mass and cost model for selecting thruster size in electric propulsion systems

7/26/2019 Mass and Cost Model for Selecting Thruster Size in Electric Propulsion Systems

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Mass and Cost Model for Selecting Thruster Sizein Electric Propulsion Systems

Richard R. Hofer and Thomas M. Randolph

Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109DOI:10.2514/1.B34525

A model of system mass and life-cycle costs is used to determine the optimal number of thrusters for electric

propulsion systems. The model is generalized for application with most electric propulsion systems and then applied

to high-power Hall thruster systems in particular. Mass and cost models were constructed for individual thruster

strings using as inputsthe numberof activethrusters,the numberof redundantthrusters,and thetotalsystempower.

Mass and cost are related through the launch cost of the propulsion-system mass, which unifies the optimization to a

single global parameter based on cost. Fault-tolerance and string cost are driving factors determining the optimum

thruster size for a given system-power level. After considering factors such as fault-tolerance, cost uncertainty,

complexity, ground-test-vacuum-facility limitations, previously demonstrated power capabilities, and possible

technology limitations,the development of twothrusters to flightstatus is suggested: a low-power model operatingat

2050 kW per thruster to support missions up to 500 kW system power and the development of a high-power model

operating at 50100 kW per thruster to support missions up to 1 MW system power.

Nomenclature

A, B, C, D, E, F, G, H, I, J = regression coefficientsC = cost k = logGl log2M = massN = number of thrustersP = power

Subscripts

ac = active thruster cab = cablinggim = gimball = learning curve slopemag = electromagnet rd = redundant thruster s = structurestr = stringsys = system tank = tankagetg = thruster and gimbaltot = totalthr = thruster Xe = xenon

I. Introduction

THE selection of electric-thruster power level is an important

consideration for technology programs supporting deep-spacehuman exploration due to the impact that this choice can have onspacecraft payload capability and life-cycle cost. The electric path

human spaceflight architecture proposed by Strange et al. [1]envisions solar electric-propulsion (SEP) spacecraft operating atpower levels of several hundred kW to enable missions to near-Earthasteroids (NEA), Phobos/Deimos, and Mars [28]. In the near term,spacecraft with 200400 kW onboard enable a wide variety of NEAtargets. What thruster technologies and individual power per thrusterare appropriate for these spacecraft power levels? Answers to thesequestions are influenced by a wide variety of factors, among thembeing the maturity of available thruster technologies (has it everflown?), the scalability of the thruster technology with power atconstant specific impulse, system efficiency (thruster plus powerprocessing), throughput capability (life), power-throttling capability,ground-test-vacuum-facility limitations (power and propellantflow rate), power density (kWm2), specific mass (kgkW), and(last but not least) life-cycle cost. Life-cycle costs are influencedby a multitude of factors such as propellant type, ground-testingrequirements, systemcomplexity (especially of the powerprocessing),reliance on exotic technologies (e.g., superconducting magnets),operating voltages, and applicability to other markets such as otherNASA directorates, commercial industry, and the military. Thereare a large number of electric-propulsion technologies that canpotentially meet the needsof specific humanspaceflight applications.Examples include Hall thrusters, ion thrusters, magnetoplasmady-namic (MPD) thrusters, field-reversed configuration (FRC) thrusters,and pulsed-inductive thrusters (PIT). However, very few of thesetechnologies can be practically applied over multiple future-missionscenarios. Among the universe of electric-propulsion technologies,Hall thrusters have been identified as strong candidates for electric

path missions for a variety of reasons [1], chief among them beingtheir long flight history dating to 1970 [9], cost-effectiveness [9],demonstrated scalability to individual powerlevels of at least 100kWoperating on xenon [1012], demonstrated capability to achieve longlifetimes [13,14], and ability to operate efficiently over a specificimpulse range (10003000 s) [15] that keeps trip times suited forhuman missions.The purpose of this paper, though, is notto provide adetailed trade amongst these various technologies. Hall thrusters areselected here as an example foruse in a generalized systemmodelthatcould equally be applied to other technologies. For a given systempower, what Hall-thruster power level is the correct choice based onmass and cost considerations?

As will be shown, due to the impact of redundancy onthe dry massof the propulsion system, there is significant mass benefit to carryingtherightnumber of electric thrusterson a spacecraft. At a givenpowerlevel, carrying toofew thrusterscausesthe mass of redundantsystemsto be an unreasonablyhighfraction of thetotaldry mass. Carryingtoomany thrusters will cause the fixed masses that must be carried with

Presented as Paper 2011-5518 at the Joint Propulsion Conference, SanDiego, CA, 31 July 201103 August 2011; received 14 December 2011;revision received 7 May 2012; accepted for publication 16 July 2012;published online 19 December 2012. Copyright 2012 by the AmericanInstitute of Aeronautics and Astronautics, Inc. The U.S. Government has aroyalty-free license to exercise all rights under the copyright claimed hereinfor Governmental purposes. All other rights are reserved by the copyrightowner. Copies of this paper may be made for personal or internal use, oncondition that the copier pay the $10.00 per-copy fee to the CopyrightClearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; includethe code 1533-3876/12 and $10.00 in correspondence with the CCC.

*Senior Engineer, Electric Propulsion Group, 4800 Oak Grove Dr., MS125-109; [email protected]. Associate Fellow AIAA.Project Systems Engineer, Mission Systems Concepts Group. Senior

Member AIAA.

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eachthruster stringto becomelarge. Somewherebetween toofew andtoo many there exists an optimal number of thrusters at which theelectric propulsion (EP) system mass is at a minimum. Similararguments can be extended to the question of system cost wheredevelopment costs substitute for string redundancy and cost savingsmay be realized through the production of multiple strings at lowerindividual power levels.

