Final Report for Research on Magnetized-Target Fusion for Space Propulsion

Summary

This final report summarizes research conducted at the University of Wisconsin-Madison on using a field-reversed configuration (FRC) as a target in a magnetized-target fusion (MTF) propulsion system for space exploration under NASA’s RASC/HOPE initiative. The study models plasma liner implosions and fusion burn dynamics using the 1-D radiation hydrodynamics code BUCKY and calculates neutron and gamma-ray heating in magnetic nozzle structures, showing that nozzle heating can be mitigated below 1% of total fusion power with proper plasma buffering.

Title Page & Cover

John F. Santarius and Mohamed E. Sawan

Fusion Technology Institute University of Wisconsin 1500 Engineering Drive Madison, WI 53706 http://fti.neep.wisc.edu

July 2003 UWFDM-1209

1 Overview

This Final Report summarizes research activities at the University of Wisconsin on using a field-reversed configuration (FRC) as the target in a magnetized-target fusion (MTF) rocket. The MTF rocket is based on a concept invented by Francis Thio, in which plasmas launched by plasma guns implode an FRC or spheromak [1,2].

The four tasks defined for this research project were: Task 1) Participate in the Revolutionary Aerospace Systems Concepts / Human Outer Planet Exploration (RASC/HOPE) project. Task 2) Undertake the modeling of the implosion of a magnetized target plasma by a high-velocity plasma liner to achieve thermonuclear fusion reactions. Task 3) Undertake modeling the fusion burn. Task 4) Undertake the modeling of the expansion of the fusion plasma against a magnetic field in a magnetic nozzle configuration.

The following sections give a brief account of project activities that address the above tasks. An Appendix in the form of a Mathematica™ [3] notebook gives further details of the calculations and figures appearing in Section 2. Tasks 2 and 3 are very closely related, so they are treated in the same section (2.2).

2 Project activities - 2.1 Task 1: Participate in RASC/HOPE

2.1 Task 1: Participate in the Revolutionary Aerospace Systems Concepts / Human Outer Planet Exploration (RASC/HOPE) project.

The main objective of the Revolutionary Aerospace Systems Concepts / Human Outer Planet Exploration (RASC/HOPE) program is to enable future NASA missions by the development of revolutionary aerospace systems concepts and related technology. The PI for this research participated in the April 16-17, 2002 RASC/HOPE meeting at NASA Langley Research Center. At the meeting, he provided expertise in fusion space propulsion, space resources including helium-3 fusion fuel, and advanced-fuel fusion power plant design. He has continued this task in discussions with Dr. Francis Thio during the time frame covered by this report. Advice was also provided to Dr. Slade White, NASA MSFC, regarding neutron interactions with the magnetic nozzle.

2.2 Tasks 2 & 3: Implosion Modeling and Fusion Burn

2.2 Task 2: Undertake the modeling of the implosion of a magnetized target plasma by a high-velocity plasma liner to achieve thermonuclear fusion reactions and Task 3: Undertake modeling the fusion burn.

2.2.1 Description of the BUCKY computer code These tasks model plasma-jet magnetized-target fusion (MTF) implosion dynamics and burn dynamics using the University of Wisconsin’s 1-D radiation hydrodynamics code, BUCKY [4,5]. BUCKY is a 1-D Lagrangian radiation-hydrodynamics code which can simulate plasmas in planar, cylindrical, or spherical geometries. It solves single-fluid equations of motion with pressure contributions from electrons, ions, radiation, and fast charged particles. Plasma energy transfer can be treated using either a one-temperature (Te=Ti) or two-temperature model. Thermal conduction is treated using Spitzer conductivities, with electron conduction being flux-limited. BUCKY includes source terms for fast ion energy deposition, fusion burn heating (D-T, D-D, D-3He), laser energy deposition, and x-ray heating. Charged products are transported using time-dependent particle tracking, and neutrons are deposited using an escape probability model.

Because there was not sufficient time to add a plasma-jet MTF magnetic-field model to BUCKY on the time frame of this project, the magnetic field was not included in the calculations. Neglecting magnetic field means alpha particles deposit energy over larger distances and thermal conductivities must be parameterized.

