AIAA-97-3208UPDATE ON COST CONSIDERATIONS FOR INTERSTELLAR FLIGHT
Dana G. AndrewsAdvanced Astronautics
4826 NE 41st, Seattle WA 98105Ph 206-524-9621
ABSTRACT
This paper examines the technical andeconomic feasibility of interstellar exploration.Three candidate interstellar propulsion systemsare evaluated with respect to technical viabilityand compared on an estimated cost basis. Twoof the systems, the laser-propelled lightsail (LPL)and the particle-beam propelled magsail (PBPM),appear to be technically feasible and capablesupporting one-way probes to nearby starsystems within the lifetime of the principalinvestigators, if enough energy is available. Thethird propulsion system, the antimatter rocket,requires additional proof of conceptdemonstrations before its feasibility can beevaluated.
Computer simulations of the accelerationand deceleration interactions of LPL and PBPMwere completed and spacecraft configurationsoptimized for minimum energy usage are noted.The optimum LPL transfers about ten percent ofthe laser beam energy into kinetic energy of thespacecraft while the optimum PBPM transfersabout thirty percent. Since particle beamgenerators are roughly twice as energy efficientas large lasers, the PBPM propulsion systemrequires roughly one-sixth the busbar electricalenergy a LPL system would require to launch anidentical payload.
The total beam energy requirement for aninterstellar probe mission is roughly 10^0 joules,which would require the complete fissioning ofone thousand tons of Uranium assuming thirty-five percent powerplant efficiency. This isroughly equivalent to a recurring cost per flight of3.0 Billion dollars in reactor grade enricheduranium using today's prices. Therefore,interstellar flight is an expensive proposition, butnot unaffordable, if the nonrecurring costs ofbuilding the powerplant can be minimized.
IntroductionInterstellar travel is difficult, but not
impossible. The technology to launch slowInterstellar exploration missions, total deltavelocities (AVs) of a few hundreds of kilometersper second, has been demonstrated inlaboratories. However, slow interstellar probes
will never be launched because no official bodywill ever start a project which has no return for1
thousands of years; especially if it can wait a fewdozens of years for improved technology andget the results quicker. Therefore, the firstcriteria for a successful interstellar mission is thatit must return results within the lifetime of theprincipal investigator. This is very difficult, butstill possible. To obtain results this quick, theprobe must be accelerated to a significantfraction of the speed of light, with resultantkinetic energies of the order of 4 x1015 joulesper kilogram. Not surprisingly, the secondcriteria for a successful interstellar mission is costeffective energy generation and an efficientmeans of converting raw energy into directedmomentum. In this paper, several candidatepropulsion systems theoretically capable ofdelivering probes to nearby star systems twenty-five to thirty-five years after launch are definedand sized for prospective missions using bothnear term technologies.
Rockets have limited AV capabilitybecause they must carry their entire source ofenergy and propellant. Therefore, they must livewith the famous rocket equation, ie.
AV = ceff*ln(Mo/Mf) 0)
Where Ceff is the effective exhaust velocity ofthe propellant, and M<yMf is the ratio of thevehicle mass with full propellant over the vehiclemass after all propellants are spent. Chemicalcombustion energy limits conventional rocketsto Ceff's < 5km/sec and Mo/Mf ratios <10 (eachstage) which means total AVs are limited to 10 to20 km/sec. Therefore, conventional chemicalrockets have their place in exploring cis-lunarspace and the nearby planets, but when weaddress interstellar missions with three orders ofmagnitude higher AV requirements we mustseek rockets with orders of magnitude increasedenergy density, or non-rockets which carry nopropellant or energy source but rely oninteractions with artificial or naturally occurringphenomena to generate thrust or drag^.
