Cohen2017ibis

Summary

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Direct Fusion Drive for Interstellar Exploration S.A. Cohen1*, C. Swanson1, N. McGreivy1, A. Raja3, E. Evans1, P. Jandovitz1, M. Khodak3, Gary Pajer2, T.D. Rognlien4, Stephanie Thomas2, and Michael Paluszek2 1 Princeton Plasma Physics Laboratory, Princeton NJ, USA 2 Princeton Satellite Systems, Plainsboro, NJ, USA 3 Princeton University, Princeton, NJ, USA 4Lawrence Livermore National Laboratory, Livermore, CA, USA Abstract The Direct Fusion Drive rocket engine (DFD), based on the Princeton Plasma Physics Laboratory’s Princeton Field Reversed Configuration machine, has the potential to propel spacecraft to interstellar space and to nearby solar systems. This paper discusses a design for a starship that would be well suited to a variety of solar system and interstellar missions. DFD employs a unique plasma heating system to produce nuclear fusion engines in the range of 1 to 10 MW, ideal for human solar-system exploration, robotic solar-system missions, and interstellar missions. This paper gives an overview of the physics of the engine. Its innovative radiofrequency (RF) plasma heating system and the fuel choice are explained. The thrust augmentation method is described along with results of multi-fluid simulations that give an envelope of expected thrust and specific impulse. The power balance is described and the subsystems needed to support the fusion core are reviewed. The paper gives the latest results for the system design of the engine, including just-completed work done under a NASA NIAC study. A mass budget is presented for the subsystems. The paper then presents potential interstellar missions. The first are flyby missions. One is the proposed 550-AU mission that would use the Sun as a gravitational lens for exoplanet research. This mission can be done without a deceleration phase. Next, flyby missions – requiring major technological advances – to the nearest star are described. Finally we sketch a mission to orbit a planet in either the Alpha Centauri A or Alpha Centauri B systems. The mission analyses include a communications system link budget. DFD can operate in an electric-power-only mode, allowing a large fraction of the fusion power to be used for the payload and communications, enhancing the scientific return. All of the missions start in low earth orbit. Keywords: Nuclear Fusion, Propulsion, Gravity Lens, 550 AU, Exoplanets, Alpha-Centauri, Interstellar Nomenclature B = magnetic field β = ratio of plasma pressure to magnetic-field energy density c = speed of light c = ion sound speed s E = ratio of plasma FRC plasma core length to diameter γ = Lower-hybrid drift instability growth rate LH I = plasma current p I = specific impulse sp MT = metric ton, 103 kg q = plasma safety factor r = FRC core plasma radius s s = 0.3 r/ρ s i S* = r ω /c s pi T = Thrust h τ = Alfvén time ~ rE/c A s s ω pi = ion plasma frequency

Introduction The idea to use fusion power for spacecraft propulsion has a long history,1,2 with its support arising from the high energy density of the fuel and the high velocity of the fusion products. Early proponents of fusion rockets that provided steady – rather than pulsed or explosive – propulsion based their designs on the fusion devices that were then in vogue, tokamaks,3,4 mirror machines5 and levitated dipoles.6 The experimental results of that period in fusion history indicated that the plasma’s anomalous transport, meaning poor plasma energy confinement, and instability would necessitate low β, D-T burning, large and powerful machines, many meters in diameter, producing over a gigawatt in power and requiring a meter or more of neutron shielding. Such large *Corresponding author, [email protected] 1

