Wensheng Huang, Rohit Shastry, George C. Soulas, and Hani Kamhawi

Glenn Research Center, Cleveland, Ohio

Farfi eld Plume Measurement and Analysis on the

NASA-300M and NASA-300MS

NASA/TM—2013-216606

December 2013

IEPC–2013–057
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Wensheng Huang, Rohit Shastry, George C. Soulas, and Hani Kamhawi

Glenn Research Center, Cleveland, Ohio

Farfi eld Plume Measurement and Analysis on the

NASA-300M and NASA-300MS

NASA/TM—2013-216606

December 2013

IEPC–2013–057

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

33rd International Electric Propulsion Conference (IEPC2013)

sponsored by the Electric Rocket Propulsion Society

Washington, D.C., October 6–10, 2013
Acknowledgments

We thank the following contributors: The NASA Space Technology Mission Directorate In-Space Propulsion project for funding 

this work, and Timothy D. Smith for managing the work; Peter Peterson for work on the design of the NASA-300M Hall thruster; 

Jonathan Van Noord of the University of Michigan and Ioannis G. Mikellides of the NASA Jet Propulsion Laboratory for work 

on the design of the NASA-300MS; Christopher Griffi th for work on the design of both the NASA-300M and the NASA-300MS; 

Thomas Haag for work on the thrust stand and Daniel L. Brown and Joseph Blakely of the Air Force Research Laboratory for 

the retarding potential analyzer; and Kevin L. Blake, George W. Readus, George P. Jacynycz, and Thomas Raly for the thruster 

fabrication, assembly of the test setup, and operation of the vacuum facility.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

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Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identifi cation 

only. Their usage does not constitute an offi cial endorsement, 

either expressed or implied, by the National Aeronautics and 

Space Administration.

Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2013-216606 1 

Farfield Plume Measurement and Analysis on the 

NASA-300M and NASA-300MS 

Wensheng Huang, Rohit Shastry, George C. Soulas, and Hani Kamhawi 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Abstract 

NASA is developing a 10- to 15-kW Hall thruster system to support future NASA missions. This 

activity is funded under the Space Technology Mission Directorate Solar Electric Propulsion Technology 

Demonstration Mission project. As a part of the development process, the NASA-300M, a 20-kW Hall 

thruster, was modified to incorporate the magnetic shielding concept and named the NASA-300MS. This 

activity was undertaken to assess the viability of using the magnetic shielding concept on a high-power 

Hall thruster to greatly reduce discharge channel erosion. This paper reports on the study to characterize 

the far-field plumes of the NASA-300M and NASA-300MS. Diagnostics deployed included a polarlyswept Faraday probe, a Wien filter (ExB probe), a retarding potential analyzer, and a Langmuir probe. 

During the study, a new, more accurate, integration method for analyzing Wien filter probe data was 

implemented and effect of secondary electron emission on the Faraday probe data was treated. 

Comparison of the diagnostic results from the two thrusters showed that the magnetically shielded version 

performed with ~2 percent higher voltage utilization efficiency, ~2 percent lower plume divergence 

efficiency, and ~2 percent lower mass utilization efficiency compared to the baseline version. The net 

change in efficiency is within the aggregate measurement uncertainty so the overall performance is 

roughly equal for the two versions of the thruster. Anode efficiency calculated from thrust stand 

measurement corroborates this finding. 

Abbreviations and Nomenclature 

GRC Glenn Research Center 

HEFT Human Exploration Framework Team 

STMD Space Technology Mission Directorate 

AFRL Air Force Research Laboratory 

LEO Low Earth Orbit 

GEO Geosynchronous Earth Orbit 

300M NASA-300M 

300MS NASA-300MS 

300MS-2 NASA-300MS configuration 2 

RPA Retarding Potential Analyzer 

CEX Charge-exchange 

SEE Secondary Electron Emission 

MCD Mean Channel Diameter 

a Anode efficiency 

v Voltage utilization efficiency 

d Divergence efficiency 

b Current utilization efficiency 

m Mass utilization efficiency 

q Charge utilization efficiency 
NASA/TM—2013-216606 2 

I. Introduction 

In 2010, NASA established the Human Exploration Framework Team (HEFT) to analyze exploration 

and technology concepts and provided inputs to the agency’s senior leadership on the key components of 

a safe, sustainable, affordable, and credible future human space exploration endeavor for the nation 

(Ref. 1). The team concluded, in part, that the use of a high power (i.e., on the order of 300 kW) solar 

electric propulsion system could significantly reduce the number of heavy lift launch vehicles required for 

a human mission to a near earth asteroid (Refs. 1 and 2). Hall thrusters were found to be ideal for such 

applications because of their high power processing capabilities and their efficient operation at moderate 

specific impulses, which leads to reduced trip times that are necessary for such missions (Refs. 2 to 4). 

Recent electric propulsion system model estimates that considered factors such as cost, mass, faulttolerance, cost uncertainty, complexity, ground test vacuum facility limitations, previously demonstrated 

power capabilities, and possible technology limitations have shown that Hall thrusters operating at power 

levels of 20 to 50 kW are strong candidates for human exploration missions operating at total powers up 

to 500 kW (Refs. 2 and 5). 

As an intermediate step towards the aforementioned higher power Hall thruster system, the Space 

Technology Mission Directorate (STMD) is investing in the development of a 10- to 15-kW Hall thruster. 

The NASA Glenn Research Center (GRC) is partnering with the Jet Propulsion Laboratory (JPL) to carry 

out this development work. The aforementioned thruster will serve as a stepping stone to higher power 

and provide a state-of-the-art propulsion system for the Solar Electric Propulsion Technology 

Demonstration Mission (SEP TDM). SEP TDM, initially announced in 2011, is aimed at demonstrating 

new cutting edge technology in flexible solar arrays, spacecraft bus, and electric propulsion that will 

increase the maturity of these SEP technologies for future commercial and government uses. Once these 

technologies have been demonstrated, they are expected to enable higher performance LEO to GEO 

transfers as well as a number of other near-Earth orbit transfers and station-keeping maneuvers. These 

technologies may also benefit a potential robotic mission to redirect an asteroid into cis-lunar orbit for 

crew exploration. In longer terms, these technologies will reduce mission costs for NASA interplanetary 

robotic missions in general, and will serve as a precursor to higher power systems for human 

interplanetary exploration. 

The magnetic shielding (MS) concept, recently developed by JPL, has the potential to greatly reduce 

discharge channel wall erosion, which is a dominant life-limiting mechanism for traditional Hall thrusters 

(Ref. 6). This concept greatly benefits Hall thruster technology development and was previously 

demonstrated on a 6-kW Hall thruster (Refs. 7 and 8). To mitigate possible risks of applying the MS 

concept to higher power thrusters, NASA GRC and JPL took a combined experimental and modeling 

approach to study the application of the MS concept on the 20-kW NASA-300M. The NASA-300M was 

developed from 2004 to 2005 for project Prometheus but was not tested until recently due to project 

cancellation (Ref. 9). With the recent renewal in interest towards high-power Hall thrusters, the 

performance of the NASA-300M was characterized in 2010 (Ref. 9). The risk mitigation activities began 

with the modification of the NASA-300M into a magnetically-shielded version of the same thruster, 

called the NASA-300MS. A series of experiments and simulations were then performed to characterize 

the difference in behavior between the NASA-300M and the NASA-300MS. For a general overview of 

the MS modification, the system performance, and the simulation work, please see Kamhawi’s paper 

(Ref. 10). For a description of the wall and interior Langmuir probe studies, please see Shastry’s paper 

(Ref. 11). This paper will focus on the plume characterization study and the accompanying efficiency 

analysis. 

The plume characterization study involved the use of a number of far-field diagnostics to study 

various plume characteristics of the NASA-300M and NASA-300MS. Measurements from these 

diagnostics can then be used to infer the effectiveness with which various performance-driving processes 

are carried out in the thrusters. Each of these processes is assigned an efficiency factor in a 

phenomenological efficiency model. By comparing the trends in the efficiency factors between the two 

thrusters, one can determine how applying the MS concept changes thruster performance and which 
NASA/TM—2013-216606 3 

performance-driving processes are the drivers. For this study, a far-field Faraday probe was swept in a 

polar fashion to map the ion current density. A Wien filter, also known as an ExB probe, a retarding 

potential analyzer (RPA), and a Langmuir probe were mounted at a fixed location on the thruster axis in 

the far-field plume. The ExB probe, so called because of the orthogonal electric and magnetic fields 

inside the probe, was used to measure the species fractions of the various charged states of xenon. The 

RPA and the Langmuir probe were used to measure the energy per charge of the exhaust plume. 

The main focus of this paper will be on the comparison of the efficiency analyses between the 

NASA-300M and NASA-300MS. This paper will also cover comparison between the NASA-300MS and 

NASA-300MS-2, which is the same as the NASA-300MS except with a shortened discharge channel. 

Other topics that will be covered include a new, more accurate, method of integration for analyzing ExB 

probe data and the effect of secondary electron emission on Faraday probe data. 

The paper begins by describing the efficiency model used in the present study in Section II, followed 

by a description of the experiments in Section III. Next, the paper will describe data analyses and 

individual probe results for the RPA (Section IV), the ExB probe (Section V), and the Faraday probe 

(Section VI). Then, the paper presents the overall efficiency analyses and comparison between the 300M 

and 300MS, as well as the 300MS and 300MS-2, in Section VII. The paper ends with the conclusions in 

Section VIII. Appendices attached after Section VIII give the derivation of the new integration method for 

analyzing ExB data. 

II. Background 

The purpose of the present study is to determine what effects the application of the MS concept has 

on the performance of a high-power Hall thruster. The performance of a Hall thruster is typically 

measured by its anode efficiency, defined in Equation (1). 

a d d

2

a 2m I V

T

η   (1) 

In this equation, T is thrust, mሶ a is anode mass flow rate, Id is discharge current, and Vd is discharge 

voltage. However, the anode efficiency alone does not provide information about the plasma generation 

and acceleration processes that drive the performance of the thruster. 

A phenomenological efficiency model is a way of breaking down and describing various physical 

phenomena that affect the overall efficiency of a Hall thruster. The purpose of a phenomenological 

efficiency model is to help researchers quantify the trends in the processes that drive the overall thruster 

efficiency. Many efficiency models have been proposed for the Hall thruster in the past. The complexity 

of these models depended on the operating environment and the state of knowledge in the community at 

the time. The model used in this paper is the same as a prior work by Shastry, (Ref. 12) which has 

evolved over time from a number of other studies (Refs. 13 to 16). The model is shown in Equations (2) 

to (7). 

a  vdbmq (2) 

d

RPA v V

V

  (3) 

2

d   (cos ) (4) 
NASA/TM—2013-216606 4 

d

b

b I

I

  (5) 

 

   















 

k k

k m m a

Xe b m Z , m e

m I

 (6) 

























 

k

k k

2

k

k k

q / Z

/ Z

 (7) 

Where a, the anode efficiency, is the same as that calculated from Equation (1), v is the voltage 

utilization efficiency, d is the divergence efficiency, b is current utilization efficiency, m is the mass 

utilization efficiency, q is the charge utilization efficiency, VRPA is the ion energy per charge, δ is the 

charged-weighted divergence angle, the Ib is the total beam current, mXe is the mass of xenon, e is the 

elementary charge constant, m is the part of mass utilization efficiency that depends on charge state 

information, Ωk is the current fraction of the k-th species, and Zk is the charge of the k-th species. 