Copyright® 1997 by the International AstronauticsFederation. All rights reserved* Member AIAA
Exploration of the nearest star systemsduring the lifetime of the principal investigatorswill require AVs of fifteen to twenty percent ofthe speed of light (45,000 to 60,000 km/sec),and twice that if the probe is to decelerate andactually explore the distant star system. Arethere candidate propulsion systems with thatlevel of performance? Actually, there are at leastthree propulsion systems with theoreticalperformance adequate to meet the extremelyhigh AV requirement. They are: the antimatterrocket, the laser-propelled lightsail, and a newconcept, the particle beam propelled magsail.Antimatter Rocket - The interstellar versionof the antimatter rocket combines antihydrogenwith a larger amount of hydrogen plasma in amagnetic nozzle, which confines and directs thecharged annililation products and ionizedhydrogen, producing thrust. Early theoreticalwork indicated that twenty-five to fifty percent ofthe annihilation energy might appear as usefulthrust.2-3 Assuming there is five times as muchhydrogen as antihydrogen onboard the rocket,the theoretical effective exhaust velocities attwenty-five to fifty percent efficiency would bebetween 60,000 and 120,000 km/sec, which isadequate for the proposed mission. Hence, ifantimatter can be produced and stored inquantity, and if antimatter rockets can be made toperform at these high theoretical levels, theninterstellar probe missions of thirty to forty yearsduration are possible. See figure 1, for aschematic of the antimatter interstellar rocket.
Liquid Anti-HydrogenMagnetic
I
o I o
O o
AnnihilationChamber
Figure 1. Antimatter Interstellar Rocket
However, later studies which simulated themixing of matter and antimatter, the annihilation,and the interaction of hydrogen with the variousannihilation products within realistic magneticnozzles have showed that only one or twopercent of the annihilation energy goes intouseful thrust.4 In addition, the large radiationlosses shown in the these simulations result inhuge shielding penalties which drive up theweight of the propulsion system. If these resultsare true, the antimatter rocket will have severelylimited capabilities for interstellar propulsion.Hence, there are still substantial doubts about
the feasibility of antimatter interstellar propulsion,and many successful experiments are requiredbefore antimatter rockets become seriouscandidates for interstellar missions.Laser-Propelled Lightsail - Laser-drivenlightsails are not rockets since the power sourceremains behind and no propellants areexpended. Therefore, the rocket equationdoesn't apply and extremely high AVs arepossible if adequate laser power can be focusedon the lightsail for a sufficient acceleration timeperiod. The acceleration, asc . of a laser-propelled lightsail spacecraft in meters persecond is:
(2)
where PL is the laser power impinging on the sailin watts, Ms is the mass of the spacecraft (sail andpayload) in kilograms, and c is the speed of lightin meters/ second. In practical units, a perfectlyreflecting laser lightsail will experience a force of6.7 newtons for every gigawatt of incident laserpower. Herein lies the problem, since extremelyhigh power levels are required to accelerateeven small probes at a few gravities.
Robert Forward in his papers on interstellarlightsail missions postulated a 7,200 gigawattlaser to accelerate his 785 ton unmanned probeand a 75,000,000 gigawatt laser to accelerate his78,500 ton manned vehicle5'6. To achievevelocities of 0.21 c and 0.5 c, respectively, thelaser beam must be focused on the sail forliterally years at distances out to a couple of lightyears. In addition, the laser beam was to be usedto decelerate the payload at the target star bystaging the lightsail and using the outer annularportion as a mirror to reflect and direct most ofthe laser beam back onto the central portion ofthe lightsail which does the decelerating. Toenable this optical performance, a one thousandkilometer diameter fresnel lens would be placedfifteen Astronomical Units (AU) beyond the laserand its position relative to the stabilized laserbeam axis maintained to within a meter. If thelaser beam axis is not stable over hours relativeto the fixed background stars (drift <10'12
radians), or if the lens is not maintained within afraction of a meter of the laser axis; the beam atthe spacecraft will wander across the sail fastenough to destabilize the system?. While thisscenario is not physically impossible, it appearsdifficult enough to delay any seriousconsideration of using the large lens/long focusapproach to laser-propelled light sails.