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and massive devices could not be launched fully assembled; upwards of 100 launch vehicles would be needed. Such daunting and expensive proposals never proceeded beyond the conceptual stage. Recently, new designs of fusion devices, bolstered by experimental successes on prototypes, have raised optimism for the prospect of considerably smaller fusion-powered rockets that are far lighter, less radioactive, and less costly. Commensurate with their reduced size, these rocket engines would produce only megawatts of power,7 nevertheless ample for a wide variety of missions in the solar system and beyond. The common feature of these rockets is the geometry of the magnetic field that confines the plasma. The “family name” for these fusion-reactor designs is field-reversed configuration (FRC), a label derived from the original plasma-formation method, not the shape of the field, as commonly thought. Importantly, FRCs have more than 10x higher β than tokamak devices, the leading contender for terrestrial fusion power production. The high β, coupled with the FRC’s quasi-linear geometry, reduce the required peak magnetic field by about a factor of 3 compared to a tokamak’s. Lighter weight magnets are possible, important for spacecraft. The higher β also allows the use of so-called aneutronic fuels, e.g., D-3He, whose main reaction produces far fewer neutrons than D-T fusion. Accordingly, less shielding (mass) is required. One member of the FRC family – the inductively driven, liner-compression Pulsed-High-Density (PHD) device – was designed to operate in a pulsed mode with D-T, producing an average power of 70 MW. Another FRC family member is the Star Thrust Experiment (STX),8 a 1-m plasma radius design, formed and heated by an RF technique called rotating magnetic fields9,10 (RMF). An STX rocket engine was predicted to be able to produce steady propulsion at a power level near ½ MW/m of length. In this paper we describe a 3rd member of the FRC family, the D-3He-fueled Direct Fusion Drive (DFD) rocket engine.11 Similar to STX in employing RMF, the DFD differs in major ways, ones that would result in a more practical rocket engine. Important differences are: 1) the DFD RMF method has different symmetry12 (odd- parity versus even parity, RMF vs RMF ), providing improved energy confinement hence allowing plasmas o e with 4-8 times smaller linear dimensions and 100-400x smaller volume and mass; 2) The smaller radius DFD plasma is far more stable than the larger STX plasma; 3) the smaller radius of the DFD plasma allows a method to improve the properties of the rocket exhaust, with specific impulse, I , to 2 x 104 s (and beyond) and thrust, sp T , to 10 N/MW; 4) DFD operation reduces neutron wall fluxes more than a factor of 1000 compared to D-T h devices, thereby reducing neutron shielding thickness by a factor of 10 and increasing engine lifetime; and 5) increased attention to the engineering details of the complete rocket engine, such as improving energy-recovery systems, raising specific power, and optimizing plasma heating and fueling systems. In section 2 of this paper we describe the physics of the DFD’s fusion core, explaining how the novel RMF method improves energy confinement, current drive, plasma heating, and plasma stability. Section 3 o described the choice of fuel, the neutron production rate, and the power balance. Section 4 describes how the energy in fusion products produced in the core is converted into directed momentum for propulsion. Section 5 describes two missions relevant to interstellar exploration. 2. The DFD rocket engine core The region where abundant fusion reactions take place is the high temperature (ca. 100 keV), moderate density (ca. 5 x 1014 cm-3) plasma region named the core. For the FRC, this region is inside a magnetic separatrix, an imaginary closed surface that demarcates open magnetic-field lines, those that leave the device, from closed magnetic-field lines, ones that stay fully inside the device, see Figure 1. The open field-line region is also called the scrape-off layer, SOL. To form the closed magnetic-field lines, a strong plasma current is needed, perpendicular to the FRC’s magnetic field. On axis, the direction of the magnetic field created by the Figure 1. FRC sketch, adapted from Ref. 26. plasma current, I , is opposite to that of the open field lines which are created by external coils. If the axes of the p two fields are not exactly parallel, MHD theory13 predicts that the configuration will strongly tilt and destroy itself. In the following subsection we shall describe how RMF generates the current and heats the plasma ions o and electrons in such a way as to allow smaller devices with excellent stability, not susceptible to the tilt mode. *Corresponding author, [email protected] 2

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2.1. Macro-stability MHD theory has shown itself to be accurate in predicting the stability of plasmas that are fluid-like.14 Fluid-like plasmas are prone to several classes of instabilities. Criteria that determine whether a magnetized plasma is fluid-like are collisionality and the ratio of particle gyro-radii to machine size. Highly collisional, that is, cold and dense, plasmas are fluid-like. Plasmas where the ion gyro-radii, ρ, are small compared to the plasma i radius, r, are likely to be fluid-like. For an FRC, the size criterion is defined by two nearly equivalent s dimensionless parameters: 𝑠 ≅ 0.3 𝑟/𝜌 and 𝑆∗ ≡ 𝑟𝜔 /𝑐, where ω is the ion plasma frequency and c the ! ! ! !” pi speed of light.15 By choosing a small, high-temperature FRC, neither fluid criterion is satisfied and the plasma is said to be kinetic rather than fluid-like. Why a kinetic plasma is stable against the tilt mode can be understood by considering the axis-encircling orbit of a single charged particle in a magnetic field, a stand-in for a hot plasma. An axial push to the particle, in an attempt to tilt its axis, causes the particle to translate along B, not to tip over. No tilt occurs. More complicated explanations can be extracted from Steinhauer’s review.16 It should be noted that several FRCs17,18,19,20 have achieved stable plasmas for durations 103 to 105 times longer than predicted by MHD theory, the Alfven time, τ . (Stability is predicted15 for S*/E < 3.) The plasma durations were limited by A power supply capabilities not instabilities. We now address how RMF heats particles and allows the size of the FRC to be relatively small. o 2.2. Confinement There are several reasons why energy confinement in FRCs can be good, that is, better than in tokamaks. We first discuss how to keep the FRC confinement from becoming poor! The net magnetic field caused by the external coils and the plasma current creates a nested set of closed field lines inside a separatrix; each closed field line circles the plasma current once poloidally before closing on itself. Closed field lines are good for confinement since they encourage charged particles to stay within the device. Open field lines allow particles and their energy to flow out of the device, i.e., confinement is poorer for open field lines. The addition of RMF to an FRC causes the field lines to open, see figure 2, while application of e RMF maintains the closure of field lines, figure 3. One explanation is that the FRC, by itself, is of odd parity.21 o Mixing parities, such as by adding RMF , causes all of an FRC’s field lines to open, hence confinement to e degrade. One experimental team22 has compared even and odd-parity electron heating on the same device and found a factor of 4 improvement in the energy confinement time. Another team19 achieved 5 to 10-fold increases in electron temperature, T , with RMF compared to other machines, e.g., Ref. 9, of the same size and heating e o power operating with RMF . e Figure 2. A very small-amplitude (B = .005), Figure 3. Magnetic field lines when a larger amplitude odd- t parity magnetic field, B = 0.04, is added to a Solov’ev FRC. uniform, transverse magnetic field (even parity) is t a) Closed field lines in the y – z plane show expansion and added to a Solov’ev FRC with B = 1. Two field lines 0 contraction but remain closed. b) Projection of field lines are mapped. Though both field lines are long, they are clearly open. This FRC’s major axis is vertical.12 originally in the x – z plane onto that plane show little change in shape. This FRC’s major axis is horizontal.12 *Corresponding author, [email protected] 3

