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An ion thruster internal discharge chamber electrostatic probe diagnostictechnique using a high-speed probe positioning system

Daniel A. Hermana� and Alec D. GallimorePlasmadynamics and Electric Propulsion Laboratory, Department of Aerospace Engineering,College of Engineering, The University of Michigan, Ann Arbor, Michigan 48109, USA

�Received 12 March 2007; accepted 28 September 2007; published online 17 January 2008�

Extensive resources have been allocated to diagnose and minimize lifetime-limiting factors ingridded ion thrusters. While most of this effort has focused on grid erosion, results from wear testsindicate that discharge cathode erosion may also play an important role in limiting the lifetime ofring-cusp ion thrusters proposed for future large flagship missions. The detailed characterization ofthe near-cathode discharge plasma is essential for mitigating discharge cathode erosion. However,severe difficulty is encountered when attempting to measure internal discharge plasma parametersduring thruster operation with conventional probing techniques. These difficulties stem from thehigh-voltage, high-density discharge cathode plume, which is a hostile environment for probes. Amethod for interrogating the discharge chamber plasma of a working ion thruster over atwo-dimensional grid is demonstrated. The high-speed axial reciprocating probe positioning systemis used to minimize thruster perturbation during probe insertion and to reduce heating of the probe.Electrostatic probe measurements from a symmetric double Langmuir probe are presented over atwo-dimensional spatial array in the near-discharge cathode assembly region of a 30-cm-diameterring-cusp ion thruster. Electron temperatures, 2–5 eV, and number density contours, with amaximum of 8�1012 cm−3 on centerline, are measured. These data provide detailed electrontemperature and number density contours which, when combined with plasma potentialmeasurements, may shed light on discharge cathode erosion processes and the effect of thrusteroperating conditions on erosion rates. © 2008 American Institute of Physics.�DOI: 10.1063/1.2800772�

I. INTRODUCTION

Ion thrusters are high-efficiency, high-specific impulse�Isp� propulsion systems that are being proposed as the pri-mary propulsion source for a variety of missions.1 Griddedion thrusters are electrostatic, in-space propulsion devices inwhich the ionization and acceleration regions can be opti-mized separately resulting in highly efficient thrusters. Theionization takes place in a discharge chamber, typically frombombardment by electrons emitted from a thermionic hollowcathode. Primary electron confinement and the dischargepropellant utilization efficiency are enhanced through a ring-cusp magnetic field topology in most NASA ion thrusters,such as the thruster used in this investigation. The ionizedgas in the discharge chamber diffuses toward a set of gridsthat accelerate the ions to high velocities by the appliedelectric field. An external neutralizer, typically a hollowcathode, emits electrons to neutralize the space charge ofthe accelerated ions and prevents spacecraft charge buildup,thereby reducing the frequency of ion impacts on the space-craft or ion thruster itself. A schematic visualizing theion thruster operation is shown in Fig. 1 and a more de-tailed description of ion thruster operation can be found inRefs. 2 and 3.

The NASA Solar Electric Propulsion Technology Appli-

cations Readiness �NSTAR� 30 cm ion thruster was the firstion thruster to be used for primary spacecraft propulsion,validating ion thruster technology and demonstrating con-tinuous operation for 16 265 h, i.e., double its design lifetimeof 8000 h.4 Potential failure mechanisms were diagnosedduring wear tests early in the NSTAR ion thruster develop-ment. One of the primary failure mechanisms identified wasthe discharge cathode erosion. A sacrificial cathode keeperelectrode was added to mitigate cathode erosion on theNSTAR thruster for the Deep Space One �DS1� mission.4,5

Adding the keeper reduced the cathode erosion rate to ac-ceptable levels in the subsequent 2000 h wear test and wasthought to have solved the discharge cathode assembly�DCA� erosion issue.6

Concurrently with the successful in-space flight, the DS1flight spare was operated for 30 352 h in an extended lift test�ELT� at the Jet Propulsion Laboratory �JPL�.7 Anomalouserosion of the DCA was observed in the ELT such that thefront face of the DCA keeper electrode was completelyeroded away, exposing the discharge cathode and heaterwire. This extensive discharge cathode keeper erosion hasyet to be understood.7–9 The thruster continued to operateeven after the keeper face plate was completely eroded awayuntil the test was voluntarily terminated after 235 kg of xe-non processed.7 The NSTAR wear tests indicate that the dis-charge cathode life may limit the thruster lifetime and there-fore there is a clear need to understand the cause of DCAerosion, how thruster operating conditions affect DCA ero-

a�Author to whom correspondence should be addressed. Present address:ASRC Aerospace Corporation at NASA Glenn Research Center,Cleveland, OH 44011. Electronic mail: [email protected]

REVIEW OF SCIENTIFIC INSTRUMENTS 79, 013302 �2008�

0034-6748/2008/79�1�/013302/10/$23.00 © 2008 American Institute of Physics79, 013302-1

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http://dx.doi.org/10.1063/1.2800772

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sion, and how to reduce DCA erosion, thereby extendingthruster lifetime.10 Mapping the internal plasma structure ofa NSTAR ion thruster, specifically downstream of the DCA,as a function of thruster operating condition is essential tounderstanding the cause of DCA erosion.