To study this optimization we have generated a generic model todetermine the optimal number of thrusters for EP systems based on

mass andcost considerations. Implicit to themodelis that thesystemsare flight qualified for the required propellant throughput and thatother mission margins (e.g., power, duty cycle [16]) are handledseparately on a case-by-case basis. These considerations arediscussed at length in the literature and the interested reader isreferred to [9,1626] for further detail. Data from a number of flightand proposed systems were collected and used to construct mass andcost models for individual thruster strings using the number of activethrusters, the number of redundant thrusters, and the total systempower to be divided between the active thruster strings as inputs. Thestring models incorporate all of the major components in thepropulsion system: thruster, gimbals, power processing unit (PPU),cabling, xenon feed system (XFS), tanks, and propellant. Althoughthe model is applied hereto Hall-thruster systems operating at tens orhundreds of kW, it is generally applicable to a wide variety of thruster

technologies and system power levels if the mass and cost inputs areadjusted for specific applications.

A simpler version of the mass model presented here was originallyderived for gridded ion thruster systems being considered for theJupiter Icy Moons Orbiter (JIMO) project [27]. We have since addedthe cost model andgeneralized them both to be applicable to most EPsystems. Mass and cost are related through the launch cost of thepropulsion-system mass. This unifies the optimization to a singleglobal parameter based on cost that provides guidance in selectingthruster power level. The combined models are applied here to Hall-thruster systems in particular due to the relevance of Hall thrusters tohuman exploration of the solar system.

Thepurpose of this studyis to informthe mission architects choiceof thruster power level in EP systems from the perspective of massand cost. The models are derived in the next section. Specific resultsfor the case of 2040 kW and 200400 kW system power levels arethen presented followed by results for systems operatingup to 1 MW.The results show that the flatness of the global cost function aroundthe optimum provides an opportunity to select thruster power levelbased on additional considerations such as ground-test-facilitylimitations. Factoring in these considerations, it is recommended that2050 kW thrusters be developed to support systems operating up to500 kW total power and 50100 kW thrusters be developed forsystems up to 1 MW.

II. Electric Propulsion System Modeling

A. Mass Model

A generic power and propulsion system consists of three major

subsystems: power generation, power management and distribution(PMAD), and propulsion. Our focus here is with the propulsionsubsystem that must accept power from the PMAD and convert it tothrust. In doing so, we neglect any dependencies between thesesystems that mayimpact thespecifictechnologies selected fora givenmission. This is justified by focusing on optimizations for a giventotal power level to the propulsion system. Any consideration of howthese optimizations scale with power then implicitly assumes acommonset of technologies. In this study, we will primarily focus onHall-thruster-based propulsion systems using xenon propellant andconventional PPU designs. Xenon is adopted because it is the onlypropellant currently used in flight systems, butit should be noted thatpropellants such as argon [28], krypton [29], magnesium [30,31],iodine [32], and bismuth [3335] are feasible. A brief look at theimpact of direct drive PPUs (DDU) will be discussed later. A DDUessentially operates a thruster directly off a high-voltage solar array.This eliminates the need for a dc-dc converter between the solar arrayand the plasma discharge, significantly reducing the DDU mass

relative to a PPU. Additional details on the impact of a DDU onspacecraft performance is provided by Brophy et al. [4].

The mass of the propulsion system is expressed in terms of threekey variables: total system input powerPsys, the number of activethrusters Nac used to process Psys, and the number of redundantthruster stringsNrd. Redundant thruster strings are used only in theevent of a failure. Robotic missions are typically single-fault tolerant(Nrd 1). Human missions may require double or triple faulttolerance. The total number of thruster strings is

Ntot Nac Nrd total number of thruster strings (1)

and the power supplied to each thruster string is

Pthr PsysNac discharge power per active thruster string

(2)

Throughout this paper thetermsthrusterpoweror input powerrefer tothe power consumed by the plasma discharge (i.e., the dischargepower) of a single thruster and do not include the power for theelectromagnets or the PPU efficiency. Strictly speaking then, thesystem power should be modified by the PPU (PthrPppu) andelectromagnet efficiency (1-PmagPthr), which can be expected to be

about 95% and 98%, respectively. Thus, for a 300 kW system, thetotal power necessary from the spacecraft power system would be3000.950.98 322 kW. We chose to use discharge powerbecause it is a fundamental scaling parameter for Hall thrusters andfurther, ourchoice of dischargepoweror total power has no influenceon our choice of thruster power level in this study.

Although many EP systems have been launched with differentfault-tolerance architectures, the broad consensus of the electric-propulsion technical community has moved towards N1; 2; 3thruster/PPU/XFS strings for primary propulsion applications[9,1626]. Here we adopt this fault-tolerance architecture byassuming that each thruster string is independent, consistent with thesystem architecture proposed for Hall thrusters in [9]. The majorcomponents of a thruster stringdepicted in Fig. 1 include the thruster,gimbal, XFS, and PPU. The XFS is composed of the high-pressure

propellantmanagement assembly (PMA) and the low-pressure xenonflow controllers (XFC). Propellant tanks are the only sharedcomponent of the propulsion system.

This fault-tolerance architecture has developed due to failuremodes related to the required high-voltage power processing that arenot present in chemical propulsion systems such as arcing, thermal/electrical component interactions, and grounding. Many of thesefailure modes require block redundancy of the thruster/PPU/XFSstrings to avoid failure propagationfrom one thruster to another.Faultprotection strategies involve redundancies at different system levelsfrom subsystem to assembly, component, and even part levels. At theelectric-propulsion-system level, the thruster/PPU/XFS strings areessentially treated as the appropriatecomponentlevel for redundancy

Gimbal

PPU

Xenon Tank PMAXFC

To S/C

Computer

To Power

Distribution

Xenon Propellant

Command & Telemetry

PowerPMA = Propellant Management AssemblyXFC = Xenon Flow Controllers

PPU = Power Processing Unit

Fig. 1 Major elements of a Hall-thruster string [9].

