The Case and Development Path for Fusion Propulsion Jason Cassibry, Ross Cortez, Milos Stanic Propulsion Research Center, University of Alabama in Huntsville, Huntsville, AL 35899 William Seidler II The Boeing Company Rob Adams NASA MSFC Geoff Statham ERC, Inc. Leo Fabisinski, ISS, Inc. Abstract The objectives of this paper are to demonstrate why fusion propulsion is needed for interplanetary space travel, show why the magneto-inertial fusion (MIF) parameter space may facilitate the most rapid, economic path for development, justify the choice for pulsed z-pinch, and provide a potential development path leading up to a TRL 9 system. We show that round trips of less than one year to Mars are only possible with fusion systems. We strongly emphasize that a fusion system will require a small on board nuclear fission reactor for reliable start ups, so fission and fusion development for space is mutually beneficial. We review the 50+ year history of fusion propulsion to serve as a reference, and we summarize results from a recent paper focused on the fusion parameter space for terrestrial power to suggest that the magneto-inertial fusion parameter space is perhaps the smallest, most economical approach for fusion propulsion development. Emerging experimental data and theory show that among MIF concepts, pulsed z-pinch fusion has solutions to some of the most deleterious instabilities, and scaling to fusion breakeven is almost within reach of current pulsed power facilities. We offer a potential development path to a TRL 9 flight system, starting from an assumed TRL 2 for the current state of fusion propulsion. Nomenclature a acceleration [m/s2] g0 gravitational acceleration at Earth's surface [m/s2] J mission difficulty parameter [m2/s3] k ratio of tank to propellant mass m mass [kg] m˙ mass flow rate [kg/s] n number density N total number of stages, number of fusion reactions P power [W] R distance traveled [m] t time [s] T total trip time, and time [s] vj jet or exhaust velocity [m/s] V reacting volume [m3] Y fusion energy yield [J] α propulsion system specific mass [kg/W] β mission type multiplication factor γ ratio of propulsion system to initial mass of nth stage Δv velocity increment [m/s] λ payload mass fraction τ characteristic time [s] subscripts 0 initial 1,2 dummy subscripts indicating different species burn propulsive burn c,coast unpowered coasting d dwell, as in dwell time τd f final jet jet, as in for jet power Pjet n number of the stage opt optimum p propulsion time pay payload pn propulsion time for nth stage (as in for Tpn) pr propellant ps propulsion system t tank I. Introduction The human predilection to explore and ultimately thrive in new environments – no matter how inhospitable or hostile – is well-known from throughout our history. We do so for many reasons: more food, preferable climate, improved trade routes, scientific discovery, and sometimes even just plain boredom. Currently, there is no conclusive economic incentive for going beyond earth orbit, and there will likely be none for a long time. And while we could fill volumes with all the potential scientific discoveries and technological spinoffs that would come from developing space worthy vehicles to carry humans throughout the solar system, we do not need to: human exploration of the solar system is already underway and will continue to get easier and become more enriching. So where should we go and how should we get there? In terms of distance, the Moon is our nearest neighbor, and can be visited readily using chemical propulsion. However, mission ∆v and crew safety may actually be more important figures of merit than simple distance. A recently proposed strategy involving piloted trips to destinations, and with robots deployed to the surface of those bodies (the 'flexible path'), could be the most feasible near-term approach to space exploration. Regardless of whether this approach is chosen, once we get beyond the Earth/moon system, other means of propulsion will have to be utilized to make the trip rapidly. II. Why We Need Fusion for Interplanetary Space Travel The rocket equation is derived from the application of Newton's second law to the motion of a spacecraft. Neglecting gravity and assuming constant exhaust velocity, it can be shown that Δv = v_j ln(m0 / mf) (1) Thus at fixed payload mass fractions, vehicle ∆v increases linearly with exhaust velocity. This does not necessarily