Recommended Practice for Use of Faraday Probes in Electric Propulsion Testing

Recommended Practice for Use of Faraday Probes

in Electric Propulsion Testing

Daniel L. Brown

∗

U.S. Air Force Research Laboratory, Edwards Air Force Base, California 93524

Mitchell L. R. Walker

†

Georgia Institute of Technology, Atlanta, Georgia 30332

James Szabo

‡

Busek Co., Inc., Natick, Massachusetts 01760

Wensheng Huang

NASA John H. Glenn Research Center, Cleveland, Ohio 44135

and

John E. Foster

University of Michigan, Ann Arbor, Michigan 48109

DOI: 10.2514/1.B35696

Faraday probes are a common plasma diagnostic used to determine the local ion charge flux of electric propulsion

plumes. Standard practices, guidelines, and recommendations are provided for experimental methods and analysis

techniques that aim to standardize community practices, to mitigate test environment effects, and to reduce systematic

measurement error in order to improve plume predictions in the space environment. The approaches are applicable

to time-averaged plasma properties in the near-field and far-field of electric propulsion plumes, with emphasis on Hall

effect thrusters and gridded ion thrusters. Considerations for other electric propulsion technologies are provided,

including electrosprays, arcjets, and electromagnetic thruster concepts. These test strategies are expected to increase

the quality of comparisons between different thrusters and vacuum environments, thereby broadening the

applicability of ground-based measurements and enhancing the fidelity for on-orbit predictions and modeling

validation.

Nomenclature

= cross-sectional geometric area, m

= Richardson constant, A · cm

−2

· K

−2

1;2

= curve-fit parameters

= thruster diameter, m

= error metric of divergence angle

= error metric of travel angle

e = elementary charge; 1.6022 × 10

−19

= thrust loss parameter

= height of collector, m

= height of guard ring, m

Axial

= axial component of ion beam current parallel to thrust

axis, A

Beam

= integrated ion beam current, A

= thruster discharge current, A

= measured ion current on the Faraday probe collector, A

j = ion current density, A ⋅ m

−2

Bohm

= Bohm ion current density, A ⋅ m

−2

= thermionic emission ion current density, A ⋅ m

−2

k = propellant charge state index; 0, 1, 2, 3, etc., for Xe

1

, Xe

2

, Xe

3

= Boltzmann constant; 1.3806 × 10

−23

J · K

−1

= ion mass, kg

m = iteration index, 0, 1, 2, :::

= total propellant flow rate, kg · s

−1

N = number axial positions

n = plasma density, m

−3

= neutral density, m

−3

Q = average ion charge

r = radial coordinate

R = radial measurement distance, m

= radius of collector, m

C-GR

= collector to guard ring resistance, Ω

= probe shunt resistance, Ω

= inner radius of guard ring, m

= near and far probe distances in two-point source

model, m

= probe radius, m

= shift in jet radial point of origin, m

= linear regression slope

T = thrust, N

= electron temperature, eV

= surface temperature, K

Beam

= thruster beam voltage, V

bias

= probe bias voltage, V

= measured shunt voltage, V

w = plasma discharge width, m

Z = downstream measurement distance, m

= ion charge state of the kth species

z = axial coordinate

= shift in jet axial point of origin, m

α = thrust reduction due to multiple charged ions

= ion divergence angle in two-point source model, rad

, α

= angle of the probe in two-point source model, rad

β = near-field gridded ion thruster divergence half-angle,

rad

1;2

= tuning parameters

= particle flux of the kth species, m

−2

· s

−1

Received 15 December 2014; revision received 1 July 2016; accepted for

publication 5 July 2016; published online 14 September 2016. This material is

declared a work of the U.S. Government and is not subject to copyright

protection in the United States. Copies of this paper may be made for personal

and internal use, on condition that the copier pay the per-copy fee to the

to reprint should be submitted to CCC at www.copyright.com; employ the

ISSN 0748-4658 (print) or 1533-3876 (online) to initiate your request.

*Chief, Liquid Rocket Engines Branch, Aerospace Systems Directorate.

Associate Fellow AIAA.

†

Associate Professor, High-Power Electric Propulsion Laboratory.

Associate Fellow AIAA.

‡

Chief Scientist for Hall Thrusters. Associate Fellow AIAA.

Research Engineer, Propulsion and Propellants. Member AIAA.

Associate Professor, Nuclear Engineering and Radiological Sciences.

Associate Fellow AIAA.