Efforts to increase thruster lifetime present an evergrowing challenge to ion thruster designs and operation asthe transition from small discovery-class missions to futurelarge flagship NASA missions takes place. NASA’s Dawnmission, the first full-up NASA science mission to use ionpropulsion, will be propelled by three 30 cm ion thrustersand is set to study two minor planets, Ceres and Vesta, thatreside in the asteroid belt between Mars and Jupiter. Each ofthe ion thrusters are required to process at least 150 kg ofxenon and operate for up to 24 000 h.11 More ambitious mis-sions will require higher power, larger beam currents, andlonger thruster lifetimes of 44 000–88 000 h.12 Since dis-charge cathode keeper wear rates are expected to be linearlydependent on the beam current density, discharge cathodeerosion becomes an increasingly important factor in the life-time of gridded ion thrusters at the higher power levels offuture deep-space missions.8

The purpose of this investigation is to provide detailed,high-resolution measurements of the plasma parameters in-side the discharge chamber of a ring-cusp ion thruster withemphasis on the near-discharge cathode region. This investi-gation presents the results of symmetric double Langmuirprobe measurements inside a 30 cm NSTAR thruster. Due tothe large number of measurements, the Langmuir probe ana-lytical technique utilized, while not entirely rigorous, pro-vides useful experimental data without an overly excessivecomputational effort. Though efforts were made to minimizethe discharge plasma perturbation due to the presence of theprobe, through fast sweep rates and small geometry probes,non-negligible perturbations of 2% and 5%–10% of thenominal discharge voltage and current, respectively, persistbut only during interrogation of the region within a few mil-limeters of the DCA orifice.

II. EXPERIMENTAL APPARATUS

A. 30 cm NSTAR ion thruster

The functional model thruster �FMT� preceded theNSTAR engineering model thruster �EMT� and the NSTARflight thruster. The principal difference in the construction ofthe FMT from the EMT is that the FMT anode is made ofaluminum while the EMT anode is constructed of spun alu-minum and titanium. The second of two FMTs, FMT2, wasmodified at the NASA Glenn Research Center �GRC� to al-low optical access to the discharge chamber for laser-inducedfluorescence �LIF� measurements.13–15

Three slots were cut into the FMT2 anode wall and cov-ered with quartz windows during LIF measurements. Thoughthese three slots replaced roughly 20% of the FMT2 anodesurface, the magnetic field, DCA, and geometry of the dis-charge chamber are identical to those of the EMT1. For amore complete comparison between FMT2 and EMT1, seeRefs. 13–15. The FMT2 thruster has been operated over theentire NSTAR power throttling range at NASA GRC and atthe Plasmadynamics and Electric Propulsion Laboratory�PEPL�, illustrating comparable performance to the EMTsand flight thrusters. The FMT2 modifications have not al-tered the discharge chamber magnetic field, the ion produc-tion efficiency, or the overall thruster performance.13–15

B. Discharge plasma containment

A discharge plasma containment mechanism replaces theside anode quartz window to permit internal probe accessover a two-dimensional data collection grid. The design,shown in Figs. 2–4, consists of a series of overlapping38-gauge slotted stainless steel sheets that slide along stain-less guide tracks. A guiding alumina tube extends from thedischarge chamber through the slotted sheets and holes in theplasma shield to ensure accurate radial sweeps of the probeat the various axial locations while maintaining thruster com-ponent isolation. Repeatable axial movement of the probe is

FIG. 1. �Color online� Schematic showing gridded ion thruster operatingprinciples.

FIG. 2. FMT2 orientation with respect to the high-speed axial reciprocatingprobe �HARP� for probe insertion. The radial zero location is on the dis-charge cathode centerline.

013302-2 D. A. Herman and A. D. Gallimore Rev. Sci. Instrum. 79, 013302 �2008�


possible without the formation of holes or tears in the sheets.Discharge plasma containment is maintained and visuallymonitored during thruster operation via an adjacent vacuum-rated camera. Hole or tear formation, while extracting abeam, leads to a surge of discharge plasma toward the holeas the high-voltage plasma escapes to grounded surfaces andcauses unstable operation.

