Optimisation of Nuclear Fusion Propulsion for ... - Icarus Interstellar

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Author's personal copyActa Astronautica 68 (2011) 1820–1829Contents lists available at ScienceDirectActa Astronauticajournal homepage: www.elsevier.com/locate/actaastroProject Icarus: Optimisation of nuclear fusion propulsion forinterstellar missions $K.F. Long a,n , R.K. Obousy b , A. Hein ca Project Icarus, UKb Project Icarus, USAc Project Icarus, Germanyarticle infoArticle history:Received 28 October 2010Received in revised form23 January 2011Accepted 25 January 2011Keywords:Fusion propulsionProject DaedalusProject IcarusICFabstractThe Daedalus spacecraft design was a two-stage configuration carrying 50,000 tonnes ofDHe 3 propellant. Daedalus was powered by electron driven Inertial Confinement Fusion(ICF) to implode the pellets at a frequency of 250 Hz. The mission was to Barnard’s star5.9 light years away in a duration of around 50 years. This paper is related to thesuccessor Project Icarus, a theoretical engineering design study that began on 30September 2009 and is a joint initiative between the Tau Zero Foundation and TheBritish Interplanetary Society. In the first part of this paper, we explore ‘flyby’ variationson the Daedalus propellant utilisation for two different mission targets: Barnard’s starand Epsilon Eridani, 10.7 light years away. With a fixed propellant mass a number ofstaged configurations (1–4) are derived for an optimal configuration but then moving toan off-optimal configuration due to the requirement for a high final science payloadmass. Some comments are then made on the ICF pellet configuration compared to thetypical pellets fielded at the National Ignition Facility (NIF) and those proposed for theVista and Longshot fusion based propulsion designs. This is a working progress report,which aims to study perturbations of the Daedalus baseline design as part of a tradestudy. This is a submission of the Project Icarus Study Group.& 2011 Elsevier Ltd. All rights reserved.1. IntroductionIn the 1970s members of The British InterplanetarySociety (BIS) designed a flyby interstellar probe aimed at aBarnard’s star mission. This was a theoretical study aimedat proving that interstellar travel was possible in principle.Fundamentally this addressed aspects of the Fermi paradox,which is the problem initially proposed by the Italianphysicist Enrico Fermi in the 1950s. His observation wasthat our theoretical expectation of encountering intelligent$ This paper was presented during the 61st IAC in Prague.n Corresponding author.E-mail addresses: kelvin.long@tesco.net,kflong@icarusinterstellar.org (K.F. Long),robousy@icarusinterstellar.org (R.K. Obousy),ahein@icarusinterstellar.org (A. Hein).life in the galaxy is in contradiction to our observations ofthere being only a single ‘intelligent’ life form – humans.Project Daedalus [1] was a landmark study covering all ofthe major spacecraft systems, comprehensively designedby application of rigorous scientific techniques. Arguably,Project Daedalus did prove that interstellar travel waspossible and so highlighting further the apparent paradoxfirst presented by Fermi.On 30 September 2009 members of the BIS in collaborationwith the Tau Zero Foundation (TZF) launched thesuccessor Project Icarus: son of Daedalus – flying closer toanother star [2]. Project Icarus aims to revisit the designand improve it with the three decades of advances inphysics, engineering and our understanding of the universe.The most critical element of the vehicle design is thepropulsion system, stipulated in the Project Icarus Termsof Reference (ToR) which are the engineering0094-5765/$ - see front matter & 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.actaastro.2011.01.010