translate into faster trip times, however. As Jahn points out, increasing exhaust velocity typically is done at the expense of thrust, because more energy per unit mass is required in order to accelerate gases for propulsion, and increased energy usually requires increased power supply mass. This tradeoff is also true in chemical propulsion, and is one of the reasons lower stages involve higher molecular weight propellants for higher thrust while upper stages frequently use LOX-hydrogen. The rocket equation can be rearranged as mf / m0 = e^(-Δv / v_j) (2) which more accurately reflects how vehicles are constrained. To the first order, the mission ∆v is determined by the destination and the exhaust velocity is determined by the propulsion technology. The optimum exhaust velocity is vehicle dependent, but will be of the same order as the mission ∆v, so as to produce a reasonable tradeoff between payload mass fraction and trip time. To further justify the remaining discussion, we consider the merits of both payload mass fraction and trip time. Shorter trip times are safer for astronauts, because they lower the radiation doses from cosmic rays and solar events. Additionally the psychological impact of long term space travel as well as the atrophy of skeletal and muscle tissue are both lessened. Increased payload mass fractions result in more room for habitation, science experiments, and recreation. Since mission ∆v's beyond the moon, but within the solar system, vary from ~10^4 to ~10^5 m/s, either we must develop propulsion systems that completely circumvent the rocket equation or investigate concepts that enable sufficiently high exhaust velocities without sacrificing thrust. While a number of advanced propulsion concepts do ‘short circuit’ the rocket equation, such as solar sails and beamed energy, the only approach that has been utilized for primary propulsion in deep space requires accelerating gases at high velocity out of a nozzle. Assuming that this continues to be the case, we must investigate concepts which accelerate gases or plasmas to high velocity. There are three common ways to add energy from an on-board source to a propellant for acceleration: 1. add enthalpy through combustion, 2. accelerate ionized gases directly via electrothermal and electromagnetic body forces (i.e. electric propulsion), and 3. add enthalpy through nuclear reactions. Combustion depends on the release of chemical binding energies and produces ~10 MJ per kg of propellant. Placing an upper limit of about 50 MJ per kg on the most advanced chemical reactions, applying a 1D energy equation to a control volume with boundaries at the combustion chamber walls and the nozzle exit, and assuming all enthalpy is converted to exhaust velocity, one obtains u_{e,max} = sqrt(2 * 50 * 10^6) = 10^4 m/s. Thus chemical propulsion reaches its practical limits for even the easiest of potential interplanetary missions: Mars. The remaining two methods will converge to the same solution based on our arguments; and we start with electric propulsion. Exhaust velocities can be quite high (10^5 m/s for ion thrusters), and some concepts may produce a sufficiently high thrust, but an external power supply is required. This demands either a solar array, beamed power, or an on-board nuclear reactor. Since solar power falls off as 1/r^2 with the distance (r) to the sun, any mission beyond Mars will require a reactor. Beamed power is a possible solution but may require a network of power stations placed throughout the solar system, or extremely long range precision vehicle targeting for deep space applications. This leaves two options for the reactor: nuclear fission or nuclear fusion. Thermal-to-electric power conversion, which is necessary for nuclear electric propulsion (NEP), is about 30% efficient and is fundamentally limited by the Carnot cycle (2nd Law of Thermodynamics) efficiency. This means that much of the thermal power has to be rejected by heavy radiators. The primary reason that fusion propulsion systems have much higher theoretical specific powers, when compared with NEP, is because the thermal-to-electric power conversion inefficiencies can be offset by the high gain of the fusion system. Direct conversion of the plasma exhaust energy, a viable approach for fusion, can yield efficiencies approaching 70% of the total fusion power, making thermal-to-electric conversion unnecessary. The third approach to