NASA/TP—2018–219996 Gradient Field Imploding Liner Fusion Propulsion System NASA Innovative Advanced Concepts Phase I Final Report M.R. Lapointe and R.B. Adams Marshall Space Flight Center, Huntsville, Alabama J. Cassibry and M. Zweiner The University of Alabama—Huntsville, Huntsville, Alabama J.H. Gilland Ohio Aerospace Institute, Cleveland, Ohio September 2018 National Aeronautics and Space Administration IS02 George C. Marshall Space Flight Center Huntsville, Alabama 35812 The NASA STI Program…in Profile Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA’s scientific and technical information. 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For more information about the NASA STI Program Office, see the following: • Access the NASA STI program home page at <http://www.sti.nasa.gov> • E-mail your question via the Internet to <[email protected]> • Phone the NASA STI Help Desk at 757–864–9658 • Write to: NASA STI Information Desk Mail Stop 148 NASA Langley Research Center Hampton, VA 23681–2199, USA Acknowledgments The authors gratefully acknowledge the support of the NASA Innovative Advanced Concepts Program during this Phase I study. Available from: NASA STI Information Desk Mail Stop 148 NASA Langley Research Center Hampton, VA 23681–2199, USA 757–864–9658 This report is also available in electronic form at <http://www.sti.nasa.gov> TABLE OF CONTENTS 1. BACKGROUND ................................................................................................................ 1 1.1 Concept Description ..................................................................................................... 1 1.2 Benefits and Challenges ................................................................................................ 4 2. PHASE I RESEARCH OVERVIEW .................................................................................. 6 2.1 Target Design ................................................................................................................ 6 2.2 Target Accelerator Concepts ......................................................................................... 8 2.3 Magnetic Field Coil Design .......................................................................................... 11 2.4 Estimating System Performance ................................................................................... 12 3. SEMI-ANALYTIC COMPRESSION MODEL ................................................................. 14 3.1 Liner Radial Acceleration ............................................................................................. 15 3.2 Pressure Terms .............................................................................................................. 16 3.3 Energy Terms ................................................................................................................ 17 3.4 Net Energy Change and Fuel Temperature ................................................................... 20 3.5 Fusion Reaction Rates .................................................................................................. 21 4. ANALYTIC MODEL: PRELIMINARY RESULTS ......................................................... 24 4.1 Model Check: Adiabatic Compression ......................................................................... 24 4.2 Initial Target Density ................................................................................................... 25 4.3 Initial Target Radius .................................................................................................... 26 4.4 Initial Target Velocity .................................................................................................. 27 4.5 Target Preheating ......................................................................................................... 28 4.6 External Magnetic Field .............................................................................................. 29 4.7 Internal Target Magnetic Field .................................................................................... 30 4.8 Magnetic Field Gradient .............................................................................................. 31 4.9 Liner Material .............................................................................................................. 32 4.10 Pulse Considerations .................................................................................................... 34 4.11 Optimized Case ............................................................................................................ 36 4.12 Summary ..................................................................................................................... 