Author's personal copyK.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829 1821requirements, to be mainly fusion based propulsion. Asthe Daedalus vehicle design utilised Inertial ConfinementFusion (ICF) technology as the main scheme for producingthrust generation (i.e. nuclear pulse propulsion) [3,4] thesame baseline is assumed for Project Icarus. This paperrepresents one trade study among many which is examiningdifferent ways of designing the Daedalus engine andoverall vehicle configuration. Thus the calculations presentedare deliberately approximate in scope and representa working progress report into studies of theDaedalus baseline design.The intention of this work is to focus on the extremesof the design envelope so as to bound the potentialperformance. We consider a comparatively distant missiontarget (Epsilon Eridani at 10.7 light years) and arelatively close mission target (Barnard’s star at 5.9 lightyears distance). Following a similar philosophy a laterstudy will aim to assess the use of ICF pellet designs suchas large configurations (as proposed for Daedalus) andsmall configurations (as proposed for next-generationcommercial fusion reactor demonstrators). It is not theintention in this brief study to produce any definitiveanswers but merely to aid in scoping the design space soas to better realise what likely options the Icarus designwill have. Currently, Project Icarus is in the Concept DesignPhase and no down select on options will be performeduntil after this phase is completed.As part of the overall propulsion work for ProjectIcarus, designers are reviewing the complete enginedesign and alternative engineering schemes. In this paperhowever, we start with the Daedalus vehicle and enginedesign as a baseline configuration and then considerperturbations thereof. We begin this paper by developingsome background theory required for the later analysis.We then describe how propellant mass and mass flowrate are related to the pellet pulse frequency. We thendevelop some 1–4-stage Daedalus-like configurations byusing optimisation equations. Further modifications leadto the configuration layout and mission profiles for eachconcept. Some equations are then developed to derive theminimum pulse frequency required for a given mission.Finally, some discussion is presented on different pelletdesigns and the maximum theoretical performanceattainable. This work is under continuing developmentand will evolve into a later more detailed analysis of thestudy, all geared towards presenting design options forProject Icarus prior to down select.2. Fundamental theoryWe firstly examine the problem of interstellar travelgenerally and remind ourselves of the ideal rocket equation,fundamental to any such studies, where v e is thepropellant exhaust velocity, M i /M f is the initial to finalmass ratio and Dv is the final velocity increment achieved:v ¼ v e LnðM i =M f Þð1ÞFigs. 1 and 2 show the basic requirements for trips tothe nearest stars calculated using Eq. (1). Fig. 1 shows thecruise velocity requirements from 8 to 20%c (wherec=3 10 8 ms 1 ), for different mission distances from 3to 20 light years, assuming different mission durationsfrom 40 to 100 years. Fig. 2 shows the mass ratiorequirements for the same mission profiles. Fig. 1 showsthat the distance attained is correlated to the final cruisevelocity and mission duration. Fig. 2 shows that the idealrocket equation imposes an exponentially increasingmass ratio in proportion to distance for a given missionduration. The distances for Barnard’s star and EpsilonEridani are highlighted with horizontal dashed lines(Fig. 1) and vertical dashed lines (Fig. 2). These lines formthe boundary of the analysis for this paper. The ProjectDaedalus engineering design is also shown with a cruisevelocity of 12.2%c, in a 50 year mission duration to 5.9light years (Barnard’s star).We next consider the potential mission duration toBarnard’s star 5.9 light years away, given different pulsefrequencies. In all calculations we assume a constantDistance light years201918171615141312111098765438100 years90 years80 years70 yearsEpsilon Eridani60 years50 years40 yearsDaedalusBarnard's Star9 10 11 12 13 14 15 16 17 18 19 20Cruise Velocity % speed of lightFig. 1. Cruise velocity requirements for interstellar travel.