The alternative approach is to build reallylarge solar-pumped or electrically powered lasersin the million gigawatt range, where we couldaccelerate a decent size spacecraft to thirty
percent the speed of light within a fraction of alight year using more achievable optics (e.g., areflector 50 kilometers in diameter). Eventhough space construction projects of thismagnitude must be termed highly speculative,the technology required is well understood andLPL systems utilizing dielectric quarterwavelightsails could accelerate at twenty to thirtymeters per second7. An example of an LPL starsystem explorer is shown in figure 2 below.
igsail Current Loop
DiamondQuarterwaveReflectors
Rotation duringLaser Boost
Payload
Shroud Lines
Side View Rear ViewFigure 2 Laser Propelled Lightsail
The Magsail current loop carries no currentduring the laser boost and is just a rotating coil ofsuperconducting cable acting as ballast tobalance the thrust forces on the dielectricquarterwave reflector. After coast when thespacecraft approaches the target star system thelightsail is jettisoned and the magsail is allowed touncoil to its full diameter (80 km for a 2000 kgprobe mission). It is then energized either froman onboard reactor or laser illuminatedphotovoltaic panels and begins its longdeceleration.
Example interstellar missions have beensimulated using state-of-the-art optics designsand the resulting LPL design characteristics areshown in Table 1 below. A constant beam poweris chosen such that the spacecraft reaches the
desired velocity just at the limit of accelerationwith fifty kilometer diameter optics.
Even though the high-powered LPLappears to meet all mission requirements, thispaper explores an alternative propulsion systemwith potential for significant reductions in power,size, cost, and complexity.
Particle Beam Propelled Magsail (PBPM)-A PBPM substitutes a neutral plasma beam forthe laser and a magnetic sail or magsail for thelight sail. The primary reason for switching fromlasers and lightsails to particle beams andmagsails is roughly six orders of magnitudereduction in the power required during initialacceleration, and a like reduction in spacecraftcost and complexity. Specific benefits foundwith this approach are: 1) improved electricalefficiency of particle beam generators relative tolasers (50% vs 25%), 2) two to three orders ofmagnitude increased force on the sail for thesame beam power, and 3) elimination of aseparate deceleration system since theacceleration magsail can serve dual purpose.
Particle beam accelerator technology iswell advanced but largely classified, so onlygeneral characteristics will be discussed in thefollowing. Magsail technology is based only ontheoretical results to date, but detaileddescriptions are readily available in references 9&10. Only a brief description of magsailcharacteristics is presented in this paper.
Use of a neutral particle beam to drive amagsail was first mentioned by Geoffrey Landisas an alternate to laser-propelled lightsails inReference 7. He suggested a particle beam toreduce the wavelength and eliminate thediffraction limit on laser lightsail optics andincrease the effective thrusting distance.
Beam Director Diameter, meters 50,000Lightsail Diameter, meters 2000Acceleration time, days 37Radius at Cutoff, AU 1114Total Beam Energy, Joules 1.6x1020
Use of a particle beam certainly reducesthe diffraction problem, but introduces two newproblems; a beam divergence caused byresidual thermal motions of the atoms afteracceleration, and a tendency for any chargedparticles to deflect off course in the solar orinterstellar magnetic field. Both these problemshave theoretical solutions discussed later, butthey have never been demonstrated outside alaboratory, and the combined effects are difficultto quantify; so an effective beam divergence of>10'9 radians has been assumed for this study.With this assumption, particle beams can providevery high thrust for limited power, but only out tomedium ranges (ie. range < thirty AstronomicalUnits (AU)).
The magnetic sail, or Magsail, is a devicewhich can be used to accelerate or decelerate aspacecraft by using a magnetic field todecelerate/deflect the plasma naturally found inthe solar wind and interstellar medium. Itsprinciple of operation is as follows: A loop ofsuperconducting cable kilometers in diameter isstored on a drum attached to a payloadspacecraft. When the time comes to accelerate,the cable is played out into space and a current isinitiated in the loop. This current once initiated,will be maintained indefinitely in thesuperconductor without further power. Themagnetic field created by the current will impart ahoop stress to the loop aiding the deploymentand eventually forcing it to a rigid circular shape.The loop operates at low field strengths, typically10'4 to 10'6 Tesla, so little structuralstrengthening is required. The proposedconfiguration for this application is shown infigure 1.
