A Titan mission using the Direct Fusion Drive
AA Titan mission using the Direct Fusion Drive
Marco Gajeri a,b , Paolo Aime a,b , Roman Ya. Kezerashvili b,c,d a Politecnico di Torino, Torino, Italy b New York City College of Technology, The City University of New York, New York, USA c The Graduate School and University Center, The City University of New York, New York, USA d Samara National Research University, Samara, Russian Federation
Abstract
The main purpose of this work is to perform an analysis of realistic new trajectories for a robotic mission toSaturn’s largest moon, Titan, in order to demonstrate the great advantages related to the Direct Fusion Drive(DFD). The DFD is a D - He fuelled, aneutronic, thermonuclear fusion propulsion system, related to theongoing fusion research at Princeton Plasma Physics Laboratory (PPPL) [1]. This fusion propulsion conceptis based on a magnetically confined field reversed configuration plasma, where the deuterium propellant isheated by fusion products, and then expanded into a magnetic nozzle, providing both thrust and electricalenergy to the spacecraft. The trajectories calculations and analysis for the Titan mission are obtainedbased on the characteristics provided by the PPPL [1]. Two different profile missions are considered: thefirst one is a thrust-coast-thrust profile with constant thrust and specific impulse; the second scenario is acontinuous and constant thrust profile mission, with a switch in thrust direction operated in the last phases.Each mission study is divided into four different phases, starting from the initial low Earth orbit departure,the interplanetary trajectory, Saturn orbit insertion and the Titan orbit insertion. For all mission phases,maneuver time and propellant consumption are calculated. The results of calculations and mission analysisoffer a complete overview of the advantages in term of payload mass and travel time. It is important toemphasize that the deceleration capability is one of the DFD game changer: in fact, the DFD performanceallows to rapidly reach high velocities and decelerate in even shorter time period. This capability resultsin a total trip duration of 2.6 years for the thrust-coast-thrust profile and less than 2 years considering thecontinuous thrust profile. The high payload enabling capability, combined with the huge electrical poweravailable from the fusion reactor, leads to a tremendous advantage compared to present technology.
1. Introduction
The emotional desire to explore and challenge the boundaries of our knowledge has allowed us to evolveand make amazing discoveries. As our ancestors searched and discovered new lands so we are exploringthe universe, looking for pleasant answers. Because of its relative proximity, human exploration began withEarth’s natural satellite, taking first men to walk on lunar soil in 1969 [2]. At the beginnings of the sixtiesfirst robotic Mars missions were designed and launched [3–5] focusing to the payload mission capability andmission time. The higher the payload mass, the more scientific instruments can be carried on-board thespacecraft and the more precious scientific data are collectable. This is very important both for robotic andmanned missions, such as those planned for the near future for the Moon and Mars. It would be significant toincrease the payload as much as possible, without excessively extend the journey time. One can say that newpropulsion concept need to be developed in order to colonize our Solar system, overcoming the limitationsrelated to chemical and electric propulsion (CP and EP respectively). In fact, considering current solutions,low power EP systems are affected by long journey time because of the extremely low thrust, even thoughtheir high specific impulse I sp ( ≈ − I sp ≈
450 s) [6], directly dependent on the fuel chemical energy.The main issue for human space exploration is the huge vastness of space, that condemns space travellersto lengthy travel times, forcing the crew to face many problems such as radiation exposure and microgravityconditions. In a long journey in space physiological response to microgravity adaptation has all the featuresof accelerated ageing involving almost all body systems [7]. Surely, before humanity can succeed in a solarsystem manned mission, a great technological advancement will have to be carried out, which must concern
Preprint submitted to Elsevier September,26 2020 a r X i v : . [ phy s i c s . s p ace - ph ] S e p any fields with a particular focus on propulsion. At present, taking for example a Mars mission, round-tripmay take up to three years and research suggests that astronauts could lose close to half their bone massbefore they return [8]. Therefore, it is natural to think about using nuclear energy to propel spacecraft whichcould reach Mars in about half the time of current missions. Using the the Direct Fusion Drive (DFD) [1]one way trips to Mars in slightly more than 100 days become possible [9], while the total mission durationfor exploration of trans-Neptunian objects takes slightly more than eight years [10].The exploration of the solar system requires advanced propulsion techniques capable of specific impulseabove 10 s and specific power in the range 1-10 kW/kg [11]. The idea of using nuclear power for spacecraftpropulsion arises from the high energy density of the fuel and the high velocity of the fusion products, whichresulted into the establishment of the NERVA project by NASA in 1960 [12]. Even today, the researchactivities related to both fission and fusion propulsion systems are in development and they will be able toovercome the limitations tied to classical propulsion systems.Our work focuses on the great advantages related to the Direct Fusion Drive project, that would enablefaster deep space missions. The paper is organized in the following way: in Section 2 is given a briefdescription of the DFD engine, its main characteristics, fuel choice, and the thrust model. The inputcharacteristics for Earth - Titan mission are presented in Section 3. Two different Titan mission profilesare analysed and discussed in Section 4 and 5: i. the thrust-coast-thrust profile; ii. the continuous thrustprofile. Section 6 highlights the differences between the two analysis performed, with particular focus on themission times, propellant consumption and payload. The conclusions follow in Section 7.