Author's personal copy1822K.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829Mass Ratio (Mi/Mf)10009008007006005004003002001000340 years50 years60 years70 yearsBarnard's StarEpsilon Eridani80 yearsDaedalus90 years100 years4 5 6 7 8 9 10 11 12 13 14 15Distance Light yearsFig. 2. Mass ratio requirements for interstellar travel.Mass Ratio160150140130120110100908070605040302010067 8 9 10 11 12 13 14 15 16 17 18Cruise Velocity, percentage of light speedFig. 3. The effect on final cruise velocity with mass ratio.propellant mass of 50,000 tonnes, exhaust velocity10 7 ms 1 , which for a Daedalus-like mass ratio of around40 is consistent with a velocity increment of 12%c (3.6 10 7 ms 1 ). The correlation between cruise velocity and themass ratio is shown in Fig. 3. For this analysis we also notethat 1 year=3.1536 10 7 s, 1l year=9.4605 10 15 m. Thetotal number of ICF pellets N totpellused during the boost phasecan be described by relating it to the boost duration t b andpulse frequency f Hz :N totpell ¼ t b f Hzð2ÞFor Daedalus, the boost phase duration was made up oftwo phases consisting of 2.05 years (1st stage) and 1.76years (2nd stage) based upon optimisation of the two-stagemasses for maximum velocity increment. For this analysiswe approximate a total boost phase for a single stagevehicle to be 3.81 years. The Daedalus pulse frequency was250 Hz, which gives a total of 3 10 10 pellets. If we nowassume this same number of pellets but for a differentpulse frequency we arrive at a modified boost duration. Fora mission with a 10 Hz frequency, this corresponds to aboost duration of around 95 years. Another way to estimatea modified boost duration is to consider the thrustdifference due to a different mass flow rate _m. If weassume a total 50,000 tonnes (where 1 tonne=1000 kg)propellant mass and a mission duration of 3.81 years thenthe average mass flow rate is related by_m ¼ M propð3Þt bThis computes to a mass flow rate of 0.416 kg s 1 .Wecan then relate this to the pulse frequency to estimate theaverage propellant mass m pell bym pell ¼_mð4Þf Hz

Author's personal copyK.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829 1823which for a Daedalus pulse frequency of 250 Hz computesto an average pellet mass of 0.0017 kg. The actualDaedalus staged pellet masses are given in Table 1. Ifwe change the pulse frequency to say 10 Hz then thisresults in a new mass flow rate of 0.017 kg s 1 , assumingthe same propellant mass. Now the vehicle thrust isrelated to the exhaust velocity and mass flow rate byT ¼ _m v eð5ÞTable 1Performance parameters for Project Daedalus engineering design.Parameter 1st stage value 2nd stage valuePropellant mass (tonnes) 46,000 4000Staging mass (tonnes) 1690 980Boost duration (years) 2.05 1.76Number tanks 6 4Propellant mass per tank 7666.6 1000(tonnes)Exhaust velocity (km/s) 1.06 10 4 0.921 10 4Specific impulse (million s) 1.08 0.94Stage velocity increment(km/s)2.13 10 4(0.071c)1.53 10 4(0.051c)Thrust (N) 7.54 10 6 6.63 10 5Pellet pulse frequency (Hz) 250 250Pellet mass (kg) 0.00284 0.000288Number pellets 1.6197 10 10 1.3888 10 10Number pellets per tank 2.6995 10 9 7.5213 10 9Pellet outer radius (cm) 1.97 0.916Blow-off fraction 0.237 0.261Burn-up fraction 0.175 0.133Pellet mean density (kg/m 3 ) 89.1 89.1Pellet mass flow rate (kg/s) 0.711 0.072Driver energy (GJ) 2.7 40Average debris velocity (km/s) 1.1 10 4 0.96 10 4Neutron production rate (n/ 6 10 21 4.5 10 20pulse)Neutron production rate (n/s) 1.5 10 24 1.1 10 23Energy release (GJ) 171.82 13.271Q-value 66.6 33.2With the average Daedalus-like pellet mass andexhaust velocity 10 7 ms 1 corresponding to a pulsefrequency this computes to an average thrust of 4.16 10 6 N. Similarly, with the reduced pellet mass flow ratecorresponding to a 10 Hz pulse frequency this computesto an average thrust of 1.7 10 5 N. So the newly derivedthrust is a factor 25 less than our Daedalus-like thrust.One should therefore expect the boost duration to beincreased by the same factor, so that 