582

JOURNAL OF PROPULSION AND POWER

Vol. 33, No. 3, May–June 2017

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= secondary electron emission yield of the kth species,

electrons/ion

δ = near-field Hall effect thruster divergence half-angle,

rad

= jet divergence angle, rad

ε = surface emissivity

= permittivity of free space; 8.8542 × 10

−12

F · m

−1

Beam

= beam divergence utilization

Current

= current utilization

Mass

= mass utilization

θ = angular coordinate

= jet travel angle, rad

= correction for ion angle of incidence

= correction for probe distance to thruster

= correction for probe ion collection area

SEE

= correction for collector secondary electron emission

λ = far-field divergence half-angle, rad

= Debye length, m

MFP

= mean free path, m

σ = collision cross section, m

=Stefan–Boltzmann con stant; 5.6704× 10

−8

W·m

−2

·K

−4

Φ = azimuthal angle, rad

φ = work function, eV

Ψ = probe angle, rad

= ion current fraction of the kth species

= charge flux-weighted average quantity

I. Introduction

ARADAY probe measurements of ion charge flux in the plume of

spacecraft electric propulsion (EP) technologies are used for sev eral

purposes, including 1) ground predictions and flight measurements of

local plume properties to determine plasma–sp acecraft interactions,

2) characterization of global plume properties to assess the thruster

plasma discharge and loss mechanisms, 3) v alidat ion data for modeling

and simulation, and 4) data for thruster acceptance tests. In addition to

EP, these diagnostics have been used for many applications, such as

space plasma experiments, dense plasma focus experiments, and laser-

produced plasma [1–4]. In its simplest form, the Faraday probe consists

of a collector electrode that measures local ion charge flux. Other

configurations use collimators, guard rings, or biased grids to filter

charged particles, such as the Faraday cup. Although Faraday probe

design and implementation is straightforward, the test methodology and

data analysis required for EP technologies are complicated by systematic

measurement errors.

This paper provides recommendations for time-averaged

Faraday probe measurements in the near-field and far-field plumes

of Hall effect thrusters (HETs) and gridded ion thrusters (GITs)

to provide common test methodologies, diagnostic design, and

analysis techniques. Although this paper is applicable to other EP

technologies, there is insufficient data in the literature to establish

standard methods for electrosprays, arcjets, and electromagnetic

thruster concepts. Section II discusses the applicability to EP

technologies and consideration s of the plasma envir onment. Sections III

and IV describe experimental apparatus and test methodologies,

respecti v ely. Section V presents data reduction and analys is techniques.

Section VI provi des information on m easurement error and uncertainty .

Section VII discusses probe design considerations. Section VIII

contains considerations for other EP technologies. A tabulated

summary of all guidelines and recommendations is provided in

Appendix A, and an analysis method to remove the cathode plume

is included in Appendix B.

The guidance in this paper uses precise definitions for the words

should and may. The word should denotes the statement is advisory;

there may be circumstances when the statement is ignored, but the

associated implications must be understood and accounted for. The

word may denotes the statement is a recommendation, and it is

considered discretionary.

II. Applicability

A. Electric Propulsion Technologies

In EP systems, electrical energy is added to the propellant from an

external power source to ionize and accelerate propellant to high

exhaust velocities; this is in contrast to chemical rockets where the

propellant exhaust velocity is limited to less than 5km∕s by the

energy released during propellant combustion processes. Thus, EP

technologies decouple the available energy from the propellant

chemical reactions, and they impart energy through electric heating,

electrostatic fields, and/or electromagnetic fields. Additional details

on EP thruster concepts and plasma processes are found in the

literature [5,6].

This paper focuses on HETs and GITs due to the flight heritage

and extensive Faraday probe measurements in ground testing,

which enables development of guidelines and recommendations.

Examples of Faraday probe measurements and analysis of HET and

GIT plumes are provided, with particular consideration for HET

plumes due to the more recent investigations that have further

improved test methodologies and analyses to reduce systematic

measurement uncertainty. In addition, HETs may have additional

complexities associated with annular geometry, oscillatory behavior,

and facility effects on the plasma ionization and acceleration

processes. The guidance for HETs and GITs may also serve as a

starting point for Faraday probe measurements of other EP

technologies, as discussed in Sec. VIII.