propellant acceleration is derived from the conversion of energy from nuclear forces, binding subatomic particles in atomic nuclei, into kinetic energy. Both fission and fusion systems release approximately 10^14 J per kg of propellant, which is a factor of 10^6 or 10^7 higher than any chemical reaction. The challenge to both fission and fusion systems is to overcome the thermal stresses and radiative flux on the nozzle, and the other vehicle components facing the reacting fuel. Nuclear thermal propulsion (NTP) accomplishes this by merely passing a working fluid – such as hydrogen – over a reactor. The heat transfer adds enthalpy to the gas, which is then expanded out of a nozzle to produce thrust. Thermal limitations to chamber and nozzle walls mean that exhaust velocities are limited to ~10^4 m/s. It is important to note that many important missions are enabled by NTP, including piloted trips to Mars; but beyond Mars the trip times become too long. Nuclear Gas Core Rockets hold promise of high thrust (10's of kN) and high exhaust velocities (20-50 km/s), but a number of problems related to uranium plasma containment may make development too costly. Nuclear pulse propulsion (e.g. Orion) involves low yield (0.1 kiloton) nuclear explosions detonating near a pusher plate, and could enable 25 to 1500 km/s exhaust velocities with a thrust-to-weight ratio of about 4. Various international treaties prohibit atmospheric testing, and there are formidable political hurdles to pursuing such an approach. Finally, there is fusion propulsion. There are two significant roadblocks against fusion. Firstly, there are currently no reactor concepts that have demonstrated breakeven (where the energy output exceeds the energy input); and secondly, typical vehicle concepts are so large, that they would require numerous launch missions and in-orbit assembly. While we do not pretend that fusion is the only concept that can potentially enable human planetary space travel, we argue that it is the most promising candidate to enable the flexibility of exploring the solar system within the orbit of Pluto and perhaps even beyond. Because of the immense gains realized with solving the physics and engineering problems of fusion, it merits serious investigation. We also do not pretend to have all the answers to these problems, but intend to present the case for what we believe to be one of the quickest, most cost-effective development paths for a working fusion propulsion system. The remainder of this paper begins with calculation of mission performance, to illustrate why fusion is needed for interplanetary travel. A brief overview of fusion confinement is then given, followed by a history of fusion propulsion concepts. Recent theoretical insights into the fusion propulsion parameters space are reviewed in the context of fusion propulsion. Next we summarize our planned approach based largely on the conclusions reached from the review of open literature, and we offer a sustainable development roadmap. III. Calculation of Mission Performance The objective of this section is to determine the relationship between distance traveled R and time elapsed T in terms of rocket parameters. These results are based on a model derived by Moeckel. For clarity and completeness, we summarize the derivation of the performance equations here. Two types of spacecraft were investigated in Moeckel's paper and are compared here, Type I and Type II (see section III.2). Type I is an approximation for impulsive propulsion systems (where the burn time is small compared to the coast time, such is the case for chemical and nuclear thermal systems), and Type II is for systems in which the burn time is comparable to the coast time (such as nuclear electric and fusion systems). Three missions are examined: flyby, rendezvous, and roundrip. Here, R is defined as the distance from the starting point to the destination. For example, a mission to Mars would be roughly 0.5 AU, and this applies to the flyby, rendezvous, and roundtrip. The equations R = f(T) are interpreted as follows. They mean: 'The distance R that can be reached by a spacecraft is equal to this function of time T and/or rocket parameters.' III.1 Type I and II calculation of mass To meet the objective, Moeckel solved the equation 'distance equals rate multiplied by time'. The most difficult part of this calculation is the determination of velocity; because the mass of the