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Neoclassical theory24 predicts that energy losses scale as (1 + q2). For tokamaks q ≥ 3 while for pure FRCs q = 0. Accordingly, FRCs should have about 10x better confinement. Sheffield prepared a survey of confinement quality in tokamaks which Kesner and Mauel updated; the results are shown in figure 4. The point denoted as C-2 represents data from a TriAlpha FRC, clearly better than the tokamak results. Whether the same improvement occurs in FRCs at higher ion temperatures needs to be tested. There are reasons to believe this improvement will occur. First, the main culprit expected25 to cause anomalous energy transport in FRCs is called the lower-hybrid drift instability (LHDI), predicted to create mm- to cm-scale turbulence that increases Figure 4. Confinement quality vs ion temperature, T i . The transport. The LHDI growth rate, γ LH , is the ratio of the TriAlpha C-2 FRC device has shown better confinement electron drift speed to the ion thermal velocity. As quality, β/χ, than tokamaks. (Adapted from Sheffield,23 ions get hotter and the plasma denser, γ gets smaller LH by Mauel and Kesner.) and the LHDI should become less important. Secondly, Rostoker26 and others27 noted that hot ions and runaway electrons in tokamaks had far better confinement than thermal electrons. The reasons proposed for the large improvement was lower collisionality and less scattering by fluctuations because, like large ships in a choppy sea, the large gyro-radii of these energetic particles made them less susceptible to small-scale fluctuations. 2.3. Plasma current drive and plasma heating RMF was proposed to drive current in the plasma, not to heat it to fusion-relevant temperatures. The e current-drive mechanism was explained as being of 2nd order, specifically, the time-varying RMF magnetic field e (in the r and φ directions) created a z-directed electric field (along B), hence a current in that direction, J . From z the JxB term in the fluid momentum equation, J z interacted with B r , resulting in the desired azimuthal current Jφ. In contrast, RMF current drive is 1st order o because of its B near the FRC’s midplane. The time z variation of that field creates an azimuthal electric field, Eφ, near the O-line magnetic null, figure 5, directly accelerating charged particles into betatron orbits near the null, figure 6a). More precisely, the trajectories are punctuated betatron orbits, separated by periods in cyclotron motion. As the particles are accelerated along the null, they gain then lose energy, figure 6b), because the (slowly rotating) Eφ reverses direction halfway around. The more energetic the particles get, the further away from the null they can circulate. In the RMF ’s rotating frame, figure 6c), o Figure 5. Snapshot of the azimuthal electric field in these punctuated betatron-orbit electrons form a the FRC’s midplane created by RMF . This field o crescent, hence move, on the average, with an rotates with the RMF . o azimuthal velocity equal to that of the RMF .28 o In an FRC reactor, these current-carrying electrons will have very high peak energy, about 5 times greater than in D-T tokamak fusion reactors, consequently their collisionality will be more than 10x less. This contributes strongly to the high efficiency of RMF for driving current. Away from the O-line null, the more o massive ions will carry an appreciable part of the current and diamagnetism will also provide a substantial part of the required current. *Corresponding author, [email protected] 4

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Figure 6a). Punctuated betatron Figure 6c). In the frame rotating orbit near the FRC midplane. At the with the RMF , the punctuated Figure 6b). As the electron moves against o start and end of the betatron betatron trajectory appears as a segments, the orbit becomes Eφ it gains energy; as it moves with Eφ, it crescent, with the betatron segments cyclotron. (B = 20 kG, r = 10 cm, loses energy, resulting in the spikes in o s “inside” the cyclotron segments. ω /ω = 0.5) energy. RMF ci Ion heating results from the same physical process, acceleration by Eφ, with an additional contribution from the RMF -created z and r electric fields. That the RMF frequency should not be far from the ion cyclotron o o frequency (at the FRC’s center) to allow quasi-resonances, particularly at higher harmonics, is seen in figure 7b). Importantly, for both electron and ion heating, the non-uniformity of the FRC’s magnetic field, especially the presence of nulls, causes orbits to lose track of the phase of the RMF, introducing stochasticity into the motion hence net energy gain.29 Near Maxwellian distributions may develop, though usually the distributions are truncated at higher energy. Note that the required RMF strengths, to ~ 200 G, and frequencies, 0.3-3 MHz, to o achieve ion energies of 100 keV are well within the capabilities of conventional RF equipment. Of course, improvements in RF amplifier efficiency and reduction of amplifier mass would provide important benefits. Figure 7b). Early time evolution of ion energy for two values of the RMF strength, 2 and 20 G. The quasi- Figure 7a). Maximum ion energy versus RMF frequency o resonances at higher harmonics, 3-5, are evident, as is the for different RMF o strengths in a 10-cm radius, 20-kG FRC. stochastic nature of the heating. Having a small FRC, allowed because of the better energy confinement, makes RMF operation better. It o improves the penetration of the RMF field to the FRC’s null line where current drive is more efficient; it o requires higher RMF o frequency, which results in higher ion energies because Eφ ∝ 𝜕𝐵 𝜕𝑡. As we shall shortly see, other important benefits accrue, ones that result in far lower neutron wall load. 3. Fuel choice, neutron production, and power balance The production of neutrons by fusion is particularly problematic for spacecraft propulsion. Neutrons cause damage and activation of nearby materials and structures, limiting their lifetime, necessitating maintenance, and increasing the mass needed for shielding. Neutrons are hard to “direct” hence may contribute little to the thrust required of a rocket engine. Having all the fusion products be charged particles solves these problems at the added cost of requiring higher plasma temperatures because of the lower fusion cross sections of the “advanced” aneutronic fuels. Of the two aneutronic fuels most commonly discussed, we choose D-3He instead of p-11B. The low energy release from p-11B fusion, plus the lower fuel density possible at fixed magnetic *Corresponding author, [email protected] 5