3.81 years 25=95 years. This result is consistent with the estimatederived above for the boost duration. We can thenestimate the distance achieved during the boost phaseby use of the following logarithmic relation whichneglects special relativistic effects, which we consider tobe appropriate for low fractions of the speed of light [1]:S b ¼ v e t b 1 LnðRÞ R 1This results in a boost distance of 3.1 light years, whichwhen subtracted from a total distance of 5.9 light yearsleaves 2.8 light years for the cruise phase. Assuming acruise velocity of 15%c we easily determine the cruiseduration by S c /v c , which is around 19 years. This meansthat for a reduced pulse frequency of 10 Hz the totalmission duration will be around 114 years. Fig. 4 showsthe results of conducting a similar calculation for a rangeof pulse frequencies and with different exhaust velocityassumptions, all for a Barnard’s star mission. The profilefor the Daedalus probe is also shown. Clearly, for a pulsefrequency that drops below 100 Hz the total missionduration will start to increase rapidly. The Project IcarusToR stipulates that the mission must be completed in lessthan a century. From these initial results much lowerpulse frequencies would seem viable for a flyby probe.However, it is also a ToR constraint that the vehicledecelerates towards the target and so mid-range pulseð6Þ120Single Stage Flyby Daedalus-like Probe BARNARD'S STAR MISSIONTotal Mission Duration, Boost + Cruise (years)11010090807060504010Variable pulse, Ve=0.8E7 m/sVariable pulse, Ve=0.9E7 m/sVariable pulse, Ve=1E7 m/sVariable pulse, Ve=1.1E7 m/sVariable pulse, Ve=1.2E7 m/sDaedalus-like pulse (42 years, 250Hz)20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250Pulse frequency (Hz)Fig. 4. Total mission duration to Barnard’s star as a function of pulse frequency.

Author's personal copy1824K.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829Total Mission Duration, Boost + Cruise (years)1201101009080706050400Single Stage Flyby Daedalus-like Probe EPSILON ERIDANI MISSIONVariable pulse, Ve=0.8E7 m/sVariable pulse, Ve=0.9E7 m/sVariable pulse, Ve=1E7 m/sVariable pulse, Ve=1.1E7 m/sVariable pulse, Ve=1.2E7 m/sDaedalus-like pulse (42 years, 250Hz)10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250Pulse frequency (Hz)Fig. 5. Total mission duration to epsilon Eridani as a function of pulse frequency.frequencies of around 100–150 Hz would seem moreappropriate for a Barnard’s star mission. Also shownbelow in Fig. 5 is a similar analysis for a mission toEpsilon Eridani 10.7 light years away. Using a Daedaluspulse frequency of 250 Hz the total mission duration willinclude a 3.7 year boost phase and a 70 year cruise phasewith a total mission duration of 74 years. A pulsefrequency of 10 Hz will require a boost phase of 93 yearsand a cruise phase of 51 years with a total missionduration of 144 years. With a pulse frequency of less than10 Hz and a slightly reduced exhaust velocity from the10 7 ms 1 nominal, total mission durations easilyapproach a millennium.3. Configuration layoutsTable 1 shows the vehicle specification and performancefor the 1st and 2nd stage Daedalus engine design. This isthe starting point in any further analysis for differentoptions, although we assume a constant exhaust velocityof 10 7 ms 1 in this paper so we refer to our baseline asDaedalus-like. We now consider different Daedalus variants,which have between 1 and 4 stages but with a constant totalpropellant mass of 50,000 tonnes and constant total structuremass of 2670 tonnes identical to our two-stage baseline.From this analysis we derive four different concepts asdescribed below.The derivation of these concepts involved severaliterations. First an approach was adopted as describedby Turner [6] to derive the optimum mass fractions foreach stage. This is defined to be some fraction of unityfrom the total wet mass and includes the stage propellant,structure and payload. This involves computing the massratio R for a single stage