Criterion for minimal operation has been developed by Mills for a system using only the DT reaction. 15,16 This model i based upon continuous injection of cold fuel where fusion temperatures are assumed to be supported by alpha heating. Mills used particle and energy conservation equations for the ion density follows: dt  n/T d 3 dt 2 + Te)] = p(1l  p)n S(T. + T ) 1 e' where = fuel ion density (ions/cm") = fuel ion injection feedrate nuclei/cm3sec) = tritium fraction of ion density = confinement time against all plasma losses including fusion (sec) = alpha particle energy from DT fusion events (3520 keV) = fraction of alpha energy retained in the plasma for heating i,e = temperature for ion and electron species respectively (keV) = DT fusion reaction reactivity or rate coefficient (cm3/sec) For steadystate operation with this model Mills found that the following equilibrium condition must be maintained if operating charac 44 2p(1 + T )  p) This result is similar to the Lawson condition but more conservative since only a fraction of th alpha particle energy i retained to sustain the plasma while none of the neutron kinetic energy is retained. addition, the Mills condition i a steadystate condition based only on the plasma while the Lawson Criterion attempts to account for all in fluences on losses tem efficiency. The constant, c, accounts for energy due to bremsstrahlung and synchrotron radiation. feature of thi work i An important the temperature difference allowed between the ion and electron speci in general, Mill s found that the electron temperature is elevated due to preferential alpha heating Figure 4 illustrates the Lawson breakeven region for to 45% efficiency com pared to the Mill ' equilibrium region = 0.8, p = 0.25 and 0.50) Since Mills' model i concerned only with alpha heating and radia tion 1 losses within the plasma, energy release to neutrons was not con sidered. Though actual power generation capabilities were not considered by Mills, comparison with the zero power condition developed in Lawson model does indicate net overall power production as expected for equilibrium operation. Fusion devices producing values above Mills equilibrium region in Fig. 4 can be operated only in the pulsed mode. similarly, devices pro viding nivalues below the Lawson region can never operate as power producing reactors, while those falling between the two criteria will 4tn, l nnvn 4n4r4n,,n C; .; n a n 1, n n + I I r.. c.,ll ..,.+., cn inhn ; $ 45 10"15 PLASMA EQUILIBRIUM REGION (c = 0.8) p = 0.25  0.50 n = 45% n = 40% n = 35% LAWSON BREAKEVEN REGION 20 40 60 Ion Temperature (keV) I, t~ 14 10 13 10 46 Plasma Thermal Stability Considerations Plasma global thermal stability studies were initiated by Mills based on the operational equilibrium studies.1517 studies Mills demonstrated that the equilibrium condition is equivalent to requiring the constancy of a function follows: = STr2p(  p)S where the socalled stability function, cm2/keVsec) varies with ion temperature Ti as S " cT~ which exhibits a broad resonance %CT1 peak around In the first approximation Mills treated the alpha energy re tention fraction as a constant. For stable equilibrium, the ogarithmic variation of i(S,T,p,T.) must vanish. Therefore, Mills found that the operational equilibrium i unstable against fluctuations in the fuel feedrate th confinement time, the fuel mixture (unl ), and the ion temperature except when the exponent in Ta falls to zero above 1 28 keV. Although the exact behavior of the confinement time with ion tem perature was not known (nor is it known today), the pfunction formaliza tion showed that if t i nuclear reactor below s independent of T. keV is impossible without stable operation of a thermo some form of control. Below , departures from equilibrium are supported due to the posi tive slope of the stability function. It is not until the negative slope region of the stability function i reached above keV that the in herent instability against fluctuations in T. is controlled and the 1 + maarnnr s I I r t i u h3Pfn4 annII 1i h nr I~ +n ar,4 km 47 In fact, most fusion reactor system design studies currently operating temperatures below 20 keV 2832 But at temperatures below keV, Mills showed that control i extreme departures from equilibrium. necessary to avoid the predicted This control can be implemented via the feedrate, the fuel mixture, the confinement time, or radiation losses dependent on injection of impurities. Initially, Mill favored control via the confinement time 5,17 but later work has emphasized feedrate control More recent studio by Ohta et al. 18 have confirmed the use of feedrate as a viable method by which to control stability. If the confinement time i temperaturedependent , then it may be useful for inherent control by introducing temperature dependency into the pfunction. Mills hypothesized Bohmtype diffusion (r ST1) as a CLT) as a possible inherent control to allow stable operation below the 28 keV cutoff indicated for constant confinement operating conditions. fixed feedrate and fuel mixture, Mill used the pfunction variationa method to demonstrate inherent stabilization of plasma equilibria for this Bohmtype diffusion for temperatures in the 7 to keV range. analyzing the dynamic behavior of thermonuclear plasmas, Mills lished the selfstabilizing influence of Bohm diffusion below estab temperatures as the perturbed plasma temperatures (ion and electron) and ion density were shown to approach equilibrium with time. Mill In this justified operation near the 12 keV temperature to take ad vantage of the optimal DT reaction rate73 without the necessity of introducing artificial control. Mills17 also presented details on calculations to evaluate the time 48 exchange between ion species as an instantaneous process. Results were reported only for plasma time behavior for attempted initial equilibrium operation about a temperature of 11 keV with 50% deuterium and 50% tritium fuel injection leading to ion densiti x 10 ions/cm stability of plasma operating conditions