masters special problem 8900

8/18/2019 Masters Special Problem 8900

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Viability of Dual Propellant with Dual Mode Electric

Propulsion for Geostationary Insertion

AE8900 MS Special Problems ReportSpace Systems Design Lab (SSDL)

Guggenheim School of Aerospace EngineeringGeorgia Institute of Technology

Atlanta, GA

Author:Marius Popescu

Advisor:Prof. Alan W. Wilhite

October 1, 2015

Signature: _________________________

Date: ______________________________

Grade: _____________________________


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Viability of Dual Propellant with Dual Mode Electric

Propulsion for Geostationary Insertion

Marius D Popescu1

Georgia Institute of Technology, Atlanta, GA, 30332

It has been known that dual modes in chemical propulsions systems provide a benefit to

overall inert mass fraction and can reduce cost. Electric Propulsion is growing in popularity for orbit

raising, station keeping, and other orbital maneuvers in order to reduce propellant usage. It is

considered that perhaps similar results may be obtained for these low thrust-long duration

maneuvers by using dual mode.

Nomenclature

g =nominal gravitational acceleration, 9.81m/s2 G =gravitational constant 6.6738e-11 m3/(kg s2)

ϵ 0 =permittivity of free space ()

k b =boltzmann’s constant

h =Plancks constant

µ =gravitational parameter (km2/s2)

a =semi-major axis (km)

r =distance from earth center (km)

v =velocity (km/s)

v eff =effective exhaust velocity (m/s)

v i =ion speed (m/s)

m =current mass (kg)

m0 =initial mass (kg)

m f =final mass (kg)

mGEO =mass delivered to geo (kg)

m p =mass of propellant (kg)̇ =mass flow rate (kg/s)M i =molecule mass (kg/ion)

T =thrust (N)

I sp =specific impules (s)

P =power (kW)

V =Voltage or Electric Potential (V)

E =Electric Field strength (V/m)

I =Current (amps) j =current/area (amps/m2)

V b =beam Voltage

I b =beam Current

V d =discharge Voltage

I d =discharge Current

x a =grid distance (m)

N =number of ions

AG =Grid Area (m2)

e =electron charge (1.6021766e-19 Coulumb)

q =charge (coulomb)

=mass utilizationε + =single ionization energy (eV/ion)c β =cosine of yaw angle β

p =pressure

I. Introduction

ROPELLANT mass fraction is an important

consideration for most space vehicles and issignificant driving factor in the overall price of the

vehicle and mission. A lower propellant mass fraction canmean one of two things: either a larger payload can be

delivered to the same destination or the size of the launchvehicle can be reduced. The first case directly affects cost

per kilogram delivered but only if it is useful to deliver

more payload to the desired orbit. On the other hand, thelatter case may result in a large reduction in overall mission

cost. Choice of propellant influences the propulsionperformance and therefore change the propellant mass

fraction. Of particular importance, choice of propellant can

influence the specific impulse of a propulsion system: ameasure of the momentum imparted by a unit of

propellant.

Propellant mass fraction is a very important driverof cost. In addition, there are many other factors that affect

cost when it comes to propulsion and, in particular,propellant choices. Propellant cost per kilogram for

instance is an obvious consideration. Other factors include:propellant density, corrosiveness, temperature, pressure,

toxicity, stability, viscosity, and development costs. These

factors may affect the overall cost of the propulsion andpropellant storage system as well. This is for instance l ikely

P


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the reason private space ventures prefer hydrocarbon

chemical propulsion systems, like kerosene, althoughsacrificing specific impulse.

Currently, Xenon is the preferred propellant of

choice for electric propulsion. Mercury and Cesium wereearly favorites due to low first ionization energies and

heavy molecular masses. Xenon was chosen later as thepropellant of choice because of its non-toxicity and easier

storage. Xenon’s cost however becomes a fairly substantial

portion of operational costs. Other propellants such asIodine, Krypton, and Argon are cheaper, but may not be as

desirable for performance and testing concerns. However,one should not consider these issues as deal breakers, as in

fact Iodine is a manageable chemical to store, and may offer

slight performance benefits to Xenon.

Electric propulsion and chemical propulsionoperate very differently however. Unlike chemical

propulsion the energy needed to create thrust is not storedin the propellant but from a separate electrical power

source. This means that vehicles using electric propulsionare inherently limited by the power supply and the power

supply is often not cheap nor light. Thrust available is alsorelated to power available and the specific impulse. Electric

propulsion (EP) devices are also able to achieve highervacuum specific impulse values than chemical rockets:

typically above 1000s while chemical specific impulsestypically range between 250 and 450. This advantage

comes with some consequences however. As mentionedearlier, higher specific impulses also tend to lower the

thrust available for a given power, this along with trying tolimit the overall size of the power supply typically resultsin a very low overall thrust to weight ratio for EP vehicles.

Low thrust to weight ratios are generally undesirable,resulting in longer trip times and additional steering,

gravitational, and drag losses.

Unfortunately, substantial improvements inpower supplies will be necessary to minimize these losses;

however, the very high specific impulse often overcomesthe downsides. Nonetheless, slight improvements in

thrusting could provide benefit. In general, slightly higher

thrust provides substantial benefit at the nodes forinclination changes, lower altitude orbit raising, and

reducing transit time, while higher specific impulse is moreimportant for high altitude maneuvers and station keeping.

As mentioned, choice of propellants provide a tradeoffbetween thrust and specific impulse. The goal of this

research is to demonstrate that a combination of cheaper,

less established choices for propellants can possibly besuperior to Xenon.

II. Literature Review

It is known that varying specific impulse and

thrust to weight on a vehicle can be advantageous.Historically this has generally been done by staging, but is

advantageous even if only one stage is used. In chemicalpropulsion, multiple fuels are often used to vary thrust to

weight and impulse between stages; it has also been shownto be beneficial in a single stage due to the tradeoff between

specific impulse which considers the efficiency of the fuelto impart momentum and density impulse which takes into

consideration the density of the fuel, which drives tank andstructure weight. Furthermore there is more benefit in

having a single engine than separate engines burning inparallel [1] which led to a few conceptual designs in dual

fuel dual expander rocket engines, which burned both

hydrocarbon and hydrogen fuel within concentriccombustion chambers and expanded through a shared

nozzle. In addition, using multiple propellants mayincrease thrust efficiency, benefit the propellant tank

system design, and reduce cost impulse (that is that one

fuel may be cheaper to provide the same ΔV). It’s possiblesimilar advantageous could be applied to electric

propulsion, and be even more effective. An electricpropulsion device that can vary its impulse and thrust over

a large range means it could be in a more optimal specific

impulse regime for different parts of the mission, ie,planetary orbital maneuvers and interplanetary travel.

Even a small range can increase performance; it alsobenefits from better flexibil ity and management of power

levels throughout a mission. For instance, as massdecreases during a mission, the optimal Isp increases, and

changes in power level or large gravity or drag losses may

optimize Isp lower. Being able to vary modes also may makeit possible to burn continuously which further reduces trip

times. It has been shown that varying specific impulse inany propulsion device and electric propulsion in particular

can provide significant reduction in propellant cost and

mass and/or trip time for interplanetary missions asshown in the figure below. [2] It is therefore of interest to

develop an electric propulsion device that can vary its

impulse aka Variable Specific Impulse Electric Propulsion(VSI EP). This is precisely the reasoning behind thedevelopment of VASIMR.