2. Direct Fusion Drive
The Direct Fusion Drive is a revolutionary fusion propulsion concept that would produce both propulsionand electric power from a single, compact fusion reactor [13]. The project, funded by NASA, is based onthe overwhelming advantages offered by the ongoing Princeton field reversed configuration (PFRC-2) fusionexperiment at Princeton Plasma Physics Laboratory (PPPL) [14]. The purpose of PPPL research is to findsolutions for the critical scientific and technological problems related to fusion technology. DFD conceptsuits to several kind of space destinations, such as Mars manned and robotic missions, heavy cargo missionsto the outer solar system or the near interstellar space [1, 9, 10, 15].
The PFRC-2 concept employs a unique radio frequency (RF) plasma heating method, known as “ odd-parity heating”, which increases the plasma temperature in order to achieve the proper physics conditionswhich enable the fusion process in a field reversed configuration (FRC) plasma [16, 17]. The FRC is aparticular magnetic field geometry, accidentally discovered in the sixties [18], in which a toroidal electriccurrent is induced inside a cylindrical plasma, creating a poloidal magnetic field. The latter is reversed withrespect to the direction of an externally applied axial magnetic field. This new heating method, inventedby Cohen and Milroy [19], is based on a magnetic field that is antisymmetric about the mid-plane normalto the axis and added to a FRC plasma maintaining its closed field line structure. It was first theorizedin 2000 [19] and demonstrated in 2006 (PFRC-1) [20]. This is a crucial point, because the “open” fieldlines let the plasma to escape and consequently reduce confinement time, which is tightly bound to optimalfusion conditions [21]. The fusion process is magnetically confined in the core, the region inside the magnetic separatrix , which is an imaginary closed surface that demarcates “open” magnetic field lines, those that crossthe device walls, from those that stay fully inside the device. The “open” field line region - also called thescrape-off layer (SOL) - is the region where the cold deuterium propellant is heated by the fusion products.The core needs a strong plasma current perpendicular to the FRC’s magnetic field to form the closedmagnetic-field lines. Otherwise, the configuration will have instability problems and it will destroy itself [22].More specifically, PFRC exploits a rotating magnetic field (RMF o ) with odd-parity symmetry, produced bythe oscillation of the current in four quadrature-phased RF antennae [1]. Two pairs operate 90 degreesout of phase on adjacent sides of the plasma and generate RMF o which is about 0 . −
5% the strength ofthe axial magnetic field. Then, the magnetic field on one side of each 8-shaped antenna has a directionopposite to the other side and closed field lines in the generated FRC keep the plasma trapped when it isheated. Therefore, a toroidal current is induced by RMF o in the plasma confined by the externally-appliedaxial magnetic field. Then, this current induces a poloidal closed magnetic field, which improves the plasma2onfinement. Therefore, RM F o generates the current and heats the plasma ions and electrons [23], leadingto compact devices with excellent stability [24] due to the fact that a small, high-temperature FRC plasma,has less problems against instability than other fusion devices. See Ref. [25, 26] for more details. Fusion of light nuclei produces much more energy per unit mass than fission processes. Usually one ofthe components of the fusion reaction is proton, deuterium or tritium. The other component involved intothe fusion of light nuclei can be another deuterium, isotopes of helium, He or He, and isotopes of lithium, Li and Li. The region where fusion reactions take place in DFD is the high temperature, moderate densityplasma region named the core. The fusion reaction of nuclei of deuterium (D) and tritium (T) is the mostpromising for the implementation of controlled thermonuclear fusion, since its cross section even at lowenergies is sufficiently large [27]. However, due to significant emission of neutron the D − T fuel is not thebest choice for the DFD and aneutronic fuel such as the mixture of the deuterium and helium-3 isotope,D − He, is most preferable. The choice of D − He fuel mixture to produce the D– He plasma is related tothe neutrons production problem. If neutrons are produced from the fusion reactions, a certain amount ofenergy is not usable, leading to not negligible losses of energy, as well as the contamination of a spacecraftdue to the neutrons emission, which should be shielded to protect the spacecraft and crew. Neutrons arehard to “direct” due to the fact that they have no charge and can not be controlled with electric or magneticfields. Therefore, it is essential to reduce the neutron fluxes in order to minimize the damage and activationof nearby materials and structures and consequently the shielding mass.Let us focus on the fusion processes in D– He plasma. Depending on plasma temperature the ignitionof D– He, D − D, and He– He fusion can occur. Therefore the D– He plasma can admit the followinganeutronic and neutron emitted primary reactions:D + He → He + p ( Q = 18 .