HOFER AND RANDOLPH 167


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of this system element. EP systems have not yet flown with humansonboard; however, in our view the proposed fault-tolerancearchitecture meets both the requirements of human missions andappropriate practices for EP systems.

The dependence of thruster mass with power level is shown inFig.2. The data was compiled from existing flight and experimental

thrusters up to 50 kW made by Aerojet, Busek, Fakel, Pratt &Whitney, andNASA. Discussions with vendors andour own analysisindicated an expectation that thruster mass scaleslinearly with power.Linear regression was applied to the data. Coefficients from theregression were used to construct an equation for the total mass of allthe thrusters in the propulsion system given by

Mthr NtotAthrPthr Bthr

Nac NrdAthrPsysNac Bthr (3)

The regression was constrained to a zero y-intercept because,otherwise, thescatter in thedata resulted in a negative thruster mass atzero input power. Because this study is concerned primarily withthrusters operating in excess of 20 kW per thruster, the behavior ofEq. (3) at low power does not significantly affect our results. Table1

compiles all of the coefficients (Athr, Bthr, etc.) used in the variouscomponent submodels for both mass and cost.

Gimbal mass is shown as the ratio of gimbal mass to thruster massin Fig. 3 for flight ion and Hall thrusters applicable to NASAmissions. The data is sourced from Moog and NASA systems.Relatively few examples exist, but we note that the gimbalrequirements are similar for both Hall and ion thrusters. From thefigure, we observe that the gimbal is 50% of the thruster mass.Discussions with gimbal vendors indicate that this relationship willcontinue as thruster power levels grow to several tens of kW. Thegimbal mass is then expressed as a fraction of the thruster mass givenabove in Eq. (3). Further, because it may be advantageous to onlygimbal a portion of the total thrusters in the entire propulsion system,we will include a factorfgim that accounts for this possibility. The

gimbal mass is then

Mgim fgimDgimMthr (4)

A combined equation for thethrusterand gimbalmass (tg) is obtainedfirst by combining the coefficients as

Fig. 2 Thruster mass versus discharge power.

Table 1 Coefficients used in the mass and cost models. Nominal values are shown

Name(subscript)

A(kgkWstring)

B(kgstring)

C (kg) D(-)

E($M)

F ($M) f (-) G (-) H(Mkg)

I(kgkW)

J(Mkg)

Basis of estimate

Mass Thruster(thr)

2.4254 0 Various Hall thrusters

Gimbal(gim)

0.5 BPT-4000, NSTAR,NEXT

PPU (ppu) 1.7419 4.654 Various Hall thrustersDDU (ddu) 0.35 1.9 Brophy et al. [4]XFS (xfs) 3.2412 4.5189 JIMO, Hall thrustersCabling

(cab)0.06778 0.7301 JIMO, Hall thrusters

Structural(s)

0.26 JPL practice

Tankage(tank)

0.04 Dawn xenon tank [38]

Xenonthroughput

(xe)

100 BPT-4000

Cost String Cost(str), 2X

2 3.4588 0.34837 Engineering estimate

String Cost(str), 3X


String Cost(str), 4X


GimbalCost

Fraction(gim)

0.08 Engineering estimate

LearningCurve

Slope (l)

0.85 Aerospace industryaverage

NRERERatio (nre)

1.5 Typical value

Xenonpropellant

(xe)

0.1 Avg. xenon cost of1 Mtand BPT-4000throughput (kgkW)

Launchcost

(launch)

0.01 Space shuttle,commercial launch

vehicles

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Atg 1fgimDgimAthr Btg 1fgimDgimBthr (5)

then combining Eq. (3) and (4) give

Mtg Mthr Mgim

1fgimDgimNac NrdAthrPsysNac Bthr Nac NrdAtgPsysNac Btg (6)

Because the regression for the thruster scaling was constrained tozero massat zero power,the same istruefor the gimbal. Althoughthefixed thruster mass can be quite small, a gimbal would not beexpected to have a nonzero mass at zero power. However, very smallthrusters are more likely to not be gimbaled at all, so the accuracy ofEq.(6) is notexpectedto be adverselyimpactedby ourapproachevenfor thrusters of just a few tens of W.

PPU mass versus string power level is shown in Fig.4using datafrom Aerojet, Busek, and Loral. Discussions with vendors indicatethat PPU mass is expected to scale linearly with power using currentdesign approaches. Thermal management in flight systems is

currently passive. Deviations from the linear trend could result ifactive schemes are employed that would be expected to improve thekgkW scaling at high power. Further, the use of a DDU couldconsiderably reduce the power-processing mass. A DDU scalingbased on the one given by Brophy et al. [4] is also listed in Table1.Under the present assumptions the mass of a conventional PPU isgiven by

MPPU Nac NrdAPPUPsysNac BPPU (7)

If a DDU is considered, the Appu and Bppucoefficients in Eq. (7) aresubstituted with the Adduand Bddu coefficients shown in Table1.