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The above table shows that despite additional

gravitational losses and not being able to utilize the Obertheffect, low thrust NEP can reduce the amount of propellant

needed, ignoring time constraints. As shown in Figure 1,adding variable impulse to the device can further improve

mass fraction. Furthermore the same paper by ActaAstronautica states:

“It is quite interesting to notice how the variable -Isp

thruster permits a 10% mean reduction of the propellantconsumption. This value is slightly lower (about 9%) if the

unavoidable upper and lower limits for the Isp are imposedat reasonable levels, but it can double in special cases (like

for long missions with gravity assist and low total

propellant mass). It has to be recognized that up to 80% ofthe achieved propellant mass savings could be obtained

using dualmode thrusters, considerably simpler to develop

and qualify.” [2]

There has been some research done exactly as towhat range of specific impulse is necessary and optimal for

a given mission or vehicle. Unfortunately, the reference dpaper does not explicitly state the bounds, but one can infer

the range to be about 2800-3500s for the mission to Mars,

furthermore the paper is not clear on what the maximumand minimum specific impulse they found when the

bounds were not imposed.[2] A similar study conducted bythe company that created VASIMR, Ad Astra, found that on

a mission to Mars allowing the specific impulse to varybetween 4000s and 30000s vs a constant specific impulse

of 5000s given a power input and initial mass allowed them

to save about 15% of propellant. [3] It is worth noting thatthe paper did not state whether or not the constant specific

impulse value was an optimized value or chosenarbitrarily, and that this range of specific impulse is not

particularly close to the currently realized range of 2000-

10000. An earlier paper did constrain the specific impulse

range to 2000-10000s and found that there would be

significant savings to an optimized constant specificimpulse and that this effect tended to be more dramatic at

higher power levels (shorter transit times), as seen in thefigures below. [4]

These studies focus on Earth to Mars missions. The

effect of variable specific impulse is expected to be more

exaggerated in interplanetary travel as compared tomissions within the Earth’s sphere of influence such as LEO

to GEO transfer. Indeed, a few papers have been publishedon the subject. A paper discussing an improvements to

analyt ical technique called Edelbaum’s approach foundthat even from a simplified analytical approach there were

positive results for variable specific impulse as seen in the

figure below. [5]


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POPESCU 4

[5]

Another earlier paper discussing a more specificexample of a LEO and GTO to GEO transfer with variable

specific impulse claiming a “almost 1% increase inpayload spacecraft mass while preserving delivery

times”[6]. The results from all of these papers demonstratesome significant predicted propellant savings.

Considering the above results, there is currently

some amount of work being done on variable specific

impulse or multi-mode EP devices. Currently, specific

impulse is principally varied by modulating electrical orheating parameters in devices. Hall effect thrusters canvary their specific impulse by increasing or decreasing the

discharge voltage and beam current. The range betweenminimum and maximum specific impulse for currently

available hall thrusters is approximately 500 to 1000s with

the typical maximum specific impulse around 3000s. Hallthrusters are currently the most commonly studied

potential bimodal electric propulsion device and mostalready have some specific impulse flexibility over a small

range. Ion thrusters might in theory derive the most benefitfrom dual propellants, they suffer from inefficiencies at

lower specific impulse operation and scalability makingthem not as practical for LEO-GEO orbit raising. There areattempts modifying ion engines to be partially bimodal, the

GIE NEXT attempts to improve upon throttle-ability andspecific impulse, but over a large range of power and

suffers technical issues. Although no other flown models

have been specifically designed for variable specificimpulse, there are some models being tested and designed,

including the T-220HT-HET currently being developed andtested in Georgia Tech’s HPEPL. In addition to more

conventional Hall thrusters, there are other short and

medium term technologies being pursued. The same paper

from Acta-Astronautica mentions some of these: Hybridelectrostatic systems like HET/GIE (ex. QinetiQ) which

combines the two propulsion systems either in parallel oras an integrated system (much the same principle as the

chemical rockets), and double stage hall-effect thrusters

(ex. SPT-MAG and LABEN-ALTA DSHET), which separates

the ionization and acceleration regions of hall effectpropulsion. Shorter term Nested Hall Thrusters (NHT)have a big potential in covering a broad range of specific

impulses and thrust levels. Of course, there are also longer

term and more novel technologies such as the VASIMR, PITand HIIPER concepts to approach the goal of VSI EP.

Currently the most prominent design considering

variable specific impulse for electrically powered marstransit vehicles is VASIMR. VASIMR stands for VAriable

Specific Impulse Magnetoplasma Rocket and is beingdeveloped by the Ad Astra Company founded and led by

former astronaut Chang Diaz. Simply stated, VASIMRessentially develops thrust by heating a gas and converting

its perpendicular motion into parallel motion,

fundamentally similar to chemical rockets. It consists ofthree stages which comprise three main subsystems: theplasma injection stage utilizing a helicon antenna, the

heating stage utilizing an Ion Cyclotron Resonance Heating

(ICRH) antenna, and the expanding stage utilizing amagnetic nozzle. The design is electrode less, meaning that

the high temperature plasma does not erode the device andcan handle high power densities. This is achieved by

magnetic confinement which ties all three stages togetherand using RF power to produce and heat the plasma. Thrust

and specific impulse is varied primarily by selectivelypartitioning the RF power to the helicon or ICRH systems,

along with adjusting the propellant mass flow.

VASIMR experiences a few technological

challenges at the moment. Contributing many of issues arethe large and strong magnetic fields it requires. This

presents 4 main issues: charged particles remainingattached to field lines causing greater beam divergence,

losses, and charging of the spacecraft, the powerful

superconducting magnets required are both complex andheavy, the shielding that would be required for both

communication and health considerations, and inducedtorques or movement of charges due to electromagnetic

interactions. In addition to this, VASIMR suffers fromsignificant thermal management considerations, requiring

rather large and potentially heavy radiators. The latterissue is only more profound when the power systems are

taken into account, which represents the most important

consideration with any electric propulsion device. VASIMRgets significant benefits from increasing power levels, and


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since its proposed roles are primarily interplanetary

and/or large payload coupled with fast transit, it isgenerally advocated that the VASIMR operates in MWs of

power. Due to this Dr. Chang Diaz has suggested nuclearpower, which additionally needs significant thermal

management, and is likely heavier than solar power.

VASIMR has also yet to demonstrate long term firing over

the ambitioned specific impulse range. As of today the VX-200 can only be fired for less than a 60 seconds with 1.2seconds being the average firing length and needs to be

cooled down over an extensive period of time, and the

specific impulse has only been optimized and controlledbetween 780s – 4900s, far less than the ambition range of

3000 – 30000s [6][7].

So far, the demonstrated VX-200 has been able toachieve maximum 51mN/kW at 1660s and 35 mN/kW at

the maximum thrust level, and thrust efficiencies variedfrom around 10% to 72% at the highest thrust level with

around 30% thrust efficiency around the maximum thrustto input power, for short periods of time. [7] On the other

hand Hall effect thrusters have demonstrated levels of

90mN/kW at similar efficiencies or better over a similarrange. NASA’s 47Mv2 Hall thruster has demonstrated

76.4 mN/kW at low power and 46.1mN/kW at max power,

with anode efficiencies between about 55 to 70%. [8]

Furthermore the specific power of VASIMR is projected toonly come down to about 1.6kg/kW for a 1MW case,

3kg/kW for 250kW case. [9] Whereas the hall effectthrusters have demonstrated 1.3 kg/kW and below at 6kW

which improves with scaling. [10] Nested hall effectthrusters are expected to improve those values even

further to perhaps 0.5kg/kW for MW levels and be able tovary impulse between 1000-5000s.[11] It should be also

considered that Hall effect thrusters have been flown and

tested extensively, and can be fired for 1000’s of hours.

They have also been shown to be fuel flexible with the

400M model operated on both krypton and xenon. Benefitsfor dual propellants can benefit any electric propulsion

device including VASIMR, which can virtually run on any

propellant and has considered propellants such asdeuterium and krypton. However, until VASIMR has

demonstrated to be more competitive with current andshorter term technologies, the focus of the research will be

more focused on demonstrated propulsion devices such asHall Effect thrusters and electrostatic ion engines.

III. Methodology

Engine Modeling

The first task in evaluating the performance of thesystem is to determine the performance characteristics for

the propulsion system. For either an electrostatically

accelerated ion engines such as gridded ion engine or hall

effect thrusters a particle will be accelerated through anelectric potential. The speed of a charged particle is given

by Equation 1 where x is the distance downstream of thethruster.

Eq. 1 is the potential change from an initialreference. In the case of Hall Effect thrusters an dropaverage potential must be used since not all the particles

will be ionized from the same potential in the thrusters. Inthe case of the gridded ion engines the net potential drop

through the grids should be used. The net potential drop of

the beam overall in either scenario is known as the beamvoltage and this generally summarizes as .Thrust is simply given by

̇ ≈ ̇ Eq. 2Where κ is some correction value. The mass flow

rate is found from the beam current:

̇ Eq. 3In the case of ion engines there is a maximum

current that can be drawn between two grids that is

dictated by Child’s Law. It is derived from the Poisson’srelation.

∇ Eq. 4Substituting equation 1 in equation 4, integrati ng

twice and substituting V = 0 at x = xa leads to Child

Langmuir law.

4

9 /

Eq. 5

It is important to note that this is the maximum

current that can be drawn between any two grids spaced xa distance apart.

The correction factor is primarily determined

from the beam divergence angle which accounts for the factthat the ions may not leave the device perfectly parallel.

This factor depends a lot on the design of the device but are

typically on the order of 5-10 degrees for ion engines and10-20 degrees for Hall Effect thrusters. In addition, the


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correction factor may include a correction for double

charged ions and neutral particles. This leads to a simplegeneralized formula.