in thi region was verified for constant confinement and shown to result in rapid plasma runaway in less than three seconds The plasma temperatures (T. and T ) were shown to 1 e runaway above or below ignition depending to extreme acc uracy on whether or not the constant plasma confinement time was too ong or too short artificial control was found to be essential below Mills17 also investigated feedback control via the fuel mixture using the monitored plasma electron temperature. When the ectron tem perature was set below a preselected control temperature, the injected fuel mixture was maintained at the original 50 D, 50 T; when the tem perature exceeded the control temperature, tritium injection was replaced with pure deuterium. effect of stopping tritium injection was to reduce fusion events and lower temperature the stabilizing effect of this mixture control feedback was achieved by making the time average of p(lp) low enough to compensate for excess ive confinement time. Control to a temperature that was too low to provide the nrequilibrium condition was found to result in the reacting plasma extinguishing itself. Mill also noted that excess ive confinement time will result in severe initial temperature overshoot. These investigations by Mill constituted the first efforts to study the dynamics and control of thermonuclear reactor plasmas. The 49 incomplete stability criteria development in Mill work is its most significant deficiency. The same stability problems of point model DT plasmas have been investigated in more detail by Ohta et al 18 but using the following global nonlinear balance equations for plasma density and temperature (energy):  n/T n ( d(nT) n2f) dt  nT+ ST (13) s where f(T)  1.12 1015 1/2 x 10 T = plasma ion density (ions/cm3) = uniform plasma temperature (keV) = particle and energy confinement times (1/sec) = fuel injection feedrate (ions/cm sec = fuel ion inject energy (keV) = alpha particle energy from DT fusion events (3520 keV 3 DT fusion reaction rate coefficient (cm /sec). Ohta addressed only the DT reaction; the fusion reaction was not considered an important loss mechanism in the particle conservation equa tion in essential agreement with Mills. and the bremsstrahlung energy 1 Both the fusion energy source terms were included in f(T) but dn dt 50 No temperature difference was allowed between the electron and ion species which is a limitation in contrast to Mill attempt to treat differing temperatures The advantages of Ohta' model include accounting for energy diffusion with particles and energetic ion inj section as well as including an explicit expression for bremsstrahlung radiation. obtained the following form of th state subscriptt o) Ohta Mills equilibrium condition for steady evaluation of the balance equations: oEE T E _o 0 (14) f(T which indicates the reduction in required nTvalues by the inclusion of Ohta's injection heating option. Efforts by Ohta to examine steadystate plasma stability can be categorized into two areas: Linear analysis establishing temperaturedependent stability criteria in possible operating regions for future fusion plasmas, and Nonlinear dynamic subject to simulation of the plasma balance equations small perturbations with and without feedback effects to verify agreement with linear stability analysis and control possibility in unstable operating regimes Linearized analysis will usually predict stability regimes. If a system is not stable, linearized analysis will not predict true con sequences of the unstabi situationhence the need for dynamic simula tions. ability criteria to predict whether small plasma perturbations will grow or diminish with time were developed by Ohta from linearized forms of the density and temperature balance Pouations. The elimination 51 and small temperature perturbations, 6T(t), which Ohta assumed to vary exponentially with time. Stability is assured provided the real part of the growth rate is negative. Ohta obtained general stability criteria by solving for the growth rate after substituting the density and temperature variations into the linearized density and temperature equations. To proceed beyond such general stability criteria , the functional dependence of both the particle and energy confinement times were re Because the exact density and temperature dependence of confine ment time was uncertain, Ohta based the analy functional dependence of confinement time on density and temperature T n Tm this genera upon the following It is the derivation of stability criteria on the basi diffusion model that represents the major contribution of Ohta s stability analysis. To obtain useful stability criteria, Ohta used three diffusion models to get specific values for and m: Constant confinement T % constant (z = 0, m = 0). Bohm confinement: T Tl (e Classical confinement: = O, m T % n'T1/2 (A = 1) = 1/2). The minimum temperature satisfying the stability criteria for each confinement model is known as the critical temperature, T temperature above which operating conditions are predicted that is, the d to be stable as described by Mill s' work. Representative temperature results pre dicted by these stability criteria are listed in Table 1XVI for both charged particle and injection heating for all three diffusion models. Ohta also dynamically simulated the balance equations to check the quired. 52 densities, however, were perturbed a small amount above and below equilibrium and th and temperature ca effect on the temporal behavior of the plasma density culated as presented in Fig. 5. Table 1XVI Critica Confinement Model Temperatures for DT Fusion Reactors c (keY) C Charged particle Heating Injection Heating* (*n E/ = 10) (n /TE  1) T = constant T T T fl *Ion Injection Energy: For the c which the ase = 150 keV. of constant confinement and charged particle heating for critical temperature T keV was found also by Mills. Ohta's results are depicted in Fig. 5 for three initial equilibrium tem peratures of 10 keV 30 keV and 50 keV. For equal magnitude density perturbations, equilibrium density is always approached with time which indicates plasma stability under isolated density perturbations. Similarly , temperature transients resulting from the density perturbations out for ca 30 keV to 50 keV) where T However, for the subcritical 10 keV initial temperature, the time evolution of temperature is unstable as shown in Fig. 5 and predicted in Table 1XVI. 53 From Ohta et al T = 10 keV ST = 30 keV T = 50 keV 0 2 4 6 8 10 Time sec) = 10 keV = 30 keV T = 50 keV 0 2 4 6 8 10 Time (sec) Figure Time variation of pointmodel plasma temperature and density for constant confinement and charged particle heating. 