Daedalus configuration (=19.73)as a fair test of the optimisation, the mass fractions A, B, Cand D for each stage is then defined byTwo-stage : A ¼ R 1=R; B ¼ 1=R;Three-stage : A ¼ R 1=R; B ¼ R 1=R 2 ; C ¼ 1=R 2 ;Four-stage : A ¼ R 1=R; B ¼ R 1=R 2 ; C ¼ R 1=R 3 ; D ¼ 1=R 3For the analysis the engine mass between the nominalDaedalus 1st and 2nd stage was found to be approximatelyin the ratio of 3.1. This same ratio was thenadopted in deriving smaller engine masses for the lowerstages. The engines masses were computed to be 988,318, 103 and 33 tonnes for the 1st, 2nd, 3rd and 4th stage,respectively, of each configuration, although no assessmentwas performed on the actual specifics of enginedesign and whether these small engines sizes are evenpossible. There would obviously be a physical limit tohow small the engine could be made, one of the reasonswhy it is no use to advance beyond 4 stages, apart fromthe diminishing gain in velocity increment. It is recognisedthat the assumption may not be valid, but for thepurposes of this crude trade study the assumption ismade until further work on potential engine designs isperformed.For the configurations derived, the aim of this analysiswas to optimise for near equal payload fraction whichwas assumed to represent a configuration with optimumvelocity increments. The payload fraction is the ratio ofpayload mass to sum of propellant and structure mass.Because the total mass has been fixed, this means that forincreased number of stages the final science payload masswill decrease. For the 3 and 4-stage configurations thiscame out as 170 and 50 tonnes, respectively, whichcompares with the 450 tonnes for the nominal 2-stagedesign. In order to get some final payload mass back aminor amount of the structure and propellant masseswere then swopped between the stages which moved theconfiguration further away from optimum, which leads to

Author's personal copy1826K.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829Distance (Light years)0.530.430.330.230.130.030-0.074-Stage3-Stage2-Stage1-Stage0.5 1 1.5 2 2.5 3 3.5 4Duration (years)Fig. 6. Mission profiles for different Daedalus-like staged configurations during boost phase.Fig. 7. Daedalus-like concept variants with 1–4 stages.This will then lead us to a revised mission profile. From anexamination of Figs. 4 and 5 we observe that thisrequirement appears to be met for a pulse frequency ofaround 100–150 Hz, which corresponds to a boost durationof around 6–9 years, as is easily demonstrated byusing Eq. (2). Minimising the pulse frequency furtherleads to an exponentially increased mission duration.The optimum pulse frequency for a given mission andvehicle parameters can best be observed by combiningEqs. (2) and (8) to give an expression for the total missionduration:t tot ¼ S totV c1 V of Hzþ Ntot pellV cV e1 LnðRÞ V c R 1In this equation V o is the initial velocity at final stageburn and V c is the total cruise velocity after final stageð9Þ

Author's personal copyK.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829 1827Table 3Daedalus variants.3-Stage concept4-Stage concept1st stage 44,081 tonnes propellant 44,149 tonnes propellant1300 tonnes structure 1150 tonnes structureDV 18,137 km/s (0.06c) DV 16,949 km/s (0.056c)Burn time 1.97 years Burn time 1.92 yearsStage distance 0.04 lightyearsStage distance 0.039 lightyears2nd stage 6218 tonnes propellant 7050 tonnes propellant1000 tonnes structure 1050 tonnes structureDV 12,587 km/s (0.042c) DV 12,179 km/s (0.041c)Burn time 1.54 years Burn time 1.45 yearsStage distance 0.187 lightyearsStage distance 0.172 lightyears3rd stage 1070 tonnes propellant 1235 tonnes propellant370 tonnes structure 360 tonnes structureDV 10,619 km/s (0.035c) DV 9035 km/s (0.03c)Burn time 0.3 years 0.38 yearsStage distance 0.375 lightyearsStage distance 0.344 lightyears4th stage236 tonnes propellant– 110 tonnes structureDV 7634 km/s (0.025c)Burn time 0.05 yearsStage distance 0.524 lightyearsFinal 170 tonnes 51 tonnespayload aCruise 