≈ cos Eq. 6Where

is the mass utilization efficiency which

is the ratio of ions to neutrals that leave the thruster,typically on the order of 90%. is the divergence angle indegrees. is the correction for current from doublecharged ions. These are summarized below.

̇̇ cos ∫ cos

+

√

++

+ ++ Where + ++ and

Eq. 7

a,b,c,d

This also leads to the relation for specific impulse.

Eq. 8Two other important values for analysis later are

the electrical efficiency and thruster efficiency. The

electrical efficiency is defined as the power input vs the

beam power.

ℎ Eq. 9And the thruster efficiency is defined as the power

of the jet vs the input power.

̇ Eq. 10With some simple substitution from equation 2,6

and 8 the thruster efficiency can be generalized as:

Eq. 11These values are unfortunately difficult to predict

analytically, and would require far more in depth analysisor powerful software than is necessary to the provide

approximation needed in this paper. Instead, values are

pulled from existing models to provide the representativemodel necessary here. Unfortunately, in order to capture

some of the effects of alternative propellants some of the

performance values will vary for each propellant and some

will have to be approximated by other means if not enoughvalues were found. In order to approximate these,

parameters for Xenon and other propellants (if they wereavailable) were found for both thrusters from various

sources, and a representative value was chosen for the

model in this paper. The tables below summarize these.

Gridded Ion Thruster Parameters

Table 1. Operating Power Range (kW)

SOURCE VALUE PROPELLANT

NSTAR [12] 0.52-2.3 Xenon25-cm XIPS [12] 2-4.3 Xenon13-cm XIPS [12] 0.42 Xenon

T-5 [12] 0.476 XenonRIT-10 [12] 0.46 Xenonµ10 ECR [12] 0.34 XenonETS-8 [12] 0.541-0.611 Xenon

NEXT [13] 0.54-6.9 XenonHIPEP [14] 10-40 XenonT-6 [15] 2.5-4.5 XenonBIT-3 [16] 0.06 Iodine

NASA DERATED [17] 0.5-5.5 Krypton & XenonNASA 1984 [18] ~1.5 Argon&Krypton

&Xenon

Table 2. Typical Operating Beam Voltage (V)


NSTAR [12] 1100 Xenon

25-cm XIPS [12] 1215 Xenon13-cm XIPS [12] 750 Xenon

T-5 [12] 1100 XenonRIT-10 [12] 1500 Xenonµ10 ECR [12] 1500 XenonETS-8 [12] 996 Xenon

NEXT [13] 1800 XenonHIPEP [14] ~5000 XenonT-6 [15] 1850 XenonBIT-3 [16] 2000 Iodine

NASA DERATED [17] ~1000 Krypton&XenonNASA 1984 [18] ~1000 Argon&Krypton

&Xenon

Table 3. Beam Current (A)


NSTAR [19] 0.51-1.76 Xenon25-cm XIPS [12] 1.4-3.05 Xenon13-cm XIPS [12] 0.4 Xenon

T-5 [12] 0.329 XenonRIT-10 [12] 0.234 Xenonµ10 ECR [12] 0.136 XenonETS-8 [12] 0.43-0.48 Xenon


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NEXT [13] 3.52 XenonHIPEP [14] ~4.8 Xenon

T-6 [15] 2.14 XenonBIT-3 [16] 0.021 IodineNASA DERATED [17] 3.2 Krypton & Xenon

Table 4. Typical Accelerator Grid Voltage (V)


NSTAR [19] -180 Xenon25-cm XIPS [20] -375 Xenon13-cm XIPS [21] -300 XenonT-5 [22] -250 Xenon

RIT-10 [23] -180 Xenonµ10 ECR [24] -350 XenonETS-8 [25] -479 XenonNEXT [26] -210 Xenon

HIPEP [27] -700 XenonT-6 [15] -265 Xenon

Table 5. Active Grid Area [~beam diameter] (m 2)


NSTAR [12] 0.0642 Xenon

25-cm XIPS [12] 0.0491 Xenon13-cm XIPS [12] 0.0133 XenonT-5 [12] 0.00785 Xenon

RIT-10 [12] 0.00785 Xenonµ10 [12] 0.00785 XenonETS-8 [12] 0.0113 XenonNEXT [13] 0.102 Xenon

HIPEP [14] 0.373 XenonT-6 [15] 0.038 XenonBIT-3 [16] 0.00237 Iodine

NASA DERATED [17] 0.0707 KryptonNASA 1984 [18] 0.0113 Argon&Krypton

&Xenon

Table 6 . Grid Transparency (%)


NSTAR [26] 80-88 XenonNEXT [26] 78-90 Xenon

HIPEP [28] ~74-82 Xenon

Table 7. Nominal Discharge Voltage (V)


NSTAR [19] 25 Xenon25-cm XIPS [20] 25 Xenon13-cm XIPS [21] 30 Xenon

T-5 [22] 42 XenonETS-8 [25] 32.5 XenonNEXT [13] 25 Xenon

HIPEP [14] 28 XenonT-6 [15] 30 Xenon

Table 8. Nominal Discharge Current (A)



25-cm XIPS [20] 18 Xenon13-cm XIPS [21] 3.4 Xenon

T-5 [22] 2 XenonETS-8 [25] 4 XenonNEXT [29] 18.2 XenonHIPEP [27] 26.9 Xenon

T-6 [15] 18 Xenon

Table 9. Thrust Available (mN)


NSTAR [12] 20.7-92.7 Xenon25-cm XIPS [12] 80-166 Xenon13-cm XIPS [12] 17.2 XenonT-5 [12] 18 XenonRIT-10 [12] 15 Xenonµ10 [12] 8.1 Xenon

ETS-8 [12] 20.9-23.2 XenonNEXT [13] 25.5-243 XenonHIPEP [14] 240-~800 Xenon

T-6 [15] 73.8-142.7 XenonBIT-3 [16] 1.4 Iodine

Table 10. Nominal Specific Impulse (s)


NSTAR [12] 1980-3196 Xenon

25-cm XIPS [12] 3420-3550 Xenon13-cm XIPS [12] 2507 XenonT-5 [12] 3200 XenonRIT-10 [12] 3400 Xenon

µ10 [12] 3090 XenonETS-8 [12] 2404-2665 XenonNEXT [13] 1400-4190 XenonHIPEP [14] ~6000-9600 Xenon

T-6 [15] 3710-4120 Xenon

BIT-3 [16] 3500 Iodine

Table 11. Decel Grid Voltage if applicable (V)


25-cm XIPS [20] ~0 Xenon

T-5 [12] -50 Xenon

Table 12. Nominal Electrical efficiency (%)


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25-cm XIPS [12] 87 Xenon13-cm XIPS [12] 71.3 XenonT-5 [12] 76.6 Xenon

RIT-10 [12] 76.5 Xenonµ10 [12] 60 XenonETS-8 [12] 78.2-79.5 Xenon

NEXT [32] ~127 (W/A)* XenonHIPEP [14] ~200 (W/A)* XenonBIT-3 [16] 62 Iodine

Table 13. Mass utilization Efficiency (%)


NSTAR [19] 88? Xenon25-cm XIPS [12] 80-82.5 Xenon13-cm XIPS [12] 77.7 XenonT-5 [12] 76.5 Xenon

RIT-10 [12] 69.3 Xenon

µ10 [12] 70 XenonETS-8 [12] 66.2-73.5 Xenon

NEXT [13] 89-93 XenonHIPEP [14] ~90-92 XenonT-6 [15] 69.3-75.3 XenonBIT-3 [16] 68 Iodine

Table 14. Max total efficiency (%)


NSTAR [12] 63 Xenon25-cm XIPS [12] 68.8 Xenon

13-cm XIPS [12] 50 XenonT-5 [12] 55 XenonRIT-10 [12] 52 Xenonµ10 [12] 36 XenonETS-8 [12] 49.7 Xenon

NEXT [13] 71 XenonHIPEP [14] ~80 XenonT-6 [15] 65.7 Xenon

* The efficiency can also be described as ion production cost in W/A.Although it is not always clear if this exactly the definition for e lectrical

efficiency.