42 5. SPFMAX THREE-DIMENSIONAL NUMERICAL MODEL ........................................ 43 5.1 SPFMaX Preliminary Results ....................................................................................... 49 5.2 Verification Test Case Plan ............................................................................................ 51 6. MISSION ANALYSIS ........................................................................................................ 55 6.1 Detailed Mission Examples .......................................................................................... 57 7. VEHICLE DESIGN ........................................................................................................... 60 7.1 Vehicle Assumptions ..................................................................................................... 61 8. OPTIONS FOR A GROUND-BASED, PROOF-OF-CONCEPT DEMONSTRATION ......................................................................................................... 63 8.1 Two-Stage Light Gas Gun ............................................................................................ 63 8.2 Test Facility Description ............................................................................................... 64 8.3 Target Projectiles .......................................................................................................... 67 8.4 Potential Test Setup ...................................................................................................... 68 9. CONCLUDING REMARKS ............................................................................................ 70 APPENDIX A—ANALYTIC MODEL BLOCK DIAGRAM ............................................... 71 APPENDIX B—ANALYTIC MODEL DATA VALUES ....................................................... 73 REFERENCES ....................................................................................................................... 76 LIST OF SYMBOLS AND ACRONYMS Al: aluminum AR: aspect ratio ARC: Aerophysics Research Center Be: beryllium CO2: carbon dioxide D: deuterium FCG: flux compression generator GUI: graphical user interface HDPE: high density polyethylene (plastic) He: helium ICF: inertial confinement fusion IMLEO: initial mass in low Earth orbit LEO: low Earth orbit LGG: light gas gun Li: lithium MagLIF: magnetized liner inertial fusion MGL: mass growth allowance MIF: magneto-inertial fusion MTF: magnetized target fusion NIAC: NASA Innovative Advanced Concepts SAMM: semi-analytic MagLIF Model SLS: Space Launch System SPFMaX: Smooth Particle Fluid with Maxwell Equation Solver SPH: smooth particle hydrodynamic T: tritium TP: Technical Publication UAH: The University of Alabama—Huntsville NOMENCLATURE A: magnetic vector potential AR: aspect ratio B: magnetic field Bi: internal magnetic field strength Bi0: initial trapped magnetic field Bv0: initial vacuum magnetic field Bz: axial component of magnetic field Cc: sound speed at critical target density c: speed of light in a vacuum cf: speed of sound in fuel region dBz/dt: rapidly changing axial magnetic field E: yield energy Ė_ad: adiabatic heating rate Ė_end: energy loss rate due to end particle losses Ė_f: time rate of change in fuel energy Ef: cumulative energy in the fuel Ė_pre: fuel preheating rate Ė_tc: thermal conduction cooling rate Ė_α: α particle heating rate F: thrust; F_ave: average thrust Isp: specific impulse Ibit: impulse P_fusion: fusion power released by the imploding target P_jet: jet power Pf: isobaric fuel pressure ρR: areal density of the target 1. BACKGROUND The advancement of human deep space exploration requires the continued development of energetic in-space propulsion systems, from current chemical engines to nuclear thermal rockets to future high energy concepts such as nuclear fusion. As NASA embarks on a program to develop near-term nuclear thermal propulsion, this NASA Innovative Advanced Concepts (NIAC) Phase I activity was funded to investigate the feasibility of an innovative approach toward highly energetic pulsed fusion propulsion. Previous concept studies have proposed the conversion of fusion energy for in-space propulsion, ranging from laser-ignited fusion systems such as Gevaltig and VISTA, to the British Interplanetary Society’s Daedalus concept and Project Icarus, to steady-state spherical torus fusion systems. Recent NIAC studies have also evaluated several innovative fusion concepts, including the acceleration and compression of field reversed configuration plasmas in time-changing magnetic fields, magnetically driven liners imploding onto plasma targets, and high current z-pinch compression of material liners onto fission-fusion fuel targets. 