Achieving the required mobility in the solar system through Direct Fusion Drive
AAchieving the required mobility in the solar system through Direct FusionDrive
Giancarlo Genta and Roman Ya. Kezerashvili , , , Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy Physics Department, New York City College of Technology, The City University of New York,Brooklyn, NY, USA The Graduate School and University Center, The City University of New York,New York, NY, USA Samara National Research University, Samara, Russian Federation (Dated: March 2, 2020)To develop a spacefaring civilization, humankind must develop technologies which enable safe,affordable and repeatable mobility through the solar system. One such technology is nuclear fusionpropulsion which is at present under study mostly as a breakthrough toward the first interstellarprobes. The aim of the present paper is to show that fusion drive is even more important in humanplanetary exploration and constitutes the natural solution to the problem of exploring and colonizingthe solar system.
Nomenclature I s specific impulse m mass m i initial mass m l mass of payload m p mass of propellant m s structural mass m t mass of the thruster m tank mass of tanks t time t d departure time v e ejection velocity F thrust J cost function P power of the jet α specific mass of the generator γ optimization parameter∆ V velocity incrementDFD Direct Fusion DriveIMLEO Initial Mass in Low Earth OrbitLEO Low Earth OrbitLMO Low Mars OrbitNEP Nuclear Electric PropulsionNTP Nuclear Thermal PropulsionSEP Solar Electric PropulsionSOI Sphere of InfluenceVEV Variable Ejection Velocity I. INTRODUCTION
To develop a spacefaring civilization, humankind must develop technologies which enable safe, af-fordable and repeatable mobility through the solar system. Half a century ago (the last year we werecelebrating the 50 th anniversary of the first human landing on the Moon) we have proven that the tech-nology then (and today, since little has changed in this field in the last 50 years) available was barelysufficient to reach the closest celestial body, – the Moon, for a number of flag and footprint missions. a r X i v : . [ phy s i c s . pop - ph ] F e b Although never yet attempted, it is possible to assess that the same technology can allow to performsome preliminary human missions to Mars [1, 2].Although it is well known that to really explore and colonize the closest celestial bodies a wide range oftechnologies need to be developed [3] – technology to exploit in-situ resources, to protect the astronautsfrom radiation, to build manufacts on the destination planet, etc. – new technologies directly related topropulsion are required. In particular, it is essential to use nuclear energy instead of chemical energy topropel spacecraft.Both alternatives of Nuclear Thermal and of Nuclear Electric Propulsion (NTP and NEP) based onnuclear fission reactions have been studied in detail, and the former was already bench tested with verysatisfactory results. NTP and NEP can allow to improve our chances of performing human missions toMars and beyond by reducing the travel time (and thus the exposure of the crew to cosmic radiation) whileat the same time reducing the Initial Mass in Low Earth Orbit (IMLEO) and thus making interplanetarymissions more affordable. An interesting comparison between the NTP and chemical approach to ahuman Mars mission is reported in the NASA Design Reference Architecture 5 (DRA5) [3, 4].Also NEP allows a notable improvement with respect to chemical propulsion, and the choice betweenthe two mentioned nuclear approaches depend mainly on political decisions about which technology todevelop to a sufficient Technology Readiness Level. Both the mentioned nuclear approaches are based onfission nuclear reactions [5].Recent advances in light weight structures and thin film solar cells make it possible to think of usingSolar Electric Propulsion (SEP) also for human planetary missions and in particular for the first humanmissions to Mars. This is a sort of ’bridge’ solution to improve the performance of interplanetary space-craft above those of chemical propulsion, while waiting that the technology for NTP or NEP becomesavailable. By comparing the performance of SEP with that of chemical propulsion and NTP, the advan-tages in terms of IMLEO are clear, while with respect to NEP they depend only on the specific mass ofthe generator α , which in the short term is more favorable for solar arrays than for nuclear generators. Ina longer term, the latter will be much better, but developing SEP means developing high power electricthrusters for human missions so that they will be ready when lightweight nuclear generator will becomeavailable.At any rate there is no doubt that to become a real spacefaring civilization we must develop rocketengines based on nuclear fusion [6, 7]. The idea to use fusion power for spacecraft propulsion has a longhistory [8]. For the fusion propulsion there are two alternatives:similar to NTP and fusion NEP. In thelast 20 years many studies have been devoted to the development of fusion nuclear power in general –mostly for general power generation – and specifically of fusion nuclear rockets. Fusion NEP requiresthe development of lightweight fusion reactors, which is something that today appears to be a difficultachievement. Moreover, also here the point is again just the specific mass of the generator α , and manyyears will pass before fusion generator will have a better value of α than fission generators [9] – apartfrom the fact that