The voltage utilization efficiency describes, on the average, how much of the voltage provided by the 

discharge supply is actually used to accelerate the ions. This factor is typically measured by the RPA. 

The divergence efficiency describes how much of the kinetic energy imparted to the ions is axial, 

thrust-producing, kinetic energy. This factor is typically measured by the Faraday probe. 

The current utilization efficiency describes how much of the discharge current is carried by ions 

instead of electrons. Electrons generate negligible thrust compared to the ions. This factor is typically 

measured by the Faraday probe. 

The mass utilization efficiency describes how much of the mass flow exiting the thruster channel is in 

the form of ions. This factor typically requires data from the Faraday probe and the ExB probe. 

The charge utilization efficiency is a number of terms representing the effects of having multiplycharged species that are not already described by the other terms in the efficiency model. 

III. Experimental Setup 

For the sake of brevity and to simplify plot labeling, NASA-300M will sometimes be referred to as 

the 300M in this paper. Similarly, 300MS is NASA-300MS and 300MS-2 is NASA-300MS-2. Operating 

conditions are labeled as www V, yy kW, where www is the discharge voltage in volts and yy is the 

discharge power in kilowatts. Unless otherwise noted, all spatial positions presented in this paper have 

been normalized by the mean channel diameter of the thrusters, which is identical for all three variants. 

The mean channel diameter (MCD) is defined as the average of the inner and outer discharge-channel 

wall diameters. 

A. Thrusters and Test Matrices 

The NASA-300M is a magnetic-layer Hall thruster. It was designed based on the principles outlined 

in Manzella’s dissertation work (Ref. 17). This thruster was originally developed for high-specificimpulse missions (Ref. 9) and has lens-type magnetic field topology (Refs. 18 and 19). For this paper, the 

magnetic field settings of the 300M were optimized to give a shape roughly symmetric about the channel 

centerline while maximizing the anode efficiency. The NASA-300MS is a magnetically-shielded Hall 

thruster created from the NASA-300M. The magnetic circuit of the thruster was modified to achieve the 

MS topology while retaining most of the original 300M thruster. As such, the physical dimensions of the 
NASA/TM—2013-216606 5 

300MS are nearly identical to that of the 300M. The biggest differences in the exterior of the two 

thrusters are the presence of chamfers on the downstream edge of the discharge channel walls. The 

physics-based modeling program Hall2De was used to validate the design of the magnetic field topology 

of the 300MS. For more details about the modifications needed to apply the MS concept and the 

modeling work, see Kamhawi’s paper (Ref. 10). Experimental verification of the plasma potentials and 

electron temperatures at the channel walls was also performed and detailed in Shastry’s paper (Ref. 11). 

For this paper, the magnetic field settings of the 300MS were set to maintain the MS topology while 

maximizing the anode efficiency. Both thrusters were operated with the same centrally-mounted hollow 

cathode, which was derived from the discharge cathode for NASA’s Evolutionary Xenon Thruster 

(NEXT) (Ref. 9). The cathode flow fraction was 8 percent. Figures 1 and 2 show photographs of the 

NASA-300M and NASA-300MS, respectively. 

The NASA-300MS-2 is a second configuration of the NASA-300MS with a shortened discharge 

channel. The modification was achieved by moving the anode downstream so that the channel length is 

roughly 20 percent shorter. This configuration was made to investigate whether the thruster could be 

made more compact to decrease mass without impacting the performance and magnetic shielding. The 

data will be used to guide the design of the 10- to 15-kW thruster. Comparisons will be made between the 

300M and the 300MS to study the effect of applying magnetic shielding, and between the 300MS and the 

300MS-2 to study the effect of shortening the discharge channel. 

The nominal operating condition of NASA-300M and NASA-300MS is 500 V, 20 kW. For the 

purpose of comparing the thruster versions, eight operating conditions have been identified as reference 

points. These eight conditions span discharge voltages from 300 to 500 V, discharge currents from 20 to 

50 A, and discharge powers from 10 to 20 kW. The thrusters operated with anode efficiencies of 65 to 

70 percent over these eight conditions. Figure 3 shows the combined test matrix for the thruster versions. 

Reference points are highlighted by red circles and will be the main focus of the paper. Data from nonreference conditions will be used to supplement plots about trends within individual thruster versions. The 

boron nitride channel walls of the 300M have accumulated 110 hours of operation time prior to the start 

of this study. The boron nitride channel walls of the 300MS were freshly manufactured for this study. 

The test campaign for the 300MS and 300MS-2 was spread over three tests. Test 1 was the 

performance and plume characterization test on the 300MS. Test 2 was the same but on the 300MS-2. 

Test 3 was the interior plasma characterization test on the 300MS. At the end of test 1, the boron nitride 

channel has seen 49 hours of operation. At the end of test 2, the channel has seen 82 hours of operation. 

At the end of test 3, the channel has seen 99 hours of operation. Figure 4 shows the 300MS prior to 

testing, after 49 hours of testing, and after 99 hours of testing. The discharge channels, especially at the 

downstream chamfers, are progressively darkened by deposited material. The data presented in this paper 

were obtained in tests 1 and 2. Details on test 3 are reported in Shastry’s paper (Ref. 11). 

Figure 1.—The NASA-300M on a thrust stand. Figure 2.—The NASA-300MS on a thrust stand. 
NASA/TM—2013-216606 6 

Figure 3.—The combined test matrix. 

Figure 4.—NASA-300MS prior to test (left), after 49 hr of testing (middle), and after 99 hr of testing (right). 

B. Test Facility 

Testing was conducted in NASA GRC’s Vacuum Facility 5. This cylindrical facility is 4.6 m in 

diameter and 18.3 m long and is pumped with a set of cryo-panels and 20 oil diffusion pumps. The 

thrusters were mounted on a thrust stand in the main volume of the vacuum facility to ensure low 

pressures near the thruster during operation. Facility pressures were monitored with one Pirani gauge and 

six ion gauges, one of which is mounted next to the thrust stand. Facility pressure uncertainties were 

estimated by the manufacturer to be within 6 percent of reading. The pressure reading, corrected for 

xenon, next to the thrust stand was less than 3.510–3 Pa (2.610–5 torr) throughout testing. 

A gas feed system made of commercially available components was used to feed xenon to the 

thruster. A 1000-sccm mass flow controller provides propellant to the anode while a 200-sccm controller 

provides propellant to the cathode. Both controllers were calibrated using xenon prior to testing. Typical 

uncertainty of measurement was 1.0 percent of reading. 

The commercial discharge power supply used is capable of supplying 2000 V at over 100 A with a 

5.5 mF output filter capacitance. A 15.3 mF capacitor bank was connected in parallel with the power 

supply at the electrical feed-throughs of the vacuum facility to filter discharge current oscillations. In 

addition, separate commercial power supplies were used to power the cathode heater, cathode keeper, and 

electromagnets. 

C. Thrust Stand and Plasma Diagnostics 

This section will describe the thrust stand and the plasma diagnostics used to obtain data for the 

efficiency model. The plasma probes used in this study included a Langmuir probe, an RPA, an ExB 

probe, and a Faraday probe. Unless otherwise stated, all probe biases were applied with commercial 

power supplies. 
NASA/TM—2013-216606 7 

The thrust stand used in this study is an inverted pendulum thrust stand designed by Haag (Ref. 20). It 

is actively cooled during operation. The nominal accuracy of this thrust stand is 2 percent (Ref. 9). 

Long-term thermal drift is corrected by measuring the thrust signal with all gas flow to the thruster off 

and then assuming a linear change in the zero-thrust value over time. The maximum thermal drift was 

found to be ~10 mN. 

A Langmuir probe, an RPA, and an ExB probe were mounted to a probe tower with accompanying 

shielding and shutters protecting the RPA and the ExB probe. This farfield probe tower was attached to a 

vertical motion stage located ~27 MCD downstream of the thruster exit plane and sitting behind a body 

shield. During the data acquisition process, each probe was moved vertically to a point roughly along the 

central axis of the thruster before measurements were taken. The probe tower retreated behind the shield 

once data acquisition was completed. Figure 5 shows a photograph of the diagnostics setup. Figure 6 

shows a photograph of the farfield probe tower. A farfield Faraday probe was mounted onto a commercially available three-axis belt-driven motion system. The motion system provides 2D rectilinear motion 

and probe rotation. Positioning accuracy is ~1 mm and 0.1°, respectively. 

For the test of the 300M, the Langmuir probe consists of a single tungsten wire protruding from an 

alumina tube. This probe was used to obtain the plasma potential at the same location as the RPA so that 

the RPA data can be corrected by this potential. For the tests of the 300MS, a disk probe was used to 

improve data fidelity. The Langmuir probe was swept at 10 Hz for 1 sec at each test point. The probe was 

connected to a custom circuit box where the probe current was passed through a shunt and the signal fed 

to an isolation amplifier. The bias voltage was passed through a voltage divider and fed to another 

isolation amplifier. Signal from the amplifiers were fed to a NI-9205 data acquisition module attached to 

a NI cDAQ-9178 unit. 

For the test of the 300M, two four-grid RPAs were used to help validate a new RPA designed by the 

Air Force Research Laboratory (AFRL), courtesy of Daniel L. Brown and Joseph Blakely. The other RPA 

(just below the Langmuir probe in Fig. 6) was of GRC design and was known to not work well at closer 

than ~25 MCD for medium to high power Hall thruster testing. Results from the 300M test show that the 

two RPAs agree with each other. Furthermore, the AFRL RPA produced data with less noise and was 

Figure 5.—Photograph of the diagnostics setup. Figure 6.—Photograph of the farfield probe tower.

 
NASA/TM—2013-216606 8 

more resistant against plasma-induced breakdown. Only the AFRL RPA was used during the 300MS tests 

and all data presented in this paper are from the AFRL RPA. During testing, the electron suppression and 

repelling grids of the RPA was biased to –30 V with respect to facility ground while the ion retarding grid 

voltage was swept. The ion retarding grid was biased by a Keithley 2410 sourcemeter while the collected 

current was measured by a Keithley 6485 picoammeter. 

The ExB probe is a commercial product of Plasma Controls, LLC. It was used to measure charged 

species current fraction. The ExB probe weights ~2 kg and is ~270 mm long. This ExB probe was the 

result of a Small Business Innovation Research project and has a proven history of usage (Ref. 15). Ions 

entering this ExB probe must first travel through a collimator, which ensures that the ions enter the ExB 

filter section along the probe axis. Perpendicular electric and magnetic fields in the filter section ensure 

that only charged particles of a given velocity can pass through to the electron suppression plate. There is 

a drift section between the filter section and the electron suppression plate which enhances probe 

resolution and makes sure bias on the suppression plate does not affect the filter section. The electron 

suppression plate has a small orifice through which ions can pass through. It was biased at –30 V with 

respect to facility ground to suppress secondary electron emission from the collector. Ions passing 

through the suppression plate were collected by the collector. The collimator used in this study has an 

entrance and exit orifice diameters of 0.76 mm. The bias plates that form the electric field in the filter 

section have a gap distance of 3 mm. The electron suppression plate orifice diameter is ~1.5 mm. The 

collector is large enough to collect all ions that pass through the electron suppression plate orifice. A 

thermocouple was attached to the case of this ExB probe to make sure it did not overheat and demagnetize. During testing, the main bias plate voltage was swept by a Keithley 6487 picoammeter, which 

also measured the collector current. 

