Pulsed Fission-Fusion Propulsion System Robert B. Adams, Ph.D. ER24/Propulsion Research and Technology Branch George C. Marshall Space Flight Center National Aeronautics and Space Administration Jason Cassibry, Ph.D. Propulsion Research Center Department of Mechanical and Aerospace Engineering University of Alabama in Huntsville NASA Innovative Advanced Concepts (NIAC) Challenges and Underlying Physics of Nuclear Processes Fission and Fusion Energy Release • Mass Defect = Mass of free nucleons - mass of assembled nucleus • Nuclear force (residual strong force) stronger than electrostatic • Nuclear Binding Energy E/A = (Δm/A) * c^2 • Fusion - Energy release by combining nuclei • Fission - Energy release by splitting nuclei [Plot showing Average binding energy per nucleon (MeV) vs. Number of nucleons in nucleus, highlighting H, He, Li, C, O, Fe-56 peak, and U-235/U-238] Source: http://en.wikipedia.org/wiki/Nuclear_binding_energy Fission and Fusion Reaction Space Reactions: (1) 2_1D + 3_1T -> 4_2He (3.5 MeV) + n^0 (14.1 MeV) (2i) 2_1D + 2_1D -> 3_1T (1.01 MeV) + p^+ (3.02 MeV) [50%] (2ii) -> 3_2He (0.82 MeV) + n^0 (2.45 MeV) [50%] (3) 2_1D + 3_2He -> 4_2He (3.6 MeV) + p^+ (14.7 MeV) (4) 3_1T + 3_1T -> 4_2He + 2 n^0 + 11.3 MeV (5) 3_2He + 3_2He -> 4_2He + 2 p^+ + 12.9 MeV (6i) 3_2He + 3_1T -> 4_2He + p^+ + n^0 + 12.1 MeV [57%] (6ii) -> 4_2He (4.8 MeV) + 2_1D (9.5 MeV) [43%] (7i) 2_1D + 6_3Li -> 2 4_2He + 22.4 MeV (7ii) -> 3_2He + 4_2He + n^0 + 2.56 MeV (7iii) -> 7_3Li + p^+ + 5.0 MeV (7iv) -> 7_4Be + n^0 + 3.4 MeV (8) p^+ + 6_3Li -> 4_2He (1.7 MeV) + 3_2He (2.3 MeV) (9) 3_2He + 6_3Li -> 2 4_2He + p^+ + 16.9 MeV (10) p^+ + 11_5B -> 3 4_2He + 8.7 MeV Ignition Requirements Fission: • Criticality is a function of: - fission cross section - Number density - And geometry • Neutrons must balance: - Lost outside reactor - Absorbed through photon capture - Fission events [Chart: U-235 Fission Cross Section vs. Energy (eV)] Fusion: • Breakeven is a function of: - Fusion cross section - temperature distribution - density • Lawson Criterion: n_e * tau_E >= (12 * k_B * T) / (E_ch * <sigma*v>) [Chart: Lawson Criterion n_e * tau_E vs. Temperature for D-T, D-D, D-He3] Fusion Confinement Parameter Space [Log-Log Graph of Plasma Energy (J) vs. Density (cm^-3)] • MFE (Magnetic Confinement Fusion) at low density (~10^14 cm^-3) and high plasma energy (~10^8 J) • MIF (Magneto-Inertial Fusion) in the intermediate regime (~10^19 - 10^20 cm^-3, ~10^6 J) • ICF (Inertial Confinement Fusion) at high density (~10^25 - 10^26 cm^-3, ~10^4 J) • Lines showing Classical Cross Field, Bohm diffusion, Electron Thermal, and chi = 1 m^2/s limits at beta = 1, T = 10 keV. Benefits of MIF Parameter Space • Fusion reactivity scales with n^2 • Magnetic field suppresses thermal conduction losses, reducing driver power • Reactor volume much smaller than MFE • These effects lead to potentially much lower cost, smaller fusion reactor, as suggested by Lindemuth and Siemon, Am. J. Phys., 77(5), May 2009 Table II: Fundamental physical parameters and cost for fusion systems: - Geometry: ITER = Toroidal | MTF example = Cylindrical | NIF = Spherical - Cost ($M): ITER = 10,000 | MTF example = 51 | NIF = 3000 - n_i (/cm^3): ITER = 10^14 | MTF example = 10^20 | NIF = 1.4 x 10^25 - rho (g/cm^3): ITER = 4.2 x 10^-10 | MTF example = 4.2 x 10^-4 | NIF = 57 - T (keV): ITER = 8 | MTF example = 8 | NIF = 8 - p (atm): ITER = 2.6 | MTF example = 2.6 x 10^6 | NIF = 3.6 x 10^11 - B (kG): ITER = 50 | MTF example = 1000 | NIF = 0 - tau_L (s): ITER = 0.9 | MTF