54 general, the quick plasma response on the order of a few seconds was found for all these anal yses of unstable plasma variations in pure fusion plasmas. Ohta' s behavior agreed with previous fusion plasma analyses. results demonstrate the need for stabilizing control to allow fusion reactors to operate below the critical temperatures as planned by current fusion reactor design studies. stabilization for the Ohta et al balance equation The case of feedback constant confinement model was also examined by Stability criteria were again derived from linearized ns. Density feedback control was introduced by adding the term, 6n(t) , but was not able to stabilize the system because the balance equations are stable for isolated density perturbations. since temperature instabilities can grow independently, various types of tem perature feedback were introduced by adding the stabilizing feedback term, 6T(t) a T T 0 tions. , to either one or both of the perturbed linearized balance equa New stability criteria were derived dependent on the value of the feedback coefficient, in implementing control ferred by Ohta et al. i . Although many parameters are possible for use , feedback via the injection feedrate was pre n agreement with Mills. Ohta demonstrated control of the temperature instability through dual temperature and density feedback which was introduced through the injection rate and its "small" variation about equilibrium as follows: an S(t) +65S T  At) where a is the feedback coefficient and At is the delay time between a 55 applicable to realistic control situations. The effectiveness of feedback stabilization was found to be dependent on both feedback parameters: and At. For the applicable plasma model Ohta found a stabilized region in the aAtplane from the linear stability analysis of thi s feedback effect. In general larger negative feedbacks and shorter delay times were found to yield more effective stabilization. At or small subcritical (T For sufficiently large feedback stabilization was found to be ineffective in all cases. As expected, Ohta found the unrealistic case of zero delay time to be the most effective feedback. However, when the delay time and feedback coefficient were within the stability region predicted by linear analysis, an equilibrium temperature was always approached; however, the amplitude of oscillations was found to increase with delay time as the limits of the stability regime were neared. Since delay times of to 3 seconds are outside the linear stability regime predicted for this case, extreme amplitude of oscillation for these delays was found as expected Usher and Campbell23'24 extended pointmodel thermal stability analyses to other fuel cycle and other plasma diffusion models with similar results and speeds of response. In addition burnup was treated in this extension of Ohta s analysis with essentially similar results for the DT fuel cycle. Stacey' point model plasma stability analysis of the DT fuel cycle extended point model plasma stability analysis of the DT fuel cycle to include more detailed plasma behavior including four balance equations to represent the following plasma parameters: 56 Alpha particle density. Electron energy density. Again the temperature instability was found in certain regimes. Effective stabilization to control operation about an unstable equilibrium point through use of controlled ion injection rate as well as controlled DT fuel mixture was demonstrated temperature instability has also been examined for radially homogeneous DT fusion plasmas by Yamato, Ohta and Mori , using partici and energy balance equations. 1921 The results of thi s inhomogeneous anal ysis support the validity of decoupling excursions in the overall particle densities and temperatures from excursions in the spatial density and temperature distributions. When the injection of fuel is uniform the temperature instability can develop only in the zero order mode. Stability criteria were developed similar to those for the uniform plasma with similar results , including feedback stabilization through temperature to allow operation below the critical temperature. There have been no investigations of hybrid plasmas to examine the temperature instability discussed in thi review. an area that requires study because large hybrid blanket energy multiplication values coupled with large plasma transients and neutron release could have con as wel as safety significance. Motivation for the Research As is evident from the preceding critical review of hybrid studies,  hn rn vmn m v n \F r r P vnn 4n 4 nncn n# i An ct M c n h r hlar c f I I rl; o c n n h ~rh ri rl c r ;I n the dynamic interaction of the two components of the hybrid system. investigations have not been reported in the literature to date. Such Thus, the objective was not to devi a new system but to take the somewhat arbitrary approach of selecting a previously establi shed hybrid concept with necessary adjustments. Many different types of hybrid machines have been proposed with many different methods of application. Powerproducing Tokamak hybrids are of most interest for control and dynamic considerations and so such a model was selected for thi work. entially thi hybrid design is compatible with various hybrid advantages Laboratory delineated in the recent Princeton Plasma tens study of Tokamak fusionfission hybrid reactors which concluded that the most economical mix of power and fuelproducing hybrids should emphasis power production An optimized hybrid machine should be a substantial power producer with a byproduct of fissionable fuel, the optimum ratio of fuel production to power pro duction being determined by economics. An early demonstration of hybrids could allow a very reassuring program for future development of the utility industry. A guarantee of future reasonable fuel costs could promote the accelerated installation of current LWR plants straints on all to fill sectors of th nearterm power needs while United States energy economy loosening con subsequent commercial development of hybrids could supplement LWR's, provide them with fue eventual 1, and take up the load of retired power stations followed by introduction of the pure fusion reactor sometime in the coming century. 