1.1 Concept Description The rapid magnetic compression of targets containing fusion fuel at high pressure offers potentially higher implosion efficiencies than other inertial confinement fusion approaches, and remains an area of active development. To successfully implode the target and trigger fusion reactions, a pulsed high current discharge in a surrounding magnetic field coil generates a rapidly changing axial magnetic field, dBz/dt, which induces a counterpropagating current in the conducting outer liner of a centrally aligned cylindrical target. The inductively driven liner current rapidly implodes the liner radially inward, compressing the fuel to the densities and temperatures required for fusion. A significant energy loss mechanism observed during liner compression and ignition of the resulting plasma is electron thermal conduction, which is mitigated by the use of strong magnetic fields to suppress cross field thermal conduction losses, generating higher plasma temperatures at lower implosion velocities. In standard θ-pinch geometries, current is pulsed through a drive coil surrounding the central target. The approach being investigated in the current Phase I activity replaces the pulsed, high current magnetic field coil and stationary central target with a fast-moving target fired axially into a static, high gradient magnetic field. This essentially decomposes the time-changing derivative of the axial magnetic field into partial derivatives associated with an axial magnetic field gradient and an axial velocity: dBz/dt = (∂Bz/∂z)(∂z/∂t) = vz (∂Bz/∂z) (1) As such, a target fired at high axial velocity into a steep magnetic field gradient will effectively experience a rapidly changing axial magnetic field and undergo the same inductive compression as a stationary target at the center of a rapidly pulsed magnetic field. 1.2 Benefits and Challenges Shifting the onus of rapid target compression from a pulsed, high current coil to a target accelerator and a static high gradient magnetic field offers several potential advantages for in-space propulsion. Eliminating the need to rapidly pulse the magnetic field coil allows the use of energy efficient superconducting field coils, which in turn reduces energy storage requirements, coil thermal losses, and associated radiator requirements. The field coils can be shaped to provide strong upstream field gradients, a high field midsection to enhance target fuel burning, and a magnetic nozzle at the downstream exit plane to convert the rapidly expanding plasma into directed thrust. Target acceleration may be accomplished using one of several possible approaches, including inductive acceleration or laser ablation, the latter also offering a possible method for preheating the target fuel. Electron and ion radial thermal losses can be suppressed by strong internal magnetic fields trapped within the target during compression, reducing energy losses and improving target gain. The linear geometry of the system, together with the axial motion of the target as it enters, compresses, burns, and expands into the magnetic nozzle region, lends itself more naturally to repetitively pulsed in-space propulsion, easing design issues associated with target placement and energy transfer to the vehicle. 2. PHASE I RESEARCH OVERVIEW The purpose of this Phase I activity is to design and evaluate a system that can rapidly inject, compress, and burn a fusion fuel target, and efficiently exhaust the resulting high temperature plasma, in a configuration suitable for in-space propulsion applications. 2.1 Target Design For this initial Phase I evaluation, a cylindrical pellet with deuterium-tritium (D-T) fuel and a conductive liner has been chosen both for simplicity of modeling and for consistency with current terrestrial MIF fusion experiments. Standard D+T -> α + n fusion reaction releases 17.59 MeV. Several low atomic number coating materials have been investigated as conductive target liners, including beryllium (Be), aluminum (Al), and lithium (Li). The ratio of target radius to liner thickness (aspect ratio AR = R/ΔR) plays a role in the evolution of disruptive Rayleigh-Taylor instabilities. Values of AR ≤ 6 have been shown to delay the onset of Rayleigh-Taylor instabilities. A key parameter for achieving fusion conditions is the areal density of the target, expressed as ρR, where ρ is the fuel density and R is the radius at maximum compression. Incorporating strong magnetic fields within the fuel can significantly reduce the value of ρR required for net energy gain at a given temperature. 