A scaling for the mass of the high-voltage cabling was determinedfrom Jet Propulsion Laboratory (JPL) flight programs that used ion

thrusters (Deep Space 1 and Dawn) as well as mass estimates from

other proposed programs (JIMO and various Hall-thruster missionproposalsdeveloped at JPLsince 2006) [27,36,37].The scaling ofthecabling mass is given by

Mcab Nac NrdAcabPsysNac Bcab (8)

Xenon flow systems currently used in Hall thrusters can be modifiedfor specific range of flow rates with little or no impact on the mass ofthe flow system [25,3840]. The XFS mass here includes all ofthe components of the system such as high-pressure regulator,proportional-flow control valves, pressure transducers, thermo-couples, latch valves, services valves, tubing/fittings, etc. Space-qualified parts from Moog, Taber, and others are used in the massestimate. The XFS mass is expressed solely as a function of thenumber of thruster strings and is given by

MXFS Nac NrdBXFS CXFS (9)

Propellant and tankage mass are computed based on the throughputcapability of Hall thrusters and a tankage fraction typical of xenontanks [38]. Qualification testing has demonstrated a 100 kgkWcapability, but this may be a lower bound based on magnetic-shielding technology that may result in throughput capability two toten times higher [13,14]. For this study, the lower bound is used inorder to be consistent with demonstrated capability. The propellantmass is given by

MXe IXePsys (10)

where the coefficientIXeis equal to 100 kgkWas shown in Table 1.Equation (10) assumes that the throughput capability of Hall thrustersis independent of power level. The tank mass is then expressed intermsof thepropellant mass througha tankage fractionand is givenby

Mtank ftankMXe ftankIXePsys (11)

The xenon tank used on Dawn, which stores 425 kg of xenon and hasa mass of 19 kg, is used to estimate the tankage fraction [38]. Underthe present assumptions note that tankage and propellant massare independent of thruster size, so they do not affect the mass

optimization. Viewed another way, this is simply a statement thatregardless of thruster size, the mission will need to process a fixedamount of propellant for a given set of requirements.

Equations (6) through (11) are then combined to find the totalpropulsion system mass given by

Msys 1fsMtg MPPU MXFS Mcab Mtank

1fsNtotfAtg APPU AcabPsysNac Btg

BPPU BXFS Bcabg CXFS 1ftankIXePsys (12)

where a structural fraction fshas been included to account for thoseelements necessary to integrate the propulsion system with thespacecraft bus.

It is illustrative to compute the total string mass for an individualthruster string. This is shown as a function of power level in Fig. 5(top), excluding structure, tankage, and propellant. That is, Fig. 5plots the string mass as

MstrPsys Pthr; Nrd 0; Nac 1

Mtg MPPU MXFS Mcab (13)

ThemasspredictedbyEq.(13) iswithin 3%of a BPT-4000 stringas itmight be implemented on a NASA mission [9]. Also included as thebottomplot in Fig. 5 is the string specific mass, expressed in kgkW.String-specific power is very high at low power because there is aminimum mass required to accommodate all of the componentsregardless of power level. The use of miniaturized and/or simplifiedcomponents could decrease the specific mass at low power, but ourmodel is not intended to capture this possibility. The string-specificmass approaches a fixed level of5.5 kgkWat high-power using aPPU. Note that improvements to the specific mass may be realized

Fig. 3 Ratio of gimbal mass to thruster mass for flight-ion and Hallthrusters applicable to NASA missions.

Fig. 4 PPU mass versus discharge power.

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through technology advances (e.g., direct drive PPUs, lightweightthrusters, etc.). For example, if a DDU is used in lieu of aconventional PPU (see Table 1), the specific mass at very high powerapproaches4.1 kgkW, a reduction of 25%.

B. Cost Model

In this section, we describe a cost model for the propulsion systemthat includes the effects of producing multiple units of the samethruster. Mass and cost are related through the launch cost of thepropulsion system mass. This unifies the optimization to a single

global parameter based on cost that provides guidance in selectingthruster powerlevel. Allcostsreportedhere are strictly rough order ofmagnitude (ROM) intended to account for variations between powerlevel (i.e., relative comparisons) and should not be relied on forbudgeting or planning purposes [21].

Thefirststep in constructinga cost model forthe entire systemis todetermine a scaling for the cost of an individual string. The cost of anindividual string is the sum of the Non-Recurring Expense (NRE)cost and recurring expense (RE) cost. NRE is the cost of developingandqualifying thethruster systemfor flight. NREcosts areamortizedover the total number of thrusters produced and will be discussedmore next. RE is the cost of procuring the string components(thruster, gimbal, PPU, cabling, XFS, tank) and the flight-systemengineering to integrate the system on a spacecraft. We constructed amodel of the stringRE cost as a function of thruster power level usingthe following assumptions:

1) The cost of a 5 kW system is of the order of $8 million [ 21].2) The minimum cost of a system is $2 million.

3) For every 10 times increase in thruster power, the cost willdouble. This trend is based on prior experience for systems operatingless than 10 kW. To account for the uncertainty of extrapolating thisexperience to systems operating at tens or hundreds of kW, a tripling

or quadrupling of cost with 10 times power increases will also beconsidered. If a 5 kW system is $8 million, then a 50 kW systemwould fall in the range of $1632 million (24 times).

4) Gimbals are approximately 8% of the system cost, as based onprior experience for systems operating less than 10 kW. This isincluded to account for the effects of hard-mounting some fraction ofthe thrusters in the system [see Eq. (4)].The resulting cost function, shown in Fig. 6 with coefficients inTable1, is given by

Cstr Estr FstrPGstrthr 11fgimGgim (14)

The string cost includes the component procurement and flightsystemintegration. Forevery10X increase in power, 2X, 3X,and 4Xincreases in cost are shown. Dueto theuncertainty implicit to thecostcurves shown in Fig.6, the cost reduction from the use of a DDUversusthe more expensive PPU is notyet incorporated. Theeffects ofall of our assumptions on the total system cost will be considered inlater sections.