58 enrichment operations run for nuclear power plants and defense purposes. The hybrid may be a better way to burn U reserves with possible elimina tion of some enrichment requirements and perhaps elimination of plutonium separation if bred plutonium i burned in situ. scenario i especially important in eight of the continuing breeder controversy the recent Three Mil Island accident ,74 which will undoubtedly delay introduction of the breeder still longer due to safety considerations. Since the hybrid represents an alternate concept for power production and orderly progression to longrange utility application of pure fusion, its characteristics require analysis central station power production. scribe hybrid prior to its being approved for One parameter frequently used to de characteristics is the global relationship for the blanket neutron energy deposition per fusion neutron QB, derived in Appendi f = [ v Li kff eff ]+E  keff where = blanket energy deposition per entering fusion neutron = fission energy deposited in the blanket per fission event (192.9 MeV)75 = average number of fission neutrons produced per fission event keff = effective blanket neutron multiplication factor = energy of the fusion neutron (14.06 PMeV) = addition due, for energy generated and deposited in the blanket example, to exothermi neutron absorption reactions + 6E 59 Several forms of the global relationship of Eq. (16) have been used tensively to describe hybrid blankets. 1,64,76, However, no results have been reported on its validity. If the parameter is to be used as a figure of merit characterizing the multiplicative capabilities of hybrid blankets, then its applicability must be verified and its limitations established. Hybrid blankets are expected to have substantial energy deposition per fusion event so it becomes imperative that safety studies be undertaken to examine the implications of this characteristic. For nonmultiplying pure fusion blankets, the energy deposition per fusion event is to be about 20 MeV. expected For hybrid blankets, even extremely modest ones with keff = 0 fusion event. .8 are predicted by Eq . (16) to have 316 MeV deposited per energy deposition and fusion energy multiplication predicted by Eq. (16) for possible blanket keff values are listed in Table 1XVII. Table 1XVII Predicted Blanket Global Response per 14 MeV Neutron Effective Blanket Blanket Energy Blanket Fusion Neutron Neutron Multiplication Deposition* Energy Multiplication keff QB (MeV) MB 0.80 0.85 0.90 0.94 0.95 0.98 0.99 439 687 872 1181 1429 3654 7364 ex 60 The accepted variation of blanket fusion neutron energy multiplica tion with blanket values of keff i depicted graphically in Fig. 6 to demonstrate the hybrid capability for high energy multiplication with in creasing but still far subcritical blanket systems. Despite the impossi ability of reaching a critical fi ssion reactor state in such stems, variations in the plasma operating conditions could cause blanket energy production rates beyond the technical limitations or the technical fications of the design. speci Even with no danger of supercritical behavior, large uncontrolled thermal instabilities in the plasma could ead to cess ive energy deposition in the powerproducing hybrid blanket. In addi tion, there is the possibility of criticality at low temperatures prior to power startup. If plasma startup is very quick, then the plasma neutron production may drive the blanket to large overpower ratings before the temperature defect can reduce the effective blanket neutron multiplication factor, keff Although relatively small quantities of therma energy are contained in the plasma a fullscale hybrid system generating 6500 MWth of steady state thermal power will require large numbers of 14 MeV neutrons. a farsubcritical blanket (keff tion of the fusion neutron fission neutrons in the blanket. Even Z 0.9) can cause considerable multiplica available as an external source for providing The component interactions as well a the control and stability of such powerproducing hybrid systems must be wellunderstood. The Lawson Criterion for hybrid reactors is modified as follows to account for fusion and fission sources of thermal power with zero energy 61 x 1014 1012 LAWSON BREAKEVEN CURVE Temperature (keV) Fioure 6. Tvoical Lawson breakeven curve for a 5050 DT plasma and 14 10 13 10 62 12 T lfl  4bT1/2 where QB is the blanket energy deposition per fusion neutron and n i usual overall system efficiency defined for the Lawson Criterion. 