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field (because of the higher nuclear charge) and the higher temperatures required, makes p-11B a dubious choice. A penalty must be paid for selecting D-3He. There are neutrons from one D-D fusion branch and possibly from the T fusion product of the other D-D fusion branch. Methods must be found to ameliorate these effects. 3.1. Reducing neutron wall load A small FRC allows solutions to these problems. The surface-to-volume ratio scales as 1/radius. For a 25-cm radius FRC, a 32-fold improvement is obtained compared to an 8-m tokamak. Additionally, fusion products born in a small FRC will have their orbits pass through the cool SOL of the FRC where the electron drag is strong. By an “airbrake”-like effect, see figure 8a), fusion products which pass through the SOL even for a small fraction of their birth orbit, will rapidly cool, from 1 Mev to 100 keV, and their orbits will become cyclotron-like, lying fully in the SOL, figure 8b). PIC studies30 of the slowing down indicate that this process will occur in under 10 ms, far quicker than the estimated 20-s T burn-up time. Once in the SOL, the T+ will be exhausted out the nozzle with the cooler propellant, to be described in section 4. Only those neutrons produced by D-D fusion will remain a problem. Figure 8a). T+ trajectory projected on the midplane of an The third step in reducing neutron production FRC. The T+ slowing down by electron drag in the SOL is to increase the ratio of 3He to D in the plasma.31 is accelerated to show the transition of the orbit from This does reduce the power density approximately betatron to figure-8 to cyclotron, the latter lying fully in linearly but the percentage of power in neutrons the SOL, the region between the red and green circles. quadratically. From a neutron-production perspective, Figure 8b). Close-up view the net effect of these 3 measures should be in of the cyclotron segment of excess of a thousand-fold32 reduction of neutron the T+ orbit, showing that the orbit eventually lies power flux to the first wall. The thickness of the neutron shielding, 100% 10B, would be 10-30 cm, fully in the SOL.32 based on the duration of the mission and of the fusion-power production. 3.2. Power balance and rocket subsystems In this section we analyze a point design for a DFD rocket engine, focusing on power balance, to see if a consistent solution exists within the stability, energy confinement, and low radioactivity constraints described above. We begin by specifying the plasma density, ion and electron temperatures, plasma radius and elongation, and the external coils inner radius, r . The latter, determined by the thickness of the SOL and of the shielding, c sets the plasma β through the Barnes relation, < 𝛽 > = 1−𝑥!/2, where x = r/r . Table 1 presents the results of ! s s c our model with r =30 cm, E = 6, T = 30 keV, T = 100 keV, n = 3x1020 m-3, and a 2:1 3He to D ratio. Flat s e i e temperature and density profiles are assumed. From these, it is relatively straightforward to calculate β, fusion power, magnetic field strength, and plasma current, I . The next step is to calculate volumetric losses from p radiation. Though Bremsstrahlung losses may also be calculated accurately, this is not the case for synchrotron losses because of plasma absorption and wall reflections. Our model assumes full emission from a 3-cm thick shell just inside the separatrix and no wall reflection. Further into the core the magnetic field is lower, hence the frequency lower; absorption of that emitted radiation occurs in the aforementioned shell. The Bremsstrahlung and synchrotron power will be absorbed in the neutron shielding. That energy is recovered with an efficiency of 60% by a Brayton cycle cooling system. Power flow into the gas box ionizes the propellant there. The energy cost is typically 50-100 eV/ion, with higher values required at lower densities. Of that power, 80-90% is deposited on the gas box walls and recovered by the Brayton cycle system. The power flows are depicted in *Corresponding author, [email protected] 6