34 MeV), (1) → T + 2 p (2) → D + D + p, (3) → Li + γ ; (4)D + D → He + n ( Q = 3 .
25 MeV) , (5) → T + p ( Q = 4 .
04 MeV); (6) He + He → He + 2 p ( Q = 12 .
86 MeV), (7) → D + D + 2 p, (8) → Li + p, (9) → Li ∗ + p, (10) → Be + γ. (11)In reactions (1) − (11) D ( H) and T ( H) are notation for the isotopes of the hydrogen – deuterium andtritium nuclei and the energy liberated ( Q value) for reactions (1), (5) − (7) are given in parentheses. Allprimary reactions in D − He are aneutronic accept the process (5), where 2.45 MeV energy neutrons areproduced. The D − D has two almost equally exothermic channel (5) and (6). The ignition of D − D fusionrequires the plasma temperature about 5 × K. Due to production of tritium (6) in D − D fusion, D − Heplasma admits the secondary fusion processes: deuterium–tritium, tritium–tritium and tritium–helium-3.These secondary processes have the following branches for nuclear reactions:3 + T → He + n ( Q = 17 . → D + D + n, (13) → He + 2 n ; (14)T + T → He + 2 n ( Q = 11 . → D + D + 2 n, (16) → He + n ; (17)T + He → He + D ( Q = 14 . → He + n + p ( Q = 12 . → He + p, (20) → He ∗ + p, (21) → Li + n, (22) → Li ∗ + n, (23) → Li + γ ( Q = 15 . − He fusion involves 3 protons as opposed to 2 with D − T or D–D fusion, the amount of heatrequired for good fusion parameters is about 90 keV. This is about 10 times greater than the amount neededfor D − T fusion. The measurements of the He+ He and T+ He fusion reactions in high-energy-densityplasmas environment were reported recently [28]. It is worth mentioning that the He+ He and T+Treactions are mirror reactions, expected to be governed by similar nuclear physics after Coulomb corrections.In experiments [29, 30] using high energy density plasmas environment were measured the neutron spectrumat very low center of mass energy 16–23 keV. The radiative capture reaction He( He, γ ) Be(11) has abranching ratio ∼ × − and is thus negligible [31]. Among the primary reactions in D– He plasma ourparticular interest is addressed to the process (5), where 2.45 MeV neutrons are produced, and reactions (2)and (6), which are the sources of tritium production. In hot D − He plasma the D–T and T–T fusion admitsreactions (12)–(17), where fast 2–14 MeV useless and undesirable neutrons are emitted. As a result of T– Hefusion the neutrons are emitted in reactions (19), (22) and (23). Undesired neutron contamination is amongthe main risk factors for damaging of spacecraft materials due to a neutron radiation occurs as a result of theinteraction of energetic neutrons with a lattice atom in the material and a crew during a mission. Thus theproblem of the contamination due to the neutron emission in these processes exists if the produced tritiumis not removed to prevent its fusion with deuterium, helium-3 and itself. The tritium removal methods havebeen proposed in Refs. [32, 33]. Also the production of neutrons is reduced by rapidly exhausting tritiumand by altering the fuel ratio to have three times the He as D, favouring the He reactions [13, 34] resultingin a great mass save.The He fuel consumption is very complex to calculate and it depends on multiple factors. We base ourestimate for fuel consumption on values calculated for other missions based on the DFD [15, 35]. The fuelconsumption is calculated by dividing the total fuel consumption by the days of mission and the fusion powerconsidered for the previous studies. In this way it has been found a fuel consumption per day per MW ofpower. This means that, for a 2.5 years mission, under the hypothesis of a 2-MW class DFD engine, themass of He required would be about 0 .