50.69 Obviously f significant energy is produced in the fissile blanket, the requisite hybrid plasma parameters can be relaxed to allow earlier utili zation of fusion power in combination with a subcritical fission reactor to take full advantage of inherent hybrid safety features. The typical effect of hybrid operation with blanket energy multipli cation is a reduction in the required n product is depicted in Fig. 7. The production of fission energy effectively reduces the need for fusion produced energy. The hybridrevised Lawson Criterion of Eq. (18) is greatly relaxed because QB is on the order of hundreds of l1eV versus the usual QB used for pure fusion systems which i s limited to about 0 [IeV including exothermic blanket reactions. As noted, this interactive multi plication demonstrates the need to examine the dynamics and controllability of hybrid systems. Previous studies have been restricted to steadystate neutron balance calculations and associated technological limitations. There has been no analysis of the timedependent behavior associated with hybrids, when subjected to reasonable perturbations in the characterizing parameters In addition, there have been no reports of analysis of hybrid plasmas in the reduced reactivity regions where plasmas are not self sustaining. The development of a model to describe the dynamic S Sl I I I .4 I r I nT + Q,) F 63 PREDICTED: MB vs. k ff 0.80 0.85 0.90 0.95 Effective Neutron Multiplication Factor Figure 7. Predicted variation of blanket fusion neutron energy multiplication with blanket effective neutron multiplication 64 hybrid system must be established when subjected to effects due to the thermal instability analyzed by Mills1517 such as those and by Ohta et al for pure fusion plasmas. The desired result was a hybrid system model whose analysis would yield useful operational characteristic then enabi of hybrid machines which could the hybrid to make a contribution to power production before the turn of the century These various investigations will only be possible if both the plasma and blanket components are modeled and coupled to allow dynamics and stability analysis to be performed. Summary of the Research The research reported here began with the Ohta plasma model18 burnup effects included after Campbell and Usher with and developed plasma stability criteria based upon source feedrate perturbations and other engineering considerations for plasma changes affecting the output neutron production rate. Essentially, an effort was made to develop an analytical model for pure fusion plasma stability and control based on a global parameter treatment of a linearized fusioning plasma model using concepts of classical control theory and transfer functions. Feedback effects were also incorporated into the model which was kept independent of specific design concepts. The analytical model and its stability pre dictions were compared with Ohta 's results to develop an engineering oriented mode which could have broad application to more sophisticated plasma models in the future. Perturbations causing plasma transients r' II .1 ... I I J  55 With the completion of this plasma stability and transfer function analysis, the effort was extended to develop a simplified hybrid model from which general stability criteria were developed for the interacting components of a hybrid system. Again, the model was kept independent of specific hybrid concepts except that the plasma confinement time was assumed to be a constant The model was , independent of plasma temperature and density. specifically developed and related to engineering con iderations of hybrid system perturbations as well as dynamic imulation and control Inherent as well as artificial feedback effects were in corporate where appropriate The entire effort was directed to develop ment of a simple, linearized closedloop model in transfer function format which could be used for future extensions of this work on dynamic and stability characteristic of hybrids. Of course the nonlinear form was retained for dynamic simulations. The hybrid analytical model was then used to examine the properties of a particular hybrid system. The various augean and symbiotic concepts and variations proposed by Lidsky2and analyzed parametrically in the Princeton Study were rejected for this research since they are not primarily intended for power production. s left essentially two choices: the possib a fast fission blanket or a thermal fission blanket. 1 need for To avoid significant enrichments and to take advantage of expected higher multiplication factors, a thermal fission concept was selected. The most advanced and promising design was reported by PNL and Livermore workers under Wolkenhauer This PNL blanket design was based primarily on existing technology 66 severely powerlimited, the only substantive change for this research wa the conversion to a Tokamakdriven hybrid versus the mirrordevice hybrid to promote larger power output and allow consideration of thermal in stability effects. Since the physical arrangement of the hybrid blanket selected cor responded to the reported PNL concept as nearly as possible, the results of oreviousl performed parametric anal yses of optimized region width ordering of zones, and region material constituents were used as the basis for extending steadystate neutronic analysis Tokamakdriven blanket design used is described Detailed neutroni of the blanket. n Appendi claculations were performed on the blanket for selected design whose thermal lattice unit cell enrichment and global temperature were the only varied parameters. The cell enrichment was varied from natural uranium up to 1 .50% enriched while the temperature was varied from 2900K up to 970K BRT16 This work was performed using the (one thermal group) and PHROG79 (three fast groups) codes to get 4group constants. The 4group CORA diffusion theory code80 was then used for criticality calculations and acquisition of fundamental flux shapes. The doppler defect was also calculated as a function of the blanket operating temperature. Only the more promising blankets with keff 0.90 at elevated temperatures were considered n detail. This limitation minimized blanket dependence on the fusion component of the hybrid system. Adjoint and perturbation calculations were performed on the system to provide parameters to characterize the kinetic property of the 67 source weighting factors, of the hybrid blanket were calculated using diffusion theory Additional inhomogeneous calculations for blankets driven by planar sources of group mate the fi fast neutrons (10 MeV ssion energy source size  0.821 MeV) were used to approxi required to produce a nominal design power of 6500 MWth. Volume source calculations