2.2 Target Accelerator Concepts To induce rapid radial compression requires an initial pellet velocity of several kilometers per second. Laser ablation was chosen for detailed initial evaluation. Treated using the rocket equation: Δv = ve ln(m0 / mf) (3) 1 - mf/m0 = 1 - exp(-Δv / (f * ve)) (4) where ve = [4 I / (nc mi)]^(1/2) and nc = me ε0 ω^2 / e^2. For a 10.6 µm CO2 laser, critical density nc = 2.52 × 10^23 m^-3. A 1 MW laser pulse can accelerate the target to 10 km/s while ablating only ~1% to 1.5% of target mass over several milliseconds. 2.3 Magnetic Field Coil Design A simple superconducting solenoid coil (up to 30 T) is assumed. Magnetic field diffusion time τ ≈ μ σ Δ r / 2 (on the order of 10^-3 s, compared to target compression time of ~10-40 µs). 2.4 Estimating System Performance Exhaust velocity ve = vz_target + [2 η E / m]^(1/2) (10) Specific impulse Isp = ve / g0 (11) Impulse per bit Ibit = m ve = m Isp g0 (12) Average thrust Fave = f(Hz) * Ibit (13) Overall Gain G = Pfusion / [ (Pin / ηin) + (Ptarget / ηtarget) ] (14) 3. SEMI-ANALYTIC COMPRESSION MODEL A semi-analytic model adapted from SAMM (McBride and Slutz) was developed. 3.1 Liner Radial Acceleration: r̈_l = (2πL/ml) [ (Pf + PBi - PBv) rl - (Pf + PBi) Δ ] (17) 3.2 Pressure Terms: Isobaric fuel pressure: Pf = ρ R Tf Internal magnetic pressure: PBi = Bi^2 / (2 μ0), Bi = Bi0 (r0/r)^2 External magnetic pressure: PBv = Bv^2 / (2 μ0), Bv = Bv0 rc^2 / (rc^2 - rl^2) 3.3 Energy Terms: Combined fuel energy rate: Ė_f = Ė_ad + Ė_pre + Ė_α - Ė_r - Ė_tc - Ė_end (41) Average fuel temperature: Tf = 2 Ef / [ 3k (ND + NT + Ne) ] (42) 3.5 Fusion Reaction Rates: Reaction rate Ṅ_D-T = L ∫ nD nT <σv>D-T 2πr dr Power PD-T = Ṅ_D-T QD-T 4. ANALYTIC MODEL: PRELIMINARY RESULTS Key sensitivity studies were performed for fuel density, radius, injection velocity, preheat temperature, external/internal B-field, and field gradient. - Optimal fuel density: ~0.07 kg/m3 - Target radius: ~1.0 cm (AR=6, liner thickness 0.16 cm, length 5 cm) - Injection velocity: 10 km/s - Fuel preheat: ~400-500 eV - External magnetic field: 30 T; Gradient: 100 T/m; Initial internal field: 1 T. 4.11 Optimized Case Results: For Li liner: - Specific Impulse: 32,200 s - Impulse bit: 780 N-s - Target Yield: 1.65 × 10^8 J - Gain (100% efficiency): 982 For Be liner: - Specific Impulse: 17,145 s - Impulse bit: 1,445 N-s - Target Yield: 1.53 × 10^8 J - Gain (100% efficiency): 323 Compression reaches peak stagnation in ~30-42 µs, generating ~5.4-5.8 × 10^19 neutrons per pulse (~1.2-1.3 × 10^8 J in neutron energy). 5. SPFMaX THREE-DIMENSIONAL NUMERICAL MODEL SPFMaX is a 3D smooth particle hydrodynamic (SPH) solver combined with Maxwell equations. It solves conservation of mass, momentum, single/two-temperature energy equations, and Maxwell potential equations (A and φ) coupled to external circuits. Preliminary simulations demonstrated successful target injection at 2 km/s into a converging/diverging coil geometry, confirming azimuthal current induction on the target surface by the gradient field (vz ∂Bz/∂z). Verification against magnetic flux compression generator (FCG) models was developed using a MATLAB GUI showing 1 MA seed current rising to 16 MA in 20 µs. 6. MISSION ANALYSIS Parametric trajectories using Zola's equivalent length method for Mars and Saturn missions were conducted: - Mars: 100–150 mt payload from LEO using two SLS Block 2 launches (260 mt IMLEO), with transit times of 40 to 60–90 days. - Saturn: 50–100 mt payload from LEO using two SLS launches, transit time of ~200 days. 7. VEHICLE DESIGN A baseline 1.2 GW vehicle concept was sized: - Payload: 50 mt - Propellant: 48.5 - 50 mt - Dry Mass: 173.2 mt (Thermal: 13.6 mt at 1,250 K rejection, Propulsion: 75.4 mt at 17.6 kW/kg, Structure: 17.3 mt, Avionics: 3.5 mt, Tanks: 5 mt, MGL 35-50%: 58.4 - 61 mt) - Total IMLEO: 271.6 - 272 mt. 8. OPTIONS FOR A GROUND-BASED, PROOF-OF-CONCEPT DEMONSTRATION Experimental validation can be performed using the UAH Aerophysics Research Center (ARC) Two-Stage Light Gas Gun (LGG), capable of launching gram-scale projectile targets at 5 to 7.5 km/s into a test chamber equipped with water-cooled magnetic coils (providing static or pulsed B-fields) and B-dot probes/high-speed videography. 9. CONCLUDING REMARKS The Phase I study shows that injecting a conductively lined target at high axial velocity into a static gradient magnetic field replicates the implosion dynamics of pulsed θ-pinch systems while using steady-state superconducting magnets. This significantly mitigates pulsed-power mass and thermal penalties, offering an attractive, viable pathway to high-thrust, high-Isp fusion propulsion for rapid human exploration of the Solar System.