The Faraday probe, which is of GRC design, was used to measure ion current density. Figure 7 shows 

a cross-sectional diagram of this Faraday probe. The collector area is a circle of diameter 17.39 mm. The 

front area of the collector is 238 mm2

. The probe has an overall diameter of ~28 mm. The collector and 

guard ring are made of molybdenum (to minimize secondary electron emission) and the insulating back is 

made of Macor. The collector and guard ring connections are mated to wires behind the insulating back 

and covered with fiberglass tape. The Faraday probe was set at 5 MCD away from the thruster because it 

needed to be far enough away from the thruster for the source of the thruster exhaust to be considered a 

point source. At the same time, the probe cannot be positioned much further away due to the effects of 

charge-exchange (CEX) and the physical size of the vacuum chamber. During each test, the probe was set 

to different bias voltages from –20 to –60 V in increments of 10 V with respect to ground. The bias was 

then set to the second most positive value that produces a consistent Faraday probe trace for recording 

data. This was done to ensure the electrons were properly repelled by the probe while keeping the sheath 

expansion negligible. Collected current was measured via a shunt and an isolation amplifier. The output 

of the amplifier was fed to another NI-9205 data acquisition module attached to the aforementioned 

NI cDAQ-9178 unit. 

Figure 7.—Diagram of the 

farfield Faraday probe. 
NASA/TM—2013-216606 9 

The experiment was conducted via a LabVIEW (National Instruments) program from a dedicated data 

acquisition computer. The motion stages were controlled by a motion controller that received movement 

commands from the computer. Encoder signals from the stages were fed into an encoder controller, which 

reports to the computer. The NI cDAQ-9178 data acquisition device and the various Keithley devices fed 

data to and were commanded by the computer. During the experiment, the computer automatically 

orchestrated the sequence of events that activated the various motion stages, shutters, and probes. 

IV. Retarding Potential Analyzer Analysis 

Data reduction was carried out in a specific sequence because, for the most part, each step of the 

analysis depended on the data obtained in the preceding steps. Though some of the analysis steps can be 

carried out independently, the accuracy of the result would have been decreased. For this study, the data 

analysis sequence was as follows, Langmuir probe analysis, RPA analysis, ExB probe analysis, and 

Faraday probe analysis. Additionally, pressure data is analyzed to help correct the ExB probe data for 

facility-background CEX effects. The data analysis as well as individual probe results will be covered in 

three analysis sections. The Langmuir probe and RPA analyses will be covered in this section. The ExB 

probe analysis will be covered in Section V. The Faraday probe analysis will be covered in Section VI. 

Differences between the presented data reduction procedures and traditional approaches will be 

highlighted with explanations for the rationale behind the new procedures. 

A. Analysis Method 

Langmuir probe analysis was carried out using simple Langmuir probe theory (Ref. 21). Since the 

Langmuir probe was swept at 10 Hz for 1 sec, 20 ramps were present in each data file. These data were 

averaged then smoothed using a Savitzky-Golay filter (Refs. 22 and 23). Then, the derivative of the probe 

current with respect to the probe voltage was plotted against the probe voltage. The voltage corresponding 

to the highest amplitude value on this plot is roughly equal to the plasma potential. This potential is 

needed to correct the RPA reading because the RPA ion retarding grid was biased with respect to the 

facility ground. The true filter voltage was equal to the ion retarding grid bias voltage minus the local 

plasma potential. 

RPA analysis was carried out by first smoothing the RPA trace then taking the negative of the 

derivative of the collector current with respect to the bias voltage on the ion retarding grid. The result, 

plotted against the bias voltage, is proportional to the ion energy per charge distribution function 

(Ref. 24). Traditionally, the most probable voltage is taken as the average ion energy per charge. The 

most probable voltage is defined as the voltage where the amplitude of the plot maximizes. However, due 

to a combination of noise and broad ion distribution, the data can sometimes contain small bumps on top 

of the main population that skewed the location of the most probable voltage. To deal with this issue, the 

average ion energy per charge was calculated via ensemble-averaging using only the part of the trace 

where the amplitude exceeded half of the maximum amplitude. This averaging approach will be referred 

to as the threshold-based averaging approach with a 50 percent threshold. For clean traces, this approach 

yield values that are at most 3 to 4 V different from the most probable voltage. For noisy traces, this 

approach yield values that are insensitive to noise spikes. Figure 8 shows plots from applying the 

threshold-based averaging approach to a slightly noisy RPA trace. The black dashed vertical line indicates 

the location of the most probable voltage, the red solid vertical line indicates the result of using the 

threshold-based averaging approach with the 50 percent threshold, and the red dashed horizontal line 

indicates the 50 percent of maximum threshold. 

 
NASA/TM—2013-216606 10 

Figure 8.—Sample RPA analysis plots. 

Note that in theory the most accurate result is obtained by ensemble-averaging the entire RPA trace. 

However, doing so often produces unphysical results because the ion energy per charge distribution as 

measured by the RPA is typically much broader than the real distribution due to the wide acceptance 

angle of the RPA. This is also the reason the traditional approach relies on the most probable voltage. 

Using the 50 percent threshold-based ensemble-averaging approach essentially strikes a balance between 

excluding broadened data and maintaining some degree of noise insensitivity. 

A full uncertainty analysis will not be carried out for every element of this study. Only uncertainties 

associated with novel parts of the study and uncertainties that are dominant will be analyzed. The 

uncertainty in the voltage utilization as calculated from Equation (3) is ~1 percent. This uncertainty is a 

combination of the uncertainty in the RPA analysis method and the Langmuir probe analysis method used 

to correct the RPA measurement. 

B. RPA and Langmuir Probe Results and Comparisons 

Figure 9 shows example RPA traces from the same reference point (400 V, 20 kW) for the 300M and 

300MS. This figure illustrates a common trend seen in the RPA data; the distributions appear to be wider 

with a longer and fatter energy tail for the 300MS than for the 300M. Note that the distributions derived 

from the RPA are broadened by the somewhat poor resolution of the probe, which has a tendency to wash 

out differences between the thrusters. Thus, the real differences between the energy distribution functions 

of the 300M and 300MS are expected to be greater than indicated by the RPA and are difficult to 

quantify. 

Table 1 summarizes the results of the RPA and Langmuir probe analyses for all three thruster 

versions across the eight reference points. At the bottom of the table, the average and standard deviation 

of the voltage utilization efficiency across the eight reference points are shown. The averages show, more 

clearly, the differences in values between the three thruster versions. The standard deviations give 

indications of the spread in values across the eight reference points. By comparing the standard 

deviations, one can get a sense of whether the spread changes with thruster versions, which may indicate 

a change in thruster physics. A change in spread can also indicate a change in the noise environment of 

the probe. Thus, care should be taken when interpreting the standard deviation, especially if the amplitude 

of the difference is lower than the uncertainty of the probe data. From Table 1, one can see that the three 

thruster versions behave largely the same in terms of voltage utilization. Both versions of the 300MS 

perform slightly better than the 300M. 
NASA/TM—2013-216606 11 

TABLE 1.—SUMMARY OF VOLTAGE UTILIZATION ANALYSIS 

Plasma potential, 

V 

Energy per charge, 

V 

Voltage utilization efficiency 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

300M 300MS 300MS-2 300M 300MS 300MS-2 300M 300MS 300MS-2 

300 10 6.3 7.6 7.2 278 285 288 0.926 0.947 0.957 

300 15 6.3 6.4 7.0 281 281 291 0.934 0.935 0.969 

400 10 6.9 7.7 8.0 377 389 395 0.942 0.972 0.984 

400 15 7.4 7.7 8.1 377 385 391 0.940 0.961 0.978 

400 20 6.9 7.2 7.2 378 390 396 0.943 0.974 0.987 

500 10 6.9 8.1 7.6 481 473 484 0.962 0.946 0.968 

500 15 7.9 8.1 8.1 472 491 491 0.942 0.980 0.982 

500 20 7.9 8.1 7.8 480 491 496 0.959 0.981 0.992 

Average: ---- ---- ---- ---- ---- ---- 0.944 0.962 0.977 

Std. dev.: ---- ---- ---- ---- ---- ---- 0.012 0.017 0.012 

Figure 9.—Comparison of ion energy-per-charge 

distributions for the 300M and 300MS at 400 V, 

20 kW. 

Note that some values of energy per charge for the 300MS and 300MS-2 are very close to the 

discharge voltage and seem physically impossible at first glance given that some ~10 V of the discharge 

voltage must be used to extract electrons from the cathode. However, one should keep in mind that the 

total possible voltage drop from anode to cathode actually includes the drop across the anode sheath. Thus 

the true maximum total voltage drop is slightly higher than the discharge voltage. While accounting for 

the anode sheath voltage is interesting, this quantity is not easy to measure. The total discharge power is 

still easiest to calculate by using the discharge voltage with the discharge current so the efficiency model 

presented here uses the discharge voltage to calculate voltage utilization. 

V. ExB Probe Analysis 

A. Analysis Method 

The ExB probe is used as a velocity filter for charged species spectrometry. Since different charged 

species are accelerated to different velocities by going through roughly the same potential drop, they will 

show up as different peaks when interrogated by the ExB probe. For a scenario where the ExB probe 

velocity resolution is at least several times smaller than the width of the ion velocity distribution function 

(VDF), the preferred method for analyzing ExB probe data is via integration. In the past, most integration 

schemes involved fitting some general distribution equation form to the ExB probe trace and calculating 

either by geometry or by numerical integration the area under the curve (Refs. 12, 25, and 26). This is 
NASA/TM—2013-216606 12 

done because the ion distributions from different charged species tend to overlap in the regions between 

peaks, making a direct integration of only one species at a time impossible without some kind of 

assumption on the form of the distribution. The domain of the curve-fit for each species usually needs to 

be bounded such that only the current signal generated by one species is being fitted at a time. 

In the process of carrying out the present study, the area under the curve was discovered to not be 

exactly proportional to the current associated with each species. A new set of integration formulas were 

derived from scratch for the purpose of analyzing ExB probe data. The results of the new derivation 

closely matches the derivation by Kim (Ref. 27), though Kim did not publish the species fraction 

formulas and did not try to calculate the current fraction (that was not his objective). As such, the new 

derivation continues where Kim’s work left off. 

Note that Kim’s work (Ref. 27) is the first published instance where the ExB probe was used to study 

a Hall thruster and strongly influenced all subsequent work in this area including all other cited work on 

ExB probe studies. 

Full derivation of the new integration formulas for analyzing ExB probe data is presented in 

Appendix A. Additional mathematical comparisons between the traditional and new integration formulas 

are shown in Appendix B. The ExB probe data presented in this paper are analyzed using the following 

steps. 

In the first step, one begins by selecting a form for the VDF. A number of different VDF forms were 

tried including the triangle, similar to what was proposed by Beal (Ref. 25), the Gaussian, first proposed 

by Linnell (Ref. 26), and the variable exponential, first proposed by Kim (Ref. 27). Two additional forms 

were also tried for this study: the twin Gaussian and skew-normal distributions. Equations (8) to (12) 

show the mathematical forms of VDFs that were tried in the present study. They are, in order, triangle, 

Gaussian, variable exponent, twin Gaussian, and skew-normal. 

 Triangle: 



         0, else

( a / b)* u c a , c b u c b f (u) j (8) 

 Gaussian: f (u) a *exp[ b (u c) ] 2

j    (9) 

 Variable Exponent: f (u) a *exp[ b u c ] n

j    (10) 

 Twin Gaussian: f (u) a *exp[ b (u c ) ] a *exp[ b (u c ) ] 2

2 2 2

2

j  1  1  1    (11) 

 Skew-Normal: 































   















    2 2

2

j

2b

d *(u c) * 1 erf

2b

(u c) f (u) a *exp (12) 

Where a, b, c, d, n, a1, b1, c1, a2, b2, and c2, are fitting constants. The term erf[] refers to the error function. 

