American Institute of Aeronautics and Astronautics1

PERFORMANCE STUDIES OF MINIATURIZED CYLINDRICALAND ANNULAR HALL THRUSTERS

A. Smirnov, Y. Raitses, and N. J. Fisch

Princeton University Plasma Physics Laboratory, Princeton, NJ

Abstract

Conventional annular Hall thrusters do not scaleefficiently to low power. An alternative approach, a 2.6cm miniaturized cylindrical Hall thruster with a cusp-type magnetic field distribution, was developed andstudied. Its performance was compared to that of aconventional annular thruster of the same dimensions.The cylindrical thruster exhibits dischargecharacteristics similar to those of the annular thrusterbut has much higher propellant ionization efficiency.Significantly, a large fraction of multicharged xenonions might be present in the outgoing ion flux generatedby the cylindrical thruster. The operation of thecylindrical thruster is quieter than that of the annularthruster. The characteristic peak in the discharge currentfluctuation spectrum at 50-60 kHz appears to be due toionization instabilities. In the power range 50-300 W,the cylindrical and annular thrusters have comparableefficiencies ( η=15-32% ) and thrusts ( T=2.5-12 mN ).For the annular configuration, the voltage less than 200V was not sufficient to sustain the discharge at lowpropellant flow rates. The cylindrical thruster canoperate at voltages lower than 200V, which suggeststhat a cylindrical thruster might be designed to operateat even smaller power.

Introduction

There is a strong interest in low-power propulsiondevices within the space community. This interest isdriven by the desire to reduce the spacecraft mass. Adecrease in a spacecraft mass can significantly reducelaunch cost and, therefore, enable new scientific andexploration space missions, which involve multiplemicrospacecraft flying in constellations. 1,2 The Hallthruster 3, as a mature electric propulsion device, seemsvery promising for low-power primary propulsion onnear-Earth missions 4 (orbit transfer, repositioning,etc.).

Scaling down the operating power of a Hallthruster requires reducing the discharge voltage or thedischarge current. The degree to which the first optioncan be accommodated is limited by the desire to keep

the exhaust ion velocity high. The second optionimplies that the propellant flow rate should bedecreased. In order to maintain high propellantutilization efficiency at low propellant flow rates, thethruster channel must be scaled down to preserve theionization probability. Then, according to Ref. (5), thelength of the acceleration region, which is mainlydetermined by the magnetic field distribution, mustdecrease linearly with the channel sizes, while themagnetic field must increase inversely to the scalingfactor. However, the implementation of the latterrequirement is technically challenging because ofmagnetic saturation in the miniaturized inner parts ofthe magnetic core. A linear scaling down of themagnetic circuit leaves almost no room for the use ofthin magnetic poles or for heat shields, making difficultthe achievement of the optimal magnetic fields.Nonoptimal magnetic fields result in enhanced powerand ion losses, heating and erosion of the thruster parts,particularly the critical inner parts of the coaxialchannel and magnetic circuit.

Currently existing low-power Hall thrusterlaboratory prototypes with channel diameters 2-4 cmoperate at 100-300 W power levels with efficiencies inthe 10-40% range. 6-8 However, further scaling of a Hallthruster of the conventional geometry down to sub-centimeter size 9 resulted in even lower efficiencies (6%at about 100 W). The low efficiency might arise from alarge axial electron current, enhanced either bymagnetic field degradation due to excessive heating ofthe thruster magnets or by electron collisions with thechannel walls. These results make the usefulness ofsimply miniaturizing the conventional annular Hallthruster debatable.

The cylindrical Hall thruster suggested in Ref.(10) features a channel with a short annular region andlonger cylindrical region, and a cusp-type magneticfield distribution (see Fig. 1a). Having larger volume tosurface ratio than the conventional annular thruster, andtherefore, potentially smaller wall losses in the channel,the cylindrical Hall thruster should suffer lower erosionand heating of the thruster parts. This makes theconcept of a cylindrical Hall thruster very promising forlow-power applications.