During the initial design of the NSTAR thruster atNASA GRC, the placement of the DCA exit plane was cho-sen based on the desired magnetic field topology, resulting inthe placement of the DCA face in the conical section of thedischarge chamber. This DCA location has direct implica-tions on the design of the containment mechanism in that themovement of the probe downstream of the DCA must takeinto account the angled wall of the mechanism with respectto the probe sweep axis. Thus, the guiding alumina tube ismounted onto a computer-controlled, single-axis ball screwtable with a lead screw accuracy of 80 �m and a range ofmotion of 20 cm. The ability to retract and extend the trans-lating alumina tube at various axial locations minimizes pro-trusion of the material into the discharge chamber and pre-vents binding of the slotted stainless steel sheets as thecoordinated movement between the translation tables re-lieves the buildup stress on the sheets during movement. Theguiding alumina tube extends 2 cm inside the dischargechamber wall at all axial locations. A spring-loaded guardring, covering the outside of the alumina tube, ensures a tightfit to prevent plasma leakage.

To minimize the likelihood of probe contamination byplasma deposition and discharge plasma perturbation, theprobe is recessed in the low-density interior of the guidingalumina tube when not in use. A rectangular aluminum platecovers the slot in the plasma shield, eliminating the line ofsight of background particles to the anode. Figure 5 showspictures that illustrate the sweeping of the electrostatic probein front of the DCA.

C. High-speed axial reciprocating probe „HARP…

A linear motor assembly provides accurate direct linearmotion of the probe with minimal discharge cathode plumeresidence times. The HARP system consists of a three-phasebrushless dc servo motor consisting of a linear “U-shaped”magnet track and a “T-shaped” coil moving on a set of lineartracks. The linear encoder provides positioning resolution to5 �m.16 A Pacific Scientific SC950 digital, brushless servodrive controls the motor. The entire table is enclosed in astainless steel shroud with a graphite outer skin. Residencetimes of the probe inside the discharge cathode plume arekept under 100 ms to minimize probe heating and dischargeplasma perturbation. The maximum relaxation times occur inregions of low number density and high electron temperature�i.e., near the anode wall�, which for ion-ion, electron-ion,and electron-electron interactions are 9�10−5, 8�10−5, and3�10−5 s, respectively.17 Thus, the sweep time in front ofthe discharge cathode plume is much longer �four orders ofmagnitude� than the plasma relaxation times over all spatiallocations investigated. Additional information of the HARPsystem can be found in Refs. 16 and 18.

D. Plasmadynamics and Electric PropulsionLaboratory „PEPL… vacuum facility

All experiments are performed in the University ofMichigan 6�9 m2 Large Vacuum Test Facility �LVTF� atPEPL. Four of the seven CVI model TM-1200 reentrant cry-opumps are used for these experiments, which provide acombined pumping speed of 140 000 l /s on xenon with abase pressure of �3�10−7 torr. Chamber pressure is re-corded using two hot-cathode ionization gauges. A completeneutral pressure map of the LVTF has shown that the wallmounted gauge is an accurate measure of the near-thrusterchamber pressure and is reported as the tank pressure in thisfacility.19 The corrected facility pressure Pc for xenon is cal-culated using the known base pressure on air �Pb�, the indi-cated pressure �Pi�, and a correction factor of 2.87 for xenonaccording to20

Pc =Pi − Pb

2.87+ Pb. �1�

FIG. 4. Schematic of the containment hardware covering the anode sideslot.

FIG. 3. Horizontal cross section of the discharge plasma containmentmechanism.

013302-3 An ion thruster diagnostic technique Rev. Sci. Instrum. 79, 013302 �2008�


A dedicated propellant feed system consisting of threeEdwards mass flow controllers regulates the xenon flowrate to the thruster. The flow rates are periodically calibratedusing a known control volume. A 2�2.5 m2 louveredgraphite panel beam dump is positioned approximately4 m downstream of the FMT2 to reduce back sputtering.The thruster is operated at PEPL using a modified stationkeeping ion telemetry package �SKIT-PAC� provided byNASA GRC.

III. DESCRIPTION OF THE ELECTROSTATIC PROBEDIAGNOSTIC

A. Probe type

Langmuir probes are one of the oldest and widely usedprobes in plasma characterization. The ease at which data aretaken, by biasing the probe with respect to another electrode�vacuum chamber, cathode common, anode, etc.� and bymeasuring the current to the probe, is offset by the difficultyin interpreting the resulting current-voltage �I-V� character-istic curve. Careful selection of the analysis method, whichdepends on the probe operating regime, can reduce the errorin the plasma parameters measured. Langmuir probes can bearranged in single, double, triple, and even quadruple elec-trode configurations. Unlike the traditional single Langmuirprobe, the double probe floats as a whole, minimizing theperturbation to the plasma. Furthermore, the I-V characteris-tic curve for a double probe has a well known hyperbolictangent shape facilitating data analysis.21,22 The symmetricgeometry of the double probe about the discharge cathodeorifice makes it the more appealing choice over triple andquadruple probes where spatial resolution in the axial andradial directions would suffer due to probe operating restric-tions, i.e., independent electrode sheaths. Because of the dis-charge chamber symmetry and the simplicity in data analy-sis, a symmetric double probe is preferable compared to anasymmetric double probe.