NRE costs can significantly vary depending on the technologyinvolved. Relatively mature technologies like ion and Hall thrusterscan reasonably be expected to scale proportionally to priorexperience. New technologies for which there is little or noexperience in developing flightsystems (e.g., MPD, PIT, FRC) couldbe substantially higher. Here, we adopt a6040 relationship betweentheNRE andRE cost to flythe first thruster. This is expressed in termsof individual string cost as

CNRE GNRECstr (15)

That is, the NRE isoneand a half times higher than the costto fly thefirst thruster. This ratio is commonly used in technology costestimation and is of the correct magnitude based on prior experiencein NASA developing EP flight systems [41,42]. Note that the NREgrows with power level due to its dependence on the string cost givenby Eq. (14), which we expect because it seems reasonable that largerthrusters are more expensive to develop. In order for this relationshipto be a constant value, though, requires that there are no significantdifferences in thetechnology as thepowerlevel increases. At least forHall thrusters, we expect this to be a reasonable assumption up tostring power levels of at least 50 kW.

To account for the decrease in average unit cost when multiplethrusters are produced, we adopt the Wright learning curve model[42,43]. Wrights model, first developed to model the cost savings ofproducing aircraft, has been shown to be generally applicable toindustrial production processes, regardless of the technologyconsidered. The key factor in a Wright learning curve model is the

Fig. 5 Top: Mass of a single thruster string versus input power usingeither a PPU or a DDU. Bottom: Specific mass of a single thruster string

versus input power using either a PPU or a DDU. Both figures excludestructure, tankage, and propellant.

Fig. 6 ROM RE cost of a thruster string given by Eq. (14) versus string

power level with all strings gimbaled.

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learning curve slope, which captures the amount of learning that maybe acquired during multiple unit production through processimprovements, economies of scale, etc. Learning curve slopes Glgenerally vary between 70% (excess capability to learn) to 100%(no learning possible). A common value used in the Aerospaceindustry is 85% [42] and will be used here. In the Wright model, theaverage cost per unit of producing Ntot thruster strings is given by

hCREi CstrNktot (16)

where the exponent variable k is

k logGl log2 (17)

The total RE cost of a system consisting ofNtot thruster strings isgiven by

CRE hCREiNtot CstrNk1tot (18)

Figure7plots the average unit cost and total cost relative to the firstunit produced as a function of the number units produced from theWright model with a learning curve slope of 85% (k 0.234).As more units are produced, the average cost declines and the totalcost increases. For example, for 10 units theaverage cost hasdroppedto 0.58 per unit and the total cost is 5.8, a savings of 42%.

Propellant costs are estimated based on specific throughput.Market conditions can substantially affect the cost of xenon, but theaverage cost over the last twenty years has been about $1 million per1000 kg ($1 million/t). This cost is then related to the specificthroughput (IXe 100 kgkW) in Eq. (10). Xenon costs are thenexpressed in terms of the system power as

CXe HXePeye (19)

Similar to the discussion of the propellant mass in the previoussection, because we base the xenon cost on the system power, thexenon cost isa constantfactorin thesystem cost sodoes notenterin tothe global optimization for selecting thruster size.The system cost iscomputed by combining Eqs. (14), (15), (18), and (19) to give

Csys CNRE CRE CXe CstrGNRE Ns1tot CXe (20)

In order to relate mass and cost, the final element of the cost model isto express the system mass in terms of the cost to launch thepropulsion system to low Earth orbit (LEO). The launch cost is then

Claunch JlaunchMsys (21)

where the system mass is given by Eq. (12). The total cost of gettingthe propulsion system on orbit is then

Ctot Csys Claunch (22)

The value of the specific launch costJlaunchthen acts as a weightingthat scales the relative importance of the mass contribution and the

system cost to the total cost. Lighter systems will have lower launchcosts such that the optimization favors system costs. Estimates ofthe specific launch cost vary significantly depending on how oneaccounts forthe life cycle costs of a launchvehicle (ofcourse, thecostto the taxpayer always includes the life cycle costs). In the case ofNASA missions, the space shuttle is a suitable analog for the heavylift launch vehicles that multihundred kW missions will require.Space shuttle LEO launch cost estimates vary approximately by afactor of five, from $10,000 to $50,000 per kg [ 44,45]. At best, thecommercial heavy launch-vehicle market can currently deliver about$5,000 per kg [45]. SpaceX is targeting a range of $1,500 to$2,400 per kg for the Falcon 9 Heavy [46]. Thus, heavy lift launchcosts, based on actual and projected costs, vary by over an order ofmagnitudefrom $1,500to $50,000 per kg to LEO. Ourbaselinevaluewill assume $10,000 per kg to reflect on one hand, the cost of

launching government payloads, and on the other hand, trends in thecommercial launch-services market aimed at reducing launch costs.Thesensitivity of this selectionon theresults will be consideredin thenext section.

III. Results

Results from the mass and cost model are presented here for thecase of 2040 kWand 200400 kW system power levels. Optimumsare found for arbitrary system powers.

A. Twenty to Forty kW System Power Levels

In preparation for much larger systems, a technology

demonstration mission that flies a high-power EP system is beingconsidered by NASA. Requirements for this mission are still beingdeveloped, but there are at least two major approaches relevant to thecurrent discussion. In the first, the mission flies a subscale SEPsystem that matches the number of active thrusters projected for thefull-scale system. In the second, the individual thruster power levelprojectedfor thefull-scale systemis flown in thedemonstration.Bothapproaches have advantages and a hybrid approach may ultimatelybe adopted. In this section, we present results for possible technologydemonstrators in the 2040 kW range. Becausethe mission is roboticonly single-fault tolerance (Nrd 1) is considered. All of the stringsare gimbaled and use conventional PPUs. The two times string costcurve shown in Fig. 6 is used. The mass and cost of xenon areexcluded because these are invariant with the number of activethrusters and therefore do not affect the optimization. Using the

values in Table1, if the full throughput capability of the propulsionsystem is demonstrated, the xenon mass and cost to support2040 kW systems would be 2,0004,000 kg and $24 million,respectively.