27 kg. This fuel mass value, on a spacecraft of multiple tonnes, canbe neglected for all trajectories calculations. Although the amount of He on the surface of Earth is limited,as discussed in [36], this value is well below the maximum availability in human hands [37]. Moreover, thereis a large source of extractable He (10 kg) on the lunar surface that have been deposited by solar wind formore than 4 · years [38–40]. Researchers at PPPL performed simulations using UEDGE software [41], a 2D multi-species fluid code,in order to model the cylindrically symmetric FRC open magnetic field plasma region of the DFD and find asteady-state self-consistent solution of continuity equations, momentum equations, and energy equations foreach chemical species. This research allows to study the plasma parameters (temperature, density, velocity)4nd power flow within the SOL, each as a function of heating power and gas input [41]. The heated plasmawill expand in a magnetic nozzle, converting its thermal energy into kinetic energy, thus providing thrust tothe system. It works as a physical nozzle, with the difference that the fluid does not directly hit any physicalwall. Researchers at Princeton Satellite Systems (PSS) considered this data to produce a functional modelof the thrust and specific impulse of the engine as a function of input power to the SOL and propellant flowrate. It is essential to underline that the input power into the SOL is only 40-50 % of the total fusion power.If only fusion products were ejected directly from the engine, they would have a velocity of 25 ,
000 km/sproducing negligible thrust [15], but interacting with cool ionized gas in the SOL, the energy is transferredfrom the hot products to the electrons and then transferred to the ions as they traverse the magnetic nozzle.The resulting exit velocity is about 10 m/s, generating a thrust of about 2 . , Table 1: Direct Fusion Drive performance. The characteristics for low and high power configuration are shown [1].
Low power High powerFusion Power, [MW] 1 10Specific Impulse, [s] 8500 - 8000 12000 - 9900Thrust, [N] 4 - 5 35 - 55Thrust Power, [MW] 0.46 5.6Specific Power, [kW/kg] 0.75 1.25Finally, due to the engine compactness, multiple modular DFDs can be combined into a cluster of manyengines, resulting in a total thrust that is the sum of the single thrusts without affecting the I sp .
3. Earth - Titan mission
Trajectory design for low-thrust propulsion systems represents a complex problem. As well known,spacecraft motion is governed by a sensitive system of non-linear differential equations and the inclusion oflow-thrust forces into this system adds complexity to the trajectory determination problem. Therefore, itis convenient to consider the orbit as the evolution of an ellipse for each temporal instant defined by theinstantaneous position and velocity vectors. Low-thrust effect causes the six formerly constant parametersto slowly vary from the Keplerian solution and it is possible to use the Gauss planetary equations to describethese rates of change [42]. It is impossible to analytically evaluate the solution in the general case and theproblem requires numerical methods to be solved. Several approaches are taken into account to furtheranalyse potential trajectories to Saturn-Titan system using the Systems Tool Kit software from AnalyticalGraphics, Inc. The purpose of the research is to study the feasibility of such kind of mission with a 2-MWclass engine and to demonstrate the advantages related to this new propulsion concept. Let us consider thatthe thrust T and specific impulse I sp are constant. The minimum estimated specific power of 0 .
75 kW/kg isselected and the power to SOL is supposed of about 1 MW, resulting in 8 N of T and about 9 ,
600 s of I sp .As a first step impulsive maneuvers are considered, computing the solution for the Lambert problem,determining the impulse that produces the orbit connecting a departure state (initial position and velocity)with a subsequent arrival point related to the target planet (final position). Lambert’s law is used for anarray of start dates and time of flights (between 2 and 5 years), and a minimum ∆ V is found. For instance,a 3-year trajectory with a start date in the next 30 years was found to require an impulsive ∆ V between37 and 45 km/s, , depending on the date of departure. The planetary positions are obtained for the dategiven using JPL’s HORIZONS system which can be used to generate ephemeris for solar-system bodies[43]. It is essential to minimize the propellant mass required, because the unburnt propellant mass mustbe accelerated along the trajectory with the spacecraft itself. Therefore, an initial rough mass estimation iscalculated through an iterative process on MATLAB using the Tsiolkovsky rocket equation [44, 45]. As wellknown, this equation shows that for a rocket with a given empty mass and a given amount of fuel, the total5hange in velocity is proportional to the specific impulse. It is also important to consider that the increaseof the mission duration, thrust efficiency, exhaust velocity, or specific power reduce the thrust duration andmass required for the mission. Increasing the payload has the reverse effect. A 25% burn duration of the3-year time of flight is 280 days. A ∆ V of 40 km/s can be achieved with a thrust of 8 N and a specificimpulse of 9,600 s, with a total initial mass of less than 7000 kg. These first rough estimates result in goodinitial guesses for the finite maneuvers analysis, which is essential to obtain accurate results for this kind oflow-thrust engine.