Table 15 Thrust Correction factor for beam divergence



13-cm XIPS [21] 0.97 XenonT-5 [31] 0.988 XenonNEXT [32] 0.96-0.98 XenonHIPEP [34] 0.99 Xenon

T-6 [15] 0.986 Xenon

Table 16 Doubles Current Fraction


NSTAR [19] 0.18 XenonT-5 [35] ~0.20 XenonNEXT [29] 0.045 Xenon

T-6 [15] 0.13-0.21 Xenon

Table 17 Nominal Discharge Cathode Keeper Current (A)*


NSTAR [19] 1.5? Xenon25-cm XIPS [33] 1 Xenon

13-cm XIPS [21] 1 XenonT-5 [22] 1 XenonETS-8 [25] 0.5 Xenon

NEXT [13] 6-12 XenonHIPEP [14]** 0.23 XenonT-6 [15] 1 Xenon

Table 18 Discharge Cathode Voltage [highest power] (V) *


NSTAR [19] 3 Xenon25-cm XIPS [33] 9 Xenon13-cm XIPS [21] 19 Xenon

T-5 [22] 12 XenonETS-8 [25] 4.2 XenonNEXT [13] 25? Xenon

HIPEP [14]** 35 XenonT-6 [15] 42 Xenon

Table 19 Nominal Neutralizer Current (A)



25-cm XIPS [33] 0.5 Xenon13-cm XIPS [21] 1 XenonT-5 [22] 22 XenonRIT-10 [36] 0.6 Xenon

µ10 [37] 0.5† XenonETS-8 [25] 0.51 XenonNEXT [13] 3 Xenon

HIPEP [14] 3 XenonT-6 [15] 1.75 Xenon

Table 20 Nominal Neutralizer Voltage (V)


NSTAR [19] 13.5 Xenon25-cm XIPS [33] 16 Xenon13-cm XIPS [21] 19 XenonT-5 [22] 0.66 Xenon

RIT-10 [36] 15 Xenonµ10 [37] 16† XenonETS-8 [25] ~16 Xenon

NEXT [13] 12 XenonHIPEP [14] 10.6 XenonT-6 [15] 25 Xenon


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Table 21 Accelerator Current (mA)


NSTAR [19] Xenon25-cm XIPS [20] Xenon

13-cm XIPS [21] Xenon

T-5 [22]


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appropriately for variances of the perveance for the

different propellants. Unfortunately optimum grid spacingand hole diameter is an analysis that will not be discussed

for this paper. The values used here were approximatedbased on the on the XIPS-25.

Table 28 Gridlet sizing

PARAMETERS VALUE

SCREEN VOLTAGE (V1) 1100 V

ACLLERATOR VOLTAGE (VACC) -450 V

DECELERATOR VOLTAGE (VDEC) -15 V

BEAM VOLTAGE (Vb) 1100 V

SCREEN TO ACCEL GRID SPACING (ℓG1) 2.5mm

SCREEN TO ACCEL GRID SPACING (ℓG2) 2mm

SCREEN HOLE DIAMETER (dS) 3mm

ACCEL HOLE DIAMETER (dA) 2.4mm

DECEL HOLD DIAMETER (dD) 3mm

SCREEN THICKNESS (tS) 1.6mm

ACCEL THICKNESS (tS) 2.5mmDECEL THICKNESS (tS) 1.6mm

The Child Langmuir law should be modified toaccount for a non-planar sheath and screen thickness. This

change accounts for the effective sheath thickness ℓe andthat the maximum current that can be drawn is determined

by the difference between the screen voltage and

accelerator voltage.

4

9 /

ℓ

Eq. 12

ℓ ℓG /4 Eq. 13Where ℓg is the grid gap spacing, t s is the screen

thickness and ds is the screen hole diameter. The maximumelectric field is still limited by the grid gap spacing. The goal

of the study is to demonstrate the ability to switch betweena high thrust lower specific impulse mode and a low thrust

high specific impulse mode, while operating at the highest

thrust to power ratio, but remaining at a constant highpower level. The beam power required per area is given by:

PB 49 /ℓ

Eq. 14

There is a constraint that the power level must

remain the same regardless of propellant, but it can be seenthat lighter propellants will drive the current higher which

in turn will drive the power requirement up if the voltageis not adjusted. Lowering the beam voltage would be

counter-productive since the beam voltage drives the ion

exit speed. Instead the extraction voltage between thescreen and acceleration grid can be altered. Since the

screen voltage and the beam voltage are generally within50V of each other, so the acceleration voltage grid should

be varied. Regarding perveance, it is assumed in this paper

that the ion optics can be operated close to the Child-

Langmuir limit for each propellant given the grid geometry .[38] This is also typically the most electrically efficientmode of operation. However, the issue of perveance limits

for the gridded ion engine and multiple propellants is

interesting and may be a future topic.

The beam divergence will be computed from

equation 15, coming from a paper on beam optics in accel-

decel systems. [39]

/.67ℓG

ℓG

ℓG

ℓG

Eq. 15

Where P is the current perveance and P 0 is theperveance as computed with Child-Langmuir law with the

grid gap instead of the effective length. f 1 and f 2 are the

focus lengths of the ion optics.

3ℓG .75 ℓGℓG / 4ℓG

Eq. 16

a,b

Where V12 and V13 are the absolute values of thedifference from the accelerator grid and decelerator grid

respectively. Unfortunately, double ion fraction andpropellant utilization is harder to predict without choosing

a specific thruster or with very rigorous computationalanalysis. The Saha equation could be used with both single

and double charged ion (Eq.17 modified from Ref. 41)where the temperature is electron temperature in the

discharge.

.

.

ℎ +

−

Eq. 17

Where ∑ /

+ ∑ + /


12/33

POPESCU 11

However, the Saha equations a re li mited in accuracy

in the highly ionized gas of the dis charge chamber. This

method is nonetheless tested and compared. Fortunately

however, there is a paper from 1971 that a nalyzed the use of

different noble gases in an ion thruster. [42] Using Table 2

from this sourc e and holding the magnetic field constant

these operating points were chosen for the nobl e gases. The

Operating magnetic field for the va lues were 3.7e-3 and

4.8e-3 Tesl a for krypton and xenon respectively . Argon

however used the reference provided in ref. 42, the paper on

SERT II operating on argon [43], si nce ref. 42 used a modified

thruster for argon, which seemed to skew the results fai rly

heavily.

Table 29. Propellant operating points

GAS DISCH.

LOSS

eV/ION

MASS

UTIL. ηm

DISCH.

VOLT-

AGE

DISCH/

BEAM

CURRENT

RATIO

XENON 248 0.9 37 8

KRYPTON 263 0.86 37 8.11

ARGON ~275 ~0.73 ~65 n/a

Another paper referenced in Ref. 42 describes the

double to singles ratio, provided below. [44]

Table 30. Doubles to Singles Current Ratio

GAS XENON KRYPTON ARGON

RATIO 0.05 0.04 0.09

Unfortunately, SERT II was never tested withiodine. An extensive literature search revealed that almost

no testing has been done on iodine gridded ion thrusters,only very recent interest has led to the development of the

Busek BIT-3, which can run on iodine. Unfortunately,Busek has released very little information regarding the

performance comparison between the two. However, usingvalues in Ref. 45 and Ref. 46, which is actually regarding

iodine use in Hall thrusters, an estimate of a comparable

performance was made.

Table 31. Iodine Estimated Performance

DISCH. LOSS

eV/ION

MASS UTIL.

ηm

DISCH.

VOLTAGE

DOUBLES TO

SINGLE RATIO

~230 0.89 36 ~0.01

Where the performance values are calculated from

the equations in Ref 18, Ref 20, and Ref 47.