Figure 8 shows the propulsion-system dry mass versus the numberof active thrusters in a single-fault tolerant system with all thrustersgimbaled. Over 2040 kW system power, the minimum mass systemis at four to five active strings or thruster power levels of 58 kW.As will be a common feature of the results of these models, the curvearound the optimum is relatively flat, providing considerable latitudein selecting the thruster power level. For example, at 30 kW systempower, the mass model optimizes at four active thrusters operatingat 7.5 kW each. However, any selection over 211 active thrusters(2.715 kW/thruster) is within 10% of this minimum mass.

Figure9 shows the cost of the propulsion system, while Fig. 10shows the total costs (launch plus system). Because the relative sizeof the launch costs are much less than the system cost, both systemand total cost optimize at two active thrusters over 2040 kW system

Fig. 7 Average RE per unit cost and total RE cost ofN units versusnumber of units produced based on the Wright Learning Curve.

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power levels. The total cost is within 10% of the minimum for anyselection of one to five active thrusters at all power levels. If thedemonstration mission is flown instead without a redundant thruster(Nrd 0), flying a single thruster is optimum. Overall, the resultsshow that the total cost of the propulsion system for system powerlevels of 2040 kW are affected by no more than 10% for anyselection of one to five active thrusters.

B. Two Hundred to Four Hundred kW System Power Levels

The electric path described by Strange et al. [1] supporting humanexploration to near-Earth asteroids requires somewhere between 200and 400 kW for the SEP system. In this section, we present modelresults for propulsion systems in this range of power levels. Double-fault tolerance (Nrd 2) is assumed because the system supportshuman missions. All of the strings are gimbaled anduse conventionalPPUs. The two times string cost curve shown in Fig. 6is used. Themass and cost of xenon is excluded because these are invariant withthe number of active thrusters and therefore do not affect theoptimization. Using the values in Table 1, if the full throughputcapability of the thrusters is required, the xenon mass and cost tosupport 200400 kW systems would be 20,00040,000 kg and$2040 million, respectively.

Figure 11 shows the propulsion-system dry mass versus the

number of active thrusters in a double-fault tolerant system with allthrusters gimbaled. Over 200400 kW system power, the minimum-masssystem isat 1622 active strings or thruster power levels of only1318 kW. Similar to the results presented above, the mass curve isquite flat around the optimum, which allows for a wide selection ofthruster power levels with only small impacts on system mass. Forexample, at 300 kW system power, the mass model optimizes at 19active thrusters operatingat 16 kWeach. However, any selectionover674 thrusters (450 kW) is within 10% of this minimum mass andany selection over 851 thrusters (638 kW) is within 5% of theminimum mass.

Figure12 illustrates the impact of fault-tolerance on the specificmass of the propulsion system for a total power of 300kW.Structure,tankage, and propellant are excluded in the figure. Fault-tolerance

significantly increases the specific mass of the propulsion system,increasingthe optimum number of thrustersat which thesystem massis a minimum. For example, if the number of active thrusters is one,the effects of carrying one, two, or three redundant thrusters is todouble, triple or quadruple the specific mass of the system. If insteadthe number of active thrusters is increased, the redundancy-masspenalty is spread amongst all of the strings, lowering the system-specific mass. However, because there is a fixed mass associated witheach string, the benefits of spreading the redundant-string mass overall the strings is eventually balanced by the fixed-mass penalty ofeach additional string. This balance between the redundant stringsand the fixed mass of each string is why there is an optimum numberof thrusters for a given system power as given by Eq. (12).

Figure13shows the cost of the propulsion system while Fig. 14shows the total costs (launch plus system) for 200 400 kW systems.Unlike the 2040 kW systems, the launch costs are now on par withthe system cost such that the total cost shifts towards the optimumbased on mass alone. The system cost curve optimizes to three active

Fig. 8 Propulsion-system drymass versusnumber of activethrusters atsystem power levels of 2040 kW.

Fig. 9 Propulsion-system cost versus number of active thrusters atsystem power levels of 2040 kW.

Fig. 10 Total cost (launch plus system) versus number of activethrusters at system power levels of 2040 kW.

Fig. 11 Propulsion-system dry mass versus number of active thrustersat system power levels of 200400 kW.

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thrusters over 200400 kW, while the total cost curve optimizes forfour or five thrusters. The total cost curve is within 10% of theminimum for anyselection of 212 thrusters (27150 kW) at300kWand any selection over three to nine thrusters (33100 kW) is within5% of the minimum cost. These rather large ranges provideconsiderable latitude in selecting thruster power level. To narrow the

range further, we consider the scaling of the optimum thruster powerlevel up to 1 MW system power level in the next section.

C. Optimum Thruster Power Levels for Systems up to 1 MW Power

Figure 15 shows the total-cost-optimized power per active thruster(top) and number of active strings (bottom) versus system inputpower. The two times string cost curve shown in Fig. 6 is used.At 1 MW system power, the total-cost-optimized power per activethruster is only 143 kW and the number of active thrusters is seven.

Figure16demonstrates the effects of redundancy on the total-cost-optimized power per active thruster versus system input power.Increasing the number of redundant strings pushes the system tolower power per thruster. If human missions ultimately impose atriple-fault tolerance on the system, the total-cost-optimized thrusterpower level is 125 kW at 1 MW system power. For single-faulttolerant systems, the total-cost-optimized thruster power level is250 kW at 1 MW system power. Thus for single- to triple-faulttolerant systems at 1 MW, the total-cost-optimized thruster powerlevel falls in the range of 125250 kW. However, over this range offault-tolerance (Nrd 13), a system of ten, 100 kW thrustersis lessthan 2% more expensive than the optimum value. Under theseconditions, the development of thrusters up to only 100 kW perthruster would seem to be sufficient to support human exploration for

the next several decades.