AIAA paper 2002-3823, Indianapolis, IN,July 7-10, 2002

American Institute of Aeronautics and Astronautics2

Magneticcore

N

N

E

B

Anode Cathode-neutralizer

Electromagnets

B

Ceramic channel

Annular part

S

S

(a)

Cylindricalceramicchannel

Anode/gasdistributor

Magnetic core

Cathode-neutralizer

(b)

A relatively large 9 cm diameter version of thecylindrical thruster exhibited performance comparablewith conventional annular Hall thrusters in the sub-kilowatt power range 10. In the present work wedeveloped and studied a miniaturized 2.6 cm diametercylindrical Hall thruster. In order to better understandthe physics of cylindrical Hall thrusters and to examinethe attractiveness of the cylindrical approach for low-power Hall thruster scaling, we compared theperformance of 2.6 cm cylindrical Hall thruster to thatof the conventional annular thruster with the samechannel diameter and length. Thruster ac and dcelectrical measurements, as well as total ion flux andthrust measurements were performed. It was found thatthe cylindrical thruster has unusually high propellantionization efficiency, compared to conventional Hallthrusters. The ratio of the total ion current to theeffective propellant mass flow current, in the case ofcylindrical configuration, could exceed 1, which clearlyindicates the presence of multicharged Xe ions in theion flux generated by the thruster. The discharge in thecylindrical thruster was also found to be somewhatquieter than that in the annular thruster: The amplitudeof oscillations in the frequency range 10 - 100 kHz wasrelatively lower for the cylindrical configuration.However, the spectrum of discharge current oscillationsof the cylindrical thruster exhibits a pronounced peak atabout 50-60 kHz, which may be due to ionizationinstabilities.11 The effects of higher ionizationefficiency and quieter operation of the cylindricalthruster are very interesting and the underlying physicsdeserves further study.

Experimental Setup

A 2.6 cm cylindrical Hall thruster shown in Fig. 1was scaled down from a 9 cm cylindrical Hall thrusterto operate at ~ 200 W power level.12 Similar to the largethruster, this miniaturized cylindrical thruster consistsof a Boron Nitride ceramic channel, an annular anode,which is also a gas distributor, two electromagneticcoils, and a magnetic core. Field lines of the cusp-typemagnetic field intersect the ceramic channel walls. Theelectron drift trajectories are closed. Magnetic fieldlines form equipotential surfaces, with E= - υe×B. Ionthrust is generated by the axial component of theLorentz force, which is proportional to the radialmagnetic field and azimuthal electron current.

The cylindrical channel features a short annularregion, approximately 1 cm long, and longer cylindricalregion. The total length of the channel is 2.6 cm. Thelength of the annular region was selected so as toprovide high ionization of the working gas at theboundary of annular and cylindrical regions. The outerand inner diameters of the channel are 2.6 cm and 1.4cm, respectively. The thruster design allows one to vary

the thruster geometry. By extending the central pole ofthe magnetic core and the central ceramic piece up tothe exit plane of the channel, the cylindrical thruster canbe converted to the conventional annular one. In thisstudy we investigated two thruster configurations,namely, cylindrical with the dimensions specifiedabove, and annular with the same channel OD, ID, andlength. The overall diameter and length of the thrusterwere both 7 cm.

Fig. 1. a) Schematic of a cylindrical Hall thruster.b) The 2.6 cm cylindrical Hall thruster.

Two electromagnetic coils were connected toseparate power supplies. The currents in the coils wereco-directed in conventional configuration and counter-directed in cylindrical configuration to produce cuspmagnetic field with a strong radial component in thechannel. Fig. 2 shows simulated results of the magneticfield distribution for the annular and cylindricalthrusters. The magnetic field was measured inside both

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these thrusters with a miniature Hall probe withdimensions 1.5 mm x 1.5mm. The results of thesemeasurements and simulations are in a good agreement.

For example, for the operating currents of 1.4 A inthe back coil and 0.9 A in the front coil, the maximumradial magnetic field is 400 G at the inner wall near theexit of the annular channel. In the cylindricalconfiguration, the radial magnetic field reaches themaximum, ~ 700 G, a few millimeters from the anodenear the inner wall of the short annular part and thenreduces towards the thruster exit.