The symmetric double probe does encounter some limi-tations compared to the other Langmuir probe configu-rations: decreased spatial resolution compared to singleLangmuir probes, the lack of distinction between primaryand Maxwellian electron populations, lack of plasma poten-tial information, and the sampling of only fast electrons. Thelatter is a result from the fact that in a double Langmuirprobe, the current from one electrode must equal the currentto the other since the double probe floats as a whole. Thus,the current to one electrode is limited in magnitude to the ionsaturation current from the other.23,24

B. Double probe hardware

While probes always perturb their surroundings, theextent of this perturbation can be minimized by makingthe probe as small as possible, thereby minimizing thecurrent collection while maintaining a measurable current.Minimizing probe size also leads to improved spatial re-solution. The electrodes of the symmetric double probe forthis investigation are sized for expected electron tempera-tures �2–11 eV� �Refs. 25 and 26� and number densities�1010–1012 cm−3�,25,27 such that the probe operates in the

FIG. 5. �Color online� Photographs taken inside the discharge chamber priorto thruster testing showing the interior of the discharge plasma containmentmechanism: �a� no probe insertion, �b� double probe is roughly half of thedistance to cathode centerline, and �c� close-up with double probe at dis-charge cathode centerline. The closest axial location to the discharge cath-ode assembly �DCA� is a few millimeters downstream of the DCA.



thin-sheath regime near the DCA. The sheath thickness, amultiple of the Debye length, will grow significantly asthe plasma number density decreases away from the DCAplume. The relationship of the Debye length ��D in cm�to the electron number density �ne in cm−3� and temperature�TeV in eV� is given by17,23

�D = 743�TeV

ne. �2�

The discharge plasma number density is expected to have amaximum on cathode centerline at the DCA exit plane and todecrease by over two orders of magnitude with increasingradius, therefore increasing the Debye length and hence theplasma sheath thickness. The result is a decrease in accuracyof the double probe measurement in areas of low numberdensity.

In the thin-sheath regime, the flux of particles en-tering the sheath can be calculated without consideringthe details about the trajectories of these particles in thesheath.24,28–30 In this case, the collection area of the electrodeis approximated as the surface area of the electrode, whichis justified for a large ratio of probe radius to Debye length�D.28–30 However, the rapid growth in the Debye length withincreasing radial distance from cathode centerline dictatesthat at some radial location inside the anode, the thin-sheathcriterion may no longer strictly apply. As a result, ourthin-sheath calculation is modified to account for the expan-sion of the sheath. The growth of the sheath is taken intoaccount by an iterative solution that will be discussed inSec. V. Typically, the traditional thin-sheath analysis is jus-tified while the electrode radius is greater than severalDebye lengths.24,28,31 However, the adjusted thin-sheathanalysis will be used in the transition regime from thin-sheath to orbit-motion limited �OML� analysis. The OMLanalysis is applicable for Debye length greater than or equalto ten times the probe radius and will be discussed later inSec. V.24,28,31

Electrodes with a large length-to-diameter ratio are uti-lized to minimize end effects. A conservative gap distance�3 mm�—the distance between the probe electrodes—maintains a minimum factor of three times the sum of thetwo electrode sheaths �i.e., 3�2�5�D� to avoid sheathoverlapping at all spatial locations. For an electron tempera-

ture of 3 eV, electrode sheaths would overlap for numberdensities less than 2�109 cm−3, over an order of magnitudeless than the minimum number density at any location in thisinvestigation. The probes used in this investigation are basedon the basic double probe design shown in Fig. 6. Two0.381-mm-diameter cylindrical tungsten electrodes, with4 mm exposed length, are held inside two double bore piecesof 99.8% pure alumina epoxied to one larger double borepiece of 99.8% pure alumina. The total length of the tungstenand alumina is approximately 46 cm �18 in.�. The “doubletier” design reduces the cross section of the probe that isinserted in front of the DCA, which decreases the dischargeperturbation.

C. Double probe electronics

The floating potential of the probe rapidly increases dur-ing probe insertion, reaching 1100 V with respect to ground,causing difficulty for most electronics. Significant errors inthe measured current can occur due to any appreciable straycapacitance in the circuit. As such, careful attention is paid tominimizing stray capacitance in the circuit design includingthe use of batteries to supply the bias voltage. The batterysupply consists of two series groups of four 67.5 V zincmanganese dioxide batteries connected in parallel. The bat-teries are capable of outputting 135 V at 100 mA. A poten-tiometer is attached to the battery output to adjust one elec-trode bias voltage with respect to the other electrode.