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figure 9, which, for this DFD, is providing primarily thrust. If more electrical power is required for station keeping or communications, the thrust power can be diverted to generating electrical power. The distribution of masses is shown in figure 10. This assumes a conservative permitted neutron flux on the superconducting coils, below 1018 n/cm2 and below 10-4 DPA, resulting in a 10-cm-thick 10B shield, sufficient for 1 year at full power. Increasing the shielding thickness to 22 cm would increase the superconducting-coils lifetime to 13 years. Table 1. Parameters for a 2-MW DFD rocket engine. Parameter DFD r (m) 0.3 s Elongation, E 6 B (T) 4.3 a I (MA) 8.0 p Ion species D-3He 3He/D 2 n (m-3) 3 x1020 e T (keV) 30 e T (keV) 100 i <β> 0.84 P (MW) 0.5 RMF ω R (radians/s) 1.6x106 Figure 9. Power-flow diagram of a 2-MW DF D. B R /B a 0.003 P (MW) 2.13 f P (MW) 0.7 synch P (MW) 0.32 Bremss P (MW) 0.1 GB τ /τ 2.7 classical Ei E s (T+) 2.3 s (4He++) 2.2 S*/E 2.8 γ 0.02 LH ψ 34 RMF penetration Isp (s) 2.3x104 Thrust (N) 12.5 B (T) 20 nozzle % power in neutrons 1.1 Wall load (MW/m2) 2x10-3 Figure 10. Mass budget of the DFD engine. We now examine the consistency of this design point with energy confinement, stability, and propulsion. The ratio of the classical confinement time, τ to the required energy confinement time is 2.7, consistent classical Ei, with the improvement in energy confinement seen by C-2 and PFRC-1. The two stability criteria are also satisfied: the LH micro-stability criterion, γ , is < 1 and macro-stability criterion, S*/E, is less than 3. One LH further criterion10 worth mentioning, named ψ , is that for RMF field to penetrate in the core of the RMF penetration FRC. This parameter was derived for RMF not RMF , so its applicability is questionable. For RMF ψ e o e RMF must be greater than 1 for penetration. For the DFD, this parameter is above 30, an encouraging margin penetration in light of the possible lack of direct applicability. *Corresponding author, [email protected] 7

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The neutron wall load for this plasma is 2500x below that specified as acceptable in D-T tokamaks, a sizeable improvement. The amount of thrust power lost in the neutron channel is small, 1%, though could be lowered by increasing the 3He/D ratio. The I predicted for the DFD depends on the propellant species and injection rate into the gas box. For sp Table 1 we have selected a low propellant injection rate, one that produces an I above 2 x 104 s. For higher sp propellant flow, I would drop and the power required in the gas box would increase along with the thrust, sp topics we describe in more detail in section 4. A pictorial representation of the subsystems is shown in figure 11 and an artist’s rendition of a DFD module is in figure 12. Figure 11. Block diagram of DFD major subsystems. Figure 12. Artist’s rendition of a 2-MW DFD module. *Corresponding author, [email protected] 8

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The scrape-off layer (SOL) and rocket exhaust The SOL of the DFD is quite different than that of any other fusion device. In tokamaks, for example, the SOL is heated and populated by diffusive transport across the separatrix of both energy and particles. The heat transport into it is local, that is, described by Fick’s law, by the local flux-surface-normal gradient in pressure. Because this diffusive transport is slow compared to the flow along the magnetic field, the SOL is onion-skin thin, 𝛿 , compared to the plasma’s radius. For example, ITER’s SOL is predicted to be ½-cm thick !”# 𝛿 while the plasma outer radius at its midplane is 9 m, !”# 𝑟 ≅ 6𝑥 10!!. It the DFD, the density profile of the ! SOL is determined by the orifice to the gas box and the field expansion between the gas box and the plasma 𝛿 midplane. For the DFD in Table 1, the SOL would be about 7 cm thick, !”# 𝑟 > 0.2 . Energy is deposited ! across the entire SOL cross section by the large gyro-radii fusion products. Thus the DFD, the SOL + FRC, is more like a navel orange, with a very thick rind. The energy is deposited in the SOL directly from the fusion products via a non-local process and is predominantly transmitted to the electrons via fast-ion drag. The random thermal energy in the SOL electrons is transferred to the cool SOL ions through a double layer at the nozzle and via expansion downstream, thus being converted into directed flow. Because of the relatively low temperature (< 100 eV) and high density (> 5x1019 m-3) of the SOL, resulting in a collisional mean-free-path of the thermal (majority) electrons less than 50 cm, it is appropriate to use a fluid model for the SOL between the gas box and the nozzle. Results from one UEDGE33 fluid-code simulation are shown in figure 13. In each, the gas box is 1-m long, at the far left, the electron heating occurs in the central 2 m, and the nozzle is located at z ~ 2 m. The inputs were P =1 MW of power and 𝑚= 0.08 g/s of D i 2 gas into the gas box. (The gas input is equivalent to a current, I = 𝑚𝑁 e/amu ~ 3.85 kA, where N is e ! A Avogadro’s number and e the charge on an electron.) From E = P/I , one can then readily estimate the upper max i e limit of ion energy to be 260 eV. As figure 13c) shows, only half that value is reached. The culprits are radiation and ionization losses and plasma energy brought to the gas box walls by plasma transport. The results of an extensive number of simulations are presented in figure 14, showing thrust reaching 10 N/MW. Figure 13a). Electron density, Figure 13b). Electron Figure 13c). Ion energy contours. n e , contours. temperature, T e , contours. Figure 14a). Thrust vs gas feed for Figure 14b). Exhaust velocity vs gas feed for powers of 0.25 to 7 MW. powers of 0.25 to 7 MW. *Corresponding author, [email protected] 9