Fig. 2. Magnetic circuit and the magnetic fielddistribution for the annular (a) and cylindrical (b)thrusters. The channel outer diameter is 2.6 cm.

The experiments took place in a 0.4-m3 vacuumchamber, equipped with a turbo molecular pumpingsystem (PPPL Small Hall Thruster facility). Themeasured pumping speed reached ~1700±300 l/s forxenon. The working background pressure of Xe wasabout 7x10-5 Torr for the total propellant flow rate of0.8 mg/s. Uncertainty in the determination of thepumping speed was caused by discrepancies in thereadings of two Bayard-Alpert tabulated ion gaugesused to measure the background pressure. Twocommercial flow controllers, 0-10 sccm and 0-15 sccm,volumetrically calibrated in the flow rate range of 1-10sccm, supplied research grade xenon gas to the anodeand the cathode, respectively. A commercial HeatWaveplasma source was used as a cathode-neutralizer. Thecathode flow rate of xenon was held at 0.2 mg/s for allthe experiments.

The total ion flux coming from the thruster andthe plume angle were measured by a movableelectrostatic graphite probe with a guarding sleeve.Graphite was chosen as a probe material because it hasan extremely low sputtering coefficient for Xe ions with

energies lower than or about 500 eV. The probe can berotated in the vertical plane ±90 deg relative to thethruster exit. The collecting surface of the probe alwayspoints at the center of the thruster. The distancebetween the probe and the thruster center is 14 cm. Yetanother probe mounted on the same movable arm wasused to measure the flux of backstreaming ions. Thesecond probe is horizontally shifted about 2 cm awayfrom the first one, and its collecting surface points outfrom the thruster.

Measurements of the thrust were performed in theElectric Propulsion and Plasma Dynamics Laboratory(EPPDL) at Princeton University. The EPPDL thruststand13 was designed to measure accurately impulse bitsfor pulsed plasma thrusters (PPTs) within the range of10-4 – 10 Ns. However, it was also theoreticallypredicted to be capable of measuring low steady statethrust, as low as 20 µN.

Fig. 3. 2.6 cm annular Hall thruster mounted on thethrust stand.

The thruster was mounted on a swinging armthrust stand.14 Fig. 3 shows a 2.6 cm annular Hallthruster attached to the arm. The thrust arm is mountedwith two flexural pivots. Thrust arm displacement fromthe equilibrium position is measured by a linear voltagedifferential transformer.

During steady-state thruster operation, thethrust generated by the thruster is directly proportionalto the displacement of the thrust arm:

T=keff(x-xequil), (1)

where keff is the effective spring constant of the thruststand. The effective spring constant is due to torsionexerted in the pivots, as well as restoring forcesproduced by the thruster wiring and the flexible silicongas line (see Fig. 3), which connect the thruster with afixed rigid part of the stand. In the present setup, it isimpossible to eliminate the contribution of the wiringand the gas line to the effective spring constant.

(b)

(a)

Magnetic core

B.Coil

B. coil F.coil

Thruster axis

Channel

magnetic core

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Although experimentally minimized, this contributionwas on the order of the torsional spring constant of theflexural pivots.

It should be mentioned that for the same dischargevoltage, coil currents, and propellant flows values of thedischarge current measured at the EPPDL vacuumfacility13 were generally about 10% lower than thosemeasured at the PPPL Small Hall Thruster facility. Thisapparently was due to the fact that the operatingbackground pressure of Xe (about 1x10-5 Torr for thetotal propellant flow rate of 0.8 mg/s) was typically 5-7times lower than that at the PPPL facility.

Experimental Results and Discussion

Ion current and V-I characteristics

The 2.6 cm Hall thruster was operated at thedischarge voltages of 150 - 300 V and xenon mass flowrates of 0.4 – 0.8 mg/s. The cathode was placed near thethruster exit at the 30 degrees angle to the thruster axis(See Fig. 1). The operation of the thruster in thecylindrical and annular configurations is shown in Fig.4.

Fig. 4. Thruster operation in the annular (a) andcylindrical (b) configurations.