D. Sensitivity Analysis

Although theinputs to themass andcost model are numerous,onlya few significantly impact the results. Redundancy has already beendiscussed and is the primary driver towards a larger number ofthrustersunder allconditions.The other potentialdriversare thefixed

Fig. 12 Specific mass of the propulsion system versus number of activethrustersand numberof redundantthrusters at a total power of 300kW.

Fig. 13 Propulsion-system cost versus number of active thrusters atsystem power levels of 200400 kW.

Fig. 14 Total cost (launch plus system) versus number of activethrusters at system power levels of 200400 kW.

Fig. 15 Totalcost (launchplus system)optimized power peractivethruster(top) and number of active strings (bottom) versus system input power.



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masses per string, using a DDU versus a PPU, the launch costs, andthe string costs. Below, we consider the relative impacts of each ofthese factors for systems in the range of 200400 kW.

The fixed mass per string is expressed as the B and Ccoefficients in Table1. Even if the fixed mass is increased by 100%,the mass- and cost-optimized number of active thrusters is onlyweakly affected for 200400 kW systems. This is the main reasonthat the minima of these curves are so flat, especially at high systempower. That is, the fixed mass does notsubstantially affect the systemmass unless a very large number of thrusters are included.

Although using a DDU versus a PPU has the potential tosubstantially reduce the power-processing mass, the effect on themass or total-cost-optimized results is to shift the optima to a lowernumber of thrusters by only one unit for system powers in the200400kW range. Because theDDU reduces thefixedmassfurther,using a DDU also flattens the mass or total cost curves further near

their respective minimums. Brophy et al. [4] also points out that theimpact of a DDU is felt beyond the propulsion system because thehigher efficiency of the DDU can reduce the solar array size slightly,reduce the waste heat, and be less expensive to develop. Powerprocessing is a major cost driver implicit to our estimates of thedevelopment and procurement costs. However, as noted previously,the uncertainty in the cost models shown in Fig. 6 is such that makingthese distinctions requires additional analysis.

Launch costs can play an important role in establishing the totalcost optimization, but only if the two times string cost curve is anaccurate model. The specific launch cost acts as a weighting functionthat determines whether the launch cost or the system cost dominatesthe total cost optimization. If the two times cost prevails for200400 kW systems, variations in the specific launch cost over

$1,50050,000 per kilogram strongly affect the optimization. Forexample, for the nominal two times cost curve and double-faulttolerant systems with 300 kW, the total cost optimized results arethree 100 kW thrusters for a 1; 500kg launch cost, five 60 kWthrusters at 10; 000kg, and eight 38 kW thrusters at 50; 000kg.If thefour times cost prevailsthough, launchcostsplay almostno rolein theoptimization, changing theoptimum stringpower by only a fewkilowatts for system powers of 200400 kW.

Lastly, Fig. 17 shows the total-cost-optimized power per activethruster versus system power for the two, three, and four times costcurvesshown in Fig. 6. As discussed in the previous section, even forthe nominal two times cost curve, the optimum thruster size is stillonly about 150 kW for 1 MW systems. If the three or four times costcurves prevail, 50100kW thrusters are sufficient forany powerlevelup to 1 MW. Thus, although the string cost model can strongly affectthe optimization of a given power level, these results still show thatrelatively low thruster power levels are sufficient for missionsspanning a few hundred kW up to a MW.

IV. Discussion

Our results imply that Hall thrusters capable of operation over arange of20100kW will easilysupportmissionsfrom a fewkW up to1 MW. The development of perhaps two thrusters to flight statuswould be required. A low-power model operating at 2050 kW tosupport missions up to 500 kWand the development of a high-powermodel operating at 50100 kW to support missions up to 1 MW.Given the insensitivity of thruster power level though, otherconsiderations affecting our choice can be weighed by the missionarchitect in this selection. Important considerations not yet addressedinclude system complexity, ground-test-vacuum-facility require-ments, and technology limitations.

Themass andcost modelsare in generalquiteflat near theminima.This results in a surprisingly high number of thrusters being eitheroptimal or near-optimal (within 510%), especially at power levels ofseveral hundred kW. Complexity was a factor that has not yet been

introduced to our model. This was because we do not expect it topresent any more than 5% impact on mass and cost. However,complexity may affect reliability, and more work is needed toconsider how to quantify these influences in themodel. Systems up to10 thrusters do not seem unreasonable, however, which is consistentwith selecting 100 kW thrusters to support 1 MW power systems.

The limitations of ground test facilities to accommodate the highflow rates and thermal loads of high-power EP systems are criticalconsiderations during the technology development process [47].Existing facilities in the U.S. are suitable for Hall thrusters operatingat several tens of kilowatts, but will be stressed for operation greaterthan 100 kW. If new facilities are needed, this capital cost mustcertainly be factored in to our analysis. However, new ground testfacilities would have to cost over $100 million in order to

significantly impact the optimization for multi-hundred kilowattsystems. The prospects for such capital expenditures lookexceedingly dim in the present era of fiscal austerity, providingfurther support for investing in thrusters that existing facilities,perhaps with modest improvements, can accommodate. Again, thispoints us towards thrusters operating at less than 100 kW.

Technology limitations are additional considerations in selectingthruster power level that are not captured in the model. Althoughthere are a large number of EP technologies that can potentially meetthe needs of specific applications, there are very few that can bepractically developed for flight applications and be applied overmultiple future mission scenarios. Among the universe of EPtechnologies, our trade studies have shown that Hall thrusters are thestrongest candidates for scaling to the thrusters sizes needed tosupport systems up to at least 1 MW. Although the practical limit forHall thrusters is not yet well-established, individual thrusters havebeen demonstrated up to 100 kW operating on xenon [1012] and140 kW operating on bismuth [33,48]. High-power Hall thrusters

Fig. 16 Effects of redundancy on the total cost optimized power peractive thruster versus system input power.

Fig. 17 Mass and cost optimized power per active thruster versussystem power for different cost curves.