today no fusion generator, even with a very high α , is available. In fusion NEP, thelower is the value of α , the higher is the optimum value of the specific impulse, so even when a lightweightgenerator will be available, much work will be required also for improving the electric thruster.The revolutionary Direct Fusion Drive (DFD) is a nuclear fusion engine and its concept is based onthe Princeton field-reversed configuration reactor, which has the ability to produce thrust from fusionwithout going through an intermediary electricity-generating step [10]. The engine development is relatedto the ongoing fusion research at Princeton Plasma Physics Laboratory. The DFD uses a novel magneticconfinement and heating system, fueled with a mixture of isotopes of helium and hydrogen nuclei, to pro-duce a high specific power, variable thrust and specific impulse, and a low-radiation spacecraft propulsionsystem. The simplest type of fusion drive is using small uncontrolled thermonuclear explosions to pushforward the spacecraft, as was planned in the Orion Project [5], but even if a continuous, controlledreaction is used, DFD seems to be much easier to realize and D − He direct fusion thrusters seem to bethe thrusters which will allow to colonize, in the medium term, the solar system.While most of the studies related to DFD deal with missions to the outer solar system or the nearinterstellar space, the aim of the present paper is studying in some detail fast human missions to Marsand to the Asteroid Belt. The result is that nuclear fusion propulsion is the enabling technology to startthe colonization of the solar system and the creation of a solar system economy.The paper is organized in the following way: In Section II we describe the thruster and its maincharacteristics. Section III is devoted to considerations of three cases for the Earth – Mars mission:i. the ideal variable ejection velocity (VEV) operations; ii. limited VEV operations; iii. slow cargospacecraft mission. The mission to 16 Phyche asteroid is considered in Section IV, and finally conclusionsare given in Section V.
II. THE THRUSTER
The solar system exploration and beyond, from robotic space voyages to manned interplanetary mis-sions, requires high-thrust, high-exhaust velocity engines. Our experience suggest that any engine engi-neered should be based on the well-understood physics of today. The emphasis on known physics andaffordability limits the scope still further to nuclear processes: fission and fusion. However, both fission-and fusion-based propulsion schemes, are well understood and realizable at power levels, while at thesame time the mass of fuel, propellant, structure, and shielding severely limit their space flight capabil-ities. A survey of rocket-engine performance for solar system missions beyond the Moon-Earth systemhas compared chemical and nuclear fission and fusion power sources [11]. One conclusion reached isthat chemical rockets have reached their practical limits, epitomized by long-duration, low-payload-massmissions. A corollary is that nuclear power will be needed for more ambitious missions [12].A nuclear fission reactor is used in a rocket design to create Nuclear Thermal Propulsion. In an NTProcket the type of nuclear reactor, is ranging from a relatively simple solid core reactor up to a much morecomplicated but more efficient gas core reactor. The fission reactions are used to heat liquid hydrogenwhich flows around the fission region inside a reactor and absorbs energy from the fission products. Hightemperature heating turns liquid hydrogen into ionized hydrogen gas, which is then exhausted througha rocket nozzle to generate thrust. As an alternative, the propellant can be heated directly by thefission fragments, like in the thruster proposed by Carlo Rubbia [13]. The specific impulse produced isproportional to the square root of the temperature to which the working fluid is heated. The hydrogenpropellant typically delivers specific impulses on the order of 850 to 1000 seconds, which is about twicethat of liquid hydrogen-oxygen chemical rocket. A second possible method, which relays on nuclearfission to generate propulsion, known as Nuclear Electric Propulsion, involves the same basic fissionnuclear reactors. Heat extracted from a fission chain reaction is converted into electrical energy whichthen powers an electrical engine. One should mention that electric specific impulse thrusters typicallyuse much less propellant than chemical rockets because they have a higher. Therefore, in both cases,the rocket relies on nuclear fission to generate propulsion. The nuclear fission propulsion is limited bythermal inefficiencies and that fusion could provide more and better mission options because of its higherpower conversion efficiency and higher energy-content fuel [11].Fusion reactions produce much more energy than fission processes. Usually one of the components ofthe fusion reaction is protium (hydrogen atom without any neutron), deuterium (hydrogen atom withproton and neutron), or tritium (hydrogen atom with proton and two neutrons). The other componentwhich involves into the fusion process of light nuclei can be deuterium, isotopes of helium, He or He,and isotopes of lithium, Li and Li. In fusion reactors use the energy released by the fusion of lightatomic nuclei. Let us focus of the fusion processes in the deuterium–deuterium (D–D), deuterium–tritium(D–T) and deuterium– He (D– He) plasma.The D–D plasma admits the following primary reactions:D + D = He (0.82 Mev) + n (2.45 Mev) + 3 .