Illustrative curves of voltage versus currentcharacteristics measured for each thruster configurationare shown in Fig. 5a. At given discharge voltage andpropellant flow rate, the discharge current, and,consequently, also the input power in the cylindricalthruster, are both larger than those in the annularthruster by factor of 1.5-2. However, the currentutilization efficiency, which is the ratio of the ioncurrent at the exit plane of the thruster to the totaldischarge current, differs on average by about 10% onlyat voltages of 250-300 V (See Fig. 5b). The reason forthis is an exceptionally high propellant ionizationefficiency of the cylindrical thruster.

The ionization efficiency of a thruster ischaracterized by a so-called propellant utilization

coefficient ηI – a ratio of the total ion current Ii at theexit plane of a thruster to the propellant flow rate µexpressed in units of electric current. ηI=IiM/eµ, whereM is a mass of a propellant atom, e is the electroncharge. In Fig. 6 ηI is plotted vs. discharge voltage forthe cylindrical and annular configurations. Propellantutilization for the cylindrical configuration can be seento be much higher than that for the annular one. Itincreases with the discharge voltage and exceeds 1 athigh voltages, which implies a presence of xenon ionsin charge states higher than +1 in the ion flux.

Fig. 5. a) Discharge voltage versus currentcharacteristics for the 2.6 cm cylindrical (C) andannular (A) thrusters (as measured at the PPPLexperimental facility). The cathode flow rate is 0.2mg/s. b) Ratio of the ion current at the exit of thethruster to the discharge current versus dischargevoltage.

The increase in propellant utilization in thecylindrical configuration might be explained byionization enhancement due to an increase in the

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Discharge current, A

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ltag

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A, 0.4 mg/s C, 0.4mg/sA, 0.6mg/s C, 0.6mg/sA, 0.8mg/s

(a)

0.35

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(b)

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electron density. As seen from Fig 5b, the electroncurrent to the anode in the cylindrical thruster is largerthan in the annular. On the other hand, the electronmobility across the magnetic field should be lower inthe cylindrical configuration, because the radialcomponent of the magnetic field is typically 1.5-2 timeslarger than that in the annular. Therefore, the electrondensity in the channel is expected to be higher in thecylindrical configuration. Simple estimates show that a25% increase in the propellant utilization (see Fig. 6)requires only about a twofold increase in the electrondensity. However, an increase in the radial magneticfield in a conventional annular thruster does not lead toa corresponding increase in the electron density,because of the onset of strong high-frequency dischargecurrent oscillations.11

Fig. 6. Propellant utilization coefficient versusdischarge voltage for the 2.6 cm cylindrical (C) andannular (A) thrusters

The fact that the ion flux produced by the thrustercan contain a substantial portion of multiply charged Xeions is of particular interest. It is worth mentioning thateven in conventional Hall thrusters, where thepropellant utilization coefficient is typically 0.8-0.9, anion flux can have rather large fractions of Xe2+ and Xe3+

ions.15 The major factor in multicharged ions formationin a Hall thruster is the ion residence time in thechannel. Simple estimates show that the time of flightof a Xe+ ion through a channel is much smaller than thetime of ionization to higher charge states. Indeed, oneexpects a plasma in a miniaturized Hall thruster to haveelectron density of about 1012 cm-3 and electrontemperature of 10-20 eV.16 For example, for Te ~ 20eV the rate coefficient for single electron impactionization Xe+1→ Xe+2 is about k1,2 ~ 4x10-8 cm3/s.17Therefore, even for a moderately energetic ion withEi=50 eV, the time of flight through a channel with

length L = 3cm τf ~L/Vi~4x10-6 s is approximately anorder of magnitude smaller than the ionization timeτ1,2 ~(nek1,2)-1~3x10-5 s. Thus, in this regime, we expectthat the number of ionization events should scalelinearly with the residue time. The presence of asignificant number of multicharged ions in the outgoingion flux might be an indication of a complex iondynamics (possibly, non-straight trajectories, trappingby ambipolar potential, etc.) which increases the ion lifetime in the channel. Formation of an ion charge statedistribution in a Hall thruster discharge deserves furtherstudy.