The double probe circuit18,32 is built around two AnalogDevices AD210 isolation amplifiers. These amplifiers pro-vide complete isolation through transformer coupling and arecapable of handling up to 2500 V of common mode voltageand provide an input impedance of 1�1012 �. The low im-pedance output �1 � maximum� is connected to a digitaloscilloscope that saves the data. Figure 7 illustrates thedouble probe circuit. High-voltage �up to 5 kV� SHV cablesand feedthroughs are used to connect the double probe elec-trodes to the battery pack outside the vacuum chamber. Theoutputs of the isolation amplifiers are calibrated with knowncurrents and bias voltages over their entire operating ranges.

IV. DATA ACQUISITION

A. Axial movement

The FMT2 is mounted on a two-axis positioning systemconsisting of two translational stages. The upper axis main-

FIG. 6. Reduced-blockage double probe tip design.

FIG. 7. Double probe circuit electrical diagram.



tains a constant radial distance between the thruster and theHARP. The lower axis controls the thruster axial locationwith respect to the probe to an absolute position accuracy of0.15 mm. The electrostatic probe is positioned radially insidethe discharge chamber using the HARP, which is fixed to thechamber wall. When actuated, the probe extends to thethruster centerline then returns to the starting location re-cessed inside the translating alumina tube. The HARP alsotriggers the oscilloscope to collect and save data. A thirdsmaller translation stage retracts and extends the guiding alu-mina tube as the axial location changes.

B. FMT2 operation

The primary thruster operating parameters for this inves-tigation of near-DCA plasma phenomena are the dischargecurrent and voltage. Therefore, for a given discharge current,the FMT2 main and discharge cathode flow rates are ad-justed until both the discharge voltage and beam currentmatch those recorded in the NASA throttling table. The datataken with beam extraction in this investigation are termedthruster operating conditions �TOC levels� instead of NSTARthrottling levels �TH� because the thruster operating param-eters considered secondary for this investigation �e.g., flowrates and accelerator current� are not matched. Table I reportsthe complete listing of the discharge parameters and thrustertelemetry for the operating conditions investigated. Thethruster was operated for at least half an hour prior to datacollection in order to reach steady operation at each operat-ing condition. Typical data collection time was 1 h for eachoperating condition.

Bias voltages are set manually using a potentiometer andthe battery supply. The probe is then swept through all spa-tial locations at each fixed bias voltage. A LABVIEW codesteps through the full axial range of motion �approximately4 cm� in 1.6 mm increments. For each axial step, the pro-gram retracts the alumina translating tube radially and trig-gers the HARP to sweep the probe radially through the dis-charge plasma. After all axial locations are interrogated, theFMT2 returns to the zero axial position located 2 mm down-stream of the DCA exit plane. The bias voltage is then manu-ally changed and the process repeats until the 31 bias volt-ages are investigated. A schematic of the two-dimensionaldata collection domain is shown in Fig. 8.

An oscilloscope records the probe position, the probecurrent, probe bias voltage, and the discharge current �from aHall sensor� as a function of time during probe insertion.From the raw data, the probe currents for a given bias volt-age are known as a function of probe position. The resultingdata are reassembled to obtain the current-voltage character-istic �I-V curve� of the double probe at each spatial locationin the radial sweep. Only data taken on the “in sweep” of theprobe are analyzed as “out sweep” data are more likely to beaffected by probe perturbation.

V. DATA ANALYSIS

The current-voltage curves from the double Langmuirprobe are analyzed according to the most appropriate oper-ating regime utilizing the scientific graphing package IGOR.33

The individual double probe characteristics are analyzed as-suming an infinite, quasineutral, and quiescent plasma. Themean free path for electron-neutral collisions �tens of centi-meters� in the discharge chamber is much larger than theprobe dimensions �millimeters�, which justifies the collision-less analysis.28,31 Particles are assumed to be collected with-out reflection or reaction inside the electrode collection area.

The presence of a magnetic field has a negligible effecton the double probe measurements. For the interrogation re-gion of this investigation, the Larmor radius for electrons is

FIG. 8. �Color online� Data collection domain. The internal discharge map-ping begins a few millimeters downstream of the DCA face and extendsdownstream with small incremental steps resulting in an axial resolution ofa few millimeters.

TABLE I. Experiment nominal thruster operating condition �TOC levels� and reference NASA throttling level �TH levels� operating parameters: beam powersupply voltage �Vs,ps�, beam current �Jb�, accelerator voltage �Va�, discharge voltage �Vdc�, discharge current �Jdc�, neutralizer keeper voltage �Vnk�, neutralizerkeeper current �Jnk�, main plenum flow rate, discharge cathode �DC� flow rate, neutralizer cathode �NC� flow rate, and discharge cathode keeper voltagereferenced to cathode common �Vck-cc�.