2.2.2 Results 2.2.2.1 Reference case (vjet = 125 km/s): Examined Lagrangian zone boundary radii versus time (0 < t < 2 µs) and density/temperature evolution. Rebounding shocks in target interact with incoming buffer plasma, repeating compression cycles.

2.2.2.2 Case with jet velocity increased to 398 km/s: A jet velocity of 398 km/s was used to satisfy a ‘perfect acoustic matching’ condition, where the contact surface velocity equals the ion-acoustic velocity in the jets, preventing outward radial shock propagation. Inertial confinement was maintained for ~100 ns, generating ~700 kJ fusion yield.

2.3 Task 4: Expansion in Magnetic Nozzle and Neutronics

2.3 Task 4: Undertake the modeling of the expansion of the fusion plasma against a magnetic field in a magnetic nozzle configuration.

Literature review supports magnetic nozzle efficiencies up to ~80% for pulsed plasma propulsion. Neutronics calculations were conducted using the ONEDANT module of the DANTSYS 3.0 code with FENDL-2 cross sections (175 neutron energy group structure) for a 5-cm thick slab of 316 stainless steel representing nozzle coils and structure.

Key finding: Absorption of low energy neutrons produces several MeV via (n,γ) reactions, but there exists a broad minimum in absorbed energy by the nozzle (<1% of total fusion energy) for neutron energies in the 200–855 keV range. A buffer plasma layer can moderate neutrons into this optimal energy window, limiting structure and magnet cryogenic heating.

3 Summary & 4 Recommendations for Future Work

3 Summary This research evaluated technical aspects of plasma-jet MTF for NASA’s RASC/HOPE program. 1-D radiation hydrodynamics simulations qualitatively reproduce implosion dynamics, though magnetic field inclusion is necessary for complete quantitative accuracy. Neutronics modeling demonstrated that magnetic nozzle heating can be held below 1% of total fusion power by buffering neutron energy to 200–855 keV using the plasma liner.

4 Recommendations for Future Work

Implement magnetic-field dependent thermal conductivity and alpha-particle deposition into BUCKY to reproduce published analytic cases and optimize burn dynamics.
Implement 2-D particle-in-cell or Monte Carlo simulations to analyze FRC equilibrium and alpha transport.
Identify optimized MTF operating points for development path experimental testing.
Perform full-spectrum neutron and gamma heating calculations in the magnetic nozzle geometry.

5 Acknowledgments & 6 Bibliography

5 Acknowledgments NASA funding through Grant NAG8-1719 is gratefully acknowledged. Valuable discussions were held with Dr. Francis Thio.

6 Bibliography [1] Y.C.F. Thio et al., Current Trends in International Fusion Research (1999). [2] Y.C.F. Thio et al., AIAA-99-2703 (1999). [3] S. Wolfram, The Mathematica Book, 3rd ed. (1996). [4] J.J. MacFarlane et al., UWFDM-984 (1995). [5] R.R. Peterson et al., Fusion Technology 30, 783 (1996). [6-16] Literature on magnetic nozzles and fusion propulsion (Hyde, Bond, Lasche, Orth, Mima, Nagamine, Zakharov, Litchford, Mikellides). [17] R.E. Alcouffe et al., DANTSYS 3.0 (1995). [18] M. Herman & H. Wienke, IAEA-NDS-176 (1997). [19] O. Motojima et al., Fusion Energy 1996, p. 467 (1997).

Appendix: Mathematica Notebook (FinalReport_PlasmaMTF_03_Appendix.nb)

The Appendix contains detailed Mathematica calculations, formulas, input decks, and plotting routines for plasma parameter evaluation (using plasma.m and fusion.m packages), BUCKY input file generation, zone mass distributions across target, jet, and buffer regions, and neutronics post-processing:

Target parameters: B_t = 1.0 T, n_it = 2.0x10^24 m^-3, T_et = 2 eV, r_t = 0.05 m.
Jet parameters: v_jet = 125 km/s to 398 km/s (perfect acoustic match), T_ej = 26.7 eV to 106 eV.
Buffer parameters: m_b = 1.8 to 2.0 g, n_ib = 4.5x10^24 m^-3.
Energy deposition tables and total cross section slowing down calculations in deuterium for 316 stainless steel nozzle components.