In HETs, propellant ionization and acceleration are achieved with

orthogonal electric and magnetic fields in the annular discharge

channel, as shown in Fig. 1 for a typical stationary plasma thruster

configuration. The guidelines and recommendations in this paper are

based primarily on numerous past experiments with stationary

plasma thrusters; however, the paper is applicable to alternative HET

configurations, including nested channel HETs and the thruster with

anode layer variants [7–9]. In HETs, a constant potential difference is

applied between the anode and cathode, where the cathode may be

located external to the thruster body (as in Fig. 1) or centrally

mounted on the thruster centerline axis. The cathode provides

electrons to the plasma discharge and to neutralize the ion beam. The

anode often serves as the propellant gas distributor. The HET electric

and magnetic fields are designed such that electrons are confined in

the plasma discharge and have a net azimuthal motion known as the

Hall effect, which is the origin of the device name. Said electrons

ionize propellant through a cascade of electron impact collisions. The

generated ions are weakly magnetized and are accelerated by the

axial electric field to generate thrust. Plasma in the HET channel is

North

South

Thruster Centerline

Magnets

Cathode with

Gas Feed

Insulator

Anode with

Propellant

Gas Feed

Neutralizing e

Propellant Xe

Ionization and

Acceleration

Fig. 1 Schematic of design features and plasma properties for HETs.

BROWN ET AL. 583

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quasi neutral, and thus the extracted current density is not space-

charge limited.

The GIT plasma is generated within an enclosed discharge

chamber via a direct current (dc) discharge, a radio-frequency (RF)

discharge, or a microwave discharge [6]. Neutral propellant gas is

injected into the discharge chamber and ionized by electrons from the

discharge cathode, as shown in Fig. 2, or by alternating electric and

magnetic field in the case of RF or microwave discharge chambers.

Magnetic fields are typically used near the anode wall to confine

energetic electrons, and thereby improve ionization processes.

Propellant ions are extracted, focused, and accelerated to generate

thrust by the ion optics, which are typically a series of closely spaced,

multiaperture grids terminating at the thruster exit plane. The ion

optics geometry determines ion trajectories, particle grid interactions,

and beam divergence. Maximum ion current density extracted though

the ion optics is limited by space-charge considerations; thus, the

maximum GIT ion beam current density is lower than a HET beam.

The exhaust ion plume is neutralized by an externally mounted

hollow cathode.

A Faraday probe is typically employed to assess time-averaged ion

current density in the plume. Time-resolved Faraday probe

measurements at tens of kilohertz are feasible (up to low megahertz

are possible) with existing capabilities, as demonstrated by local

plasma measurements with ion saturation reference probes at fixed

bias voltages that were used in experiments with high-speed dual

Langmuir probes in the near-field of HETs [10,11]. However, time-

resolved Faraday probes have not been used to map an EP plume or to

evaluate facility effects. Although certain guidelines related to time-

averaged Faraday probe measurements may be applicable to time-

resolved measurements, there may be significant differences in the

probe configuration, data acquisition, data analysis, measurement

error, and quantification of ion beam parameters. These differences

are beyond the scope of this paper.

The guidelines in this paper were generated for inert, nonreactive

propellants such as the noble gases. Faraday probes may also be used

with low vapor pressure (“condensable”) and reactive propellants,

such as bismuth, iodine, mercury, and ionic liquids [12,13]. Although

this paper is applicable to HETs and GITs with these propellants,

additional issues may arise that should be accounted for. For

example, a possible concern with condensable propellants is the

potential for contamination of dielectric surfaces leading to electrical

leakage from the collector. Laboratory HET measurements with

iodine propellant showed negligible accumulation on test coupons in

the plume [14]. Mercury GITs on the Space Electric Rocket Test 2

(SERT II) spacecraft were successfully fired on orbit for 4000 h,

where most critical spacecraft surfaces, such as solar arrays, were too

warm to permit mercury condensation and no evidence of condensate

accumulation was expected [15]. However, the issues unique to

condensable and reactive propellant should be carefully considered for

each application, such as deposition of propellant upon probe

electrodes, deposition on ceramic surfaces leading to reduced electrical

isolation, leakage current, and material degradation due to corrosion.

B. Plasma Plume Characterization

The plume of EP thrusters is associated with dynamic and complex

processes that must be considered for Faraday probe measurements.

Examples include downstream regions of ion acceleration, spatial and

temporal gradients in plasma properties, and interactions with neutrals.

In addition, there are thruster specific processes such as beamlet

interactions downstream of GIT ion optics or HET ion beam merging

from opposing sides of the annular channel. These challenges will be

addressed with regard to experimental configuration, test methods, and

analysis in Secs. III, IV, and V, respecti vely.