example = 9 x 10^-7 | NIF = 6.6 x 10^-12 - M (mg): ITER = 350 | MTF example = 1.7 | NIF = 0.01 - a (cm): ITER = 240 | MTF example = 0.6 | NIF = 3.5 x 10^-3 - V (m^3): ITER = 8.3 x 10^2 | MTF example = 4.0 x 10^-6 | NIF = 1.8 x 10^-13 - E_plas (J): ITER = 3.2 x 10^8 | MTF example = 1.6 x 10^6 | NIF = 9.3 x 10^3 - P_heat (W): ITER = 1.3 x 10^8 | MTF example = 9.0 x 10^10 | NIF = 1.1 x 10^14 - I_heat (W/cm^2): ITER = 18 | MTF example = 1.0 x 10^10 | NIF = 7.5 x 10^17 PuFF Concept Introduction to PuFF Concept Diagram Components: • Magnetic field lines • Magnetic nozzle coils • UF6 fuel • D-T fuel • Cathode • Lithium liner and radiation shield Operation of a Z Pinch Components and Principles: • Evacuated Chamber • Vaporized Wire Array / Plasma Cylinder • Current I flowing axially • B, Magnetic Flux compressing the plasma column radially (Lorentz J x B force) • Anode and Cathode configuration Fission-Fusion Energy Balance Layers and Energy Interaction Pathways: • Layers (outer to inner): Lithium -> U235 -> DT • Power Flow Legend: 1: Fusion reactions within DT core 2: Fusion-to-fission energy coupling (neutron heating/fission initiation) 3: Fission energy generated in U235 liner 4: Power outflow/expansion towards nozzle and lithium liner 5: Reflection/thermal confinement feedback between U235 and DT Research Status Heating Mechanisms Included in Model Mechanisms Illustrated in FRC/Liner Model: • DT FRC Target Plasma • Fissionable liner • Magnetic Field Lines • Fusion heating power • Fission heating power • Neutron induced Fast fission reactions • Bremsstrahlung and Cyclotron Radiation losses • Axial and Radial Thermal conduction losses Fission-Fusion Power Balance Key Insights: • Synchrotron Radiation Dominates at low rho*R • Fission Power Dominates as Neutron Count Becomes Significant • Parameter space for ignition: - Greatly broadened with embedded magnetic field - Marginally improved with 6Li and thorium liners - Significantly enhanced with uranium liners (235U and 238U) Our Approach: Solve Maxwell's Equations Coupled to Multifluid (Ions, Electrons, Neutrals) Equations of Motion Maxwell's Equations: • Solve with Smooth Particle Electromagnetic Variant of Finite-Difference Time Domain (FDTD) method • FDTD well documented, highly accurate grid-based method for analyzing the time evolution of electric and magnetic fields • Can interpolate charged fluid particles to grid to model conductivity or charge and current density Multifluid Equations of Motions: • Solve with Smooth Particle Hydrodynamics (SPH) • Gridless Lagrangian technique • Vacuum/plasma boundary well defined • Leverage same engine as Maxwell Equation Solver Both methods yield to 'vectorized' coding, making multiprocessor (parallel) computing easy. Equations of motion (completed): • Continuity for electrons: ∂n_e/∂t + ∇·(n_e * u_e) = 0 • Continuity for ions: ∂n_i/∂t + ∇·(n_i * u_i) = 0 • Momentum for electrons: n_e * m_e * ∂u_e/∂t + ∇p_e + e * n_e * [E + u_e x B] = R_e • Momentum for ions: n_i * m_i * ∂u_i/∂t + ∇p_i - Z * e * n_i * [E + u_i x B] = R_i • Energy for electrons: 3/2 * n_e * ∂(k*T_e)/∂t + p_e * ∇·u_e = -π_e : ∇u_e - ∇·h_e - (u_e - u_i)·R_e - Q_i • Energy for ions: 3/2 * n_i * ∂(k*T_i)/∂t + p_i * ∇·u_i = -π_i : ∇u_i - ∇·h_i - Q_i Transport effects (planned), which can be based on nonequilibrium distribution functions (kappa and power law): • Friction force R_a • Scalar pressure p_a • Viscous stress tensor π_a • Heat flux vector h_a • Energy exchange term Q_a Initial Pulsed Nozzle Model • Test thermal expansion of gas