vehicle changes as the propellant is expelled over the course of time, while the thrust may be relatively constant or impulsive. The basic concept is that the vehicle consists of N stages, and once the fuel is burned for one stage, that stage is ejected so that the new vehicle mass does not include the propulsion system or tankage for the previous stage: m_{0,n+1} = m_{0,n} - m_{pr,n} - m_{t,n} - m_{ps,n} (3) A linear relationship is assumed between the tank and propellant mass, and propulsion system of the nth stage to the initial mass of the nth stage (k ≡ m_{t,n} / m_{pr,n} and γ ≡ m_{ps,n} / m_{0,n}). Inserting these definitions into the mass equation and solving for the new to previous stage initial masses, m_{0,n+1} / m_{0,n} = 1 - (1 + k) (m_{pr,n} / m_{0,n}) - γ (4) The propellant mass is given by the rocket equation m_{pr,n} = m_{0,n} (1 - e^(-Δv_n / v_j)) (5) Equation 4 becomes m_{0,n+1} / m_{0,n} = 1 - (1 + k)(1 - e^(-Δv_n / v_j)) - γ = (1 + k)e^(-Δv_n / v_j) - k - γ (6) This expression can be considered the kernel upon which the performance model developed by Moeckel is built. The vehicle has N stages. Consider the net payload to be in the N+1 stage. Using Eq. 6, m_{pay} / m_{0,N} = (1 + k)e^(-Δv_N / v_j) - k - γ (7) Assuming all the Δv's are the same for all stages, (m_{pay} / m_{0,N}) (m_{0,N} / m_{0,N-1}) ... (m_{0,2} / m_{0,1}) = \prod_{n=1}^N (m_{0,n+1} / m_{0,n}) = m_{pay} / m_{0,1} = [(1 + k)e^(-Δv_N / v_j) - k - γ]^N (8) One of the main points of this exercise is to calculate a velocity increment. We now can do that by solving for the velocity increment, Δv = N Δv_n = N g0 I_sp ln[(1 + k) / ((m_{pay}/m_{0,1})^(1/N) + k + γ)] (9) III.2 Type II rockets For Type II rockets, Moeckel made the approximation γ >> k. k is roughly fixed regardless of type of rocket, based on material choice for the tank and the surface to volume ratio. γ is bigger for type II because it tends to be electrical, where electrical storage has a much lower energy density then chemical systems. What it means is that the propulsion system mass is large, and similar to the rest of the vehicle. For type II rockets under this assumption, Eq. 4 becomes m_{0,n+1} / m_{0,n} = [1 + (α J_n / 2γ)]^(-1) - γ (10) and propellant mass ratio is m_{pr,n} / m_{0,n} = 1 - [1 + (α J_n / 2γ)]^(-1) (11) where α is the propulsion system specific mass α ≡ m_{ps} / P_{jet} = m_{ps} / (0.5 m˙ v_j^2) = 2 m_{ps} / (m˙ (I_sp g0)^2) (12) and Jn is the mission difficulty parameter for stage n J_n ≡ \int_0^{T_{pn}} a^2 dt ≡ a_0^2 T_{pn} (13) Differentiating Eq. 10 with respect to γ, setting to 0, and solving for γ, finds the optimum gamma which maximizes the n+1 stage mass to the n stage mass ratio, gives γ_{opt} = (α J_n / 2)^(0.5) [1 - (α J_n / 2)^(0.5)] (14) Substitution of Eq. 14 For γopt into Eq. 10 gives m_{0,n+1} / m_{0,n} = [1 - (α J_n / 2γ)^(0.5)]^2 (15) The payload ratio for N stages becomes m_{pay} / m_{0,1} = [1 - (α J_n / 2)^(0.5)]^(2N) (16) Solving this expression for α Jn gives α J_n = 2 [1 - (m_{pay} / m_{0,1})^(1/(2N))]^2 (17) The overall mission difficulty is N Jn. By the definition, then the overall propulsion time is then T_p = N T_{pn} = N J_n / a_0^2 (18) or J = T_p a_0^2 (19) The velocity increment Δv is related to the acceleration and propulsive time according to Δv = a_0 T_p = sqrt(J T_p) (20) With Eqs. 17 and 18, Moeckel concluded Δv = sqrt(2 N T_p / α) [1 - (m_{pay} / m_{0,1})^(1/(2N))] (21) III.3 Mission Performance, R vs T equations for Type I and II Rockets We are now ready to obtain expressions for distance in terms of trip time and rocket parameters. We do this by superposition (adding) of acceleration periods and coasting periods. Burn periods are of the form R_{burn} = (1/2) a_0 T_p^2 (22) Coast periods are R_{coast} ≡ R_c = v_0 T_c = T_c a_0 (T - T_p) (23) For a flyby mission, R = R_c + R_{burn} = (1/2) a_0 T_p^2 + a_0 T_p (T - T_p) (24) With a = sqrt(J / T_p) (25) R = sqrt(J / T_p) (T_p T - (1/2) T_p^2) (26) Differentiation with respect to Tp gives T_opt = 2/3 T. Then R = Δv (2/3 T) (27) We can then make the substitution for Δv into this equation as was first done by Moeckel. It is more convenient to put this in terms of R, and specify a destination. The equation is identical, apart from a factor β, for the flyby, rendezvous, and roundtrip missions. Type I: T = (3 β R / 7) / [N v_j log10((1 + k) / (λ^(1/N) + k + γ))] Type II: T = (3/2) [(8 β R sqrt(α / 2N)) / (1 - λ^(1/(2N)))]^(2/3) (28) where λ ≡ m_{pay} / m_{0,1}. According to Moeckel, the trip distance R for rendezvous and roundtrip are 1/2 and 1/8 of the flyby. This means that for a given set of rocket parameters and time T, one could travel R, 1/2 R and 1/8 R. These fractions are multiplied by the f(T) side. When solved for T, one multiples R by the reciprocal of these factors, and this is how β is defined, Table 1. Table 1. Values of β as a function of trip type. Trip | β Flyby | 1 Rendezvous | 2 Round Trip | 8 III.4 Payload Mass Fraction We solve the equations in the previous section for λ. We have Type I: λ = [(1 + k) / (10^((3 β R) / (7 N v_j T)) - k - γ)]^N Type II: λ = [1 - (2/3 T)^(-3/2) β R sqrt(α / (2N))]^(2N) (29) These equations are plotted below for Mars and Saturn missions of interest. One assumes values for N, α, and λ, and picks a distance R. For example, R~5.0 AU for Jupiter, and that applies for flyby, rendezvous, and roundtrip. 1.0 AU is about 1.5 × 10^11 m. Figures 1–4 illustrate how difficult it is for chemical systems to reach interplanetary destinations in a short time compatible with human piloted missions. For the Mars mission, it becomes feasible with nuclear thermal and advanced nuclear electric propulsion, but cannot become routine unless fusion propulsion becomes possible. Missions to Saturn are not realistic at all unless advanced fusion systems are built. IV. Introduction to fusion and fusion confinement The basic challenges to fusion for propulsion are two-fold. First, thermonuclear fusion requires fuel temperatures of ~10^8 K or greater. Second, the reaction products are born with kinetic energies in the MeV-range. Such products are difficult to thermalize in short distances, which leads to large reactor size. Perhaps more importantly, the neutron flux is roughly an order of magnitude greater than that from nuclear fission, and this requires significant advancements in materials compared with fission reactors. Because of these challenges, fusion is often classified according to the method utilized for confining the plasma. Among the most commonly studied approaches to nuclear fusion are Magnetic Confinement Fusion (MCF), Inertial Confinement Fusion (ICF), Magneto-Inertial Fusion (MIF), and Inertial Electrostatic Confinement Fusion (IEC). IV.1 Magnetic Confinement Fusion (MCF) MCF utilizes strong magnetic fields to confine low-density plasma over a large spatial and temporal scale (ion density ~10^15 cm-3, a volume of hundreds of cubic meters and a continuous, steady state operation), establishing the conditions for thermonuclear fusion. The primary type of device used to confine the fusion is the tokamak, although there are numerous spin-offs which differ primarily in geometry of the magnetic field i.e. spheromaks, Reversed Field Pinch (RFP) and stellarators. IV.2 Inertial Confinement Fusion (ICF) ICF utilizes a spherically symmetric distribution of high-energy laser pulses or heavy ion beams to compress a solid-state ~2 mm target. The target is typically a hollow shell with stratified layers consisting of hydrocarbons doped with various additives in the outer layers and deuterium-tritium (DT) ice on the inside. The process of target implosion can be broken into four phases: ablation, implosion, stagnation, ignition, and burn. IV.3 Inertial Electrostatic Confinement (IEC) Inertial electrostatic confinement (IEC) involves a (typically) spherical electrostatic field produced by a grid or other means to radially confine ions. The ion energies are determined by the potential well depth, and the simplicity has facilitated a sizable number of researchers and hobbyists to build table top fusion reactors. IV.4 Magneto-Inertial Fusion (MIF) Magneto-inertial fusion (MIF) uses a magnetic field in an inertially confined fusing plasma to reduce thermal losses and to enhance alpha particle self-heating of the fuel. This reduces the areal density (ρr) threshold for ignition. Success of the MTF approach relies on the liner, which must be energetic enough to compress the target to ignition, behave as a stable magnetic flux conserver, and confine the target long enough so the fusion yield exceeds the liner driver and target generation energies. Plasma liner driven magneto-inertial fusion (PLMIF) aims to overcome solid liner damage issues. IV.5 Fission fusion hybrids Fission-fusion hybrid reactors have been established for over a half-century, but research has mainly