Discharge Oscillations

Typical spectra of the discharge currentoscillations are shown in Fig. 7. Although the amplitudeof oscillations is relatively lower for the cylindricalconfiguration, the discharge at low propellant flow ratesis not as quiet as it was found to be in the large 9 cmcylindrical thruster.10 The characteristic peak atfrequencies ∼ 50-60 kHz may be due to an ionizationinstability, which appears because of the depletion ofneutral atoms in the ionization and accelerationregions.11 The characteristic frequency of theseoscillations scales as f ~υn/Li, where υn is the thermalspeed of a neutral atom and Li is a length of theionization region. Apparently, the characteristicfrequency, which was typically ∼ 20 kHz for a 9 cmannular Hall thruster,10 almost triples as Li together withthe thruster sizes are reduced by about factor of 3.

Fig. 7. Spectra of discharge current oscillations forthe annular and cylindrical thrusters at Ud=300Vand anode flow rate of 0.4 mg/s.

Thrust and Efficiency

As mentioned above, the thrust stand had not beenspecifically designed to suit the experimentalenvironment of a steady state Hall thruster operation.

0.4

0.6

0.8

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1.2

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A, 0.4 mg/s C, 0.4 mg/sA, 0.6 mg/s C, 0.6 mg/sA, 0.8 mg/s

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Thruster operation showed that the heat generated bythe thruster brought about a weak long-timescalethermal drift of the thrust stand equilibrium position.The larger the thruster operating power was, the morevisible this effect became. However, it wasexperimentally found that the thrust stand moment ofinertia remained almost unaffected by a temperaturechange due to the thruster operation.

Fig. 8. An exemplary trace of thrust arm positionvs. time. At t≈196.3 s the thruster was turned off.Time interval from 198 s to 203 s is used for curvefitting with a damped linear oscillator responsefunction (solid line) to determine the instantaneousequilibrium position. A 2-sec interval (solid line)before the turning off is used to determine thedisplacement of the arm caused by the producedthrust.

In order to minimize the uncertainty of the thrustmeasurements caused by the equilibrium position drift,a procedure to determine an ‘instantaneous’ equilibriumposition and keff, was developed. Once the steady stateoperation of the thruster was achieved (about 20 min.from the ignition of the discharge), the dischargevoltage, coil power, and gas flow to the anode andcathode were turned off, and oscillations of the thrustarm position x(t) were recorded (see Fig. 8).

The position of the thrust arm x0 corresponding tothe firing thruster was determined from averaging x(t)over a 2-second interval immediately before the turningoff. The instantaneous equilibrium position xequiltogether with keff was determined from fittingapproximately half of the period of oscillations rightafter the turning off with a damped linear oscillatorresponse function.13 The thrust was calculated thenaccording to Eq. (1). For each set of operatingparameters the thrust measurement was repeated severaltimes to minimize the statistical error. Thismeasurement procedure ensured good repeatability ofresults.

Figure 9 shows measured thrust versus dischargevoltage and efficiency versus input power for differentanode flow rates for the cylindrical and annularconfigurations of 2.6 cm Hall thruster. In all regimesbut one, the estimated error bars on thrust andefficiency are ±3% and ± 6%, respectively, which iscomparable with typical values of errors for most of thelow-thrust measurements.6,7 In the case of cylindricalconfiguration with anode flow rate of 0.7 mg/s the errorbars are ±6% for thrust and ± 12% for efficiency. Theserelatively larger measurement errors are due to the morepronounced thrust stand thermal drift, observed at highoperating power, and, partly, to the unstable operationof the anode in this particular regime. Unstableoperation of the anode was supposedly caused by theanode overheating.

Fig. 9. a) Measured thrust vs. discharge voltage andb) efficiency as a function of input power fordifferent anode flow rates for the 2.6 cm cylindrical(C) and annular (A) thrusters. The estimated errorbars on thrust and efficiency are ±3% and ± 6%,respectively, for all regimes except for the case ofcylindrical configuration with anode flow rate of0.7 mg/s, where the error bars are ±6% for thrustand ± 12% for efficiency.