MagsailCurrent Loop
Rear ViewTop ViewFigure 1. Magsail Configuration at
Angle of Attack
In operation, charged particles entering thefield are deflected by the B-field, thus impartingmomentum to the loop. If a net plasma flow, suchas the solar wind, exists relative to thespacecraft, the magsail loop will always createdrag, and thus accelerate the spacecraft in thedirection of the relative flow. When a neutralbeam of charged particles are directed at themagsail a similar reaction occurs, at least incomputer simulations. When the dipole field isinclined to the flow vector the magsail alsogenerates a force perpendicular to the flow (i.e.lift). This feature allows the magsail to centeritself in the particle beam, which is especiallyimportant when the magsail is light minutes fromthe particle accelerators.
SolarWind
Bow'Shock
iwagneiospnere
Payload
ShroudLines
Magsail CurrentLoop
Figure 2. Dipole Plasma Interaction
The magsail also makes an excellent brakefor an interstellar spacecraft travelling at fractionsof the speed of light. The rapidly movingmagnetic field of the magsail ionizes theinterstellar medium and then deflects theresulting plasma, creating drag whichdecelerates the spacecraft. The ability to slowdown spacecraft from interstellar tointerplanetary velocities without the expenditureof rocket propellant results in a dramatic loweringof the total mission mass, as we shall show in asystems performance trade presented later.
PBPM System DescriptionThe acceleration phase of the PBPM
system is shown schematically in figure 3. Equalnumbers of positive and negative particleaccelerators are ganged together on an asteroidor airless moon, which serves as a solid base,heat sink, and momentum absorber. Theganged projectors produce a collimated streamof equal numbers of positively and negativelycharged atoms (probably hydrogen atoms).
These charged particles form a neutral streamingplasma which should have little tendency todiffuse since it contains equal numbers ofoppositely charged particles. However,interplanetary space is not empty, but filled by anoutward streaming solar wind with magneticfields which were frozen in as the plasma left thesolar corona.
The rapidly moving plasma stream willinteract with the interplanetary medium in twoways. The simplest interaction is elastic particleto particle collisions between the plasma stream
Airless Moonor Asteroid
and the particles in the solar wind. This will notbe a factor since the mean free path is over10+20 meters for hydrogen ions at theproposed energy levels. The second interactionis with interplanetary magnetic field, whichalthough quite weak (10"̂ Tesla at three AU),could deflect the plasma beam. Fortunately, theinterplanetary magnetic field spirals out from thesun in fairly homogeneous sectors whichbecome more radial in direction as they travel outfrom the sun (Figure 4).
Particle BeamGenerators
Not to ScaleFigure 3. Beamed Momentum propulsion Schematic
With careful timing and a launch base at threeAU, the particle driven portion of the launchcycle (seven or eight hours) could take placewith the plasma beam closely aligned with theinterplanetary magnetic field. Those times whenthe beam and the field are not perfectly alignedshould result in some charge separation as the
negative and positive particles try to turn inseparate directions. Since all the particles havethe same mass, the center of mass will remain oncourse and the electric field caused by theseparation of charges will prevent significantspreading (The electric forces exceed themagnetic forces after millimeters of separation).