The twin Gaussian and the skew-normal forms were tried in an attempt to capture the tail that is often 

observed in the VDFs of accelerated ions in a Hall thruster. In particular, the twin Gaussian form 

generally gives much better fits to the data than any other form. However, it can generate erroneous 

results if the curve-fit boundary is not properly chosen. For instance, if the boundary includes peaks from 

two different species, the computer will fit the twin Gaussian form to both peaks and treat them as a 

single species. Analysis of the 300M ExB probe data, which show relatively little overlap between 

neighboring peaks, showed that while the twin Gaussian form fitted very well, it did not generate results 

that were much different from the other forms. This behavior suggests that properly capturing the width 

and height of the distribution was sufficient to obtain accurate results in the absence of strong overlap. 
NASA/TM—2013-216606 13 

Unfortunately, the 300MS ExB probe data showed strong overlap between neighboring peaks, and the 

cause was hypothesized to be a combination of wide VDFs and large high-velocity tails (Fig. 9). The use 

of the skew-normal distribution was an attempt to obtain useful data despite the strong overlap between 

peaks. Compared to a normal distribution, the skew-normal distribution has an additional parameter that 

controls skewness and collapses into a normal distribution when that parameter is equal to 0. The skewnormal distribution retains the general shape of the normal distribution but has skewness. Note the 

Gaussian is essentially a normal distribution. Skew-normal was chosen as the VDF form to use for the 

present study because the associated efficiency analysis results were the most consistent across all three 

thruster versions. 

In the second step, the selected VDF form is inserted into Equation (13) 

  j P

3

P

0 f

P

j

3

P,j P 1 j P ~ V f V

B D

V I (V ) K n V f 













  (13) 

Where IP,j is the contribution of the j-th species to the ExB probe collector current, nj is the number 

density of the j-th species, VP is the ExB probe bias, B0 is the magnetic field magnitude in the ExB filter 

section, and Df is the gap between ExB bias plates. K1 is a constant that will be derived in Appendix A. In 

practice, K1, nj, B0, and Df are constant with respect to the bias voltage and can be rolled into the fitting 

constants of the VDF forms. Curve-fits are then performed using Equation (13) for each charged species 

in the ExB probe data in order to obtain the values of the various fitting constants. 

For this study, the curve-fit process starts with the singly-charged species peak. The fitted curve is 

then subtracted out of the data and the remainder is curve fitted for the doubly-charged species peak. The 

process is repeated until the quadruply-charged species peak is fitted. Boundaries are used to make sure 

the curve-fit is performed over domains that are dominated by only one charged species at a time. For 

each species, the left boundary is set to 0.667 times the voltage location of the corresponding species 

peak; the right boundary is set to halfway between the peak location of this species and the peak location 

of the next higher charged species. 

The voltage location of the singly-charged species is first manually determined from many ExB probe 

traces. A second-order polynomial fit of this location against the discharge voltage was performed and 

found to have an R-squared value of 0.995. The ratio of the locations of the remaining peaks to the 

location of the singly-charged peak is assumed to be constant and found by manually studying several 

ExB probe traces. The analysis code then uses the discharge voltage, the second-order polynomial fit, and 

the peak location ratios to predict the location where each charged species should be located. For ExB 

probe traces with distinguishable peaks, visual inspection of the curve-fit process shows the code 

accurately predicts the peak locations. 

Figure 10 shows a set of analysis plots generated by the program that performs the ExB probe 

analysis. The thruster is the 300M and the operating condition is 500 V, 20 kW. For convenience, the 

paper will refer to the six subplots in order from left to right, top to bottom as (a) to (f). Subplot (a) shows 

the raw ExB probe data as black data points with red dashed vertical lines showing the location of the first 

four peaks. Subplots (b), (c), (e), and (f) show the four sub-steps in the curve-fitting process. The program 

fits the appropriate equation to the 1st peak, subtracts the fitted data, then fits the 2nd peak, and so on. The 

data prior to the fit at each curve-fit sub-step is shown as black dots, the red solid line shows the curve-fit, 

the magenta dashed vertical lines show the curve-fit boundaries, and the blue dashed line shows the 

leftover result after subtraction. Subplot (d) shows the raw data in black dots with a red solid line that 

represents the sum of all four curve-fit sub-steps super-imposed on top. Figure 11 shows the same for the 

300MS. 

 
NASA/TM—2013-216606 14 

Figure 10.—ExB probe analysis plots for the 300M operating at 500 V, 20 kW. 

Figure 11.—ExB probe analysis plots for the 300MS operating at 500 V, 20 kW. 

In the third step, the IP,j of all the species are substituted into Equations (14) and (15) to calculate the 

species and current fractions, respectively, 





 



  

k

P 0 3

P

P,k P

P 0 3

P

P,j P

k

k

j

j

dV

V

I (V )

dV

V

I (V )

n

n

 (14) 

 



 



  

k

P 0 2

P

P,k P

k

P 0 2

P

P,j P

j

k

k

j

j

dV

V

I (V ) Z

dV

V

I (V ) Z

I

I

 (15) 

 
NASA/TM—2013-216606 15 

Where Ij is the current contributed by the j-th species at the entrance of the ExB probe collimator. Since 

the entrance orifice area is a constant across all Ij’s, Ij and Ik can be replaced with the corresponding 

current densities. Note that Ij is not the same as IP,j, which is current at the collector of the ExB probe. In 

this study, Xe4+ was not accounted for in the current and species fraction calculation because those 

typically comprise less than 0.5 percent of the beam current. 

In the fourth step, CEX interactions between beam ions and facility background neutrals were 

accounted for. CEX depletes lower-charge-state species more than higher-charge-state species, causing 

the ExB probe to read more higher-charge-state species than when in the vacuum of space. This effect is 

especially prominent for high-power thruster tests. The CEX model used to correct the ExB probe data is 

described in Shastry’s work (Ref. 12). The model describes the effect of CEX as a set of attenuation 

factors that diminishes the detected current at the ExB collector. Equations (16) to (18) show the 

equations used to calculate the attenuation factors (Ref. 12). 

(J/J ) exp( n z), 87.3 13.6 log(V ) 0 Xe   01 1   1 (16) 

(J/J ) exp( n z), 45.7 8.9 log(2V ) 0 Xe2   02 2   2 (17) 

(J/J ) exp( n z), 16.9 3.0 log(3V ) 0 Xe3   03 3   3 (18) 

Where J is the recorded current density at distance z away from the thruster exit plane, J0 is the current 

density that would have been recorded at the thruster exit plane, and n0 is the average background neutral 

density. The numerical formulas for the CEX cross-sections, σ1, σ2, and σ3, are given in units of Å2

(10–20 m2

). The ion energy per charge, V1, V2, and V3 for Xe+, Xe2+, and Xe3+, respectively, are assumed 

to be equal to the average ion energy per charge as measured by the RPA. The value of n0 is calculated by 

converting the average of the pressure measurement from four ion gauges. Two of these gauges were 

located on the chamber wall at the same axial position as the farfield probe tower, one of the gauges was 

next to the thrust stand, and the last of the gauges was on the chamber wall at an axial location close to 

the thruster. Note that one can assume the ion energy per charge is equal to the discharge voltage for the 

purpose of these calculations. Doing so removes the dependence of the ExB probe analysis on the RPA, 

though with a small increase in uncertainty. See Shastry’s work for an estimate of this uncertainty 

(Ref. 12). 

The uncertainty in the charge utilization as calculated from Equation (7) is no more than 0.5 percent. 

This value is small because the charge utilization is very insensitive to the values of the current fractions. 

For the 300M, the charge utilization varied from 0.975 to 0.984. For the 300MS, the charge utilization 

varied from 0.965 to 0.973. 

ExB probe data is also used to calculate the m term in the mass utilization. Total uncertainty of the 

mass utilization will be discussed in Section VI; this paragraph will focus on the uncertainty in m. 

Based on the equations derived in the appendix, the average velocity resolution of the ExB probe was 

2.7 percent. This value is higher for ions with higher energy per charge and is no more than 4.0 percent 

for the detectable ion populations with the highest energy per charge. This resolution is sufficiently fine 

so that the aforementioned ExB probe analysis method is applicable. The ExB probe resolution primarily 

affected broadening of the measured VDF and has minimal effect on the current fractions. For the 300M, 

the uncertainty in the current fraction is expected to be dominated by the uncertainty in the average 

background neutral density measured by the ion gauges. For the 300MS, additional uncertainty is 

introduced by the strong overlap between charged species peaks. This added uncertainty arises from not 

being certain about whether the analysis program really only captured contributions from one charged 

species at a time. For now we will focus on the uncertainty in the ion gauge measurements. The ion 

gauges are nominally 6 percent accurate. However, they only measured the neutral density in their 

immediate vicinity. Factors like conductance losses and un-compensated temperature effects on the 
NASA/TM—2013-216606 16 

electronics are expected to raise the uncertainty of the neutral density measurement to ~15 percent. 

Substituting in a 15 percent neutral density uncertainty into the CEX correction formula yielded average 

uncertainties of 0.034, 0.024, and 0.011 for the Xe+

, Xe2+, and Xe3+ current fractions, respectively. 

The corresponding average uncertainty for m is ~2 percent. Since much is still not known about the 

strong overlap between peaks found in the ExB probe traces of the 300MS, the uncertainty in m for the 

300MS will be tentatively set to twice that of the 300M. Thus, the uncertainty in m is 2 percent for the 

300M and 4 percent for the 300MS. 

B. ExB Probe Results and Comparisons 

Figure 12 shows example ExB probe traces from the same reference point (400 V, 20 kW) for the 

300M and 300MS. This figure illustrates a common characteristic of ExB probe traces from the 300MS 

and 300MS-2; there is strong overlap between the different charged species, to the point that the multiplycharged peaks appear to merge into a single large structure. Generally speaking, this overlap trend is 

strongest for the lower voltage and higher power operating points. Figure 13 illustrates the change in ExB 

probe trace with discharge voltage for the 300MS. Figure 14 illustrates the change in ExB probe trace 

with discharge power for the 300MS. 

Figure 12.—Comparison of ExB probe traces for the 

300M and 300MS at 400 V, 20 kW. 

Figure 13.—Comparison of ExB probe traces for the 

300MS at 300 and 600 V, 15 kW. 

Figure 14.—Comparison of ExB probe traces for 

the 300MS at 500 V, 5, 10, and 20 kW. 
NASA/TM—2013-216606 17 

Table 2 summarizes the results of the ExB probe analyses for the 300M and 300MS across the eight 

reference points. Results for the 300MS-2 were almost identical to the 300MS and will not be tabulated 

separately. The table shows the Xe2+ and Xe3+ current fractions. The sum of the current fractions Xe+

, 

Xe2+, and Xe3+ is 1. Also shown are the average charge state, m, and charge utilization efficiency. The 

average charge state is calculated using Equation (19). 

  

k

Z Zk k (19) 

As with the RPA and Langmuir probe data, averages and standard deviations are shown to aid the reader 

in comparing the 300M to the 300MS. 