4. Thrust-coast-thrust profile mission
The objective of the mission is to reach Saturn near the descending node referred to the ecliptic planealong its orbit around the Sun, in order to solve a nearly 2-D problem, with huge advantages at numericaland computational level. Once the spacecraft is orbiting around Saturn, the Titan orbit insertion maneuverconcludes the mission. The T-C-T profile mission is divided into four different phases: Earth departure,interplanetary trajectory, Saturn orbit insertion and Titan orbit insertion. The mission start time hasbeen estimated considering both the Earth and Saturn orbits and taking into account the time constraintrepresented by the rendezvous with the planet target. The inputs for this rendezvous problem are the DFDengine parameters, initial and final radii r and r , payload and spacecraft mass (initial guesses). Travel timeand mission start time estimations are obtained after several iterations, starting from initial guess related tothe impulsive approach and considering some crucial constraints, for instance, related to the total mass ofthe spacecraft. Let us follow Fig. 1, where the first three phases of the mission are shown. Figure 1: Thrust-coast-thrust profile for the Titan mission. It is possible to observe three segments of the trajectory, the redsolid curves suggest that the spacecraft thrust is active and the green line represents the coasting phase without active thrust.
The first red solid curve starts from the Earth initial position and contains both the escape maneuver fromEarth and the burn which puts the spacecraft along the heliocentric hyperbolic trajectory to Saturn. Thesecond red solid curve shows the Saturn orbit insertion. While the green curve indicates the interplanetarytrajectory without thrust. In the following subsections each phase is analyzed.
A logic solution for the Earth departure phase could be to insert the spacecraft directly into a heliocentricorbit. Our simulations show that the Earth departure from a low Earth orbit (LEO) uses reasonablepropellant mass and takes between 25 and 71 days depending on the DFD engine parameters and initialmass considered. The results obtained are very close to those published in Ref. [15]. This solution allows touse almost any launch vehicle, dramatically reducing launch and overall mission costs. The initial consideredorbit is a circular orbit with an altitude of about 386 km and inclination of about 24 degree which allowsthe spacecraft to escape from Earth gravitational influence along the Ecliptic plane. A simulation for thespiral trajectory is presented to evaluate propellant mass consumption and maneuver time. As a first step,an Earth point mass model is considered and we neglect all orbital perturbations. This is a representativemodel because the influence of all orbital perturbations leads only to a small difference in terms of propellantmass and maneuver duration. The results of calculations related to the Earth escape maneuver are listed6n Table 2. We approximated the optimal thrust steering law [46] with a model where the thrust is mainlyaligned with the velocity vector. However, the thrust vector has a small positive radial component too.
Table 2: Earth departure spiral analysis. The final results are obtained considering the Earth point mass model and a geocentricreference system.
Departure phaseMission start time 2 Nov 2046Maneuver duration 76.2 daysPayload mass 1800 kgInitial mass 7250 kgPropellant consumption 559.5 kgVan Allen belt time 17 days∆ V V CE ≈
30 km/s) and it is achievedacting on the waiting time in LEO. Therefore, as a consequence of a long iterative process which dependsby several variables involved in all mission phases, the maneuver start time is obtained with a given waitingtime in LEO.
Figure 2: Spiral trajectory for the escape maneuver. The escape trajectory (blue) is shown using the Earth centred referencesystem. The red solid line starts when the spacecraft is outside the Earth gravitational sphere of influence, moving intointerplanetary space.
Due to the electromagnetic nature of the engine and because of safety reasons for the spacecraft itself, itis preferable to spend less time possible inside the inner Van Allen radiation belt. This time is about 17 daysand it is calculated as the time spent between 1 ,
000 and 6 ,
000 km altitude. In order to simulate the entireEarth departure phase the analysis stops when the spacecraft reaches the external surface of the Earth’sgravitational sphere of influence (radius r ⊕ ∞ ≈ km). The escape maneuver ends when the eccentricityreaches the unit value after 71 days of burn with a propellant consumption of about 520 kg. Once the Earth departure phase is completed, the spacecraft is in an elliptic orbit around the Sun and theinterplanetary trajectory mission phase begins. Many days of acceleration are needed at this point to obtainan heliocentric hyperbolic orbit, where the thrust vector is aligned with the velocity of the spacecraft. This isessentially the continuation of the previous maneuver, since the engine still generates thrust while it is exitingfrom the Earth gravitational sphere. It comes from an iterative process where the launch date, maneuverduration and thrust direction components are the main independent variables. After the acceleration phase,it is necessary to include a proper coasting segment, which duration has a strong impact on the followingmaneuvers. The main goal of this phase is to reach a spatial region on the ecliptic plane, pointing at the7escending node of Saturn’s heliocentric orbit. It is necessary to include a 1.6 year long coasting segmentbefore the deceleration maneuver when the spacecraft is approaching the target planet, ensuring that thespacecraft and Saturn velocities are comparable. The parameters related to this phase are shown in Table3.