∗ [ − ̇ − ]− Eq. 18Where

̇ ̇ Eq. 19̇ 4 Eq. 20

4

Eq. 21

Where C0 is the primary electron utilization factor,̇ is the current equivalent flow rate, εp* is the baselineplasma ion energy cost, determined by the mean energy it

would be to produce an ion if all primary electrons wouldhave an inelastic collision with an atom (thus resulting in

ionization or excitation). ϕ0 is the neutral grid

transparency, σie is the total electron-atom cross section, Ag is the total grid area exposed to discharge chamber, v 0 is

the atom thermal velocity,

8 / Eq. 22

vp is the primary electron velocity given by

/ Eq. 23τp is the average confinement time of the primary

electrons which can be approximated by

≈ Eq. 24Where Ap is the average loss area for the primarieswhich can be given by

Eq. 25Where B0 and T0 are the surface magnetic field and

chamber averaged neutral temperature, rp is the Larmor

radius of the primary electrons, and Lc is the magnetic cusp

length. Assuming a cylindrical chamber, it is possible toalso make the approximation that the chamber volume is

approximately Lc times the grid area Ag so that Eq. 24becomes

≈

Eq. 26

Rewriting

ℓp 4ℓp Equation 18 can be rewritten


13/33

POPESCU 12

∗ [ −− / ]− Eq. 27From Ref 44, an electron discharge voltage of 36

eV is assume. While not at the absolute highest ionizationcross section, this also reduces the doubles ionization cross

section, so that the single ionization cross section is 5.93 Å 2

and a double ionization cross section of 0.032 Å2. Using thiselectron temperature and the operating magnetic field of4.8e-3 Tesla, the Larmor radius is 4.273 mm. Assuming a

neutral temperature of about 400K and neutral grid

transparency of 50% and using the Xenon data for SERT IIfrom Ref 42, an average confinement time estimate of 13μs

is used. To find the baseline plasma ion energy cost foriodine is found by solving for ∗ simultaneously using[from Ref 18]

∗ +

〈〉 + + 〈+ 〉 / Eq. 28

And

∗ /+ 〈+ 〉 + Eq. 29Thus finding the appropriate Maxwellian to

primary ratio as well. Where

8 / Eq. 30 43 Eq. 31

〈+ 〉 ∫ + ∞ ∫ ∞ Eq. 32

/ 4− Eq. 33

Where +is the cross section for single ionization,+ is the cross section for single ionization at primaryelectron energy, is the cross section for excitation, isthe energy lost to the anode from Maxwellian electrons, + is the single ionization energy, is the lowest excitationstate, TM is the Maxwellian temperature, and VA is the

anode sheath potential taken as 2V.

The doubles and singles current could also be

determined using the equation in the Brophy text;however, Ref 46 seems to suggest that with a Xenon

multiple charged current fraction of ~0.05 the equivalent

for Iodine would be approximately 0.01 (since charged I2 provides additional mass which reduces the impact of

multiple charged ions).

Ignoring scaling effects the appropriate thrusterefficiencies are calculated for each propellant below at the

given design point.

Table 32. Summary of Propellant Performance

GAS γ ηe ηm ηT Isp

IODINE 0.985 0.827 0.89 0.714 3655

XENON 0.972 0.816 0.9 0.694 3586

KRYPTON 0.978 0.807 0.86 0.664 4315

ARGON 0.987 0.8 0.73 0.57 5354

Note that the total efficiency for the propulsion

system will also include the PPU efficiency which isassumed to be 94% across the board since input power to

thruster will not vary during operation. PPU efficiency willlikely be higher than other models since thrust will be

varied by propellant not by voltage.

LEO to GEO Transfer

The first task is to find the performance

requirements for the low earth orbit to geostationary orbit

transfer. Specifically, it is important to determine the deltaV requirement and power requirement for trip time. As

seen in Figure 1, thrust to weight can impact the total deltaV requirement for the transfer. Low thrust to weight ratios

suffer from steering and gravitational losses: the optimal

transfer being an impulsive transfer. Also as can beobserved in the figure, there is a region of little change in

either the high thrust or low thrust to weight ratios.Fortunately, there are appropriate approximations for


14/33

POPESCU 13

both of these regimes. However, the middle region, where

there is a clear dependence on thrust to weight ratio,requires a more rigorous trajectory analysis typically a

computational orbital trajectory optimization tool is used.It was found that this region will not likely be needed for

the focus of this study.

Electric propulsion systems utilizes generatedelectrical energy instead of stored chemical energy to

produce thrust, which results in a far heavier propulsionsystem for the same amount of thrust, at least with current

technology. A given thrust and specific impulse results in a

jet power, which with a thruster efficiency from the abovesection can be used to compute the electrical power system

requirement for the propulsion system. Power systems are

often described in specific mass, αsp, which is the mass in

kg per kW of electrical power demand of the propulsionsystem. Using this value we can use the relationships below

to compute the delivered mass, or the mass that represents

everything besides the propulsion system, ie. Structure,payload, tanks, avionics, habitats.

Eq. 34 Eq. 35 Eq. 36 − ∆ Eq. 37

− ∆

Eq. 38

− ∆ Eq. 39

− ∆ − ∆ Eq. 40

Figure 1. Altitude and thrust to weight ratio effect on Delta-V requirement. From [41]


15/33

POPESCU 14

Using this equation and representative delta-V’s

and specific impulses for the orbital transfers seen in thispaper, figure 2 and 3 show the dependence of the mass

delivered on the initial thrust to weight ratio. The knee infigure 1 where thrust to weight starts showing appreciable

benefit is around 0.01. Current technology for state of the

art solar panels have specific masses at approximately

5kg/kW and thruster systems including PPU can be as lowas 2kg/kW leading to an appoximate best case 7kg/kWtotal propulsion alpha. [40 and citations needed]

Unfortunately, even the ambitious propulsion specific

mass of 0.5kg/kW cannot deliver any mass, or hence closea design, for a delta-V requirement of 5km/s, which is close

to a LEO-GEO transfer. Thus for current technology and theLEO-GEO transfer, thrust to weight ratio will not play a

significant role in the analysis. In reality, most satellites are

delivered to a Geo-Transfer-Orbit (GTO) instead of LEO. Inthis scenario, thrust to weight plays a bigger role in the

delta-V requirement and because there is also generallymuch less delta-V required, picking a higher thrust to

weight system may be more feasible, and possibly providesome benefit. This will be discussed in a later section.

For the LEO-GEO transfer, a low thrustapproximation for delta V and trip time may be used. In

particular, the Edelbaum approximation is used. The

Edelbaum approximation reduces the delta-V requirementto a simple formula from the change in speed. The method

is explained in good detail in reference 48, but summarizedhere. For low thrust - low eccentricity approximation the

following can be assumed. Eq. 41 cϑ Eq. 42 Eq. 43

cϑ /

−/

Eq. 44Where f t and f h are the tangential and out of plane

acceleration determined by the yaw angle β. Using onlythese basic assumptions the necessary condition is simply

given by.

tan Eq. 45

It follows from the cost function that

tan Eq. 46From this the steering law can derived.

Eq. 47

This can be plugged into equation 45 and

integrated and squared to yield

Δ Δ Eq. 48In order to determine the initial yaw angle,

equation 48 can be plugged into equation 46 and

integrated

00.10.20.30.40.5

0.60.70.80.9

1

0.00001 0.0001 0.001 0.01

D e l i v e r e d M

a s s F r a c t i o n

Thrust to Weight Ratio

5000 4000 3000 2000

1500 1000 500

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.00001 0.0001 0.001 0.01 0.1

D e l i v e r e d M a s s F r a c t i o n

Thrust to Weight Ratio

0.5 1 2 4 8 12 20

Figure 2. Thrust to weight ratio sensitivity to specificimpulse. αsp = 10 kg/kW, delta-V = 5km/s.

Figure 3. Thrust to weight ratio sensitivity to specific mass.Isp = 4000, delta-V = 5km/s


16/33

POPESCU 15

Δ < / Δ > / Eq. 49Using some trig identities and the steering law,

Edelbaum’s original constant -acceleration circle to

inclined circle transfer delta V equation can be derived.[48]

∆ cos ∆ Eq. 50The major limitation by this approximation is that

acceleration is assumed to be constant, this approximationis generally valid for most electric propulsion even if the

acceleration increases significantly as the mass of thevehicle decreases, since the term truly depends on the

vehicles orbital velocity change from initial as can be seenin equation 50. However, this precludes any firingstrategies that would take advantage of multiple modes. In

particular, it is advantageous to use higher thrust on thenodes to maximize inclination change, while the lower

thrust better specific impulse could be fired with less yawangle to reduce steering losses. There is a slightly better

method that was formulated by a paper by Lorenzo

Casalino and Guido Colasurdo that addresses this issue[49] and even better approximation discussed in the

introduction that includes variable Isp during a revolution

[5]. If Edelbaum’s original equations are used; however, only starting and final orbital radius and inclination matter

for delta V calculation. A plot for a 200km starting orbit isshown below.