25 MeV, (1)D + D = T (1.01 Mev) + p (3.03 Mev) + 4 .
04 MeV. (2)In Eqs. (1) and (2) the values in parenthesis are the energy of that particular fusion product. The D–Tplasma admits both deuterium–deuterium reactions (1) − (2) and deuterium–tritium processes. Theprimary energy reactions in the D–T plasma in addition to (1) and (2) are the following:D + T = He (3.52 Mev) + n (14.06 Mev) + 17 . He (3.52 Mev) + 2 n + 11 . ∼
40 keV (about 5 × K).The fusion reaction of nuclei of tritium and deuterium is the most promising for the implementationof controlled thermonuclear fusion, since its cross section even at low energies is sufficiently large [14].However, the problem of the contamination due to the neutron emission in the primary processes stillexists. Although the D–D fuel burning is also accompanied by a neutron flux, they are weakened incomparison with the D–T process (3).Now let us consider the reaction that are admitted in D– He plasma. The primary processes whichoccur in D– He plasma are the aneutronic fusionD + He = He (3.52 Mev) + p (14.7 Mev) + 18 .
34 MeV (5)and reactions (1) and (2) that involve the D–D fusion. One should mention that reaction (5) is thesecondary process in the D–T plasma. Due to the D–D fusion, the D– He plasma also includes undesiredneutron channel (1). The two branches of the D–D fusion reaction produce He and tritium. Theonly neutrons produced are medium-energy neutrons (2.45 MeV). If the produced He (Helium-3) is notremoved, it will react with deuterium producing charged particles protons and He with no additionalneutrons. On the other hand, if the produced tritium is not removed, it will react with deuteriumproducing 14.1 MeV neutrons. However for the D – He plasma with equal deuterium and Helium-3densities, the fraction of the fusion energy carried by neutrons from the D–D reaction is 1/3 [12, 15].The undesired tritium produced via reaction (2) will increase the neutron flux due to reactions (3) and(4), which are secondary for D– He plasma. In Refs. [16, 17] a method of tritium removal from theplasma before it can fuse has been proposed. Removing tritium produced by D–D fusion and recyclingpart of it after it decays to Helium-3 isotope significantly reduces the fraction of fusion energy carriedby neutrons in a D–D system [17]. The latter results in significant lifetime enhancement of structuralmaterials. In summary, the main reactions in D– He fusion produce far fewer neutrons than D–D fusion.Consequently, a lower mass of shielding materials is required, which will reduce the total mass of thestructure. Calculations show that for obtaining useful energy the temperature of ions in a plasma for theD + D reaction should be about 10 K and for the D + T reaction about 10 K [18].The experimental study of the D– He plasma led to the proposal of a new kind the fusion-based thruster- the Direct Fusion Drive (DFD), which has field-reversed configuration (FRC) reactor for an originalplasma-formation. The FRC employs a linear solenoidal magnetic-coil array for plasma confinement andoperates at higher plasma pressures. One should note that several FRCs [19–22] have achieved stableplasmas. The DFD employs the radiofrequency technique called rotating magnetic field (RMF) to formand heat plasma. An important figure-of-merit for fusion reactors is β , the ratio of the plasma pressureto the magnetic energy density. The innovative radiofrequency RMF method, which heats particles andallows the size of the FRC to be relatively small was suggested in Ref. [23]. In Refs. [10, 12, 15, 24] wasconsidered a compact, anuetronic fusion engine, which enables more challenging exploration missions inthe solar system and beyond. The DFD concept is result of the Princeton Field-Reversed ConfigurationReactors which employ heating method invented by