Table 2 shows that the 300MS is producing ~70 percent more multiply charged particles than the 

300M on the average. This rise in multiply charged species has a much more prominent effect on the 

value of m than on the charge utilization efficiency. The low magnitude of the standard deviation shows 

that the difference in m between the 300M and 300MS is not a statistical fluke. While Table 2 shows the 

average trends across thrusters, detailed trends are difficult to visualize from Table 2. Figure 15 shows a 

plot of the average charge state as a function of the discharge current. Since the channel cross section 

(upstream of the chamfers) was kept the same between the 300M and 300MS, the discharge current is 

proportional to the current density. Note that this figure is augmented with data from operating points 

beyond the eight reference points. A rather interesting trend can be seen in this figure. Whereas the 

TABLE 2.—SUMMARY OF CHARGE UTILIZATION AND ΑM ANALYSES 

Current 

fraction, 

Xe2+

Current 

fraction, 

Xe3+

Average charge 

state 

m Charge 

utilization 

efficiency 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

300M 300MS 300M 300MS 300M 300MS 300M 300MS 300M 300MS 

300 10 0.18 0.34 0.04 0.05 1.097 1.195 0.884 0.800 0.980 0.971 

300 15 0.24 0.31 0.03 0.08 1.125 1.201 0.858 0.793 0.977 0.968 

400 10 0.21 0.33 0.05 0.03 1.122 1.181 0.861 0.811 0.976 0.973 

400 15 0.19 0.32 0.06 0.07 1.116 1.205 0.865 0.789 0.976 0.968 

400 20 0.18 0.32 0.05 0.09 1.102 1.214 0.878 0.781 0.978 0.967 

500 10 0.22 0.27 0.06 0.12 1.134 1.207 0.851 0.786 0.975 0.965 

500 15 0.19 0.31 0.05 0.06 1.115 1.187 0.867 0.805 0.977 0.970 

500 20 0.20 0.33 0.06 0.09 1.123 1.222 0.858 0.776 0.975 0.967 

Average: 0.20 0.32 0.05 0.07 1.117 1.201 0.865 0.793 0.977 0.969 

Std. dev.: ------- ------ ----- ----- ----- ----- 0.011 0.012 0.002 0.003 

Figure 15.—Average charge state as a function of 

discharge current for the 300M and 300MS. 
NASA/TM—2013-216606 18 

average charged state of the 300M remained comparatively constant (to within 0.03), the same of the 

300MS increase quite noticeably with discharge current (and current density). This rise is most rapid at 

lower discharge current and tapers off at higher discharge current. The change in multiply charged species 

content is one of the biggest differences between the 300M and 300MS. 

VI. Faraday Probe Analysis 

A. Analysis Method 

Faraday probe data are used to calculate the plume divergence angle and the total ion beam current. 

The cosine of the momentum-weighted plume divergence angle is defined as the average axial velocity of 

the particles divided by the average total velocity of the particles. However, momentum-weighted 

divergence angle is difficult to measure. The typical approach is to measure the charge-weighted 

divergence angle, which is approximately equal to the momentum-weighted divergence angle if the 

current fraction is roughly constant across the interrogated domain. For a polarly-swept probe, 

Equation (20) can be used to calculate the charge-weighted divergence angle. 



 



   

   

  / 2

0

2

FP

/ 2

0

2

FP

2 R j( ) sin d

2 R j( ) cosθ sin d

cos δ (20) 

Where δ is the charged-weighted divergence angle, θ is the polar angle and is equal to 0° for particles 

traveling parallel to the firing axis, and j(θ) is the ion current density as a function of the polar angle. RFP

is the distance from the Faraday probe collector to the thruster center at the exit plane and is constant for a 

polarly-swept probe. Note the denominator is equal to the total ion beam current. 

For a nude Faraday probe with a guard ring like the one used in this study, the effective collector area 

is not exactly equal to the collector frontal surface area. Current that enters the gap between the collector 

and the guard ring can be collected by the side surfaces of the collector (Ref. 28). According to work by 

Brown, the current entering the gap is collected by the collector and the guard ring in ratio proportional to 

the ratio of exposed gap area (Ref. 28). For the probe design used in the present study, the area inside the 

gap is dominated by area connected to the guard ring (Fig. 7). However there is enough area connected to 

the collector that some level of correction is needed. Note that only the part of the gap with direct 

exposure to the incoming ion beam is used in the gap area calculation. Using the approach recommended 

by Brown, the effective collection area is ~4 percent greater than the collector frontal area. The effective 

collection area is used for all Faraday probe analysis. 

Much like in ExB probe data analysis, CEX is a factor in Faraday probe data analysis. However, 

whereas CEX is an attenuating factor for ExB probe data, it is a re-distributing factor for Faraday probe 

data. This is because CEX ions have a different trajectory than the ion it is born from and will tend to 

show up in the wings of a Faraday probe trace. The region considered the “wings” of a Faraday probe 

trace can be seen in Figure 16 as the region outside of the two outermost dashed vertical lines. An ExB 

probe does not see CEX ions because of a combination of small acceptance angle and a tendency to deemphasize low speed ions. The ExB filter resolution has a dependence on the square of the particle speed 

and CEX ions have only a small fraction of the speed of beam ions. The best way to correct for the redistributing behavior of CEX on Faraday probe traces is to take data at multiple distances and facility 

background pressures (Ref. 28). This could not be carried out for the present study due to space 

constraints. Instead, an extrapolated-wing approach was used to remove the parts of the trace that are 

believed to be dominated by re-distributed CEX ions. The extrapolated-wing approach begins by plotting 

the ion current density on a semi-log scale. Exponential curve-fits are then performed on the data from a 

polar angle of 10° to 25°. The curve-fit result is then extrapolated to 90°. Note an exponential function of 

 
NASA/TM—2013-216606 19 

Figure 16.—Illustration of the extrapolated-wing 

method for analyzing Faraday probe data. 

TABLE 3.—SUMMARY OF SEE DATA FOR 

XENON ION BOMBARDMENT OF 

MOLYBDENUM (REFS. 32 AND 33) 

Bombarding particle SEE yield of 

molybdenum 

Xe+ 0.022 

Xe2+ 0.20 

Xe3+ 0.70 

the polar angle shows up as straight lines on the semi-log plot. Figure 16 shows a graphical representation 

of the extrapolated-wing method. The black solid line is the raw data. The dashed vertical line in the 

middle is the center of the trace (θ is not quite equal to 0° here due to a minor mis-alignment in the 

physical setup). The left two and right two dashed vertical lines indicate the boundary for the data used to 

perform the curve-fit on the respective side. The light green solid lines represent the curve-fit results. 

In past studies, low secondary electron emission (SEE) yield materials like molybdenum and tungsten 

have been used for the collector (Refs. 29 to 31). Secondary electrons born on a negatively biased probe 

will accelerate away from the probe. This effect adds extra current to the probe measurement that is 

indistinguishable from the collected ion current. By selecting a low SEE yield material, researchers had 

believed that the effect of SEE is negligible and can be ignored. While singly-charged xenon-induced 

SEE yield for molybdenum and tungsten are indeed negligible (0.013 to 0.022), the doubly-charged 

xenon-induced SEE yield are roughly 10 times higher than the singly-charged yield, and the triplycharged SEE yield are roughly 35 times higher than the singly-charged yield (Refs. 32 to 34). 

Furthermore, Hagstrum discovered that metastable singly-charged xenon induces roughly the same SEE 

yield as doubly-charged xenon (Ref. 35). Thus, as long as the plume of the thruster is composed of mostly 

ground-state singly-charged xenon ions, the assumption of negligible SEE effect holds. 

During the present testing, the assumption of negligible SEE effect was discovered to not hold. The 

material used for the present study is molybdenum, which is considered a low SEE yield material. The 

reason SEE effects are not negligible is because high-power Hall thrusters appear to produce 20 to 

40 percent doubly- and triply-charged ions by current fraction. Combined with the high SEE yield 

associated with bombardment by higher charge ions, the effect of SEE can be non-negligible. To correct 

for SEE effects on the Faraday probe measurement, we turn to data published by Hagstrum. Table 3 

summarizes the SEE yield values used in the data analysis of the present study. The singly-charged and 

doubly-charged xenon-induced yields are averages of the SEE yield data for ion energies in the range of 

200 to 800 eV in Hagstrum’s 1956 work on molybdenum (Ref. 33). For both of these parameters, the 

value measured by Hagstrum varied by no more than 10 percent of the listed average. A published value 

for the triply-charged xenon-induced yield of molybdenum could not be found. The value in Table 3 is a 

projected value based on the similarity in yield between tungsten and molybdenum. The ratio of triplycharged induced yield to doubly-charged induced yield for tungsten is 3.5, so the yield for molybdenum is 

projected to be 3.5 * 0.2, or 0.7 (Ref. 32). 
NASA/TM—2013-216606 20 

Equation (21) shows the relationship between the actual ion current density and the ion current 

density measured by the Faraday probe due to SEE effect. 

  



k k

FP k k

Z

1

1

J

J

 (21) 

Where J is the actual ion current density, JFP is the current density measured by a nude Faraday probe, and 

k is the SEE yield in number of electrons per ion associated with bombardment by the k-th species. For 

the present study, the ion current density measured by the nude Faraday probe is 4 to 7 percent higher 

than the actual current density. The amount of metastable singly-charged ions is assumed to be negligible. 

This assumption is an extrapolation from controlled ion beam work done by Hagstrum (Ref. 35). In his 

experiment, Hagstrum varied the energy of the electrons used to generate his singly-charged ion beam 

from 10 to 70 eV. The SEE yield he measured jumped quickly up from 0.022 to 0.025 when the electron 

energy was ramped up from 25 to 30 eV, and then plateaued out at 0.025 all the way up to 70 eV. While 

the Hall thruster ionization zone and an ion beam discharge chamber are not exactly the same they do 

share many of the same operating principles, including a reliance on impact bombardment ionization. 

Since the amount of metastable ions was so small that the SEE yield increased by only 0.003 for 

Hagstrum’s experiment, we assumed the effect will be of similar magnitude in a Hall thruster and is 

therefore negligible. 

The Faraday probe data is used in the calculation of several efficiency factors, the uncertainties of 

each which will now be treated. For the divergence efficiency, the important sources of uncertainty 

include background CEX effects and SEE effects. Based on prior work by Brown, Faraday probe data 

taken at 5 MCD away from the thruster should have an uncertainty of no more than 2 percent for the 

facility background pressure found during the present study (Ref. 28). However, Brown’s work was done 

on a lower power thruster (nominal 6 kW) compared to the 300M and with a correspondingly shorter 

distance between the probe and the thruster. We estimate the uncertainty associated with CEX to be 

~3 percent based on the extra distance between the probe and thruster. The effect of SEE on the 

uncertainty of the divergence efficiency is more difficult to calculate due to lack of prior experience. 

However, as long as the current fraction only undergoes small changes as a function of polar angle, the 

overall effect will be small. This is because SEE represents a relatively small correction to the local 

current density, so small changes to a small correction should be negligible. Thus, the overall uncertainty 

in the divergence efficiency is estimated to be 3 percent. 

The uncertainty in the current utilization is primarily influenced by uncertainties associated with 

calculation of the effective collector area, CEX effects, and SEE effects. The effective collector area is 

expected to be accurate to ~1 percent based on different ways in which the gap current can be distributed 

between the collector and the guard ring. The use of the extrapolated-wing approach should remove much 

of the uncertainty associated with the CEX effect, but without additional knowledge about how much 

uncertainty is removed, we will assign the same 3 percent uncertainty here that was assigned for the 

divergence efficiency. The uncertainty in the SEE calculation is tricky to estimate because it depends on 

the uncertainty of the current fractions calculated from the ExB probe data. Substituting in uncertainties in 

the current fractions previously calculated into the SEE correction equation (Eq. (21)), the uncertainty in 

the beam current due SEE correction is 1 percent. The total uncertainty in the current utilization, 

calculated from standard error propagation, is 3.3 percent. 