Figure 4. Delta V for various inclination changes to GEO

The transfer time can simply be found then using

∆ ∆ Eq. 51

For a given specific impulse this reduces to

∆ ̇ Eq. 52The transfer time is the driving factor for the

power required by determining the necessary propellant

rate, as shown in equation 53. ̇ Eq. 53Noting that this is the required average propulsive

power. With the simple Edelbaum equation, dual mode is

easily characterized by a fraction of delta V for each mode,

∆ ∆ ∆ ∆ Eq. 54a,b

Such that the propellant mass fraction is

− ∆ − ∆ Eq. 55a,bThe time requirement holds that

∆ ∆ ∆ Eq. 56Where

∆

̇ ∆

̇ Eq. 57

Since the power will be fixed on the orbit

̇ ̇ Eq. 58Where η is the total efficiency from the power

supply to the jet power. This leads to the relationship for

the power required from the time required with dualmodes:

0

1 − ∆11 12 − ∆11 1 − ∆22 222∆ Eq. 59

The distribution of the time is arbitrary, only thefraction of time spent by each mode matters for the

equations; however, in reality, the higher thrust mode

should be used deeper in the gravity well to reducepotential gravitational losses. Another note is that for now

this assumes 100% duty cycle, most operations run 90-

0

2

4

6

8

10

12

0 20 40 60 80 100 120

D e l t a V i n k m / s

Incl ination Change in degrees


17/33

POPESCU 16

98% duty cycles. It is fairly reasonable to assume the

power required is ′ ,% / /.Finally, it is also important to recognize that this is thethruster input power required, and that the propulsion

system includes the PPU and its associated efficiency. referenced in the rest of the paper is propulsive system

requirement, which is

from Eq. 59 divided by

.

When considering geostationary satell ites there isan additional delta V cost associated with station keeping.

This amounts to roughly 50 m/s a year for the duration ofthe satellite lifetime. Unlike orbital raising, there is no

appreciable power requirement. Smaller low thrust

systems are considered to reduce weight; in addition,higher specific impulse is desired to reduce propellant

weight as long as reduced weight overcomes any increasedmass in the propulsion system. This has been the initial

reason for using electric propulsion in geostationary

satellites. In addition, a 7% margin on delta V is added toaccount for any errors in steering or orbit insertion.

System Sizing

The final and most important step is determiningthe mass of the vehicle. This was broken down into

subsystems: propulsion, tanks, attitude control, structure,power, thermal management, and payload. Payload will

include GN&C, Communications, and data handling.

Propulsion Sizing

As shown in the orbital mechanics section,

propulsion system size is typically determined by thepropulsive power requirement and the specific mass. Thepower required is driven by the delta V and the transfer

time requirement. The specific mass is difficult to predictanalytically, instead a best fit curve based on data is used

to predict the specific mass for a given power requirement.

A propulsion system, however, consists of a thruster, apower processing unit (PPU), a propellant management

system (PMS), and sometimes requires a digital controllerinterface unit (DCIU). In contemporary designs, the PPU

and DCIU are often combined into one unit. Unfortunately,

it is not always clear what is included in the electrical

design from some thrusters, so unless otherwise specified,it is assumed that the mass for the thruster electricalsubsystem includes both the PPU and DCIU although this

may have led to slightly poorer curve fit.

Once the propulsive power requirement isdetermined from equation 59 and the thruster efficiency

from table 32, the specific mass of the propulsion

subsystems can be easily determined from the plot. Oncethe specific mass is found, it may be multiplied by the

power as in equation 36, to find the overall mass of thepropulsion system and power conditioning. Where not

explicitly stated, it was assumed the mass of the engine didnot include a gimbal. Therefore, an additional 20% of the

mass is added to include a gimbal, which agrees with most

gimbal systems.

Propellant Feed Sizing

The Propellant management system (PMS) begins

from the high pressure feed from the propellant tanks andends at the thruster. The PMS does not depend on the

power requirement as much as it depends on the pressuredrop and mass flow rate requirement of the thruster.

For the noble gases the PMS typically consists of

two parts called the Pressure Regulation Module (PRM)and the Flow Control Modules (FCM or XFS for Xenon),

where the PRM is multiple string and is mostly a pressuredrop assembly, propellant filter, and distribution system

y = 2.9514x-0.211

R² = 0.6446

y = 9.5913x-0.368

R² = 0.9455

0

2

4

6

8

10

12

14

16

18

0.01 0.1 1 10 100 1000

a l p h a ( k g / k

W )

Input Power (kW)

engines

ppu

Enginealpha curve

PPU alphacurve

Figure 5. Specific Mass Curve Fits


18/33

POPESCU 17

across multiple strings and the PFS is a single string unitfor distribution and fine control of flow to individual

components of a thruster. Plenum tanks are often used inbetween the two stages, most often each FCM contains its

own plenum tank. Some models, especially newer ones,combine the two stages into one unit, which makes more

sense if only one thruster is being used. For convenience

and due to lack of enough models and predictive behavior

for multiple propellants, an available model is chosen forthe PMA and PFS, and scaled holding the mass to maxpropellant flow constant. Using the values from reference

50 on the NEXT propellant feed system, the HPA (PMA) andLPA (FCM) are 1.9 kg and 3.1kg respectively. The totalpropellant rate is approximately 62 sccm or about 6.1

mg/s. Thus the feed sys tem is approximately 0.82

kg/(mg/s) of propellant flow for a single string, but couldbe slightly less if multiple strings are used. The HPA may be

slightly heavier if a higher pressure propellant is used. Thisscaling factor is simply the ratio of the pressure compared

to 18.6MPa which is used on the NEXT.

For Iodine, the container is not pressurized but thepropellant needs to be heated to be vaporized and fed into

the thruster through heated lines. Fortunately, this does

not require too much energy especially since the tanks maybe stored next to propulsion elements that will emit heat

and the propellant sublimes with a reasonable vaporpressures at temperatures under 100C. The plumbing and

propellant feed systems for Iodine are more complicatedbecause oxidization and deposition must be considered.

Unfortunately, no information could be found on any

existing iodine feed systems. For this reason the same massapproximation is used; however, it should be noted that

this is likely a slight overestimation.

Propellant Storage and Plumbing Sizing

Composite overwrapped tanks (COPV) are a

popular choice for highly pressurized and supercriticalstored propellants such as Xenon. COPV tanks are assumed

for the noble gases. Iodine is stored as a solid and will bediscussed later.

The propellant tank weight is driven largely by thevolume and pressure of the propellant. The empty weight

of the tank is calculated using the material properties forTitanium, specifically sheet TI-6Al-4Va-AMS-4911, and

Carbon fiber, specifically Torayca T1000G with Epon Resin826, and a safety factor. The following equations were used

to estimate the weight and the table of values and

constants.

∗ ∗ ∗ % Eq. 60 cos Eq. 61 % /% Eq. 62 .6 Eq. 63

Eq. 64 Eq. 65 Eq. 66 Γ( ) Eq. 67

Table 34. Material Properties and Constants

PROPERTY Value

TITANIUM YIELD STRENGTH 910 MPa

TITANIUM DENSITY 4430 kg/m3

TITANIUM LINER PERCENT

“STRENGTH THICKNESS” %t

13% (Xe), 11%(Kr), 9% (Ar)

CARBON FIBER YIELD STRENGTH 3040 MPa

CARBON FIBER DENSITY (60% FIBER) 1550 kg/m3

CARBON FIBER OVERWRAP %t 1-%tTi

SAFETY FACTOR f 1.5

WIND ANGLE ΘW 15°

OVERWRAP WIND FACTOR β 3/2

PORT AND MOUNT FACTOR ξ 2.5

PLUMBING FRACTION κ 0.002

STRUCTURE FRACTION Γ 0.02

Table 33. Error in Tank Mass Predictions Compared to Psi-Pci Models

NAME

EMPTY

MASS

CALCULATED

MASS VOLUME

CALCULATED

VOLUME

%ERROR

MASS

%ERROR

VOLUME

%ERROR

MASS/VOLE

80386-101 6.4 9.034516 0.0321 0.05 41.16431 55.76324 -9.3725180412-1 7 7.629832 0.05 0.052281 8.997603 4.562314 4.24176680458-201 12.2 13.07574 0.0541 0.058966 7.178174 8.995033 -1.66692

80458-101 19.05 19.8328 0.1197 0.123185 4.109187 2.911687 1.16361980458-1 20.4 21.19244 0.1328 0.137404 3.884491 3.467047 0.403456


19/33

POPESCU 18

A cap eccentricity of 0.707 is used. Table 33

demonstrates the closeness in prediction of actual weightof xenon tanks. The first tank is slightly more off in

prediction, but that is likely because of i ts irregular shape.In order to find the surface area the volume of the tank

must be figured out. Then surface area can be found from

the following relation using the aspect ratio [ARcyl = length

of cylindrical section as multiple of diameter]:

ℎ .5 Eq. 68 4 6 4

Eq. 69

{[ ]

atanh }

Eq. 70

A cylinder aspect ratio of 1 is assumed for thetanks. In order to determine the volume of the tank, the

mass and density of the propellant must be known. Since a

pressurant such as Helium shouldn’t be used, the minimumpressure with which the propellant may be retrieved from

the tank must also be known. From ref 50, it was estimatedthat the minimum pressure the HPA could operate was

around 300 kPa. Using this we get the relation:

, , Eq. 71Since the initial pressure is very high, the density

can no longer be considered ideal (the final pressure,

however, may be assumed ideal) the density should befound from a table or real gas law. The temperature is

assumed to remain the approximately the same unless thepropellant is cooled initially, as letting the temperature

raise will increase the amount of propellant that is able to

be extracted.