were also run to investi gate the difference in the worth of the diffusion theory group 1 source neutron power production depending on the point of introduction into the blanket This investigation was accomplished to analyze the validity of global parameter relationship for the blanket energy deposition per fusion neutron presented in Eq. (16). relationship was expected to yield reasonable agreement with diffusion theory simulations since the source neutrons were introduced at nearly fission spectrum energy The series of diffusion theory results were used essentially as scoping calculations to select the best enrichment for further, more detailed and exact transport theory analysis using the AMPX code package available from ORNL The blanket neutronic analysis performed with the XSDRNPM code82 from AMPX was the first reported application of the ORNLdeveloped AMPX package to such hybrid studies. using the AMPX package In P2S4 analysis , the fusion neutron source energy was treated more nearly as a true 14 MeV source. The required source strength for pro during the 650 MW design power was determined for the toroidal to establish finally the applicable degree of validity expected in cal culating or predicting the blanket energy deposition per entering fusion neutron using Eq (16). The flux hapes were also investigated again but 68 On the basis of the XSDRNPMpredicted fusion neutron source strength required for a 6500 MWth hybrid plant, the required plasma conditions were estimated. The corresponding plasma temperature, density, constant con finement time, source feedrate, and injection energy characteristics were then parametrically varied to establish reasonable hybrid plasma operating conditions. Perturbations in various parameters with emphasis on plasma feedrate and temperature were then simulated to investigate the thermal instability of the hybrid plasma and the results compared with stability predictions and expected dynamic behavior under transient conditions. way the plasma component of the hybrid plant was examined with respect to the thermal instability to establish operational characteristics necessary for planning proper deployment of hybrid power plants. Finally transient phenomena, time variations driving the bla since hybrid plasmas are expected to be subjected to various especially thermal instabilitydriven transients, n the design magnitude of the 14 MeV neutron source nket were considered on the basis of those transients resulting from the perturbed behavior of the hybrid plasma examined pre viously. Kinetics calculations representing the effects of plasmacaused perturbations on the fusion neutron source driving the blanket were run and changes in power level were examined for one patial dimension and six delayed neutron groups These kineti calculations were performed using the spacetime kinetics code GAKIN II83 with si neutron groups whos group constants were obtained from the previous XSDRNPM, P2S4 calculations. Although no timedependent feedback effects were examined, the speed of response of the system was determined for typical transients CHAPTER THE PLASMA MODEL Introduction to the Plasma Model First generation fusion power plants are expected to utilize the basic deuteriumtritium (DT) fuel cycle 2 3 D + T S 4He (3.52 MeV) + 1 2He (3.52 PMeV) + On (14.06 MeV (19) Because of its large cross section and reactivity, its minimized plasma temperature requirements and its relatively large energy rel ease reaction, no other fuel cycle is given serious consideration for use in early pure fusion power reactors. and demonstration fusion power syst Certainly the near term experimental ems are expected to use DT fuel 29,32,84 The United States Department of Energy effort toward implementation of central station fusion power plants has clearly recognized the superiority of this fuel cycle in the overall development programs 8587 Even the utility industry has recognized the need for future choices in types of power generating systems and is supporting the effort to develop fusion reactors using the DT fuel cyc1 The major magneti confinement efforts to produce fusion power in other countries have also been directed toward the DT fuel cycle. 89,90 Even so, DT fueled fusion 70 The complexity and difficulty involved in achieving fusion power is amply demonstrated in full scale commercial fusion power plant design studies. 2830 Because economic fusion power is such a large made the technological challenge, no factor can be dismissed which wil development proceed more easily. designs The one common factor in different for fusion power plants in a closed, steadystate mode of opera tion (Tokamak) has been the universal selection of the DT fuel Hence, although the DT fuel cycle has the drawback of producing high energy, penetrating neutrons serious choi Mill , its other advantages make it the only for fusion fuel for many years. demonstrated that the fusion reaction rate and fusion power production are maximized for thermonuclear plasmas which have a 50% deuterium50% tritium fuel ion composition. the most favorable fuel cycle This 5050 DT mixing ratio for the production of fusion energy. With thi cycle, not only i the demonstration of scientific breakeven in a selfsustaining fusioning plasma more easily accomplished but the steadystate production of net energy in a fusion power plant can be accomplished at minimized evel of plasma particle density, temperature, and confinement time. These inherent advantages of the DT fuel cycle in reducing plasma requirement have been illustrated in various analyses of equilibrium requirements and conditions including those of Lawson in which the criterion for energy breakeven was first presented.50 of the 5050 DT fuel The superiority cycle for reaching and maintaining thermonuclear powerproducing conditions has been uniformly demonstrated in extensive 71 Because fusionfission hybrids are expected to serve as an inter mediate energyproducing stepping block between current LWR plants and the eventual development of pure