The uncertainty in the mass utilization is dominated by the uncertainty in the measured anode mass 

flow rate, the total beam current, and the current fraction-dependent factor, m. The mass flow rate 

measurement has an instrumentation uncertainty of ~1 percent. The uncertainty in the total beam current 

is the same as the uncertainty in the current utilization (3.3 percent). The uncertainty in m, which is 

calculated from the current fractions, is dominated by uncertainty in the average background pressure and 

 
NASA/TM—2013-216606 21 

effect of overlap between ExB probe peaks. The uncertainty in m was calculated in the preceding section 

to be 2 percent for the 300M and 4 percent for the 300MS. The total uncertainty, calculated from standard 

error propagation, in the mass utilization is 4 percent for the 300M and 5.3 percent for the 300MS. 

B. Faraday Probe Results and Comparisons 

Figure 17 shows example Faraday probe traces from the same reference point (400 V, 20 kW) for the 

300M and 300MS. The two traces are normalized by the peak probe current to better illustrate the 

difference in the shape of the traces. This figure illustrates a common trend seen across the reference 

points; the current density distribution, measured by the Faraday probe, is generally wider for the 300M 

than for the 300MS. 

Tables 4 and 5 summarize the results of the Faraday probe analyses across the eight reference points 

for divergence and current utilization efficiencies, respectively. Table 4 quantifies the degrees by which 

the divergence of the 300MS and 300MS-2 are greater than the 300M. On the average, the divergence of 

the 300MS is ~2.5° greater than that of the 300M, which translates to ~2.5 percent lower divergence 

efficiency. For the 300MS versus the 300MS-2, there is practically no difference in divergence. Table 5 

shows a small difference in current utilization efficiency between the three thruster versions. However, 

given that the uncertainty in current utilization measurement is bigger than this difference, part of the 

difference may not be real. 

Figure 17.—Comparison of Faraday probe 

traces for the 300M and 300MS at 400 V, 

20 kW. 

TABLE 4.—SUMMARY OF DIVERGENCE ANALYSIS 

Divergence angle, 

degree 

Divergence efficiency 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

300M 300MS 300MS-2 300M 300MS 300MS-2 

300 10 15.1 20.5 21.0 0.932 0.878 0.871 

300 15 18.4 19.7 20.6 0.901 0.887 0.877 

400 10 14.9 17.3 16.8 0.934 0.912 0.917 

400 15 14.6 17.3 17.2 0.937 0.911 0.913 

400 20 14.4 18.4 18.5 0.938 0.900 0.899 

500 10 15.3 14.8 15.9 0.931 0.935 0.925 

500 15 15.2 16.6 16.4 0.931 0.919 0.921 

500 20 14.7 17.9 18.2 0.936 0.906 0.903 

Average: 15.3 17.8 18.1 0.930 0.906 0.903 

Std. dev.: 1.3 1.8 1.9 0.012 0.018 0.020 

 
NASA/TM—2013-216606 22 

TABLE 5.—SUMMARY OF CURRENT UTILIZATION ANALYSIS 

SEE correction factor Beam current, 

A 

Current utilization efficiency 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

300M 300MS 300MS-2 300M 300MS 300MS-2 300M 300MS 300MS-2 

300 10 0.958 0.945 0.946 26.2 26.9 28.0 0.783 0.807 0.834 

300 15 0.954 0.941 0.942 39.7 39.5 41.9 0.786 0.787 0.823 

400 10 0.953 0.948 0.947 20.2 20.8 20.9 0.796 0.833 0.832 

400 15 0.953 0.941 0.941 30.0 30.8 30.8 0.799 0.818 0.822 

400 20 0.955 0.938 0.941 39.3 40.3 40.8 0.790 0.806 0.820 

500 10 0.951 0.936 0.939 16.5 16.4 17.2 0.817 0.811 0.835 

500 15 0.954 0.944 0.944 24.4 25.1 25.0 0.809 0.827 0.831 

500 20 0.952 0.938 0.942 32.3 33.0 33.5 0.802 0.826 0.836 

Average: ----- ----- ----- ----- ----- ----- 0.798 0.814 0.829 

Std. dev.: ----- ----- ----- ----- ----- ----- 0.012 0.015 0.006 

TABLE 6.—SUMMARY OF MASS UTILIZATION ANALYSIS 

Anode mass 

flow rate, 

mg/s 

αm Mass utilization efficiency 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

300M 300MS 300MS-2 300M 300MS 300MS-2 300M 300MS 300MS-2 

300 10 32.3 29.3 29.3 0.884 0.800 0.802 0.976 1.000 1.044 

300 15 42.0 40.0 40.0 0.858 0.793 0.791 1.102 1.066 1.128 

400 10 25.3 23.8 23.8 0.861 0.811 0.806 0.938 0.968 0.963 

400 15 34.9 33.2 33.2 0.865 0.789 0.789 1.010 0.997 0.999 

400 20 43.7 40.9 40.9 0.878 0.781 0.795 1.076 1.048 1.078 

500 10 20.7 20.4 20.4 0.851 0.786 0.799 0.924 0.858 0.917 

500 15 29.1 27.4 27.4 0.867 0.805 0.802 0.991 1.005 0.998 

500 20 36.4 34.2 34.2 0.858 0.776 0.797 1.037 1.021 1.065 

Average: ----- ----- ----- ----- ----- ----- 1.007 0.995 1.024 

Std. dev.: ----- ----- ----- ----- ----- ----- 0.063 0.063 0.068 

Table 6 summarizes the mass utilization analysis, which depends strongly on both the ExB probe and 

the Faraday probe analyses. Note that the average of the mass utilization is very close to unity and 

individual entries may not be physical. On the other hand, earlier calculations showed that the mass 

utilization has the highest uncertainty of all the efficiency factors. Error in the mass utilization in one 

direction could be offset by error in another direction in the other efficiency factors. Instead of artificially 

capping the mass utilization at unity and thereby introducing systematic error, they will be left as they are 

for the overall efficiency analysis. Additionally, the anode mass flow rate indicates that for a given 

discharge current, the 300MS used less propellant than the 300M. One possible explanation is that the 

higher average charge state of the 300MS led to a higher current to mass ratio. 

VII. Results and Discussions 

Before we proceed to the overall efficiency analysis, the associated uncertainties will be treated. The 

uncertainty in the anode efficiency as calculated by Equation (1) from the measured thrust is dominated 

by the uncertainty in the thrust and is 4 percent when calculated via standard error propagation. The total 

uncertainty in a calculated via Equation (2) depends on the uncertainties associated with each of the 5 

efficiency factors. Using standard error propagation, the total uncertainty in anode efficiency calculated 

from the phenomenological efficiency model is 6 percent for the 300M and 7 percent for the 300MS. 

 
NASA/TM—2013-216606 23 

We are now ready to study the full physical picture of the 300M, 300MS, and 300MS-2. Since the 

previous sections have shown how similar the performance of the 300MS-2 is compared to the 300MS, it 

will not be listed separately. Results and trends shown in this section that pertain to the 300MS also 

pertain to the 300MS-2. Tables 7 and 8 shows the thrusts and the various efficiency factors calculated 

during the present study for the 300M and 300MS, respectively. The probe-derived ηa refers to the anode 

efficiency derived from the use of probe data with the phenomenological model (Eqs. (2) to (7)). The 

thrust-derived ηa refers to the anode efficiency calculated from thrust measurement via Equation (1). 

Tables 7 and 8 show several interesting trends. On the average, the 300MS data shows ~2 percent 

higher voltage utilization efficiency, ~2.5 percent lower divergence efficiency, and ~1.5 percent higher 

current utilization efficiency than the 300M data. Although the 300MS produced quite a bit more 

multiply-charged particles in comparison to the 300M the absolute quantity is fairly modest. Since the 

charge utilization efficiency equation is largely insensitive to differences of such a modest magnitude, the 

difference in the charge utilization is less than 1 percent. The two thrusters have roughly the same values 

in mass utilization efficiencies to within the measurement uncertainties. The anode efficiency calculated 

from the probe data is nearly identical on the average, though values for individual reference points vary 

by up to ~6 percent. This variation is similar in magnitude to the uncertainty in the anode efficiency 

derived from probe data and is likely dominated by uncertainty in the mass utilization. Tables 7 and 8 also 

show that the anode efficiency calculated from the thrust is, on the average, nearly identical between the 

300M and 300MS; the values for individual reference points differ by up to ~2 percent. From the two 

different methods for calculating the anode efficiency, one can conclude that the NASA-300MS had 

roughly the same discharge performance as the NASA-300M to within the measurement uncertainties. 

One can also conclude that the ~6 percent variation in anode efficiency calculated from probe data is 

likely due to uncertainties in the probe data. 

TABLE 7.—SUMMARY OF THRUST MEASUREMENT AND EFFICIENCY ANALYSIS FOR THE 300M 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

Thrust, 

mN 

ηv ηq ηd ηb ηm Probederived, 

ηa

Thrustderived, 

ηa

Difference 

300 10 652 0.926 0.980 0.932 0.783 0.976 0.647 0.654 –0.008 

300 15 912 0.934 0.977 0.901 0.786 1.102 0.713 0.651 0.061 

400 10 581 0.942 0.976 0.934 0.796 0.938 0.641 0.657 –0.017 

400 15 852 0.940 0.976 0.937 0.799 1.010 0.694 0.692 0.002 

400 20 1099 0.943 0.978 0.938 0.790 1.076 0.736 0.693 0.043 

500 10 528 0.962 0.975 0.931 0.817 0.924 0.659 0.668 –0.009 

500 15 770 0.942 0.977 0.931 0.809 0.991 0.687 0.673 0.014 

500 20 1004 0.959 0.975 0.936 0.802 1.037 0.728 0.686 0.042 

Average: ---- 0.944 0.977 0.930 0.798 1.007 0.688 0.672 0.016 

Std. dev.: ---- 0.012 0.002 0.012 0.012 0.063 0.037 0.017 0.029 

TABLE 8.—SUMMARY OF THRUST MEASUREMENT AND EFFICIENCY ANALYSIS FOR THE 300MS 

Disch. 

voltage, 

V 

Disch. 

power, 

kW 

Thrust, 

mN 

ηv ηq ηd ηb ηm Probederived, 

ηa

Thrustderived, 

ηa

Difference 

300 10 615 0.947 0.971 0.878 0.807 1.000 0.651 0.646 0.005 

300 15 883 0.935 0.968 0.887 0.787 1.066 0.674 0.646 0.028 

400 10 578 0.972 0.973 0.912 0.833 0.968 0.695 0.700 –0.005 

400 15 832 0.961 0.968 0.911 0.818 0.997 0.691 0.693 –0.002 

400 20 1067 0.974 0.967 0.900 0.806 1.048 0.716 0.694 0.022 

500 10 515 0.946 0.965 0.935 0.811 0.858 0.594 0.644 –0.051 

500 15 755 0.980 0.970 0.919 0.827 1.005 0.726 0.685 0.041 

500 20 978 0.981 0.967 0.906 0.826 1.021 0.724 0.700 0.024 

Average: --- 0.962 0.969 0.906 0.814 0.995 0.684 0.676 0.008 

Std. dev.: --- 0.017 0.003 0.018 0.015 0.063 0.045 0.026 0.029 

 
NASA/TM—2013-216606 24 

In terms of the fidelity of the efficiency analysis, Tables 7 and 8 show that the combination of the 

phenomenological model with the data analysis methods and probe design presented in this paper 

performed very well. On the average, the anode efficiency calculated from probe data matched the anode 

efficiency calculated from the thrust to within 2 percent. With that said, values for individual reference 

points were up to 6 percent off indicating possible room for improvement. In statistical terms, the 

efficiency analysis was very accurate but only moderately precise. 