Table 3: Characteristics of the interplanetary phase. The results related to the finite maneuver after the Earth escape are listedin the upper part of the table. The second half shows the coasting phase, which starts when the spacecraft shuts down thethrust generation. The velocities are shown in an heliocentric reference system.
Acceleration phaseManeuver duration 130.1 daysPropellant consumption 955.18 kg∆ V The Saturn orbit insertion (SOI) maneuver puts the spacecraft into Saturn’s orbit. The main purpose ofthe SOI is to obtain a proper velocity vector which allows the spacecraft to orbit around Saturn at a radiuscomparable to that of Titan. Let us adopt a Saturn centred reference system. It is required that after theSOI maneuver the spacecraft orbit switches from a hyperbolic trajectory to an elliptical orbit around thetarget planet. At arrival, however, the heliocentric transfer orbit usually crosses the target planet’s orbitat some angle, φ as shown in Fig. 3. The heliocentric spacecraft velocity, V , and the orbital speed ofthe target planet, V CS , should be comparable in magnitude with a relatively small angle φ between them.Otherwise, only a trajectory variation occurs (fly by or gravity assist) with a net accelerative effect whichdepends on the angle θ and the velocity of the spacecraft relative to the target planet V [47]. As a first step,a simple impulsive problem allows to evaluate the hyperbolic excess velocity V ∞ on the approach hyperbolato Saturn and other physical parameters. This important estimations are necessary to have accurate initialguesses of the velocities magnitude and periapsis radius of the approach trajectory, for the finite numericalanalysis. It is essential to consider the Titan orbital parameters in order to initially define the periapsisradius r p of the approach trajectory. As the distance of closest approach to Saturn we consider the meandistance from the center of Saturn to the Titan, assuming a comparable value r p ≈ · km. An iterativeprocess is used to estimate the velocity V when entering in the Saturn influence, which is clearly bound tothe spacecraft velocity V relative to Saturn. A good initial guess for the arrival velocity is slightly higherto the descending node Saturn’s orbital speed ( V CS = 9 .
17 km/s).8 igure 3: Fundamentals parameters for rendezvous mission. φ is the angle between the spacecraft heliocentric velocity vector V and the orbital velocity of the target planet at arrival V CS . V is the velocity of the spacecraft relative to the planet target. The necessary change in velocity is not achievable only decelerating the spacecraft, but also varying thedirection of V acting on the radial component of the thrust. Since V is the result of the cross product( V CS and V ), if the φ angle decreases, the resulting hyperbolic excess velocity rotates and decreases inmagnitude, as noticeable in Fig. 3. Finally, analysing the problem taking into account finite maneuvers,both deceleration and direction changes are studied. In order to avoid an excessive deceleration, whichwould extend the mission time, a trade-off between time requirements and propellant mass consumptionallows to find a solution. The SOI maneuver is divided in two segments. Near the end of the first segmentthe spacecraft is entering the planet gravitational sphere of influence and starts to be increasingly attracted. Table 4: Approach to Saturn. Results related to the entire Saturn orbit insertion maneuver in a heliocentric system.
SOI maneuverManeuver duration 142.2 daysPropellant consumption 1044 kg∆ V . · km,for about 170 days before starting the last mission maneuvers. Different solutions are considered also for the Titan orbit insertion (TOI) phase. In order to properlydeal with the mutual gravitational interaction between Saturn, Titan and the spacecraft it is necessary toaddress the three-body problem. This problem consists of determining the perturbations in the motion of9 igure 4: Saturn orbit insertion maneuvers. Figure ( a ): One of the solution for the SOI maneuver. The red solid curverepresents the finite maneuver which let the spacecraft to orbit around Saturn on the same orbital plane of Titan. The greensolid line is the waiting orbit, leading up to the the TOI maneuver. Figure ( b ) Alternative solution, the red solid curve representsthe finite maneuver which let the spacecraft to orbit around Saturn on the same orbital plane of Titan. The blue solid linemarks the start of the TOI maneuver. one of the bodies around the central body, produced by the attraction of the third. The Moon’s orbit aroundthe Earth, as disturbed by the Sun is an example. In order to numerically solve the problem and obtainaccurate results we use a perturbation model that takes into account the gravitational influence of bothSaturn and Titan. The purpose of this phase is not only to achieve orbital parameters very similar to thoseof Titan, but also to perform a rendezvous. Therefore, a strong time constraint has to be considered to solvethe problem. Let us adopt the following maneuver strategy: i) a first finite burn where the thrust vectoris directed along the anti-velocity direction; ii) a coasting segment; iii) a phasing maneuver where thrustcomponents along anti-velocity and co-normal direction are considered; iv) the final Titan orbit insertionmaneuver. The different segments of the TOI maneuver can be seen in Fig.5. The phasing angle, which isthe angle between the spacecraft and Titan position vectors, with respect to Saturn, decreases during thisentire maneuver because of the different orbits travelled by the chaser (spacecraft) and the target (Titan)resulting in different velocities, as shown in Fig. 5. Figure 5: Titan orbit insertion phase. Central body: Saturn. The blue line marks the start of the required TOI maneuver,subsequent the SOI maneuver (red). It is possible to observe the portion of the waiting orbit (green) travelled by the spacecraftbefore the phasing maneuver starts (red).Table 5: Titan orbit insertion phase. Results related to the required insertion maneuver which let the spacecraft (chaser)reaches Titan (target), orbiting around Saturn. The results are related to a Saturn centred reference system.