Sector Boundary
OutgoingMagneticField Lines
Sector Boundary ParticleBeamAsteroid
Interplanetary 'Magnetic Field
'Particle BeamFigure 4. Schematic of Interplanetary Magnetic Field
Once the neutral plasma beam reachesthe magsail it is slowed and deflected by thedipole field in much the same way the solar windplasma is deflected by the earth's magnetic field.This results in a momentum transfer to thecurrent loop which can be calculated usingcomputer models.8
Assuming; that plasma velocity can bevaried incrementally, and that all atoms in thebeam impact the dipole field, we can calculatethe force per watt of particle beam power asfollows:
Vs/c
= m (Vp- Vs/c) (3)
where FS/C is the thrust on the spacecraft, m isthe total mass flow through the particleaccelerator, Vp is the average velocity ofparticles in the beam (ignoring solar gravitationallosses), and Vs/c is the instantaneousspacecraft velocity. However,
(4)
where PB is the total beam power, andequations (3) and (4) can be combined into;
(5)
which can be differentiated with respect to Vp
and set equal to zero
(6)
which reduces to Vp = 2 Vs/c, and means thatthe thrust per watt of beam power is maximizedwhen the particle velocity is twice the spacecraftvelocity. We can then plot thrust per gigawatt asa function of spacecraft speed assuming theparticle velocity is always twice the spacecraftspeed. This relationship is shown in figure 5.
Therefore, transfering momentum usingparticles instead of photons is more energyefficient until the spacecraft approachesapproximately one third the speed of light. Note,that relativistic effects are ignored in theseanalyses.
PBPM Performance - Computer simulationsof the acceleration process for a hypotheticalinterstellar probe payload were generated forvarious assumptions. If power is not a problem,then design a probe for intense acceleration anddo the entire job with the battery of particleaccelerators and a heavy duty magsail. Themagsail is an ideal device for high accelerationsbecause each element is in tension and modernhigh strength to density fibers make for alightweight system capable of handling verylarge forces. Figure 6 shows the range ofspacecraft accelerations necessary to achieveinterstellar exploration velocities within ten AUrange of our proposed particle beam accelerator.This data assumes constant acceleration, whichwould be the case only if the spacecraft is alwayswithin the range where the magsail dipole fieldcapture diameter is greater than the particlebeam diameter.
10,000
1000
g. 1°i
o<DO.
TParticle Beam PropelledMagsail Thrust
Laser LightsallThrust (6.7 newtons)
10" 10 1010 10 10Spacecraft Velocity,
Figure 5. Spacecraft Thrust per gigawatt of Beam Power
Computer simulations were generated tomodel the acceleration and decelerationprocesses for the PBPM propulsion system.These simulations assume a design limit onacceleration and increase beam power tomaintain that limit as velocity increases. Thesame typical payloads of two, twenty, and fiftymetric tons were used to determine scaleeffects. The results of these simulations areshown in Table 2 below. Note that the smallermagsails optimize at higher accelerations whichprovides more efficient coupling of the particlebeam with the magsail (less beam divergence tocause losses). Larger payloads optimize at loweraccelerations and consequently spend moretime further out in a diverged beam.
Assumes ConstantAcceleration forTen Astronomical Units
Power ConsiderationsWith the short operating times
characteristic of the PBPM system, an electricpowerplant based on nuclear fission power and alarge energy storage facility would seemappropriate. A series of large particle bed or gascore reactors driving a Brayton cycle system andusing the natural heat sink of a nickel ironasteroid would seem ideal to power a system ofthis type. Basing the system in the outerasteroid belt has advantages too. If the magsailstarts at three AU, we can use conventionalsuperconductors for the magsail because thetime spent in the inner solar system is so short.
The particle beams are accelerated inRadio-Frequency Quadrapoles (RFQs). CurrentRFQ designs can handle tens of kilowatts ofpower efficiently, and scaled-up versions arethought to be capable of Terawatt powerlevels^, in addition, because the magsail forceis proportional the area within the current loopwhile the mass is proportional the perimeter, themagsail provides a large effective target area inwhich the particles will be deflected for a lowmass penalty. Also, because the magsail
Explorer20,00026,7000.31.08X1020
3x10-9
3.5x1020
30002.8x1016
6.26.8
2.0x1016
15.7
Manned50,00076,7300.33.1X1020
3x1O'9
1.05X1021
20005.0x1016
12.513.5
1.0X1017
15.3
structure is entirely in tension, it is capable ofhigh acceleration. Our computer simulationsindicate that even the larger magsails can beaccelerated at up to 1000 gees. This enablesthe spacecraft to reach near-realivistic speedswithin the effective range of near-termtechnology particle beams. In the case ofmanned spacecraft, it will be necessary tosubmerge the crew in water for the few hours ofacceleration. Preliminary centrifuge testing ofsubjects submerged in water while wearingSCUBA gear indicated no discomfort to above10 gravities.