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Missions We describe two missions, one to place a 1-m telescope at 550 AU where it can use the sun as a gravitational lens to image exoplanets and the second to deliver a 1 MT payload to Alpha Centuri. 5.1. 550-AU mission The 550-AU mission will carry a camera and other instruments to a distance of 550 AU (and beyond) from the Sun. At that distance, unique interstellar and solar system observations can be conducted. Using the Sun as a gravitational lens for imaging exoplanets is the one considered here. Conventional rocket technology would result in a 30-year transit to 550 AU; data collection would start in 2060. Using the Direct Fusion Drive (DFD), the transit time to 550 AU would be 13 years. Even accounting for development time, data collection will start 15 years earlier than with conventional technology, in 2045 rather than 2060. In transit and on arrival, the DFD would provide a megawatt of power for science, communication, and station-keeping. Furthermore, DFD allows a much smaller launch vehicle to be used, reducing mission costs substantially. The mission objectives include the objectives of the Innovative Interstellar34 and the 550 AU mission.35,36 One instrument is an infrared telescope capable of looking back toward the Sun to assess the solar system dust that causes IR extinction as we look outward from Earth. It was too heavy for the Innovative Interstellar Explorer mission. The instruments are given in Table 2. The Exoplanet Imaging instrument would be a 1-m telescope with a large focal plane with a 0.4° field-of-view. The baseline communications system is a 40-GHz, Ka-band system with a 4-m-diameter transmit dish and 500-kW power. The data rates as a function of distance are shown in figure 15, sufficient to return a 1080p HDTV image every 6 seconds. (A 1-µ laser could increase the data rates 100-fold.) Table 2. Instrument packages.37 The power is that necessary to operate the instrument, not for communications. Acronym Instrument Mass (kg) Power (W) Data rate (bps) MAG Magnetometer 8.81 5.30 130.00 PWS Plasma wave sensor 10.00 1.60 65.00 PLS Plasma parameters 2.00 2.30 10.00 EPS Energetic particle spectrometer 1.50 2.50 10.00 CRS-ACR/GCR Cosmic-ray spectrometer: anomalous and 3.50 2.50 5.00 galactic cosmic rays CRS-LoZCR Cosmic-ray spectrometer: 2.30 2.00 3.00 electrons/positrons, protons, helium CDS Cosmic dust sensor 1.75 5.00 0.05 NAI Neutral atom detector 2.50 4.00 1.00 ENA Energetic neutral atom imager 2.50 4.00 1.00 LAD Lyman-alpha detector 0.30 0.20 1.00 EXOI Exoplanet Imager 20 100 3 x 106 IRD Infrared camera for solar system dust 10 100 3 x 106 Total resources 35.16 229.40 6 x 106 The exoplanet telescope focus extends semi-infinitely. A 1-meter telescope, with coronagraph components, could resolve 3-km features on a planet 30 parsecs away. The light from the exoplanet appears as a ring around the sun, whose disc of light is blocked. There are many complexities38 to the data analysis: pointing; focal properties of the sun are different in the radial and azimuthal directions; signal to noise; the exoplanet moves across the field of view; etc. The spacecraft is translatable perpendicular to the focal length vector to produce an image. High-spectral-resolution spectroscopic data is available for every 3-km pixel. The unprecedented spectral resolution allows LANDSAT-like characterization of the exoplanet surface. Geological and material features of the 3km x 3km areas can be determined. Weather patterns can be tracked in real time. If the target exoplanet were Earth, the extent of industrial and agricultural use would be available for each 3km x 3km area. *Corresponding author, [email protected] 10

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Figure 16. Example of what the telescope Figure 15. Data rate for a Ka-band communication system. might be capable of resolving from 30 parsecs.39 A list of select spacecraft specifications is shown in Table 3. The fuel mass does not include that for the outgoing spiral. The “efficiency” is the fraction of power that goes into thrust; the fuel “tank fraction” is the ratio of its mass to that of the fuel. Once the spacecraft departs from Earth, it takes 13 years to reach 550 AU. The same spacecraft could be put into solar orbit at 550 AU in 18 years. The additional time is due to deceleration. Orbiting at 550 AU could not be done with a solar sail or laser light sail. Launch windows for gravity-assisted missions can be decades apart while a direct flight does not require any particular launch window since it does not employ any flybys of the planets. It can be launched as soon as it is ready. Figure 17 shows a transfer (flyby) trajectory. The Earth departure spiral requires 400 kg of fuel from an ISS orbit and is shown in Figure 18. The spacecraft total mass of 5282 kg is low enough to be launched on any currently available launcher, as shown in Table 4. The spacecraft is in the inner radiation belt for 11.7 days. Achieving the spacecraft performance values listed in Table 3 will be challenging. The specific impulse corresponds to 2.6 keV deuterons. In the lab40 magnetic nozzles have produced only ~100 eV ions, though at considerably lower power (density) than the DFD. Higher I studies would require kinetic codes rather than sp fluid ones because of the reduced collisionality. Table 3. Select spacecraft specifications for the 550 AU flyby mission. Parameter Value Units Final position 555.6 AU Final velocity 479.1 km/s Final time 13.0 yr Fuel 3217.6 kg Mass Total 5282. kg Mass Engine 1700. kg Mass Payload 300. kg Exhaust Velocity 510. km/s Power 1.7 MW Thrust 4.0 N Specific power 1.0 kW/kg Efficiency 0.30 Tank fraction 0.02 Figure 17. Flyby trajectory parameters.41 *Corresponding author, [email protected] 11