TOI maneuverManeuver duration 33.5 daysPropellant consumption 77 kg∆ V Figure 6: Titan orbit insertion from a Titan centred inertial reference system. After the phasing maneuver, the red solid curverepresents the orbit insertion maneuver which results in the final orbit around Titan (green solid curve).
In summary, the T-C-T mission profile is based on the assumption that the DFD will be capable ofturning off and on the thrust generation. This is an important hypothesis which requires that the enginewill not produce thrust during the coasting phase, which is in theory possible but not yet certain. Morespecifically, because of the robotic nature of the mission, it could be possible to think to turn off the enginein order to save both deuterium propellant and precious fuel ( He). The total fuel consumption for the entiremission is ≈ .
112 kg. Another possible solution, which could be more feasible, is based on the DFD abilityto turn off and on the thrust generation without shutting down the engine, still generating the electricalpower from the nuclear fusion reactions. In this case the reactor still provides energy for the entire mission,and the He consumption would be around 0 .
282 kg.
5. Continuous thrust profile mission
The natural alternative solution to the T-C-T mission profile is represented by the continuous thrust(CT) profile mission where the engine is always on, generating a constant thrust during the previous fourdifferent mission phases.
Figure 7: Planar trajectory for the continuous thrust profile mission. At the end of the blue curve there is the change indirection of the thrust (switch time). The trajectory follows Earth’s orbit for some time before a nearly straight trajectory toSaturn.
An iterative process is necessary to define the spacecraft initial mass, in order to define the propellant massfor the entire mission, which is directly related to the total duration of the trip. Starting from the same11rbital initial conditions of Section 4.1, calculations are performed with the additional constraint on thethrust. The results from the first phase analysis are listed in Table 6.
Table 6: Earth departure spiral analysis. The results are obtained considering an Earth point mass model and a geocentricreference system
Departure phaseMission start time 25 Sep 2047Maneuver duration 93 daysPayload mass 1000 kgInitial mass 9015 kgPropellant consumption 686.99 kg∆ V Table 7: Interplanetary phase. The results are related to the acceleration and deceleration phases for the heliocentric orbit.
Acceleration phaseInitial mass 8313 kgBurn duration 383.05 daysPropellant consumption 2812 kg∆ V V
6. Scenarios comparison
Let us consider the two mission scenarios analysed, the T-C-T and CT, and compare them to one ofthe most successful scientific mission, Cassini-Huygens, which studied the Saturn system for more than 10years. A summary for the entire scenarios studied are given in order to make a comparison of missiondurations, payload masses and propellant consumptions. In Table 8 along with results of our calculationsare also presented data for the Cassini-Huygens mission taken from Refs. [49–52]. It is worth noticing that
Table 8: Comparison between the thrust-cost-thrust profile, the continuous thrust profile and Cassini-Huygens missions. TheCT profile mission results into an even shorter time travel - less than two years - still with a heavier payload than previousmissions.