Cost AnalysesEven though the power producing and
momentum producing elements of the systemwill be expensive, they are reusable and couldbe used for generations. For the LPL system,the major cost is in the powerplant since freeelectron lasers appear to scale up favorably andcan handle tremendous power loadings. Spacequalified solar panels are currently about a milliondollars per kilowatt, but new terrestrial solarpanels are being designed for mass production
and will sell at about $2000 per kilowatt. Theprice per watt for solar cells has decreased anorder of magnitude over the last ten years as theproduction rate rises, and this trend could wellcontinue for the next thirty years because thecost of the raw materials and the energy ofmanufacture are only pennies per kilowatt.
As solar panels become a major part ofterrestrial and then space based civilization,volume production and competition will rapidlydrive the price down. With three orders ofmagnitude cost reduction from current cells,solar power would be $2 per kilowatt and a basicpowerplant to drive a 5.0x1013 watt laser wouldbe $3.3x1011. This would be a majorinvestment, but divided over 9 launches per yearfor thirty years, it works out to $1.2 Billion permission. About what we're paying now forinterplanetary probes. If the price of solar cellscan be reduced another order of magnitude,then the total power system cost would bearound a thirty billion dollars and the resultingcost per mission about one hundred milliondollars.
For the PBPM system, with an accelerationperiod measured in hours, it makes sense toselect a high specific energy power source suchas a Magnetohydrodynamic (MHD) generator, orundersize the powerplant and store energy for aburst of acceleration. For example, assuming agas core nuclear reactor heating hydrogenworking fluid for use in a MHD generator, theprimary cost of a single interstellar flight would bethe recurring cost of the uranium energy source(hydrogen is cheap once you have access to acomet). Unenriched uranium is currently $20 perkilogram. In theory a very large gas core reactorcould operate as a fast reactor using minimallyenriched uranium.
The bottom line is the cost of energy, andit is essential to move beyond reactor gradeuranium, which is currently about 300$/kg. Iffusion reactors are not attainable in the timeframe of interest, then a shift to thermonucleardevices driving major MHD power generatorsseems warranted. If a PBPM probe requires 1020
joules of energy, this is equivalent to 1200 two-hundred megaton bombs which cost a smallfraction of the equivalent enerrgy in reactorgrade uranium.ConclusionsThese data show that interstellar exploration isfeasible, even with near term technologies, if theright system is selected and enough resourcesare available. Therefore, once the technologyfor low cost access to space is available, theprimary risk to any organization embarking on aserious effort to develop interstellar exploration/transportation is affordability, not technicalfeasibility.. The primary issue with respect to any
of these systems actually being built is cost, bothdevelopment cost and operating cost in theprice of energy.
The most energy efficient interstellarpropulsion system yet proposed, particle beampropulsion, may not be the most cost effective,but does offers potential for affordable, rapidexploration of nearby stars. With the capability oflaunching probes to 0.3 c in less than twelvehours, the launch rate will be determined by therate of power generation and the energy storagefacilities at the launch site. It is quite conceivablethat probes to all stars within twenty lightyearscould be launched during the first few months ofoperations.
The laser propelled lightsail, while not asefficient as the PBPM, could well be the systemof choice if the price of solar panels continues todrop over the next thirty years. Either way, wecan watch the cost of space-based energy falland predict the time when interstellar explorationbecomes affordable.
[1] Andrews, D. G., and Zubrin, R. M.,"Magnetic Sails and Interstellar Travel," IAF-88-553, 1988.
(2) Forward, R. L, "Antimatter Propulsion,"JBIS, Vol 35,pp 391-395, 1982.
[3] Forward, R. L., Cassenti, B. N., and Miller,D., "Cost Comparison of Chemical andAntihydrogen Propulsion Systems for High AVMissions,"AIAA Paper # 85-1455, 1985
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