LevelVb,ps

�V�Jb

�A�Va

�V�Ja

�mA�Vdc

�V�Jdc

�A�Vnk

�V�Jnk

�A�Main flow�SCCM�

DC flow�SCCM�

NC flow�SCCM�

Vck-cc

�V�

TOC 4a 1100 0.71 −150 2.72 25.65 6.05 19.93 2.0 8.9 4.94 3.47 7.00TOC 4b 1103 0.71 −150 2.68 25.60 6.05 17.68 2.0 8.6 5.43 3.47 6.84TOC 8 1101 1.10 −180 4.84 25.10 8.24 17.40 2.0 15.3 4.02 3.68 6.49

TOC 15 1100 1.76 −180 8.30 25.14 13.2 ¯ ¯ 25.1 2.96 3.60 5.53TH 4 1100 0.71 −150 1.93 25.61 6.05 16.26 2.0 8.30 2.47 2.40 ¯

TH 8 1100 1.10 −180 3.14 25.10 8.24 15.32 1.5 14.4 2.47 2.40 ¯

TH 15 1100 1.76 −180 5.99 25.14 13.2 14.02 1.5 23.4 3.70 3.60 ¯



smallest near the discharge cathode where the magnetic fieldis the largest. In the bulk discharge plasma, the electron Lar-mor radius is on the order of a few millimeters, an order ofmagnitude larger than the probe electrode radius. Near theDCA, the magnetic field strength is on the order of 100 G,giving a Larmor radius that is only twice as large as theelectrode radius. The double probe analysis infers the num-ber density from the ion saturation current and therefore isunaffected by the reduction in electron saturation currentcaused by the presence of a magnetic field.23,24,28–30 Themagnetic field can also cause electron energy distributionfunction �EEDF� anisotropy. Passoth et al. determined thatEEDF anisotropy depends on the ratio B / p0, where p0 is theambient pressure �in this case the discharge chamberpressure�.34 It has been shown experimentally that EEDFanisotropy is negligible for B / p0�2.5�106 G / torr.35 Inthe FMT2, the magnetic field has a maximum �downstreamof the DCA� on the order of 100 G and the pressure inthe discharge chamber is estimated to be �10−4 torr. Sincethe maximum B / p0 ratio for any interrogated domain in thisinvestigation is of order 106, no substantial anisotropy in theEEDF is expected.

Post-test inspection of the raw data revealed asymmetricI-V curves. The asymmetry is most extreme closest to theDCA, decreasing with increasing axial distance from theDCA. The asymmetry is larger than can be accounted for bythe error in electrode lengths during fabrication. The mostprobable cause is an electrode-to-orifice misalignment duringevacuation of the vacuum facility. The HARP, and thus theelectrostatic probe, is mounted to the wall of the chamber,while the thruster rests on a platform inside the vacuum fa-cility. During pumpdown, the walls of the chamber com-press, resulting in a shift of the probe tip. A vertical shiftof 1 mm would result in one electrode lying directly in frontof the discharge cathode plume. The disappearance of theasymmetry far from the plume supports the misalignmenttheory. Mounting both the thruster and the HARP on a com-mon structure, independent of the chamber wall, wouldeliminate this problem.

The unexpected asymmetric characteristics also bring tolight another more important limitation of the double probemeasurement for this specific application. To eliminate elec-trode sheath interaction and satisfy the plasma isolation con-straint requires the electrodes to be placed millimeters apart.The required spacing of the electrodes and magnetic confine-ment of the electrons from the hollow cathode to a narrowplume results in an inadequate characterization of the ex-treme near-cathode plume. A single Langmuir probe is moreappropriate to characterize the extreme near-DCA plasma.However, the double probe results are accurate over a major-ity of the spatial domain and can be used to confirm singleprobe measurements. To account for the misalignment shift,the electrode collected current and bias voltage data corre-sponding to the larger collected current, i.e., the electrodemore in the discharge cathode plume, are mirrored and theresulting I-V curve is used.

The data are initially analyzed assuming a thin sheath.The initial calculated number density and electron tempera-ture from the measurement allow an iterative solution for the

sheath size and final number density. Based on the ratio ofthe Debye length �based on the final parameters� to probeelectrode radius, either the modified thin-sheath result is usedor an OML calculation is performed.

A. Thin sheath data analysis

Each I-V characteristic is fitted with the theoretical hy-perbolic tangent curve for a symmetric cylindrical doubleprobe, Eq. �3�, incorporating the Levenberg-Marquardt fitmethod,21,22,28,36