Figure 18 shows a plot of the voltage utilization efficiency as a function of discharge voltage. For a 

typical Hall thruster, like the 300M, the voltage utilization efficiency increases with discharge voltage. 

Since the portion of the voltage used by the thruster to draw electrons out of the cathode and the anode 

sheath drop tends to be relatively constant compared to the change in discharge voltage, thrusters 

operating at higher discharge voltage are able to allocate more of that voltage drop to accelerating the 

ions. From this figure, one can see that the voltage utilization efficiency of the 300MS and 300MS-2 

display the same behavior. 

Figure 19 shows a plot of the divergence efficiency as a function of discharge voltage. For a typical 

Hall thruster, like the 300M, the divergence efficiency typically rises with the discharge voltage. One 

hypothesis is that the forces that are responsible for the radial component of the ion velocity (neutral 

thermal drift, ambipolar field, radial sheath drop, CEX) are relatively constant with rising discharge 

voltage. Since the accelerating electric field is mostly axial, the ratio of axial to radial ion velocity 

components rises with the discharge voltage. This trend gives rise to a more focused plasma plume at 

higher discharge voltage, which leads to a higher divergence efficiency. From this figure, one can see that 

the divergence efficiency of the 300MS and 300MS-2 display the same trend. 

The charge and current utilization efficiencies are largely constant and will not be plotted. Charge 

utilization is largely constant due to the general insensitivity of the charge utilization equation to current 

fractions of the multiply-charged species. The invariance of the current utilization with operating 

conditions have been seen in past work (Refs. 14 and 16). The exact value of current utilization is related 

to electron mobility and is an ongoing area of research. Since the value of the current utilization is largely 

constant for both the 300M and 300MS and are roughly equal, the same transport mechanisms are likely 

to apply for both thrusters. 

Figure 18.—Divergence efficiency as a function of the 

discharge voltage. 

Figure 19.—Mass utilization efficiency as a function of 

the discharge current. 
NASA/TM—2013-216606 25 

Figure 20.—Mass utilization efficiency as a function of 

the discharge current. 

Figure 21.—Illustration of the anchor locations for 

the magnetic field of conventional and 

magnetically-shielded Hall thrusters. 

Figure 20 shows a plot of the mass utilization efficiency as a function of discharge current. For a 

typical Hall thruster, like the 300M, the mass utilization efficiency typically rises with the discharge 

current. The reason is that as the discharge current rise so does the current density and the plasma density. 

Since the ionization rate scales with the electron density, denser plasma means higher ionization rate, 

which give rise to higher mass utilization. The mass utilization efficiency of the 300MS and 300MS-2 

display the same trends. Note that a value of mass utilization above unity is unphysical. There are two 

potential sources of error that may explain some of the high mass utilization values. As previously 

mentioned, the mass utilization draws heavily on both the ExB probe measurement and the Faraday probe 

measurement. Inaccurate accounting of the multiply charged species such as poor handling of the overlap 

region between charged peaks can give rise to incorrect values of αm and, by extension, the mass 

utilization. For the Faraday probe data, the probe may be capturing more CEX than can be removed by 

the extrapolated-wing method. If data from either (or both) probe(s) have a positive systematic error, the 

mass utilization and the associated anode efficiency will be too high, which may explain why the probederived anode efficiency is ~1 percent higher than the thrust-derived efficiency. With that said, the error 

being examined here is around the same as or below the uncertainty of the measurements. 

From the tables and figures in this section, one can conclude that the NASA-300MS likely operates on 

the same ionization and acceleration physics as the NASA-300M. The implementation of magnetic 

shielding did not change the fundamental laws that govern the basic operating principles of the 300M. 

The performance of the thruster remained largely unchanged. We will now turn to the small differences 

that have been observed during the present study and possible physical explanations. 

Generally speaking, the plume of the 300MS contains more multiply charged species and has a higher 

divergence than the plume of the 300M. One possible cause for the higher amount of multiply charged 

species is the presence of higher temperature plasma associated with reduced wall moderation. The key 

idea behind magnetic shielding is to maintain a layer of low-temperature, low-density plasma at high 

plasma potential near the channel walls that extend all the way to the thruster exit (Ref. 8). The anchor 

points of the magnetic lines of force that travel through the bulk plasma are moved out of the channel and 

onto the front pole where plasma density is much lower (Fig. 21). As a result the wall area effectively 

“wetted” by the plasma is reduced by orders of magnitude. In a typical Hall thruster, like the 300M, 

where the lines of force that pass through the bulk plasma terminates in the ceramic discharge channel 

walls, electron temperature tends be moderated. Ceramics, like boron nitride, have relatively high 

secondary electron emission coefficients. When high energy electrons from the bulk plasma impact the 

wall they are preferentially de-energized and secondary lower-energy electrons are released, resulting in a 

net decrease in the average electron energy. The electron temperature in a typical Hall thruster does not 

rise much above some wall-material-dependent critical value even as the discharge voltage increases 

(Refs. 36). Since the wetted area is much reduced with a magnetically shielded thruster, the electron 
NASA/TM—2013-216606 26 

temperature can rise as seen in more typical plasma discharges that are not moderated. This increase in 

electron temperature is seen in simulations though not yet confirmed by interior plasma probing (Ref. 8). 

Assuming the plasma temperature in a magnetically-shielded thruster is higher than its more typical 

cousin, the increase in multiply charged species production will result as a natural consequence. The 

ionization energies for doubly and triply charged xenon are 21.2 and 32.1 eV, respectively. The average 

electron temperature found in the ionization zone of a typical Hall thruster is 20 to 30 eV (Refs. 7 and 37). 

For a plasma with such a temperature, even a small rise in average plasma temperature will mean a large 

increase in the fraction of electrons (in the high energy tail of the electron energy distribution) that have 

enough energy to produce multiply charged ions via impact-ionization. 

A possible explanation for the increased divergence is that, as a consequence of the magnetic shielding 

topology, the ionization and acceleration zones of the 300MS are further downstream than the 300M. This 

change in zone locations was previously seen when the H6 was modified for magnetic shielding (Ref. 8). 

In such a case, ions with radial momentum are less likely to strike the channel walls and more likely to 

reach the far-field. Indeed, the main purpose of the magnetic shielding concept is to prevent high-energy 

ions from striking the channel walls. Another possible explanation is that the magnetically shielding 

topology has small regions, near the anchor points of the line of force, where the electric field is tilted 

sideways (Fig. 21). These regions of non-axial electric field correspond to low plasma density so the 

amounts of ions that escape through them are small. The added radial momentum may explain the small 

rise in plume divergence. 

VIII. Conclusion 

This paper has presented an in-depth efficiency analysis of the NASA-300M, a 20-kW thruster, and 

the NASA-300MS, a magnetically shielded version of the 300M. The results of the phenomenological 

model with combined inputs from the Langmuir probe, RPA, ExB probe, and Faraday probe shows 

excellent agreement with thrust stand measurements. On the average, the 300MS data shows ~2 percent 

higher voltage utilization efficiency, ~2.5 percent lower divergence efficiency, and ~1.5 percent higher 

current utilization efficiency than the 300M data. The two thrusters have roughly the same values in 

charge and mass utilization efficiencies. The general conclusion is that the 300M and 300MS have very 

similar performance as measured by the anode efficiency. Further testing with a second configuration of 

the 300MS with a shortened discharge channel shows essentially identical performance as the 300MS. 

The data acquired in the present study will greatly benefit the design of a flight-like magnetically-shielded 

Hall thruster in the 10 to 15 kW class for SEP TDM. 

As part of the current study, a new set of integration formulas were derived for ExB probe analysis. 

Two VDF equation forms were tried as a part of the analysis. The results show excellent consistency with 

data obtained from both the 300M and the 300MS. The presence of strong overlap between peaks for the 

ExB probe data of the 300MS is a new phenomenon in the use of ExB probe in a Hall thruster plume 

environment. New advances may be needed in the area of Hall thruster charged species spectroscopy to 

keep up with the newly developed magnetic shielding concept. 

Another discovery during the current study is the need to account for secondary electron emission 

effects on the nude Faraday probe even when a low SEE material is used as the collector. The correction 

factor for SEE effects were found to vary from 4 to 7 percent and must be accounted for if high fidelity 

results are needed. 

Lastly, several physical explanations are provided to explain the increase in multiply charged species 

and plume divergence found in the 300MS when compared to the 300M. The discharge of the 300MS is 

speculated to contain higher temperature electrons and is further downstream than the 300M. 

 
NASA/TM—2013-216606 27 

Appendix A—Derivation of New Integration Formulas 

for ExB Probe Analysis 

The process for deriving the integration formulas for ExB probe analysis start by relating the current 

collected by the ExB probe collector to the velocity distribution functions (VDFs) of the various charged 

species. To accomplish this, the velocity resolution of the ExB probe is derived in terms of various 

physical and geometrical properties. The results are used to relate the species and current fraction to the 

VDFs, culminating in the new integration formulas. This appendix will be written in a stand-alone 

manner. 

To figure out the relationship between the species and current fraction and the ExB probe trace we 

will first look at the physical description of what exactly the ExB probe is collecting at a given plate bias 

voltage. This is shown in Equations (22) to (24). 

I (V ) I (V ) P

j

P P  P,j (22) 





  0 j

0 j

u u

u u IP,j(VP ) Zj

eAPn j ufj(u)du (23) 

0 f

P

0

0

0 B D

V

B

E

u   (24) 

Where IP is ExB probe collector current, VP is the plate bias voltage, IP,j is the contribution to the 

measured current by the j-th species, Zj is the charge state of the j-th species, e is the elementary charge, 

AP is the probe entrance area, nj is the number density of the j-th species, u is particle velocity, u0 is the 

particle velocity corresponding to the applied electric and magnetic field magnitude, E0 and B0, 

respectively, as shown in Equation (24), uj is the half-width of the ExB velocity resolution and varies 

with species, fj is the velocity distribution function (VDF) of the j-th species, and Df is the gap between 

the ExB bias plates. 

To continue, we need to derive the relationship between uj and other known constants and variables. 

The derivation will be carried out for a single species so the subscript j will be dropped temporarily. 

Figure 22 shows the design of a generic ExB probe with a drift section. This simplified and 

exaggerated diagram also represents the ExB probe used for the present study. Starting from the left of the 

diagram, we have the collimator with a circular entrance orifice of diameter a1, a circular exit orifice of 

diameter a2, and a length of Lc. The particle is injected at the maximum collimator acceptance angle, α, 

and enters the filter section. The filter section is of length Lf and is sufficiently wide that the particle does 

not hit the bias plates (grey rectangles). The electric and magnetic fields in the particle path are uniform, 

perpendicular, and of magnitude E0 and B0, respectively. The example particle in this derivation is 

traveling slightly faster than the filter velocity u0, which is equal to E0/B0. The velocity of the particle is 

assigned to be u0+Δu. Because the particle is slightly too fast, it experiences a net downward acceleration 

in the filter section and passes into the drift section. The drift section is of length Ld. The particle is just 

slow enough to pass through the circular orifice of diameter a3 in the SEE suppression plate. The collector 

is sufficiently large as to collect all ions passing through the orifice on the SEE suppression plate. In some 

ExB probe designs, an exit collimator replaces the SEE suppression plate. The diameter of the entrance 

orifice for the exit collimator would become a3. Two assumptions will be used in this derivation. One, the 

acceptance angle is small enough that small angle approximation applies. Two, Δu << u0, so the equation 

can be linearized. 