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Table 4. Launch vehicles to put spacecraft into LEO. 1 Family Launch Vehicle LEO (kg) ISS (kg) 0.5 Atlas 401 9800 8910 411 12030 10260 0 431 15260 13250 501 8210 7540 -0.5 511 11000 10160 -1 531 15530 14480 551 18850 17720 -1.5 Delta IV Medium 9190 8510 -2 Medium+ (4.2) 12900 12000 -2.5 Medium+ (5.2) 11060 10220 -3 Medium+ (5.4) 13730 12820 Heavy 28370 25980 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 x (km) 105 Falcon 9 Block 1 9000 8500 Figure 18. Earth departure spiral.41 Block 1.1 13150 12420 5.1.1. Spacecraft Design The spacecraft design is shown in figure 19. The 4-m-dia Ka-band high gain antenna dominates the spacecraft. A single DFD engine is used. While a second engine would give the system some redundancy, it may be better just to fly two spacecraft. For other missions, multiple engine modules offer strong benefits, noted later. The solar panels are for the spacecraft LEO checkout phase. The deuterium (propellant) tank is the larger of the two and is cryogenic. It has a cryo-cooler to recirculate boil-off. Helium-3 is stored as a gas in the smaller tank. The antenna, small blue vertical panels) and radiators (large black horizontal panels) are deployable. Figure 19. Spacecraft design. The large tank is for liquid D, the smaller tank is for gaseous helium-3. 5.2. An interstellar mission Interstellar missions require much longer burn durations, and higher I and specific power than the 550 sp AU mission. Figure 20 shows the rendezvous distance as a function of specific power and thrust for a 325-year- duration mission. The power is fixed at 100 MW. The exhaust velocity is found by solving the power equation, 2𝜂𝑃 𝑢 = (1) ! 𝑇 where 𝜂 is the power to thrust efficiency, ~ 0.3. Figure 21 shows the same but for a flyby. The maximum distance at each specific power is achieved for different thrust levels. At low specific powers, higher thrusts send the spacecraft further. This is not true at high specific powers. At a specific power, the maximum distance is achieved with 4 N thrust, not 8 N. There will be an optimal thrust for every duration and specific power. The exhaust velocity assumed is a sizeable fraction of that of the full energy of the fusion products. The distance as a function of time for intercept is 𝑚 𝑚 𝑚 𝑚 𝑚 𝑑 =𝑢 𝜏− ! 𝑙𝑜𝑔 1− 𝜏 (1− )− 𝑡 − ! 𝑙𝑜𝑔 1− 𝑡 +𝑡 −𝜏 +𝑣 𝜏 (2) ! 𝑚 𝑚 𝑚 ! 𝑚 𝑚 ! ! ! ! ! ! *Corresponding author, [email protected] 12 )mk( y 105 35.4 day 39.3 day 43.3 day 47.2 day

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where 𝑚 is the mass at switch time, 𝑚 is the mass flow rate, 𝑢 is the propellant exhaust velocity, 𝜏 = 𝑡 −𝑡 , ! ! ! ! 𝑚 = 𝑚 − 𝑚𝑡 , and 𝑣 is the velocity at switch time, ! ! ! ! 𝑚 𝑣 =𝑢 𝑙𝑜𝑔 1 − 𝑡 (3) ! ! 𝑚 ! ! The switch time is found from the quadratic equation 𝑡!−2𝛾𝑡 +𝛾𝑡 =0 (4) ! ! ! where 𝛾 = !! . The solution for 𝑡 that is less than 𝑡 is the correct solution. ! ! ! Figure 20. Rendezvous distance in 325 years for Figure 21. Flyby distance after 325 years of different thrusts and specific powers.41 constant thrust.41 Entry into the star system is similar to entry into a planetary orbit within the solar system. The approach geometry is shown in figure 22. The final orbit adjust maneuver is shown in figure 23. By the time such a mission is launched, accurate information about planetary orbits should be available so that the maneuvers can be planned in advance. Once in orbit the spacecraft would have up to 100 MW of power to transmit data back to earth. The data rate from interstellar space using a 95 MW laser transmitter is shown in figure 24. Alpha-Centauri Orbital Plane B 1.5 From Earth 1 Thrust 0.5 Normal to Orbital Plane 0 VFP A −0.5 ! = 17 deg −1 VFP Orbit Lowering Maneuver Final Orbit, 1 AU −1.5 Distance at Orbit Plane Insertion −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 Figure 22. Approach to Alpha-Centuri.41 Figure 23. Final orbit adjust.41 If the engine burns for 500 years it could go further, reaching Alpha-Centauri, with specific power of 25 kW/kg, in 500 years. This is shown in figure 25 for a rendezvous. Currently our best estimates of attainable specific power are from 0.3 to 1.5 kW/kg, woefully inadequate for these missions. To achieve the high numbers in these plots would require a number of revolutionary improvements, such as: *Corresponding author, [email protected] 13