I = Isat tanh� �

2 � TeV� + A1� + A2. �3�

In Eq. �3�, Isat is the ion saturation current, � is the probebias voltage, the parameter A1 accounts for sheath expansionin the ion saturation region, and A2 accounts for any offsetcurrent due to stray capacitance. Figure 9 illustrates repre-sentative I-V traces and their corresponding curve fits. Elec-tron temperature can be determined immediately from thefit parameters. Using the Bohm approximation for ionvelocity,17,23,28 the ion number density is calculated accord-ing to

ni =Isat

0.61Ase�MXe

kTeV. �4�

In Eq. �4�, e is the electron charge, MXe is the mass of thexenon ion, k is Boltzmann’s constant, and As is the electrodecollection area, which is initially set to the physical electrodesurface area. The true collection area depends on the thick-ness of the sheath surrounding the probe. Knowledge of thenumber density and electron temperature allows the Debyelength to be calculated according to Eq. �2�. Assumingquasineutrality neni �in cm−3� readily gives �D �cm�.The sheath thickness � is then calculated using the massof an electron �m�, the mass of the xenon ion �MXe�, and theDebye length ��D� according to30,31

FIG. 9. �Color online� Sample of I-V curves �� and fit curves �� to rawdata for DL 4A. Curves are at the furthest axial position along the centerlineat the following radial locations: 0 mm �red�, 1 mm �orange�, 2 mm �yel-low�, 5 mm �green�, 10 mm �light blue�, 20 mm �dark blue�, 30 mm�purple�, and 40 mm �light purple�.



� = 1.02�D�1

2ln� m

MXe��1/2

−1�2 1/2

��1

2ln� m

MXe��1/2

+ �2 , �5�

and the sheath area �As� follows in Eq. �6�, where Rp is theprobe electrode radius and Ap is the exposed probe electrodesurface area,24

As = Ap�1 +�

Rp� . �6�

The above equation ignores the circular area of the end of theelectrodes, which is negligible due to the large length-to-diameter ratio of the electrodes. New plasma parameters arecalculated from this new collection area and the process isiterated until convergence. This iterative process attempts totake into account the departure from the thin-sheath regimeand is used in all calculations in which an OML analysis isnot warranted. The iterative calculation is most useful whenthe probe is operating in the transitional regime. For a ratioof probe radius to Debye length of less than or equal to 3, theconverged thin-sheath iterative result is used.

B. OML data analysis

For a ratio of probe electrode radius to Debye length ofgreater than or equal to 10, the thin-sheath calculation ofelectron temperature is still appropriate; however, the num-ber density is calculated from the slope of the ion current �Ii�squared versus probe bias voltage �Vp� according to the fol-lowing equation:34,37,38

nOML =��− ��Ii2�/�Vp�MXe

0.2e3Ap2 . �7�

C. Transition analysis

When the final iterated Debye length calculation reveals10� �Rp /�D��3, the probe is not operating in either thin-sheath or OML regimes. In this case, a weighted average,based on the range of probe electrode radius to Debye length,is used to blend the two regimes.

VI. RESULTS AND DISCUSSION

A. Number density contours

The number density measurements are illustrated inFig. 10. Due to export control restrictions, all spatial di-mensions have been nondimensionalized by the dischargecathode keeper outer diameter. There is little variation be-tween the number density contours over the range of operat-ing conditions investigated. The structure of the number den-sity contours is intuitive. There is an on-axis maximum nearthe DCA �in its plume� that decreases gradually in the down-stream �axial� direction. A more extreme density gradientexists in the radial direction as the discharge chamber mag-netic field confines electrons and resulting ions created to anarrow plume particularly at axial locations near the DCA.

The number density falls off by more than an order of mag-nitude from the cathode centerline to the cathode keeperouter radius.

As the discharge current and flow rates are increased, themagnitude of the number density plume increases slightly.All number densities measured in the 2D domain fall withinthe range of 1�1010–8�1012 cm−3. Foster and Pattersonhave measured the number densities of a high-current12.7-mm-diameter hollow cathode inside a NSTAR-typedischarge chamber, i.e., without beam extraction. Their ex-periment, though unable to capture the effects of the beamcoupling to the discharge plasma, accurately captures thedischarge chamber geometry and magnetic field topology ofa gridded ring-cusp ion thruster. Radial measurements taken3 mm downstream of the keeper plate report a maximumnumber density of approximately 2�1012 cm−3 on axiswith steep radial gradients, similar to the present data. Their

FIG. 10. �Color� Number density profiles for �a� TOC 4a, �b� TOC 4b, �c�TOC 8, and �d� TOC 15.



results also indicate an increase in number density with in-creasing discharge current, which is also consistent with re-sults of this investigation.27