T-C-T profile CT profile Cassini-Huygens mission
Travel time (to Saturn), [days] 958.50 714.05 2422Initial spacecraft mass, [kg] 7250 9015 5712Payload mass, [kg] 1800 1000 617.4Propellant mass used, [kg] 2658 5347 2950Fuel ( He) mass used, [kg] 0.282 0.201 –Maximum trip velocity (Sun), [km/s] 34.560 47.814 –12n the CT case, the DFD is capable of really fast travels, rapidly reaching extremely high velocity. In thelast mission phases, when a great amount of propellant has already been consumed and the spacecraft massis decreased, the DFD can reach the required speed in a relatively short period, reducing of many yearsthe time of flight with a payload decrease since the propellant consumption has doubled. The reduction inpayload mass can be explained looking at the Earth departure phase: the higher the initial mass, the longerthe time necessary to escape from Earth. Then, a payload of about 1000 kg has been obtained throughan iterative process, in order to provide a relatively fast spiral Earth departure comparable with the firstscenario solution. Collectively, such kind of maneuvers would be too demanding for any kind of presentpropulsion systems. The total trip duration is below 2 years for the CT profile mission, which is more thanthree times less the duration of the Cassini spacecraft travel to Saturn, which has been possible due to severalgravity assists. It is important to emphasize that also the payload has increased significantly, delivering 1000kg in the fastest solution or 1800 kg in the T-C-T profile mission. For comparison, the Cassini spacecrafthad a total payload of about 617 kg, including the Huygens lander (349 kg) [48]. Another advantage relatedto the shortening of total mission duration is the reduction of precious fuel mass ( He), compared with thescenario of the T-C-T profile mission. In the case of a robotic mission, such as Cassini mission, it couldbe possible to shut down the engine, saving precious He fuel. Otherwise, for a manned space mission thiscould not be reasonable due to the fact that the electrical power generation could be vital for the crew.Finally, there are two possible solutions related to the operative phase of the mission. The results leadto two different feasible mission concepts. The high payload capability for both mission profiles allows toconsider a parachute descent through Titan’s dense atmosphere performed by a lander probe, containing arover or even better a rotorcraft, carried on the main spacecraft (orbiter) [53, 54]. In this case, during theTOI maneuver, the orbiter will release the lander and keep orbiting around Titan or, by performing a propermaneuver, it can orbit again around Saturn. In the first case, the lander can be designed to collect scientificdata for the entire mission, sending it to the powerful orbiter that is capable to receive and retransmit backdata to Earth. In the second case, the lander will send data to the orbiter only during the atmosphericdescent and a period after the landing, limited by the orbiter spacecraft trajectory and the lander powercapability. Therefore a maneuver that changes the path of the orbiter requires a negligible ∆ V of tens m/sorder of magnitude to perform the data relay during the descent.
7. Conclusions
Realistic trajectories analysis to accomplish a rendezvous interplanetary mission are presented. Ouranalysis confirm that a Titan mission using a 2-MW class DFD engine is not only feasible, but the departurefrom LEO dramatically reduces launch and overall mission costs. The strong advantages related to thisnew propulsion technology result in a great reduction of travel time with respect to the previous performedmissions [48, 55–57] and a tremendous payload increase with a huge availability of on-board electrical power.The DFD would be a true game-changer for any robotic missions to asteroids, solar system planets andmoons, and any other deep space mission become faster and cheaper. There are many missions that can beaccomplished now with a small amount of He from terrestrial sources, and enormous reserves are presumablyavailable on the Moon for future missions [39, 40]. Results of calculations obtained are extremely promisingalthough the conservative assumptions on the DFD engine specific power. We estimate the mission phasesduration and the propellant mass consumption for all the required maneuvers. In order to accomplish thisgoal, the proper thrust vector orientation and maneuver duration are numerically estimated. Most of thetime the thrust vector is considered updated throughout the maneuver to maintain the required thrustdirection. This choice forces the thrust vector to the desired direction at every instant during the burn,rotating with a specified coordinate system or tracking with the spacecraft’s inertial velocity vector. Wedemonstrate that the total Earth-Titan mission duration is about 2.6 years for the T-C-T profile, and lessthan 2 years for CT profile, which is more than three times less the duration of the Cassini spacecraft travelto Saturn.In future research works, it could be more appropriate to consider an inertial at ignition conditionduring the insertion phases, where the thrust vector direction is defined at ignition and remains the samethrough the maneuver. This option does not require a continuous attitude change and it could make themaneuver more simple. However, this choice does not affect significantly the results. We performed a basicoptimization process, which has proven to be useful to approximate the optimal thrust direction, minimizing13he duration of burns, hence the propellant used. The payload increase, combined with the huge electricalpower availability generated by the fusion reactor, leads to a tremendous growth of scientific data. In fact,for any robotic mission, the higher the payload, the more scientific instruments can be carried on-board andthe more precious data can be collected. This is a key aspect, also thinking to the near future lunar andMars missions [9, 58, 59] where it would be essential to maximize the payload, without excessively extendthe journey time.
Acknowledgements
We thank S. A. Cohen and his research team at Princeton Plasma Physics Laboratory, who provided insightand expertise that greatly assisted the research.
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