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• Replace the Brayton cycle heat engine with a method of direct conversion from x-rays and waste heat to radio-frequency power. Direct conversion of heat to electricity is done now but is only about 5% efficient. Direct conversion of x-rays is done in x-ray machines but the efficiency is very low. • Use DFD staged modules - consume then jettison. This is similar to chemical rockets today, with the significant difference that all remaining DFD modules provide thrust until they and their propellant tanks are jettisoned. The performance improves with the logarithm Figure 24. Data rate from interstellar space for of the mass of the extra stages.42 Employing 100 a 95-MW transmitter. DFD units, a flyby of Alpha-Centuri within 350 years is then achievable at a specific power of 5 kW/kg, an improvement compared to requiring 30 kW/kg for a single 100 MW DFD, as depicted in figure 21. • Make superconductors that can last 300-500 years in the face of neutron bombardment. • Make superconductors that retain their superconducting properties at higher temperatures, to reduce the need for cryo-coolers. • Lower mass structures. • Increasing 3He supply, perhaps by T-suppressed D-D fusion reactors. The currently available 3He supply is (x1000) inadequate for a 100-MW-power, 300-year mission. Closed cycle method for recycling propellant/coolant during electrical power generation mode of • operation, to reduce the system mass. Figure 25. Rendezvous distance after 500 years.41 Figure 26. Mass of a 100 MW power plant as a function of specific power.41 Figures 27 and 28 show example trajectories for the 325-year rendezvous and flyby missions. The parameters for these cases are: a constant thrust of 4 N; a specific power of 100 kW/kg; engine power of 160 MW; and an exhaust velocity of 24,000 km/s. Note the switch time is beyond the halfway point as the spacecraft continues to become less massive. Using multiple engine modules, and jettisoning them and empty propellant tanks along the way, could reduce the required specific power a factor of 10 while keeping the trip duration and payload the same. These jettisoned modules could act as relay stations for communications, increasing the data rates enourmously. *Corresponding author, [email protected] 14

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Figure 27. Sample flyby trajectory for T = 4 N.41 Figure 28. Sample rendezvous trajectory for T = 4 N.41 6. Summary The physics basis for low-radioactivity, FRC fusion reactors has steadily grown over the last two decades, with innovative contributions from theory, modeling, and experiments. Importantly, stability limits, once thought to be a major issue, have been exceeded by a factor of 105 and energy confinement quality, seen in experiments and measured by the ratio of β to plasma thermal conductivity χ, is a factor of 10 better than in the mainline fusion reactor designs. Scaling predictions to hotter FRC plasmas is favorable. More recently, attention has been given to technical and engineering aspects, such as reducing the weight of subsystems, increasing electrical efficiency, and identifying components with high resistance to radiation damage. From this foundation, we extrapolate to a Direct Fusion Drive rocket engine that would permit high scientific-return interstellar research missions in the 2030 time frame, provided advances are made in achieving fusion and producing the predicted thrusts and specific impulse levels. A DFD-powered spacecraft could be used for the 550-AU gravitational lensing mission. An Alpha Centauri flyby and orbital mission would require a ten- fold increase in mission duration and place far more difficult demands on the technical components. DFD has the potential to reduce the cost and increase the scientific return for most solar system robotic missions and human missions to nearby planets. The paper illustrates, once again, the critical relationship between specific power and mission performance. The current estimated DFD specific powers are between 0.3 and 1.5 kW/kg. Far higher specific powers are desired for missions to other star systems, ones that will also require much better methods of recycling waste energy and components that are far less sensitive to neutron irradiation. Near-term work includes the completion of the PFRC-2 ion heating experiment, detailed mission analysis, and subsystem designs for the engine components. Design work on higher efficiency RF heating systems and on superconducting magnets is underway. Design of PFRC-3 will begin once the ion heating experiments are complete. This will be about 50% larger than PFRC-2 and aims at higher plasma temperatures and pressures. The succeeding facility, the PFRC-4, is aimed at demonstrating fusion power generation with D- 3He. Additional work will be done on the integration issues of multiple engine modules, including the effect of one engine’s field on another. A critical point is that the engineering challenges in the DFD design, though large, are greatly reduced, compared to all previous fusion rocket engine concepts, because of its small, clean, steady- state, and high-β modular nature. The DFD design allows ambitious missions throughout and outside the solar system. Direct Fusion Drive has the potential to revolutionize space exploration. Near term research and development aim to move the technology to operational status by 2030. This work was supported by the US Department of Energy Contract No. DE-AC02-76-CHO-3073 and NASA grant NNX16AK28G. *Corresponding author, [email protected] 15

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