S. Cohen. The Scrape-off Layer (SOL) of the DFDis quite different than that of any other fusion device. The energy is deposited in the SOL directly fromthe D– He fusion products via a non-local process and is predominantly transmitted to the electronsvia fast-ion drag. The random thermal energy in the SOL electrons is transferred to the cool SOL ionsthrough a double layer at the nozzle and via expansion downstream, thus being converted into directedflow of a propellant fluid. The heat transport into SOL is described by Fick’s law [25], by the localflux-surface-normal gradient in pressure. In Refs. [10, 26] is used a fluid model for the SOL betweenthe gas box with the propellant and the nozzle and dependencies of the thrust and specific impulse ongas input flow for powers of 0.25 to 7 MW transferred to the SOL are studied. The calculations areperformed using UEDGE [27] fluid-code for simulations. Results of these simulations for the propellantgas input 0.08 g/s yields to the data given in Table I. The nuclear fuel for such a thruster is D– He andthe propellant fluid is atomic or molecular deuterium, which is heated by the fusion products and thenexpanded into a magnetic nozzle, generating an exhaust velocity and thrust. Adding propellant to thisflow results in a variable thrust, variable specific impulse exhaust through a magnetic nozzle. The thrustof the DFD depends on the input gas flow and varies from about 4 N for the power 0.25 MW to 60 N,
TABLE I: DFD propulsion parameters based on UEDGE Model spacecraft based on the DFD studies in Refs.[10, 26, 35] Total Fusion Power, MW 1 1 . I s , s 10 ,
000 12 ,
000 12 , T, N 8 10 11Fusion Efficiency 0 . − . . − . when the power is 7 MW. The results of simulations show that when the gas input flow increases from0.08 to 0.7 g/s the thrust increases from 4 N to 60 N. For the specific impulse the preferable gas feedfor the power 0.25 MW to 7 MW is 0.08 – 0.3 g/s [10, 26]. Approximately 35% of the fusion power goesto the thrust, 30% to electric power, station keeping and communication, 25% lost to heat, and 10% isrecirculated for the radio frequency heating. The current estimated DFD specific powers are between0.3 and 1.5 kW/kg [10]. One could considered as a conservative estimate the power to thrust efficiency,about 0.3 – 0.5.A full-sized D– He fusion reactor is perfectly suited to use as a rocket engine for two reasons:i . the configuration results in a radical reduction of neutron production compared to other D– Heapproaches;ii. the reactor features an axial flow of cool plasma to absorb the energy of the fusion products.In other words, the cool plasma flows around the fusion region, absorbs energy from the fusion products,and then is accelerated by a magnetic nozzle.The ratio of the total mass of fuel and propellant to the mass of He is about 670 and to get a specificpower 0.18 kW/kg the small amount of He is needed – about 0.53 kg. The most Helium-3 used inindustry today is produced from the radioactive decay of tritium. Tritium is a critical component ofnuclear weapons and it was produced and stockpiled primarily for this. At present, Helium-3 is onlyproduced as a byproduct of the manufacture and purification of tritium for use in nuclear weapons. Themain source of Helium-3 in the United States is the federal government’s nuclear weapons program [28].There are extraterrestrial sources of He. Materials on the Moon’s surface which contains Helium-3 atconcentrations between 1.4 and 50 parts-per-billion in sunlit and shadowed areas [29–31]. There is maybe Helium-3 on Mars also [32]. The analysis of fusion fuel resource base of our solar system is given inRef. [33].A spacecraft driven by a fusion thruster was studied at the turn of the century by NASA: its goal wasto perform a human mission to Jupiter or