41,343 km/s (0.138c) 45,796 km/s (0.153c)velocityTotal burn 3.81 years 3.81 yearstimeBoostdistance0.375 light years 0.524 light yearsCruise time 40.09 years 35.22 yearsBS bTotal 43.91 years 39.03 yearsmission BSCruise time 74.92 years 66.66 yearsEE cTotalmission EE78.74 years 70.48 yearsa Refers to science payload.b BS=Barnard’s star.c EE=Epsilon Eridani.Table 4Minimum pulse frequency requirements and maximum allowable boostperiod duration.Configuration Barnard’s star (Hz) Epsilon Eridani (Hz)2-Stage 5 203-Stage 3 64-Stage 2 3burn. R is the mass ratio of the final stage. Any numbersput into this equation must be self consistent with adesigned mission profile and vehicle configuration. Thiscan then be re-arranged to find the minimum pulsefrequency required to achieve the stated mission durationof 100 years:f Hz ¼ N totpell1 V oV cV e1 LnðRÞ S 1tott totð10ÞV c R 1 V cIf we assume an exhaust velocity of 10 7 ms 1 , totalpropellant number 3 10 10 , and the final cruise velocitiesachieved for each configuration derived and their respectivefinal staged mass ratios, this leads to the resultsshown in Table 4 for the minimum pulse frequencyrequired for a 100 year mission, but for flyby (nodeceleration) only.5. ICF pelletsThe discussion above assumed the nominal DaedalusDHe 3 pellet design. However, we ideally also need toconsider the use of a DT propellant combination as well asa different type of pellet design. For this we can turn to adesign that is much smaller, something typical of aNational Ignition Facility (NIF) baseline target [5]. Theobvious fact to point out is that the much smaller pelletswill have much less mass to potentially ignite and soproduce a much smaller amount of energy. The differenceis an energy release of tens to hundreds of GJ for theDaedalus-like pellets compared to only 10–20 MJ for theNIF-like pellets. This will inevitably affect the accelerationprofile and thereby elongate the boost duration. The twodifferent pellet geometries can be chosen to representextremes of design mass and radii. It is assumed that anyICF pellet design chosen for the Icarus vehicle will likelybe smaller than those used for Daedalus (to minimisepropellant mass) but much bigger than those being usedfor NIF (in order to get the required energy out). Fig. 8shows the Daedalus and NIF pellets compared. Futureresearch will consider these two extremes in pellet designas applied to the vehicle configuration layouts and missionprofiles derived in this paper.It is worth comparing the pellet sizes discussed aboveto those for other theoretical design studies that utilisedICF based propulsion schemes. The first was Project Longshot[7], a US Naval Academy study conducted in the1980s for a mission to Alpha Centauri in around 100years. It proposed the use of DHe 3 fuel with pellet massesbetween 0.005 and 0.085 g detonated at a pulse frequencybetween 14 and 250 Hz. Another (more credible) studywas Project VISTA [8] led by a designer from LawrenceLivermore National Laboratory in the late 1980s and wasdesigned for interplanetary missions. This was again anICF based engine design but would use a DT propellantcombination and the ignition by a 5 MJ laser driver wouldbe enhanced by the use of a Fast Ignition technique toproduce 7500 MJ per pellet, which would allow highenergy gain up to 1500. The pellets would be detonatedat a rate of between 0 and 30 Hz and each had a mass of0.066 g. Comparing the pellet configurations proposed forthese vehicles to the designs proposed for Daedalus weobserve that these are a lot lower than the 1st stage pelletmass, although this could be a result of lack of a properdesign evaluation for LONGSHOT and a less ambitiousmission requirement for VISTA. However, it does makeone question the large 1st stage pellet masses proposed