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,mN

A, 0.4 mg/s C, 0.4 mg/sA, 0.6 mg/s C, 0.6 mg/sA, 0.7 mg/s C, 0.7 mg/s (a)

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0.15

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Eff

icie

ncy

A, 0.4 mg/s C, 0.4 mg/sA, 0.6 mg/s C, 0.6 mg/sA, 0.7 mg/s C, 0.7 mg/s

(b)

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Measured thrust ranges from about 3 mN (200V,86 W) to 12 mN (300V, 320W) for the cylindricalconfiguration, and from about 2.5 mN (200V, 63W) to10 mN (300V, 225W) for the annular configuration. Forany given discharge voltage and anode flow rate in therange of parameters investigated, the thrust generated inthe cylindrical configuration is larger than that in theannular configuration. This is another indication thatthe cylindrical configuration has a better propellantionization capability (see Fig. 6).

It should be mentioned that the cylindrical thrustercan be operated at the discharge voltage lower than 200V, while for the annular configuration such voltage isnot sufficient to sustain the discharge at low propellantflow rates. In Fig. 9, the voltage is kept at least at 200 Vonly in order to make comparison between the twoconfigurations.

The efficiency η was calculated, using themeasured thrust T, flow rate µ and power P, asη=T2/2µP. The cathode power and propellant flow andthe magnet losses were not taken into account.Therefore, the efficiency plotted in Fig. 9b is a so-called ‘anode’ efficiency. As can be seen from thegraphs, the cylindrical and annular thrusters havecomparable efficiencies. This, in principle, gives anopportunity to develop a low-power Hall thrustercapable of generating a variable thrust at givenefficiency and thruster power. The use of a variable-thrust thruster is required for optimization of apropellant expenditure on satellites.18 Thrust variationcan be achieved in the 2.6 cm Hall thruster by changingthe length of the central magnetic pole and channelpiece. At constant power, one can increase the thrust(and decrease the ion exhaust velocity) by convertingthe thruster from the cylindrical to the annularconfiguration. For example, at power of about 120 W(see Fig. 9a and 9b), the transition between µ=0.4 mg/sand Ud=250 V in the cylindrical configuration andµ=0.6 mg/s and Ud=200 V in the annular configurationdecreases efficiency by less than 2%, while the increasein thrust is 21%.

Conclusions

Annular conventional Hall thrusters do not scaleefficiently to small sizes because of the large surface tovolume ratio and the difficulty in miniaturizing themagnetic circuit. An alternative approach, which maybe more suitable for scaling to low power, is acylindrical Hall thruster. A 2.6 cm miniaturizedcylindrical Hall thruster was developed and operated ina broad range of operating parameters. Its performancewas compared to that of a conventional annular thrusterof the same dimensions. Several interesting effects wereobserved.

The ion flux and thrust measurementsshowed that propellant ionization efficiency of thecylindrical thruster is much higher than that of theannular. Therefore, gases or gas mixtures that areharder to ionize than xenon may be used as apropellant; for example, one can use argon to generatelarger ion exhaust velocities. In the cylindrical thruster,at high propellant flow rates, a significant fraction ofmulticharged xenon ions can be present in the outgoingion flux. This may indicate complex ion dynamics thatincrease the ion life time in the channel. The formationof multicharged ions in a cylindrical Hall thrusterdischarge, which may be very different from that in anannular thruster, is a subject of ongoing research.

Discharge characteristics of the cylindricalthruster are comparable to those measured for theannular thruster. Although relatively quieter operationof the cylindrical thruster was observed, the dischargeat low propellant flows is not as quiet as it was found tobe in the large 9 cm cylindrical thruster. Thecharacteristic peak at frequencies ∼ 50-60 kHz may bedue to an ionization instability, whose frequencyapproximately triples as the thruster sizes are reducedby a factor of 3.

At given discharge voltage and propellant flowrate, the discharge current and input power of thecylindrical thruster are higher than those of the annularone. The higher power and current would tend to erodethe thruster faster; on the other hand, the cylindricalthruster has a lower surface to volume ratio and fewerinner parts. The lifetime comparison, therefore, remainsan open question.

In the power range 50-300 W, the cylindrical andannular thrusters have comparable efficiencies (η=15-32%) and thrusts (T=2.5-12 mN). Since theseconfigurations may be controlled electronically, it maybe possible to develop an efficient low-power Hallthruster with a variable thrust.