The mass of the propellant must include a marginfor errors such as missed thrust, fill error, and startup. Thismargin is chosen to be 10% as recommended by JPL in

their paper in ref 51. In addition to this, there is ullagevolume and trapped flow associated with the propellant

feed system. This is approximated as 2% and 1%respectively of the total volume as the middle of range

recommended in the “Space Propulsion Analysis and

Design” text. Thus Eq. 71 becomes:

..97 Eq. 72No boiloff volume is assumed since no cryogenic

tanks are used. The mass of the actual plumbing is ignored

and considered part of the structural mass. The noble gasstorage conditions that are used are below.

Table 35. Summary of Propellant Performance

GAS Xenon Krypton Argon

MEOP (MPa) 18.6 22 24

DENSITY (kg/m3) 1680 1013 491

Noting that argon must be insulated and kept at atemperature of 262K instead of the approximated 300K for

the other two, this only adds marginal mass to the tanks if

only a matter of placement in the satellite. For iodine thecontainer does not need to be pressurized, thus eliminating

significant mass in the tank. Indeed, the propellant feedsystem also does not require a depressurization, but

requires a heating element. Iodine also has the advantagethat is far denser than noble gases at 4900 kg/m 3 and as a

solid does not require much structural support. Toestimate the mass for the container is very simply

approximated as 3% of the mass of the propellant.

Power Sizing

The mass of the power system can be found in a

similar fashion as the propulsion system, using the powerrequirement and specific mass the mass of the power

subsystem can be found. The overall power requirement

includes all subsystems: propulsion, propellant feed,GN&C, and payload. Thermal management is assumed to be

passive or at least not contribute much power requirementto avoid an iterative sizing process, but this is a reasonable

approximation to make. It is clear that solar power will be

used. As such battery power must also be considered forwhen the satellite is in the shade.

For the solar panel size, the solar panels must

provide enough power for all the subsystems and enough

excess power to charge the batteries for operation in thedark. Time of the year and inclination make a difference in

the time spent in shadow. At geostationary orbit for

instance, at solstice the orbit may never be in the earth’s

shadow, while at equinox it may spend up to 1.2 hours in

shadow. Time spent in the shade of the earth isapproximately:

≈ τsin− / Eq. 73


20/33

POPESCU 19

Where τ is the orbit period. This is an

underestimation usually particularly at lower altitudes dueto atmosphere but a safety factor of 10% on the battery

requirement provides a conservative estimate for thebattery size; likewise a 10% safety factor is applied for the

power requirement as recommended in ref 51 and a 95%

efficient electrical bus. Thus the total power required is

∗ ∗./.95 Eq. 74This ratio is largest closer to earth, and for a 400

km circular orbit for instance this ratio is about 1.64decreasing to about 1.05 at geostationary orbit. This is a

nice fact, as this decrease is larger than the degradation of

the solar panels. This is also a very large multiplier on thepower required, resulting in much larger solar panels and

batteries than if the spacecraft was to thrust only when insunlight, especially at lower altitudes. However, for worst

case scenario and convenience it is considered here.

Since the spacecraft will not change its relativedistance from the sun very much, it can be assumed that the

solar irradiance is constant. Often times the specific massof solar panels is also given at 1 AU. In this case, the specific

mass for solar panels is chosen to be 6.6 kg/kW which is

close enough to the ATK UltraFlex’s achieved 17W/kg andaccounts for some degradation and the electrical bus. It is

noteworthy that this is a rapidly developing technologyand that specific masses of 2-3kg/kW may be achievable in

the near future.

For the type of batteries, Li-ion is chosen as theprimary battery for LEO-GEO transfer. Although nickel

hydrogen batteries have been popular in the past, they

have up to 30 times higher self-discharge rates and requireup to 10 times more thermal rejection. In addition, Li-ion

improve significantly the energy density, both in mass andvolume advantage and have no memory effect like NiH2.

[53] NiH2 batteries were popular for their long lifetime,relatively light weight, tolerance to abuse and deep

discharge, and ease of charge monitoring. However, Li-ion

technology has improved significantly, extending the lifetime. However, this requires the depth of discharge (DOD)

to be limited to around 40% for the application for GEO.[54] This is also levels out the voltage over the discharge.

Indeed Li-ion has been successfully implemented on a

multitude of contemporary geostationary satellites. Themass of the battery system can be estimated as

∗ . ∗ ./.4 Eq. 75As 1.2 hours is approximately the longest time

spent in shadow, there is a 10% margin on power, and a

40% DOD is assumed (DOD is lower throughout most of the

mission resulting to allow longer lifetime). The specificenergy mass for the battery is the inverse of energydensity (Wh/kg), which for Li-ion is variable and dependson the power requirement. The minimum battery specific

power will be given by:

, ∗ ./ Eq. 76Which can be substituted back into the previousequation.

.4. /3 κE Eq. 77It is of course desirable to maximize energy

density. Given this constraint the values can be looked up

on a ragone plot of available li-ion batteries. The pointchosen is 150 W h/kg and 50W/kg.

A note on the power requirement for

communications: while this consumes power it is often thatthis accounted for by a duty cycle.

Thermal Management Sizing

A simple model for radiator, heat pipe, and heatersizing was initially considered, but it would probably be

not significantly more accurate than lumping the thermalcontrol elements and simply stating:

and choosing the specific mass to be 0.2kg/kW assuggested in the “Spacecraft Propulsion Analysis and

Design”. The power that must be dissipated can be easilyapproximated by:

∑ = Eq. 78Or the summation of each subsystem’s input

power times its difference from 100% efficiency. Assumingthat the solar panels dissipate its own heat, only the bus

must be considered. If only the propulsion string isconsidered and the other components’ rejected heat

considered negligible and the battery power is used

instead of solar. Then this is simply:

Eq. 79This can actually be more easily be estimated as:

Eq. 80


21/33

POPESCU 20

This is also conservative as this does not include

the ionization energy that leaves with the propellant, albeitsmall, and assumes that all thermal energy must be

rejected by the thermal management system. The powerrequired for the thermal management system is simply

estimated as 1% of the energy rejected.

Attitude Control System Sizing

The attitude control system normally consists of a

few small lightweight thrusters. Often times, this same

system also serves the role of station keeping and electricpropulsion suits both of these applications well. The main

propulsion system can participate in this role if 2 or 3thrusters are used. This reduces the overall size of the

attitude and station keeping system easily overcoming anyadditional mass associated with adding an additional

propulsion string. For the most part this is almost sufficient

for steering, but it is likely a couple small thrusters such as

resistojets or arcjets may be necessary. Steering loss andmissed thrust is included in the 10% total propellantmargin for orbit raising. Using values from chapter 10 in

the “Space Propulsion Analysis And Design” book, the

accumulated momentum control impulse of 1200Ns perroughly 3 tons per year of payload needed by the attitude

control system. The attitude thrusters can very well besmall RF ion thrusters as the absolute minimum thrust

required is about 30µN per 3 ton payload per thruster. TheBIT-3 thruster can use any of the propellants and provides

the thrust necessary at only 200 grams and 60W which is

essentially negligible mass and power even consideringthat each thruster still requires a PPU and feed system [16].

Station keeping can be accomplished by the primarythrusters. Both of these systems would use the higher

specific impulse propellant if available. The approximate

specific impulse for the BIT-3 on different propellants isbelow.

Table 36. ApproximateBIT-3 Propellant Performance

GAS Xenon Iodine Krypton Argon

ISP 3500 3550 4000 4850

It turns out the formula to compute the propellantrequired is quite simple for this requirement.

, 3 ∗ Eq. 81Where years is the lifetime of the satellite in years

in geostationary orbit, and the mfinal once placed in thegeostationary orbit. These thrusters have an additional

requirement for North South and East West Station

Keeping and end of life De-orbt. These values are chosen

as:

Table 37. ACS Additional Requirements per 5.8 Years

NSSK EWSK De Orbit

ΔV (m/s) 272.6 29 10

As suggested in reference 56. 53m/s per year isrecommended in the “Space Propulsion Analysis and

Design” book and these values agree for 10 year service.Additional BIT-3 thrusters would be added to als o meet

this requirement if necessary, although the main thrusterscould be used in part, so the added mass is not consideredfor now. The bare minimum acceleration to be provided is

1.5E-06 m/s2 for N-S axis and 1.6E-07 m/s2 for E-W axis

although at least 5 times as much is practical.

