PSFC/RR-11-1 A Fission-Fusion Hybrid Reactor in Steady-State L-Mode Tokamak Configuration with Natural Uranium Reed, M., Parker, R., Forget, B.* *MIT Department of Nuclear Science & Engineering January 2011 Plasma Science and Fusion Center Massachusetts Institute of Technology Cambridge MA 02139 USA A Fission-Fusion Hybrid Reactor in Steady-State L-mode Tokamak Configuration with Natural Uranium Mark Reed, Ronald R. Parker, Benoit Forget Massachusetts Institute of Technology January 2011 Abstract The most prevalent criticism of fission-fusion hybrids is simply that they are too exotic - that they would exacerbate the challenges of both fission and fusion. This is not really true. Intriguingly, hybrids could actually be more viable than stand-alone fusion reactors while mitigating many challenges of fission. This work develops a conceptual design for a fission-fusion hybrid reactor in steady-state L-mode tokamak configuration with a subcritical natural or depleted uranium pebble bed blanket. A liquid lithium- lead alloy breeds enough tritium to replenish that consumed by the D-T fusion reaction. Subcritical operation could obviate the most challenging fuel cycle aspects of fission. The fission blanket augments the fusion power such that the fusion core itself need not have a high power gain, thus allowing for fully non-inductive (steady-state) low confinement mode (L-mode) operation at relatively small physical dimensions. A neutron transport Monte Carlo code models the natural uranium fission blanket. Maximizing the fission power while breeding sufficient tritium allows for the selection of an optimal set of blanket parameters, which yields a maximum prudent fission power gain of 7.7. A 0-D tokamak model suffices to analyze approximate tokamak operating condi- tions. If the definition of a \reactor" is a device with a total power gain of 40, then this fission blanket would allow the fusion component of a hybrid reactor with the same dimensions as ITER to operate in steady-state L-mode very comfortably with a fusion power gain of 6.7 and a thermal fusion power of 2.1 GW. Taking this further can determine the approximate minimum scale for a steady-state L-mode tokamak hybrid reactor, which is a major radius of 5.2 m and an aspect ratio of 2.8. This minimum scale device operates barely within the steady-state L-mode realm with a thermal fusion power of 1.7 GW. This hybrid, with its very fast neutron spectrum, could be superior to pure fission reactors in terms of breeding fissile fuel and transmuting deleterious fission products. It 1 2 Mark Reed could operate either as a breeder, producing fuel for pure fission reactors from natural or depleted uranium, or as a deep burner, fissioning heavy metal and transmuting waste with a cycle time of decades. Despite a plethora of potential functions, its primary mission is deemed to be that of a deep burner producing baseload commercial power with a once-through fuel cycle. Although hybrids are often purported a priori to pose an elevated proliferation risk, this reactor breeds plutonium that could actually be more proliferation-resistant than that bred by fast reactors. Furthermore, a novel method (the \variable fixed source method") can maintain constant total hybrid power output as burnup proceeds by varying the neutron source strength. As for engineering feasibility, basic thermal hydraulic analysis demonstrates that pressurized helium could cool the pebble bed fission blanket with a flow rate below 10 m/s. The Brayton cycle thermal efficiency is 41%. This device is dubbed the Steady-State L-Mode Non-Enriched Uranium Tokamak Hybrid (SLEUTH). The purpose of this work is not any sort of elaborate design, but rather the exploration of an idea coupled with corroborating numerical analysis. At this point in the hybrid debate, viable conceptual designs are persuasive while intricate build-ready designs are superfluous. This work conceives such a conceptual design, demonstrates its viability, and will perhaps, incidentally, spur a profusion of pro-fusion sentiment! A Fission-Fusion Hybrid Reactor 3 Contents 1 The Fission-Fusion Concept 13 1.1 Hybrid History . 13 1.1.1 Nascence . 13 1.1.2 Renaissance . 14 1.2 Present Limitations . 15 1.2.1 The Limitation of Fusion: Plasma Stability . 15 1.2.2 The Limitation of Fission: Criticality . 16 1.3 A New Conceptual Design . 16 1.3.1 Geometry and Fission Power Gain . 17 1.3.2 Pebble Bed Blanket . 19 1.3.3 Subcritical Operation . 19 1.3.4 Fast Spectrum . 20 1.3.5 Natural or Depleted Uranium . 20 1.3.6 Tritium Breeding . 24 1.3.7 Shielding.................................. 24 1.4 Mission ...................................... 24 1.5 ScopeandOutline ................................ 25 2 Fission Blanket Monte Carlo Code 26 2.1 Path Length Sampling in Toroidal Geometry . 26 2.1.1 Flight Distance in Toroidal Geometry . 