The values of efficiency for both configurationsare comparable to those of other currently existing Hallmicrothrusters. For example, BHT-200-X2B 6 haschannel diameter d=2.1 cm and operates at powerP=100-300 W with efficiency η = 20-45%, SPT-30 7has d=3 cm, P=100-260 W, andη=16-34%.

For the annular configuration, a voltage less than200 V was not sufficient to sustain the discharge at lowpropellant flow rates. However, the cylindrical thrustercan operate at low voltages (Ud < 200V). Operation atlow voltage is important for three reasons: one, certainmissions may require lower ion exhaust velocity. Two,voltages lower than 200 V may be accommodated bydirect drive power, which could simplify enormouslythe power processing unit on a small satellite. Three,the operation at low voltage suggests that furtherminiaturization may be possible, thereby permittingeven lower power operation.

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Acknowledgments

The authors would like to thank Prof. Edgar Choueirifor the provided opportunity to work with the EPPDLthrust stand, Kurt Polzin for his assistance in the thrustmeasurements, and David Staack for the help in theexperiments at the PPPL facility.This work was supported by grants from AFOSR andDARPA.

References

1. R.M. Jones, Journal of the BritishInterplanetary Society, 42(10), 2588 (1989)

2. R.L. Ticker, D. McLennan, Proceedings ofIEEE Aerospace Conference, Big Sky, MN,2001

3. A.I. Morozov and V.V. Savelyev, in Review ofPlasma Physics, edited by B.B. Kadomtsevand V.D. Shafranov (Consultants Bureau, NewYork, 2000), Vol. 21, p. 203.

4. J. Mueller, in Micropropulsion for SmallSpacecraft, edited by M.M. Micci and A.D.Ketsdever (AIAA Progress in Astronautics andAeronautics, 2000), Vol. 187, p. 45.

5. J. Ashkenazy, Y. Raitses, and G. Appelbaum,Proceedings of the 2nd InternationalSpacecraft Propulsion Conference, Holland,1997.

6. V. Hruby, J. Monheiser, B. Pote, C. Freeman,and W. Connolly, IEPC paper 99-092, 26th

International Electric propulsion Conference,Kitakyushu, Japan, June 1999.

7. D. Jacobson and R. Jankovsky, AIAA paper98-3792, 34th Joint Propulsion Conference,Cleveland, OH, July 1998.

8. O. Gorshkov, AIAA paper 98-3929, 34th JointPropulsion Conference, Cleveland, OH, July1998.

9. V. Khayms and M. Martinez-Sanches, inMicropropulsion for Small Spacecraft, editedby M.M. Micci and A.D. Ketsdever (AIAAProgress in Astronautics and Aeronautics,2000), Vol. 187, p. 45.

10. Y. Raitses and N.J. Fisch, Phys. Plasmas 8,2579 (2001).

11. J.P. Boeuf and L. Garrigues, J. Appl. Phys. 84,3541 (1998).

12. A. Smirnov, Y. Raitses, and N.J. Fisch, IEPCpaper 01-038, 27th International Electricpropulsion Conference, Pasadena, CA,October 2001.

13. E.A. Cubbin, J.K. Ziemer, E.Y. Choueiri, andR.G. Jahn, Rev. Sci. Instrum. 68 (6), 2339(1997).

14. Full description of the thrust stand, thecalibration procedure, as well as themeasurement procedure for PPTs are given inRef. (13). In the present paper we describe thethrust stand features relevant to a steady stateHall thruster operation only.

15. L.B. King and A.D. Gallimore, AIAA paper98-3641, 34th Joint Propulsion Conference,Cleveland, OH, July 1998.

16. A. Bishaev and V. Kim, Sov. Phys. Tech. Phys23, 1055 (1978).

17. E.W. Bell, N. Djuric, and G.H. Dunn,Phys.Rev A 48(6), 4286 (1993).

18. J.P. Marek, in Optimal Space Trajectories,Elsevier, Amsterdam, 1979, pp. 7-19, 38.

Thrust and Efficiency