nozzle with various initial conditions: - Nozzle geometry - Gas: • Temperature • Density • Radius • Length • Composition • Lays groundwork and expectations for magnetic nozzle • 3D Simulation domain showing nozzle wall, initial gas cylinder from z-pinch, and direction of motion. Preliminary results - Initial state of plasma expansion simulation in 3D nozzle geometry. Preliminary results - Onset of plasma puff expansion and particle spreading within the nozzle wall. Preliminary results - Mid-stage expansion of heated plasma particles moving outward through the nozzle exit. Preliminary results - Advanced expansion with significant axial exhaust beyond the nozzle boundary. Preliminary results - Full exhaust plume dispersal and directed thrust generation simulation. NIAC Phase I Goals Crewed Mars Mission Concept Vehicle Configuration & Subsystems (Polsgrove, T. et al., 2010 AIAA Aerospace Sciences Meeting): • Z-Pinch Nozzle • Lithium Hydride Radiation Shield (.25 m thick) • SMES Envelope (1.8 m x 1.8 m x 2.4 m) • Stacked Capacitor Module (2) (10 m long x 3.6 m x 7.2 m, 8 plcs) • Deuterium-Tritium Tank (2.4 m dia., 4 plcs) • SP-100 Reactor • Lithium 6 Tank (4.8 m long x 2.6 m dia., 4 plcs) • Two-Sided Crew/Avionics Radiators (176 m^2 total area) • Two-Sided Med. Temp. Radiators (608 m^2 total area) • Two-Sided High Temp. Radiators (1910 m^2 total area) • 4-Pod RCS 700 lbf MR_80B 3 Hydrazine Thrusters, RCS Tank (.86 m dia.) and RCS Helium Pressurant Tank (.64 m dia., 8 plcs - 4 Aft and 4 Forward) • Lander • Surface Habitat • Transhab • ISRU Mission Concepts Trajectory Performance Table: • Parameter | Mars 90 | Mars 30 | Jupiter | 550 AU • Outbound Trip Time (days) | 90.2 | 39.5 | 456.8 | 12936 • Return Trip Time (days) | 87.4 | 33.1 | 521.8 | n/a • Total Burn Time (days) | 5.0 | 20.2 | 6.7 | 11.2 • Propellant Burned (mT) | 86.3 | 350.4 | 115.7 | 194.4 • Equivalent DV (km/s) | 27.5 | 93.2 | 36.1 | 57.2 Engine Specifications: • Isp = 19,400 sec • Thrust (T) = 38 kN • 10 Hz pulse freq. Vehicle Specifications: • M_dry = 552 mT • M_pay = 150 mT • 30% MGA Source: Polsgrove, T. et al. Design of Z-Pinch and Dense Plasma Focus Powered Vehicles, 2010 AIAA Aerospace Sciences Meeting. Mating SPFMaX and MCNP • SPFMax gives: - Ability to model 3d effects - Can propagate magnetic fields in vacuum - Easily editable • MCNP: - Track neutron life, fission reactions - Flexible geometries • Second half of NIAC is to run codes concurrently: - Synchronize neutron population vs. time - Optimize energy output: • As function of geometry • As function of composition: - Mix of UF6, D-T - Lithium liner thicknesses Single turn Magnetic Nozzle • Gasdynamic nozzle performance to be compared with magnetic nozzle to assess loss mechanisms in magnetic nozzles, e.g.: - Field/plasma instabilities - Plasma detachment • Diagram illustrating 3D single turn coil geometry with indicated direction of current. Charger - 1 Test Facility • A test facility for high power and thermonuclear fusion propulsion concepts, astrophysics modeling, radiation physics • Located in the UAH Aerophysics Lab at Redstone • The highest instantaneous pulsed power facility in academia – 572 kJ (1 TW at 100 ns) Long Range Plans NIAC Phase II: • Complete Charger 1 refurb • Ignite PuFF plasma • Continue magnetic nozzle research Charger II: • Construct breadboard PuFF system capable of 10-20 Hz operation - Upgrade to flight weight hardware – NASA - Optimize pulse for maximum power output – DOE - Astrodynamics, radiation protection, other research goals - Various