Saturn as described in the Movie 2001, a Space Odyssey. Thespacecraft was aptly named Discovery II [34]. The main characteristics of the thruster (in the versionfor the Saturn mission) which were obtained in that study were: specific impulse I s = 47,205 s andspecific mass of the propulsion system α = 0.00016 kg/W and are listed in Table II. These values are veryfavorable indeed. DFD, with a specific impulse in the range of 10,000 to 20,000 seconds and a specificpower about 1 kW/kg, is suitable for almost any interplanetary mission. In NASA solicitation for rapid,deep space propulsion, four candidate missions were identified: Mars, Jupiter, Pluto, and 125 AU for aninterstellar precursor mission. In Ref. [35] has sized a DFD engine for each candidate mission. The maincharacteristics of the spacecraft are reported in Table I. A more recent study for a DFD driven spacecraftis reported in Ref. [10]. Although showing a small spacecraft aimed at the focal line of the gravitational TABLE II: Main characteristics of the Discovery II and a spacecraft based on the DFD thruster studied in Ref.[10] Spacecraft Discovery II DFD [10]Specific impulse I s , s 47,205 23,000Specific mass of the propulsion system α, kg/W 0.000116 0.0018 lens of the Sun and an interstellar probe aimed at Alpha Centauri, the basic values there reported fora 2 MW fusion rocket can be considered as a conservative estimate for a larger unit aimed to power aninterplanetary piloted spacecraft. III. EARTH – MARS MISSIONA. Ideal Variable Ejection Velocity operations
In our consideration of the Earth – Mars mission we use the parameters for the DFD thruster givenin Table II. As it was shown by the authors in a previous paper [36], a thruster with such a high specificimpulse and low specific mass must operate in a continuous thrust mode. A first study of an Earth-Marstransfer was performed assuming that it can operate in an optimal (unlimited) Variable Ejection Velocity(VEV) conditions. The study was performed using the IRMA 7.1 computer code [37] with the followingdata: launch opportunity: 2037; specific mass α = 1 .
25 kg/kW; overall efficiency η = 0 .
56; tankage factor k tank = 0 .
10; height of circular starting LEO: 600 km; height of circular arrival LMO: 300 km.The optimal trajectory for a 120 days Earth-Mars journey starts 66.6 days before opposition, spends 8.4days spiraling about Earth, 105.8 days in interplanetary space and finally 8.4 days spiraling about Marsto reach the final LMO. The mass breakdown and the jet power are reported in Table III, second column.Notice that the ratio between the installed power and the vehicle mass is of the order of magnitude ofthat of a modern small car, showing that traveling fast in the solar system does not require enormousamounts of power!The optimum specific impulse is shown in Fig. 1. The specific impulse ranges between 1,790 s at startand 60,250 s at midcourse, which is 60 days after starting.
B. Limited Variable Ejection Velocity operations
The minimum and the maximum values of the specific impulse are certainly beyond the possibilitiesof the thruster, so the computation was repeated limiting the specific impulse between 9,900 and 12,000s. In this case the optimal strategy is increasing the duration of the planetocentric phases (the specificimpulse is higher than the optimal one in these phases, and keeping their duration at the optimal valueof the unlimited case would result in an unacceptable increase of the jet power) and introducing a coastarc at the interplanetary mid course, introducing a bang-bang regulation of the thruster.The orbit-to-orbit bacon plot is reported in Fig. 2: at equal transfer time the payload mass fractionis slightly lower and thus to maintain the same payload fraction a slightly longer travel time has to beaccepted.