been for military applications. Winterberg’s concept involves a relativistic central electron beam to magnetize and preheat a central fuel target with a high voltage pulse, with compression and confinement provided by a surrounding liner driven by a high current z-pinch. V. Summary of past fusion concepts The main problem of fusion propulsion is the fact that fusion energy with gain in excess of unity has only been achieved in weapons, not in terrestrial reactors. Nevertheless, there has been over a half century of research conducted. V.1 Early Fusion Propulsion History The idea of thermonuclear fusion for propulsion has at least been around since the late 1950's. Notable works come from Englert and Hilton, who primarily discussed the magnetic mirror approach. Bussard ramjet was proposed in 1960. Reinmann in 1971 discussed magnetic mirror concepts. Daedalus was an early feasibility study for an unmanned interstellar probe. V.2 Major NASA Programs The longest sustained NASA program dedicated to fusion energy for space propulsion and power ran from 1958 to 1978 (Pilot Rig, Electric Field Bumpy Torus). Later, Norman Schulze published a major 1991 technical memorandum titled 'Fusion Energy for Space Missions in the 21st Century'. In the late 1990s, NASA MSFC focused on plasma jet-driven magneto-inertial fusion (PJMIF/MTF). V.3 Other Efforts Other efforts examined IEC (Bussard, Polywell), Gasdynamic Mirror (Kammash and Lee), Closed Field Magnetic Confinement (spherical torus, FRC, plasmoids), Inertial Confinement (VISTA, Project Icarus), and Pulsed Z-pinch (Schumlak's ZAP concept). VI. A set of guiding parameters suitable for in-space propulsion The path to fusion propulsion will be shortened by reducing the development cost and reactor mass. These two factors are coupled, because the cost of a system depends on the reactor size. VI.1 Fusion parameter space Scaling of reactor depends on the type of confinement approach. Lindemuth and Siemon determined that the estimated cost for developing a fusion breakeven facility minimizes in the MIF parameter space, based on the assumption that cost scales with the total energy and power required for the system. VI.2 Fusion fuels The reaction rate is given by dN/dt = n1 n2 <σv>12 V. While DT has the highest reactivity, alternative fuels include D-3He, p-11B, and D-6Li. D6Li exists as a solid salt at room temperature with mass density ~800 kg/m3 (number density ~10^29 #/m3), eliminating the need for compressional work to reach solid density and avoiding cryogenic storage. VII. Summary of Proposed Pulsed Zpinch Concept VII.1 Description of the Charger 1 Facility UAH obtained a 3 TW pulsed power machine, the Decade Module 2 (DM2), from DTRA. Renamed Charger 1, it is a ~500 kJ facility capable of 2 MA discharges at 3 TW instantaneous power. VII.2 Planned Experiments Planned experiments include testing wire array diodes (Cu/Al, lithium wires with D6Li cores, molten lithium and D6Li injection) and magnetic nozzles. VII.3 Estimates for D6Li Fusion Energy Scaling with Current Z-pinch yields scale as ~I^4. Experiments with D6Li diodes benefit from solid starting densities, resulting in 8 orders of magnitude higher reactivity prior to compression. VII.4 Fusion Propulsion Roadmap Beginning With Charger 1 - TRL 3: Proof of concept experiments on Charger 1 (ignition mechanisms, fuels, magnetic nozzle). - TRL 4: Prototype ground test facility utilizing Linear Transformer Drivers (LTD), demonstrating scaling to breakeven and automated pulsing (10 Hz for 1 s). - TRL 5: Upgrading facility with flight-weight and high-durability components for continuous long-duration runs. - TRL 6: Vacuum environment testing and engine mass optimization. - TRL 7: Construction and checkout of a new flight-weight engine for a high-ΔV robotic demonstration mission. - TRL 8-9: Deployment on operational deep space robotic and crewed exploration missions. VIII. Summary This paper provides the motivation, technical justification, and development roadmap for pulsed z-pinch magneto-inertial fusion propulsion, which offers the most compact and economical route to rapid solar system exploration. IX. Acknowledgments The authors thank Dr. Raymond Sedwick, Dan Dorney, and Nikki Werkheiser for their valuable contributions. X. References Includes 90 citations covering foundational fusion propulsion literature, magneto-inertial fusion, pulsed power systems, and related mission studies.