Structural Sizing

A simple 7% of the dry mass of the satellite isassumed to be structure. This includes the plumbing and

RCS thrusters.

IV. Results

For initial consideration, a Delta IV Medium to LEO

is around 8200 kg assuming a 600kg attach fitting at 400km circular orbit. Initially consider a 160 day transit and

the inclination to be 0° and 12 year service life.

Figure 6. 100% Argon


22/33

POPESCU 21

Figure 7. 100% Krypton

Figure 8. 100% Xenon

Figure 9. 100% Iodine

160 day transit is chosen in particular because thistransit time is associated with an opportunity to perform

the transit without being eclipsed. Therefore the batteryand power requirement can be drastically reduced.

Repeating the same cases, it can be seen that the lowerspecific impulse propellants no longer have as much

advantage. Only 3 minutes of max power battery life is

provide.


23/33

POPESCU 22

Figure 10. 100% Argon

Figure 11. 100% Krypton

Figure 12. 100% Xenon

Figure 13. 100% Iodine

Below are the results for the differentcombinations of propellants for 160 day transfers.


24/33

POPESCU 23

Figure 14. 0 degrees inclination

Figure 15. 28.5 degrees inclination


Power drives much of the trends. Only one case:

the Xenon Krypton with a small amount of krypton mode

showed benefit. If the transit time is allowed to be

increased to 1 year a few more points show benefit.




0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.63

0.64

0.65

0.66

0.67

0.68

0.69

0.7

0.71

0.72

Mode DV Fraction

PayloadF

raction

Xe-Ar Xe-Kr Kr-Ar I-Ar I-Ar Xe-I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.54

0.56

0.58

0.6

0.62

0.64

0.66

Mode DV Fraction

PayloadFraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

Mode DV Fraction

Pa

yload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.74

0.745

0.75

0.755

0.76

0.765

0.77

0.775

0.78

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.67

0.68

0.69

0.7

0.71

0.72

0.73

Mode DV Fraction

PayloadFraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.59

0.6

0.61

0.62

0.63

0.64

0.65

0.66

Mode DV Fraction

Payload

Fraction



25/33

POPESCU 24

Extending this time to 1.5 years shows that as the

transit requirement reduces and hence the power, the

benefit of dual mode inc reases.





The 1 year cases are repeated with a 90% duty cycl e

and worst case eclipsed time, and 15 year service li fe, and 28

degree l aunch with vari ous power systems speci fic mass .

Figure 24. power systems alpha = 6.6 kg/kW

Figure 25. power systems alpha = 5 kg/kW

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.804

0.806

0.808

0.81

0.812

0.814

0.816

0.818

0.82

0.822

0.824

Mode DV Fraction

PayloadFraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.76

0.765

0.77

0.775

0.78

0.785

0.79

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.7

0.705

0.71

0.715

0.72

0.725

0.73

Mode DV Fraction

PayloadFraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.66

0.665

0.67

0.675

0.68

0.685

0.69

0.695

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.675

0.68

0.685

0.69

0.695

0.7

0.705

0.71

0.715

0.72

0.725

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.695

0.7

0.705

0.71

0.715

0.72

0.725

0.73

0.735

0.74

Mode DV Fraction

PayloadFraction



26/33

POPESCU 25



To assess the scalability of this concept the mass is

varied from 100 kg to 100000 kg. The transit is 1 year and

launched from Kodiak Island, 15 year service life, 200kmLEO, 92% duty cycle.

Figure 28. LEO Mass = 53000 kg

Figure 29. LEO Mass = 28800kg



0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.734

0.736

0.738

0.74

0.742

0.744

0.746

0.748

0.75

0.752

0.754

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.74

0.745

0.75

0.755

0.76

0.765

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.59

0.6

0.61

0.62

0.63

0.64

0.65

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.58

0.59

0.6

0.61

0.62

0.63

0.64

0.65

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.58

0.59

0.6

0.61

0.62

0.63

0.64

0.65

Mode DV Fraction

PayloadFraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.55

0.56

0.57

0.58

0.59

0.6

0.61

0.62

0.63

Mode DV Fraction

P

ayload

Fraction



27/33

POPESCU 26




Mass breakdown for 8200kg payloa d, 28.5

inc li nation change 1 year transi t, and 15 year service.

Figure 35. Propulsion fraction

Figure 36. High Specific Impulse Propellant fraction

Figure 37. High Thrust Propellant fraction

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.53

0.54

0.55

0.56

0.57

0.58

0.59

0.6

0.61

0.62

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5

0.51

0.52

0.53

0.54

0.55

0.56

0.57

0.58

0.59

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.42

0.44

0.46

0.48

0.5

0.52

0.54

0.56

0.58

Mode DV Fraction

Pay

load

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.028

0.03

0.032

0.034

0.036

0.038

0.04

0.042

0.044

0.046

0.048

Mode DV Fraction

Propulsion

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

Mode DV Fraction

Prop

2

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.05

0.1

0.15

0.2

0.25

Mode DV Fraction

Pro

p

1

Fraction



28/33

POPESCU 27

Figure 38. Dry Mass fraction

For the sake of interest, the beam voltage was

reduced to 650V (clos er to a hal l thruster). The

corresponding propell ant performance is below. 8200kg

ini tial mass at 200km LEO, 92% duty cycl e, 1 year trans it,

partia lly eclipsed, 15 year service.

Table 38. 650 Beam Voltage Propellant Performance

GAS γ ηe ηm ηT Isp

IODINE 0.979 0.739 0.89 0.63 2792

XENON 0.97 0.724 0.9 0.613 2750

KRYPTON 0.975 0.712 0.86 0.582 3307

ARGON 0.981 0.702 0.73 0.5 4090

Figure 39. 0 degree inclination

Figure 40. 28.5 degree inclination


8200kg initia l mass at 200km LEO, 95% duty cyc le,

160 day trans it, no ecli pse, 15 year service.


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

Mode DV Fraction

Dry

Fra

ction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.71

0.715

0.72

0.725

0.73

0.735

0.74

0.745

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.645

0.65

0.655

0.66

0.665

0.67

0.675

0.68

0.685

0.69

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.53

0.54

0.55

0.56

0.57

0.58

0.59

0.6

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.6

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

Mode DV Fraction

Payload

Fraction



29/33

POPESCU 28

Figure 43. 28.5 degree inclination


Repeated with power systems alpha of 2kg/kW and

1 year transit.

V. Conclusion

From this analysis it can be concluded that dual

mode electric propulsion can result in a slightly largerpayload to geostationary orbit, up to roughly 2% more than

Xenon alone in some cases. This is not very impressive, buta result nonetheless. One of the reasons for this, is that any

benefit gained in propellant mass and tank mass is offsetby an increasing power system requirement. This is the

reason why the effect is more pronounced when the powersystem sizing is less important: lower specific mass or

longer transit times.

Of course this simplified delta V calculation doesnot represent all the benefit dual mode can provide. In fact,

dual mode trajectories can be much further optimized bystrategic thrusting. Such thrust strategies include using

higher thrust at nodes to increase the effectivity of

incl ination changes, or perigee and apogee burns to

increase the effect of orbit raising, or even both. In addition,the GTO to GEO transit would be of interest for a dual modevehicle. These would be an excellent areas to pursue in

further research for better payload and dry mass fractions.

Lastly, this research has not entirely taken intoaccount the cost of dual mode. It is true that most of these

alternative propellants are significantly cheaper. In some

cases it can be seen that 100% Argon or 100% Kryptonhave higher payload fractions, however, the subsequent

increase in power, propulsion, and tank subsystems mayoffset the cost advantage.

It should be noted that Iodine significantly out

performs in this simplified study. While this may not becompletely reflected in a more extensive study, it

nonetheless demonstrates that Iodine holds much promiseas an alternative propellant to Xenon.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.5

0.52

0.54

0.56

0.58

0.6

0.62

Mode DV Fraction

PayloadF

raction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.36

0.38

0.4

0.42

0.44

0.46

0.48

0.5

0.52

0.54

Mode DV Fraction

Payload

Fraction


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.59

0.595

0.6

0.605

0.61

0.615

0.62

0.625

Mode DV Fraction

Payload

Fraction



30/33

POPESCU 29


31/33

POPESCU 30

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