fusion power, the usual 5050 DT fuel cycle was logically sel ected for this hybrid analysis. This choice was aimed at optimizing the time scal for th implementation of the hybrid powerproducing concept. The Point Model Plasma In this work , timedependent point model balance equations were first established for the plasma ion density, n(t), the plasma energy density, 3n(t)T(t), and the volumetri plasma neutron production rate, qp(t) these three balance equations for the plasma ion (particle) density, temperature, and neutron production rate state variables are presented as follows: Plasma Ion (Particle) Density: dn(t = S(t) n(t) t) Plasma Energy Density: d[3n(t)T(t)] n2 (t) =D + T(t) 3n(t)T(t) t)   bn(t)T1/2(t) Plasma Volumetric Neutron Production Rate: n (t) t4" 72 Conventional definitions for symbol equations are listed below: n(t) T(t) used in these nonlinear point model 3 = plasma ion density for 5050 DT plasma (ions/cm3 ) = plasma temperature (keV) = external fuel volumetri injection rate ions/cm sec) = volumetri Ts(t 7 fusion neutron production rate (#/cm sec) = external particle (ion) injection energy (keV) = particle confinement time (sec) = energy confinement time sec) = completely plasma confined fusionproduced alpha particle energy (3520 keV) = DT fusion reaction rate coefficient (cm3/sec) = proportionality coefficient for plasma energy loss rate via Bremsstrahlung radiation (3.36 x 1015 cm3 keV1/2/sec)18 the plasma in this analysis was treated as a global system, only a single average plasma temperature was considered that i distinction was made between ionic species or between ion and electron temperatures. The inclusion of the burnup term in the plasma ion density equation i an improvement to the model used by Ohta corporate by others 23,24,95 18 that has been in In stability studies on pure fusion devices this burnup term and its effects have frequently been neglected because burnup causes small changes in the stable e temperature operating regimes of DT fusion systems. This analysis was intended for application to a hybrid system where most of the energy would be produced in the blanket so burnup predictions were even lower than in pure fusion devices that , plasma temperature and plasma density are both expected to be lower 73 burnup increases due to temperature increases will be directly respon sible for lowering neutron yields which are proportional to the square of the ion density All of the alpha particle energy produced in fusion was assumed to be deposited within the plasma to help heat the system. Others have assumed fractional deposition, but there is no loss of applicability in assuming full alpha energy deposition. For this initial analysis of point model kineti the plasma volume, , was treated as a constant; for linearized stability analysis, thi adequate because only small plasma system perturbations were considered. For timedependent, nonlinear analysis energy and neutron production are overpredicted by the assumption of constant volume since both are pro portional to the square of the ion density. More detailed anal yses the future will incorporate temperaturedependent as well as magnetic and other dynamic conditions that can affect the volume occupied by the plasma independent of whether the plasma density has changed. liminary global analy Some pre of such plasma volume variations have been 1921,96 reported for pure fusion models and additional work is under 97,98The analysis was directed ultimately to the kinetic behavior of the hybrid so the inclusion of the added complication of a variable plasma volume in this initial treatment of the plasma neutron source driving a powerproducing blanket was not justified. The inherent behavior and characteristic of the point model fusion ing plasma used for analysis in thi study i completely described by Eq. (20), Eq. (21), and Eq. In fact , the plasma response to any input perturbation as well as its equilibrium characteristic 74 with the driven nature of the hybrid subcritical blanket, the third equation for the specific neutron production rate was also necessary; without neutrons produced in and hence output from the plasma, no inter action i possib between the two component halves of the hybrid system. Note that these neutrons are produced in the plasma and inherently drive the blanket; however, there i plasma is affected by the neutrons themsel no inherent reverse effect whereby the or by the blanket itself. The neutrons and their effects are strictly feedforward in nature. The volumetric neutron production rate q (t), is an intrinsic variablecharacteristic of the condition of the plasma represented by the state variabi of ion density and temperature only. The volumetric neutron production rate was multiplied by the effective plasma volume, V to obtain the total plasma neutron production rate, Q (t follows: Qp(t) = q (t) 'p p (23) where the total neutron production rate is an extrinsic variable charac teristic of a specific plasma with constant effect volume, V other words, Q (t) is characteristic not of all plasmas in a state de scribed by an ion density and a temperature but only of those specific plasmas whose volumes satisfy Eq. (23) This extrinsic variable could useful for relating specific blanket; however, for this genera plasmas to the corresponding hybrid development, the volumetric neutron production rate was more useful since it is the intrinsic variabi from which any specific pure fusion or hybrid plasma can be analyzed. Indeed, 75 constant volume will be simply multiplicativethe larger the plasma, the greater the system power production. The density equation was rewritten in the following simplified form: dn(t)= S(t) =S(t)  n(t) f2 nf (T)n (t n where the temperaturedependent coefficient, fl(T), was defined as follows to simplify the burnup term: f,(T) Similarly, Eq 2 1) for the plasma energy density was also simplified preparatory to linearization by rewriting it in the following form after Ohta: d[n(t)T(t)] dt f,(T)n n(t)T(t) + fE TsS(t) where the temperaturedependent