Author's personal copy1828K.F. Long et al. / Acta Astronautica 68 (2011) 1820–1829Fig. 8. NIF/Daedalus ICF pellet design comparison.Table 5Fusion reaction energy release from single reaction assessment.Propellant/productsDT/He 4 +nDHe 3 /He 4 +pDD/He3+nDD/T+pExhaust velocity (km/s)26,400 (8.67%c)26,500 (8.85%c)12,500 (4.17%c)13,900 (4.64%c)for Daedalus and to aim for something smaller in thedesign. This will be the subject of future research.It is also constructive to consider what is the maximumperformance that you can get from a fusion basedrocket engine? This is also important in determining thetype of fuel to use in an ICF pellet. We can approach thisquestion in terms of exhaust velocity. We shall calculatethe maximum performance based upon two methods.Firstly, we shall simply look at the difference in massbetween the two reacting particle species and then considerthe kinetic energy of the excess mass.Next we shall examine the question from the standpoint of enthalpy. We begin by examining the DHe 3reaction, which gives the products of He 4 and a proton.Looking at the atomic mass unit balance between thereaction products and the released products we have:2.013553+3.014932-4.001506+1.007276. The differencein mass between the two sides of the reaction is0.019703. We next consider what kinetic energy is associatedwith this mass difference. The fractional energyrelease e for the DHe 3 combination is simply the massdifference divided by the total mass of the reactingproducts 0.019703/(2.013553+3.014932)=0.00392. A similarcalculation for the DT propellant combinations will yield afractional energy release of 0.00375. We then work outthe thermal exhaust velocity V e by inverting the equationfor kinetic energy:V e ¼2E 1=2kinð11ÞmThen using E=emc 2 , the mass cancels and we are leftwith an equation for the exhaust velocity as a function ofthe fractional energy release to be V e ¼ð2eÞ 1=2 c 0:088c.This is nearly 9%c and corresponds to a velocity of26,500 km/s. The performance for the two propellantcombinations is shown in Table 5. This is the maximumtheoretical performance of a fusion based engine althoughsubsequent energy from reacting products will alsoincrease this maximum. In reality, efficiency issues willcome in such as burn fraction and this will reduce thepotential exhaust velocity. Neutron energy losses will alsoreduce the DT exhaust velocity, not an issue for DHe 3which produces protons in the reaction (also useful formagnetic thrust directivity due to the charge). For comparisona Daedalus-like engine has an exhaust velocity ofaround 10,000 km s 1 , much less than the theoreticalvalues shown in Table 5.6. ConclusionsIn this paper we have assessed two mission profilesand discussed two types of ICF pellet configurations for anuclear pulse propulsion based engine. These results formthe lower and upper bound extremes of the designenvelope to aid further design discussions. The conceptspresented are not claimed to be ‘designs’ or even properlyoptimised but merely configuration concepts to assist inscoping the design envelope. In fact the need to maintaina high final science payload mass took the configurationsoff-optimal. The 3 and 4-stage configurations presentedabove were not optimum designs and future work willaim to continue to evolve these concepts towards a fullyoptimum layout. These results suggests a trade-off whereyou can have either a low final science payload mass (andmaintain an optimal configuration) or much higher finalscience payload mass (but for a non-optimal configuration).The problem is more pronounced the higher thenumber of stages, hence a move to a 4-stage configurationshould be avoided and even a move to a 3-stage configurationwould require some thought for a fixed totalvehicle wet mass.The results show that within a constrained totalpropellant and total structure mass increased stagingleads to a decreased final payload mass. Hence to maintaina constant payload one must either increase the totalmass or be satisfied with a lower staging layout. In orderto reach a destination further in distance one must eitherincrease the cruise speed attained or elongate the totalmission duration. Within the constraints of a total vehicle