B. Electron temperature contours

Figure 11 illustrates the measured electron temperaturesfor the various thruster operating conditions. Each contourcontains an off-axis maximum region that was unexpected.Electron temperatures range from 2 to 5 eV over most ofthe spatial locations and operating conditions investigated.The off-axis maximum is located at the boundary betweenthe discharge cathode plume and the bulk discharge plasmaas confirmed by plasma potential measurements inside theFMT2 thruster.39,40 The increased electron temperature onthis boundary in ion thrusters is due to the electron accelera-tion across the radial potential gradient structure producingelectron energy distribution functions that become stretchedtoward higher energies and in some cases become double

peaked.39,41 The measured electron energy distributionfunctions indicate that in this transition region between thecathode plume and discharge plasma, the assumption ofMaxwellian electrons is no longer valid and therefore de-scribing the electron energy by an electron temperature is notappropriate. It does, however, add qualitatively to the discus-sion of the ion thruster internal discharge plasma. Figure 11also illustrates that the magnitude of the maximum off-axiselectron temperature region increases as the thruster isthrottled up to higher power levels. This observed increase,combined with comparison of electron temperature mea-surements in the FMT2 thruster without beam extraction,illustrates the changes in the ion thruster internal plasmawith beam extraction.42 These effects may be partially due tothe decreased neutral density in the discharge chamber thatalters the electron energy distribution function when a beamis extracted.

Noise in electron temperature contours is evident. Aspreviously stated, the double probe electron temperaturecalculation is proportional to the ion saturation current di-vided by the slope of the I-V characteristic evaluated at zero.As a result, errors in calculating both the ion saturation cur-rent and slope at the zero location lead to large variations inelectron temperature measurements. In single Langmuirprobe measurements, the electron temperature calculation issolely determined by the slope of the I-V curve in theelectron-retarding region and therefore may yield smoothercontours.23,24,28–30

VII. ERROR ANALYSIS

Typical estimates for the error in electron temperatureand electron number density Langmuir probe measurementsare 20% and 50%, respectively.22 While these traditional er-ror estimates are large, they are absolute uncertainties. Largecombinations of effects are lumped into these percentages:the uncertainty of electrode collection area, applicability ofprobe theory, noise in the collected signal, circuit calibrationerrors, and additional measurement errors to name a few. Theerror between measurements made using identical setups willgreatly reduce the contribution of systematic errors with re-gard to relative comparisons of the data obtained. The appli-cable regions of thin-sheath, transition, and OML theoriesare displayed in Fig. 12.

Another source of measurement error is the dischargeperturbation due to the presence of the probe in the plasmaenvironment being interrogated. The discharge voltage in-crease �not shown� less than 0.5 V, �2% of the nominal

FIG. 11. �Color� Electron temperature profiles for �a� TOC 4a, �b� TOC 4b,�c� TOC 8, and �d� TOC 15.

FIG. 12. Illustration of the different probe regimes in the 2D domain foroperating condition TOC 4a: thin sheath, OML, and transition.



discharge voltage, when the probe is inserted into the dis-charge plasma. The largest perturbations occur only duringprobe sweeps within a few millimeters of the DCA, for largemagnitude bias voltages where the probe is in ion saturation,and only when the probe is directly in front of the cathodeplume. Figure 13 shows that the discharge current perturba-tion and bias voltage drop during probe insertion. For themost extreme conditions, the discharge current perturbationis typically 5%–10% of the nominal discharge current, whichis considered to be minor. Outside of this very extreme near-DCA region, i.e., over a vast majority of the interrogationregion, the discharge current perturbation due to probe inser-tion is negligible. In the extreme near-DCA region, the per-turbation is still minor but not negligible. The error intro-duced would cause a minor reduction in the measuredelectron number density but is considered well within the50% error bars on this value.

VIII. CONCLUSIONS

An internal ion thruster discharge diagnostic techniquehas been demonstrated. Double Langmuir probe electrontemperature and number density measurements inside thedischarge chamber of a 30 cm ring-cusp ion thruster are pre-sented for multiple operating conditions with beam extrac-tion. Electron temperature magnitudes, 2–5 eV, are compa-rable to those measured by other researchers in electronbombardment discharge plasmas. Number density contours,with a maximum of approximately 8�1012 cm−3 on the cen-terline, show very little variation over the range of operatingconditions investigated. The perturbation of the dischargecurrent, 5%–10%, by the probe was minimized though re-mains non-negligible. Number density magnitudes agreewith data taken by other researchers in simulated ion thrusterdischarge chamber environments. Double probe spatial reso-lution is found to be insufficient in the very-near DCA loca-tions. Thus, single Langmuir probes may be more suitableclose to the DCA.

ACKNOWLEDGMENTS

We would like to thank Michael Patterson of the NASAGlenn Research Center �GRC� for the financial support ofthis research through research Grant No. NAG3-2216 and forthe use of government furnished equipment. We would liketo acknowledge Dr. Matthew Domonkos, Dr. John Foster,

and Dr. George Williams who have been principal technicalcontacts at NASA GRC. Additional support was provided bya Department of Defense NDSEG fellowship.

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FIG. 13. Sample discharge current perturbation and probe bias voltage�20 V probe bias, 13.13 A discharge current, 25 V discharge voltage� forradial sweep at the closest axial position to the DCA.



an ion thruster internal discharge chamber electrostatic ......large ﬂagship nasa missions takes...

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