 
NASA/TM—2013-216606 28 

Figure 22.—Simplified diagram of a generic ExB 

probe with drift section. 

Applying the equations of motion to the collimator section, we can obtain Equation (25) for the 

acceptance angle of the collimator. Note the use of the small angle approximation. 

c

1 2

2L

a a sin tan

    (25) 

Applying the equations of motion to the filter section, we obtain Equation (26) for the x-axis and 

Equation (27) for the y-axis. Note the use of the Δu << u0 assumption in Equation (26). 

f  Lf u0  (26) 

0 f

2

f 2

1

f y  a   u sin   (27) 

a

ZeB

m

u

0

    (28) 

Where f is the dwell time of the particle in the filter section, Δyf is the change in y-position of the particle 

between where it enters and where it exits the filter section, Δa is the net acceleration on the particle due 

to the velocity of the particle deviating from the filter velocity, m is the mass of the particle, and e is the 

elementary charge. The relationship between Δu and Δa is derived from force balance in the filter 

section and shown in Equation (28). Applying the equations of motion to the drift section, we obtain 

Equation (29) for the x-axis and Equation (30) for the y-axis. 

d d 0   L u (29) 

d y,d d f d 0 d y  u   a    u sin (30) 

where d is the dwell time of the particle in the drift section, Δyd is the change in y-position of the particle 

between where it enters and where it exits the drift section, and uy,d is the y-velocity of the particle as it 

enters the drift section. uy,d is calculated from the equations of motion for the filter section. Next, we note 

that the total change in the y-position of the particle between where it enters the filter section and where it 

exits the drift section is equal to the negative of the difference in y-position between the upper lip of the 

collimator exit and the lower lip of the orifice on the SEE suppression plate. This relationship is expressed 

in Equation (31). 
NASA/TM—2013-216606 29 







 





 

     2

a a

y y 2 3

f d (31) 

Substituting Equations (25) to (27), (29), and (30) into Equation (31) and re-arranging some terms, we 

obtain Equation (32). Lastly, substituting Equation (32) into Equation (28), we obtain an expression for 

the maximum deviation in velocity that a particle can have and still reach the collector. 

2

0

d f

2

f

2 3 1 2 f d c u

L 2L L

a a (a a )(L L ) / L

a 

















   

   (32) 



















   

 

d f

2

f

2 3 1 2 f d c

0

2

0

L 2L L

a a (a a )(L L ) / L

ZeB

mu

u (33) 

Note, if the acceptance angle of the ExB probe is larger than the angle subtended by the plasma source, 

the angle α is no longer the limiting parameter. Instead, the angle β (Eq. (34)) should be used and the 

form of Equation (33) changes to Equation (35). 

ExB

PS

2R

D

sin   (34) 



















   

 

d f

2

f

2 3 f d

0

2

0

L 2L L

a a 2sin (L L )

ZeB

mu

u (35) 

where DPS is the diameter of the plasma source and RExB is the distance between the ExB probe and the 

plasma source. For the probe used in this study, the acceptance angle is sufficiently small that Equation 

(35) does not apply. 

For an ExB probe without a drift section, we can set Ld to 0 in Equation (33), which simplifies into 

Equation (36). 















   

  2

f

2 3 1 2 f c

0

2

0

L

a a (a a )*L / L

ZeB

mu

u (36) 

Comparing Equations (36) to (33), we see that the addition of the drift section will generally improve the 

resolution of the ExB probe. Note that a1, a2, a3, Lc, Lf, Ld, and RExB are all geometric constants for a given 

experimental setup. DPS is also typically a constant (though one can never be too careful when 

generalizing about plasma sources). We can now write a scaling equation for the maximum accepted 

deviation in velocity of a generic ExB probe, which is shown in Equation (37). 

G

ZeB

mu

u

0

2

0   (37) 

where G is a geometric constant. 

Here are some quick observations about the maximum accepted deviation in velocity for an ExB 

probe. One, the numerator of Equation (37) contains the ion kinetic energy while the denominator 

contains the ion charge. In other words, Δu scales with the ion energy per charge of the incoming 
NASA/TM—2013-216606 30 

particles, which is slightly lower than the discharge voltage of a Hall thruster. The implication of this 

trend for a Hall thruster is that Δu is species-insensitive because all charged species undergo similar 

voltage drop and have similar ion energy per charge. When calculating ExB probe resolution as a relative 

percentage, the value for the singly-charged species will always be the biggest. That is because Δu is 

roughly constant while u0 increases with species charge. 

Two, dividing both sides of Equation (37) by u0, we obtain Equation (38). 

G

ZeB

mu

u

u

0

0

0

  (38) 

This equation says that for a given charged species, the ExB probe resolution in relative percentage 

increases with the velocity of the particle. For instance, an ExB probe with a 2 percent resolution when 

probing the plume of a 250-V thruster would have a 4 percent resolution when probing the plume of a 

1000-V thruster. The probe resolution in relative percentage scales as the velocity of the particles, which 

scale as the square root of the accelerating voltage. This is part of the reason why ExB probe traces for 

ion thruster are typically unable to resolve the VDF of the plume particles. The high accelerating voltage 

(1000+ V) associated with an ion thruster means Δu will generally be large. The combination of low VDF 

spread and large Δu means that Δu is generally larger than the VDF spread for an ion thruster. This 

interesting trend also means that an ExB probe used to interrogate the plume of a Hall thruster operating 

at high discharge voltage should have tight dimensions to ensure Δu is several times smaller than the 

width of the ion VDF. 

Having related Δu to known constants and variables, we now put back the subscript j in the 

appropriate places to indicate species-dependence. Mass is normally species dependent; however, Hall 

thrusters typically operate on a single atomic species so we will use a single atomic mass constant. The 

result is shown in Equation (39). 

G

Z eB

mu

u

j 0

2

0  j  (39) 

For an ExB probe with good velocity resolution, that is to say uj << u0, the integral term in 

Equation (23) can be approximated as fj(u0)*2uj. Taking the uj << u0 approximation and substituting 

Equation (39) into Equation (23), we arrive at Equation (40). 

0

P

j j 0 0

3

P, j P 0 0 B

2A mG I (V )  K u n f (u ), K  (40) 

where K0 is a constant for a given probe design. Further substituting Equation (24) into Equation (40), we 

arrive at Equation (41). 

0 f

2 3

0 f

0

j 2 P 1

3

P,j P 1 j P B D

1 , K

(B D )

K

I (V )  K n V f (K V ), K   (41) 

Where K1 and K2 are constants for a given probe design. Depending on which VDF form is in use, the 

associated equation is substituted into fj, and Equation (41) is fitted to the ExB probe trace to solve for the 

fitting constant. Note, Equation (13) is the same as Equation (41). The formulas presented so far, though 

appearing in different forms, matches previously published work (Refs. 12 and 27). It is the formulas to 

follow that are original and diverge from past work. 
NASA/TM—2013-216606 31 

To calculate the species fraction and current fraction, we now need the integral equations relating 

each quantity to the ExB probe collector current. To find the species fraction, we begin by re-arranging 

the VP

3

 term, then integrating both sides of Equation (41) with respect to VP from 0 to ∞. Since nj does 

not depend on VP it can go outside the integral. The result is shown in Equation (42). Since the integral of 

fj from 0 to ∞ is unity, we can further simplify the result, which is shown in Equation (43). 

P 0 3

P

P,j P

P 0 1 j j 2 P dV

V

I (V ) K n f (K V ) dV    

 (42) 

P 0 3

P

P,j P

1

j dV

V

I (V )

K

1

n 



 (43) 

Equation (43) relates nj to the ExB probe collector current and can be used to calculate the species 

fraction. The integration formula for species fraction is shown in Equation (44). 





 



  

k

P 0 3

P

P,k P

P 0 3

P

P,j P

k

k

j

j

dV

V

I (V )

dV

V

I (V )

n

n

 (44) 

To find the current fraction, we begin by relating the current of the j-th species entering the ExB probe, Ij, 

to the probe collector current. The current of the j-th species is defined in Equation (45). Substituting 

Equation (24) into Equation (45) yields Equation (46). 





 0 j j P j 0 j 0 0 I Z e A n u f (u ) du (45) 





 0 j P j 2 P P

2

j j P 2 I Z e A K n V f (K V ) dV (46) 

Next, we rearrange Equation (41) by dividing both sides by VP

2

, then integrate both sides with respect 

to VP from 0 to ∞ to obtain Equation (47). Substituting Equation (47) into Equation (46) yields 

Equation (48). 

   

 0 P 2

P

P,j P

1

P 0 j P j 2 P dV

V

I (V )

K

1

n V f (K V ) dV (47) 





 0 P 2

P

P,j P

1

2

j P 2

j dV

V

I (V )

K

Z eA K

I (48) 

Equation (48) relates Ij to the ExB probe collector current and can be used to calculate the current 

fraction. The integration formula for the current fraction is shown in Equation (49). 

 



 



  

k

P 0 2

P

P,k P

k

P 0 2

P

P,j P

j

k

k

j

j

dV

V

I (V ) Z

dV

V

I (V ) Z

I

I

 (49) 
 
NASA/TM—2013-216606 33 

Appendix B—Traditional Versus New Integration Formulas 

for ExB Probe Analysis 

Recall, the traditional approach to analyzing ExB probe data involves calculating either by geometry 

or by numerical integration the area under the curve, which is assumed to be proportional to the current of 

the corresponding species entering the probe. The traditional integration formula for the current fraction 

can be written as Equation (50). 





 



  

k

P 0 P,k P

P 0 P,j P

k

k

j

j

I (V ) dV

I (V ) dV

I

I

 (50) 

While Equation (50) is mathematically incorrect, it turns out to be a pretty good approximation of 

Equation (49) for analyzing the plume of a Hall thruster, especially when the VDF is narrow. To see why 

this is the case, let us calculate the current fractions for both integration formulas in the limit of very 

narrow VDFs. 

The current fraction calculated from the old (traditional) approach will be labeled with Ωj

O and the 

current fraction calculated from the new approach will be labeled with Ωj

N. Assuming the incoming ion 

beam is composed of species with very narrow VDFs and all charged species undergo the same voltage 

drop, Equation (49) can be simplified as shown in Equation (51), and Equation (50) can be simplified as 

shown in Equation (52). 

   



       



k

3/ 2

k k

3/ 2

j j

V

Same

k

k k k

j j j

VDF

Narrow

k

P 0 2

P

P,k P

k

P 0 2

P

P,j P

j

N

j

n Z

n Z

Z n u

Z n u

dV

V

I (V ) Z

dV

V

I (V ) Z

d

 (51) 

  

        



k

3/ 2

k k

3/ 2

j j

V

Same

k

3

k k

3

j j

VDF

Narrow

k

P 0 P,k P

P 0 P,j P O

j

n Z

n Z

n u

n u

I (V ) dV

I (V ) dV

d

 (52) 

The simplified expressions for the two integration approaches are equal. The voltage drop is typically 

very similar between the charged species, thus any difference in the results between the new and old 

approaches arise mostly from differences in the way the two approaches account for the spread in the 

VDF. During the present study, the difference was found to correspond to a change in anode efficiency of 

only 1 to 2 percent on the average. 
NASA/TM—2013-216606 34 

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