coefficient, f2(T), was used to account for charged alpha particle heating and bremmstrahlung radiation, respectively CclV>D T~c fo(T) (27) bT32 3 Although it was not so complicated, the equation for the volumetric neutron production rate was also redefined as follows: qn(t) = g(T)n2(t) (28) v 76 It is noteworthy that g(T) in the neutron production equation and fl(T) in the burnup term of the particle a factor of two (2) density equation differ only by follows: = 2fl(T) which simply means that two (2) ions must undergo fusion burnup for each neutron produced. The Linearized Plasma Mode The global plasma equations were linearlized in order to facilitate analysis of stability regimes in the frequency domain. At this point contrary to previous work 3,24,95 specific perturbations were intro duced into the point model plasma equations Since the feedrate, is the only external influence appearing in both the density and tem perature point model equations, the feedrate was chosen as the typical source perturbation for the choice was logical examination of global plasma stability the driving force for the entire fusioning energy producer is ultimately supplied by the plasma feedrate. The same depen dence on feedrate is applicable for the hybrid stem, since the hybrid will be entirely dependent for energy production on the plasmaproduced neutrons because of the blanket subcriticality. neutrons is ultimately governed by the state of But the production of ' the plasma (ion density and temperature) which itself i driven and sustained by the feedrate of energetic fuel ions. Therefore, examination of the hybrid system response .. ~ L. .1 fl 5" J*% .n S in L.. 5 S La  S . j**. ri .,. S. . n .. d 4 1  S(t), 77 For inherent stability and control analyses, the system response to small external or internal perturbations was a primary concern. Depen dent variable perturbations about steadystate values were used to generate a dynamic variation in the point model equations. the following necessarily small variabi For linear analysis perturbations were used: n(t) T(t) + 6n(t) (31a) + 6T(t) (31b) + 6S(t) (3) qp(t) = qPo + 6qp(t) (31d) where the subscript "o" was used to designate a system variable at an initial steadystate equilibrium value about which a small perturbation in the variable, represented by 6terms was introduced so the system could subsequently examined for stability in linearized form. In other words, the timedependent arbitrary perturbations in ion density, 6n(t), plasma temperature, 6T(t) source feedrate (t), and volumetric neutron pro duction rate 6qp, were required to be small to validate the lineariza tion of the point model equations. These perturbed variable were sub stituted into the point model dynamics equations along with first order linear expansions for all the density and temperaturedependent coeffi clients in these equations. The objective was to obtain linearized perturbed equations from the three original nonlinear plasma dynamics equations for the plasma ion density, temperature, and volumetric neutron 78 The inverse confinement time coefficients were examined using pro cedures from previous analyses of global plasma behavior. 15,16,23,24 Both the particle and energy confinement times were assumed to depend exclusively y on the plasma ion density and temperature state variabi = F(n,T) Therefore , fo owing the example of Ohta both inverse confinement times were expanded about an initial steadystate in first order Taylor series in the dependent density and temperature variables as follows: Tn(t) 5T(t) 6n(t) 1 6T(t) n T, T (33a) 1~ 1 ~  The constants 1/1,nl 1 6n(t) + E 0 6T(t) 6n(t) + 1 6T(t) n E,, T ITT, , 1/nl, ,and (33b) /rT1 were used to reduce complexity of analytical manipulations. to denote quantiti The subscript "o" was used again in an initial steadystate condition about which the system was somehow to be perturbed and subsequently examined for stability  + *1 1 T 79 Each of the other three temperaturedependent coefficients (no density dependence) was also From the particle expanded expanded in a simple linear Taylor series. equation the temperaturedependent coefficient was as follows: 6T(t) The temperaturedependent bremsstrahlung and alpha heating coefficient in the energy density equation was expanded af2(T) fjTi Finally similarly: 6T(t) , the temperaturedependent coefficient in the equation for the volumetric neutron production rate becomes: g(T) = g(To) + aT) yv 4 6T(t) (36) A linearized system of plasma equations can now be produced by substitu tion of the perturbed variables from Eq. (33) and the various coefficient expansions into the plasma model equations. Substitution of the first order variable and coefficient expansions into the plasma particle equation yields the following equation: + 6S(  [+ 1 C + n 0 ,..r\ n( t) 1 i 6T(t) n  ]no + an(t)] dan(T) dt fl f2(T~)+ 80 The steadystate condition in the expanded particle equation was eliminated using the steadystate equilibrium condition. Two additional coefficients were defined from the effect of including burnup via fl (T) in thi model specifically, the effective confinement time for particle burnup effects. due to any 1 Certainly mechanisms is reduced by including , fusion of particles is a loss mechanism. subscript "b" was used in defining inverse confinement time terms to account for the increased loss of plasma ions by fusion as follows: S= 2n f T. o0 1 af, (T = n T o o (39) By eliminating the steadystate solution and neglecting all terms above the first order in the perturbed variables and coefficients, the following linearized equation for the perturbed plasma ion density was obtained: d6n(t) dt 6S(t) 1_ + n T + 1 n(t) 1 6T(t) b, o T1 b, o .(40) The inclusion of burnup results in an additional burnupdependent inverse confinement time term as well as the usual density and temperatureperturbed terms. This dual effect fc the dependence of burnup on both state variables. allows directly from Note that the addition of inverse confinement time terms results in lowered overall particle 