TABLE III: Timing and mass breakdown of the missions studied in the present paper.Destination Mars PsycheType Unlimited Limited fast Limited cargo t d (days) 66.6 71.9 189.9 120 t t (days) 120 123 350 250 t (days) 8.4 20.6 94.5 27.6 t (days) 105.8 96.0 219.2 222.3 t (days) 5.8 6.4 36.3 0.1( m l + m s ) /m i m p /m i m t /m i m tank /m i P jet /m i (W/kg) 75.62 175.35 40.09 134.60 FIG. 1: (Color online) Time history of the Specific impulse during a 120 days Earth – Mars transfer.FIG. 2: (Color online) Bacon plot, i.e. the contour plot of the surface ( m l + m s ) /m i as a function of t d and t tot ,for an Earth – Mars transfer. A slightly longer transfer time, t t = 123 days, is chosen. The trajectory starts 71.9 days beforeopposition. The mass breakdown and the jet power are reported in Table III, third column. Thetrajectory is shown in Fig. 3, while the time histories of the acceleration, the ejection velocity, the thrustand the power of the jet are shown in Fig. 4The limitation of the minimum exhaust velocity reduces the propellant consumption but causes anincrease of the installed power and thus of the mass of the thruster. The overall result is a decrease ofthe payload mass at equal total journey time. C. Slow cargo spacecraft
A slow cargo ship able to carry to Mars large payloads in an inexpensive way can also be built with thistechnology. Assuming a travel time of almost one year (namely 350 days) and starting from Earth orbitabout 190 days before the opposition, the results reported in in Table III, fourth column are obtained.The payload and structures mass fraction is quite high, above 70% (namely 0.715), which means that
FIG. 3: (Color online) Earth – Mars trajectory for the fast crew spacecraft.FIG. 4: (Color online) Time histories of the acceleration, the ejection velocity, the thrust and the power of thejet during an Earth-Mars journey − fast crew spacecraft. using a single superheavy launcher able to carry 130 t in LEO, a cargo of about 93 t (minus the structuralmass) can be carried into LMO.Also the power of the jet is quite small, of about 40 W/kg (referred to the IMLEO). IV. MISSION TO 16 PSYCHE ASTEROID
Asteroid 16 Psyche, which belongs to the asteroid belt, is a metal asteroid extremely rich in nickel andiron, but also in gold. NASA plans a mission to survey this asteroid which should be launched in Augustof 2022, and arrive at the asteroid in early 2026, following a Mars gravity assist in 2023. The asteroidhas a mass of 1.7 × kg and an average diameter of 226 km.Using the DFD thruster here described a mission to the same asteroid can be performed in a quite shorttime: for instance, using the launch opportunity of 2037 (the opposition is on March 4, 2037) and starting120 days before the opposition, a mission lasting only 220 days can be performed. This figure must becompared with the roughly 3.5 years of the mentioned NASA proposal, based on chemical propulsion andgravity assist. The mass breakdown and the jet power are reported in Table III, last column. FIG. 5: (Color online) Trajectory for a 250 days journey to the metal asteroid 16 Psyche.
The payload and structure fraction is quite high (0.241) and the travel time is low enough to imagineeven a human mission to a metal asteroid of the main belt like 16 Psyche − since the planetocentric partof the trajectory lasts almost one month, a human mission in which the astronauts reach the spacecraftat the exit from the earth sphere of influence would last about 225 days, roughly like most of the humanMars missions presently planned. V. CONCLUSIONS
From the study here performed it is clear that the development of a nuclear fusion rocket engine basedon the D − He technology will allow to travel in the solar system with an ease never before attained,opening almost ’science fiction’ possibilities to humankind.One way travels to Mars in slightly more than 100 days become possible and also journeys to the asteroidbelt in about 250 days After the return to Earth orbit the spacecraft can be refitted and refurbished tomake another travel in the following launch opportunity: a sort of commuting Earth-Mars service aimedat the colonization of the red planet. A spacecraft able to carry 30 t in 120 days or 85 t in 350 days toMars may be launched from the Earth surface with a single superheavy-lift launcher (slightly bigger thanthe Saturn 5 or the Energia). A cargo ship able to carry to LMO the propellant required for the returnjourney and much cargo is also possible.However, the performance of such devices is still hypothetical and the value of its specific mass hereassumed is conservative also taking in mind that this technology has very ample margins for improvements − as an alternative to chemical propulsion which has already reached the limits of this technology. If0a lower value of the specific mass (a higher value of the specific impulse) will prove to be feasible, evenfaster interplanetary spacecraft could become possible.The spacecraft described in the present paper still require much research and development, but it ispossible that they become feasible in less than two or three decades (the launch opportunity here studiedis that of 2037, – 17 years from now), which is a fairly favorable one for Mars, while, on the contrary isnot a very good one for 16 Psyche however with such powerful spacecraft the difference between a ’good’and a ’bad’ launch opportunity is smaller than when using chemical propulsion.If a DFD could be made available in time for the first human Mars missions − as the launch opportunityhere chosen implicitly implies − , the latter would become much easier, safer and affordable than whatis today thought. 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