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were studied extensively by NASA in the early 2000s and designstudies were conducted for thrusters operating up to 150 kW[1012,4954]. Two possible limitations on thruster size are theability to maintain an adequate magnetic field topography acrosslarge channel widths [52] and the ability to manufacture large-diameter ceramic discharge chambers capable of surviving launchloads. The emergence of nested-channel Hall thrusters (NHT)[8,49,50,5558] hasprovidedan alternate developmentpath for50 tomultihundred kilowatt thrusters by circumventing channel-width and

diameter limitations with the use of multiple nested channels. NHTsalso have a high potential to achieve much lower specific mass thansingle-channel devices and high throttling capability (10005000 sspecific impulse and power throttling of2001) [50,55]. Thebenefitsof NHTs are likely to begin to pay off somewhere in the 50100 kWrange.Althoughthe upper limit of NHTpower levelis notyet known,it is worth noting that NHTs operating at 200500 kW would besuited for systems operating at 25 MW.

Although we doubt that systems consisting of more than tenthrusters would ever be flown, it is interesting to consider theimplications of systems with a large number of thrusters. Spacecraftwith many thrusters would have considerably higher controlauthority than those operating with just a few. This can allow the EPsystem to provide not only primary propulsion but attitude control aswell [59]. Control authority can also be traded with mass and cost by

fixing some of the thrusters instead of gimbaling. Fixing half of thethrustersin a 300 kW systemwould decrease the dry mass by6% andthe cost by 4%. Clusters of thrusters certainly present new challengesin spacecraft integration with regards to launch-vehicle packaging,thermal integration, and plume interactions. However, it bearspointing out that none of these systems would be integrated on anyspacecraft that would be considered small. There is ample real estateto accommodate the thrusters for these high-power missions. Manystudies have also been conducted on the effects of clustering onthruster operation, plume formation, etc. [6064]. None of thesestudies have revealed any significant issues with thruster-to-thrusterinteractions. We conclude based on these basic considerations thatclusters up to at least ten thrusters are unlikely to present significantissues and may in fact prove beneficial to the operation of thespacecraft.

V. Conclusions

A generalized model of system-mass and life-cycle costs ofelectric propulsion systems has been applied to the particular case ofhigh-power Hall thruster systems due to their relevance to humanexploration of the solar system. Mass and cost are related through thelaunch cost of the propulsion-system mass. This unifies theoptimization to a single global parameter based on cost that providesguidance in selecting thruster power level. The model is populatedwith data from a number of flight and proposed systems with thenumber of active and redundant thrusters and the total system powerbeing the primary inputs. Fault tolerance and string cost are drivingfactors determining the optimum thruster size for a given system

power level. The flatness of the global cost function around theoptimum provides an opportunity to select thruster power levelbasedon other considerations. Our results indicate that thrusters in the2050 kW range are strong candidates to support systems operatingupto500kWtotalpowerand50100kW thrustersare well-suited forsystems up to 1 MW. Nested-channel Hall thrusters (NHT) operatingat 200500 kW per thruster could potentially extend the applicablerange of Hall-thruster technology to 25 MW.

Our analysis primarily considered systems in three categories oftotal systempower: 2040 kW, 200400 kW, and upto 1 MW. For the2040 kW systems being considered for a near-term technologydemonstration mission, any selection of one to five active thrusters iswithin 10% of the minimum total cost. This allows the selection ofthruster power level for this mission to be based on other factorswithout significantly affecting the mass or cost of the propulsionsystem. Similar results were found for 200400 kW systems, where,for example, the total cost curve is within 10% of the minimum forany selection of 212 thrusters (27150 kW) at 300 kW. This rather

large range provides considerable latitude in selecting thruster powerlevel. To narrow the range further, we also considered the scalingof theoptimum thruster powerlevelup to 1 MW systempowerlevels.At 1 MW system power and a fault-tolerance range of one to threeredundant thrusters, we findthe total-cost-optimizedpower per activethruster to range from 250 kW for single-fault tolerance to125 kW for triple-fault tolerance. However, over this same fault-tolerance range, a system of 10, 100 kW thrusters is less than 2%more expensive than the optimum. After factoring in additional

considerations such as complexity, ground-test-vacuum-facilitylimitations, previously demonstrated power capabilities, and possibletechnology limitations, we conclude that thrusters operating less than100 kW are strong candidates for supporting human explorationmissions operating at several hundred kW.

The relatively low individual thruster power levels suggested bythese considerations is a powerful guide to directing technologyinvestments in high-power EP systems. Hall thrusters capable ofoperation over a range of 20100 kW could support missions from20 kW up to 1 MW. The development of perhaps two thrusters toflight status would be required. A low power model operating at2050 kW to support missions upto 500kWand thedevelopment of ahigh power model operating at 50100 kW to support missions up to1 MW. The extensibility of Hall-thruster technology to even higherpower levels may also be realized with nested Hall thrusters.

Although a practical upper limit of NHT power level has not yet beenestablished, NHTs operating at 200500 kW are likely possible andwould be suited for systems operating at 25 MW. Based on theseresults, it is expected that Hall-thruster technology will be sufficientto support human exploration for the next several decades.

Acknowledgments

This research was carried out at the Jet Propulsion Laboratory,California Institute of Technology, under a contract with NASA.Thanks to John Brophy, Dan Goebel, Steve Snyder, and John Ziemerfor their input and assistance during the formulation of this paper.Special thanks to Ryan Dougherty for his work during the Jupiter IcyMoons Orbiter project developing the mass model for ion thrusters.

The inputs provided for the mass model from the various vendorsmentioned in the study as well as Hani Kamhawi at NASA GlennResearch Center (GRC) is greatly appreciated.

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A. GallimoreAssociate Editor

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mass and cost model for selecting thruster size in electric propulsion systems

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