26 2.1.2 Sampling Algorithm . 29 2.1.3 Tokamak Wall Neutron Flux . 31 2.1.4 Quartic Solution Comparison . 34 2.1.5 Cylindrical Comparison . 35 2.2 Monte Carlo Methodology . 36 2.2.1 ENDF Cross-Sections . 36 2.2.2 Elastic Scattering . 36 2.2.3 (n,xn) and (n,α) Reactions . 39 2.2.4 Inelastic Scattering . 40 2.2.5 Fission................................... 41 2.3 MCNP Benchmark . 42 2.4 Pebble Homogenization . 44 3 Fission Blanket Analysis 62 3.1 Blanket Parameter Analysis . 62 3.1.1 Uranium Layer Thickness . 64 4 Mark Reed 3.1.2 Lithium Layer Thickness . 67 3.1.3 Lithium Enrichment . 68 3.1.4 LayerPositioning ............................. 73 3.1.5 Li-Pb Content . 77 3.2 The Optimal Fission Blanket . 79 4 A Tokamak Fusion Core Model 92 4.1 Concept and Geometry . 92 4.2 0-D Core Model Overview . 94 4.3 0-D Core Model System Parameters . 94 4.3.1 D-T Fusion Rate Coefficient . 98 4.3.2 Elongation vs. Aspect Ratio . 98 4.3.3 Plasma Current and Sustainment . 98 4.4 L-modeandH-mode ............................... 101 5 Pure Fusion Core Analysis 103 5.1 0-D Allowable Parameter Space . 103 5.1.1 Allowable [R,q*,FG]Space........................ 104 5.1.2 Allowable [R,q*,R/a]Space ....................... 114 5.1.3 Allowable [R,q*,R/a,Q]Space...................... 117 5.2 Minimum Tokamak Scale Defined . 117 5.3 TechnologyLimits ................................ 120 5.3.1 Maximum On-Coil Magnetic Field Bmax ................ 120 5.3.2 Blanket Fusion Power Density PF /AS .................. 123 5.4 Aspect Ratio R/a Considerations . 125 5.5 A \Reactor" Defined . 128 6 Coupled Fission-Fusion Analysis 131 6.1 Effect of Tokamak Geometry on Fission Blanket . 131 6.2 Solenoid Size vs. Blanket Thickness . 131 6.3 Steady-State L-mode ITER-PBR . 133 6.4 Minimum Scale Steady-State L-mode Fission-Fusion Hybrid . 139 6.4.1 1-D Profiles . 143 6.4.2 RadiativePower.............................. 151 6.4.3 Operating Point Access . 152 6.5 Implications.................................... 154 A Fission-Fusion Hybrid Reactor 5 7 Burnup and Fuel Cycle 155 7.1 Subcritical Burnup Implementation . 155 7.2 Maintaining Constant Hybrid Power . 156 7.3 Breeding...................................... 161 7.4 Viability of a Thorium Fuel Cycle . 169 7.5 Non-Proliferation . 172 7.6 Waste ....................................... 174 7.7 CycleTime .................................... 176 7.8 TwoOptions ................................... 177 8 Pebble Structure, Thermal Hydraulics, and Safety 178 8.1 PebbleStructure ................................. 178 8.2 Thermal Hydraulic Analysis . 181 8.2.1 Coolant Flow Rate and Pressure Drop . 183 8.2.2 Heat Transfer and Temperature . 190 8.2.3 Summary ................................. 197 8.3 Brayton Power Cycle and Electric Power . 198 8.4 Safety ....................................... 201 9 Ramifications 202 9.1 Comparison to Other Studies . 202 9.1.1 Tokamak Pebble Bed Hybrids (ITER-PBR) . 202 9.1.2 Other Tokamak Hybrids (SABR) . 205 9.1.3 Inertial Confinement Hybrids (LIFE) . 207 9.2 The Hybrid Debate . 209 9.3 Overarching Conclusions . 209 A Fusion Model 215 A.1 0-D Core Model . 215 A.2 1-D Density, Temperature, and Power Profiles . 218 A.3 1-D Current Profiles . 220 A.4 1-D q Profile . 222 A.5 Auxiliary Power for Operating Point Access . 224 B Toroidal Monte Carlo Code 228 C Cylindrical Monte Carlo Code 261 6 Mark Reed D Plasma Surface Neutron Flux Code 265 D.1 Toroidal Flux Monte Carlo . 265 D.2 Toroidal Volume - Spiric Sections . 270 E k1 Monte Carlo Code 271 F Elastic Scattering 281 G Thermal Hydraulics Model 282 H Conversion Ratio Model 285 I MCNP Input Files 289 I.1 Full Toroidal Hybrid Blanket . 289 I.2 k1 for U and UO2 ................................ 291 I.3 Infinite Array of UO2 Pebbles in H2O Pool (Simple Cubic) . 292 I.4 Typical Fast Reactor Spectrum . 293 A Fission-Fusion Hybrid Reactor 7 List of Tables 3.1 Optimal Blanket Parameters . 79 6.1 Steady-State L-mode ITER-PBR Operating Parameters . 138 6.2 Minimum Scale Steady-State L-mode Operating Parameters . 142 7.1 Fissile Nuclide Conversion Ratios . 168 7.2 Comparison of Thorium and Uranium Breeding Ratios . 171 7.3 239Pu One-Group Cross-Sections (barns) . 173 7.4 Fission Product Equilibrium Concentrations . 175 8.1 Pebble Bed Blanket Thermal Hydraulic Parameters . 197 8.2 Ideal Brayton Cycle Parameters . 199 9.1 Comparison of Graphite Matrix Pebbles to UO2 Pebbles . 204 8 Mark Reed List of Figures 1.1 A fission blanket coats a tokamak. 17 1.2 The total 238U cross-section showing constituent parts as a function of energy. 21 1.3 Normalized constituent parts of the total 238U cross-section as a function of energy........................................ 22 1.4 Normalized constituent parts of the total 235U cross-section as a function of energy........................................ 23 2.1 Simple elongated toroidal geometry.