Facility effects influence thruster operation and the plasma plume,

and they are well characterized in the EP literature [16–21]. These

interactions are present in both the near-field and far-field regions,

including the influence of facility background neutrals, backsputtering

of facility surfaces, pressure gradients due to facility configuration and

pumping, and the thruster discharge circuit in a grounded vacuum test

facility. The interactions are inherent in ground-based EP plume

investigations, and thus cannot be completely eliminated to fully

replicate the space environment. The two primary facility interactions

on the thruster plume are related to facility background neutrals, and

they are illustrated in Figs. 3 and 4 for HETs and GITs, respectively.

The first interaction is collisional processes between facility neutrals

and the thruster beam, where ion-neutral charge exchange (CEX)

collisions are the dominant interaction. The second interaction is

ingestion, ionization, and acceleration of facility neutrals.

The influence of collisional processes between facility neutrals

and the thruster beam may be evaluated with respect to the neutral

particle populations in EP plumes, as shown in Fig. 5 for simulations

of the BPT-4000 HET [22]. In Fig. 5, the ambient facility neutral

density exceeds the thruster neutral density beyond approximately

0.02 m, which is comparable to GIT plumes for a similar propellant

flow rate [23]. The mean free path (MFP) in Eq. (1) represents the

mean distance a fast particle will travel in a background of stationary

neutrals before a collision:

Thruster

Centerline

Neutralizer

Cathode with

Gas Feed

Ion Optics

Neutralizing e

Anode

Plasma

Generator

Propellant

Gas Feed

+, +2,…

Beam Ions

Discharge

Cathode

with Gas

Feed

Electrostatic Ion

Acceleration

Fig. 2 Schematic of design features and plasma properties for GITs.

+, +2,…

Beam Ions

North

Thruster Centerline

Magnets

Cathode with

Gas Feed

Insulator

Anode with

Propellant

Gas Feed

Background Xe

Ionization and

Acceleration

+, +2,…

Accelerated

Background

Ions

↔Xe

CEX Collision

Fast Xe

Slow Xe

Fast Xe

Slow Xe

Ingested

Background

South

Fig. 3 Diagram of HET plasma interactions of facility background

neutrals.

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MFP

n

σ

−1

(1)

In Eq. (1), n

is the neutral density and σ is the particle collision

cross section. The MFP may be used to determine the dominant beam

collisional processes in the plume region; an overview of particle

collisions and relevant cross sections was described elsewhere

[6,24,25]. The cross section for CEX collisions between ambient

xenon neutrals and xenon ions has been experimentally measured as

5 × 10

−19

to 8 × 10

−19

[25], which was much larger than the cross

section for xenon-neutral elastic scattering (10

−20

), as well as

xenon ionization and excitation cross sections (10

−20

) [6,26]. The

CEX collisions between background neutral particles and beam ions

generated high-velocity neutrals and low-energy scattered ions. The

CEX collisional processes scattered beam ions and increased ion

current density on the periphery of the plume, thereby increasing

thruster plume divergence [18,27,28]. Based on Eq. (1), the xenon

ion-neutral MFP of CEX collisions is shown in Fig. 6. For a HET or

GIT operating at a 300 V discharge condition, the relative velocity

between the xenon ions and neutral atoms was approximately

17;000 m∕s and the CEX cross section was 6 × 10

−19

[25]. For a

background neutral pressure of 1.3 × 10

−5

torr of xenon gas

(torr-Xe), the neutral number density was 4.2 × 10

−3

[29] and

the ion-neutral CEX collision MFP was 3.97 m. The MFP values in

Fig. 6 are on the order of the far-field spatial measurement region, and

they are consistent with far-field experimental results showing

increased plume divergence at elevated facility pressure in Sec. V.

Although the ion-neutral CEX MFP is larger than the near-field

spatial region of interest for most HETs and GITs, the difference is

not significant; thus, CEX collisions are expected to have a

nonnegligible effect in the near-field plume. These observations will

be discussed with experimental results in Sec. V.

The second dominant facility interaction is associated with

ingestion of facility background neutrals near the thruster discharge

exit, which increases the amount of propellant used by the thruster.

These ingested neutrals undergo ionization and subsequent

acceleration, which increases the amount of propellant available to

the thruster. The ingested facility neutrals may be ionized and

accelerated downstream of the peak electric field, and thus manifest

as a low-velocity divergent ion population in the beam. In GITs, the

accelerator grid current may become prohibitively high at an elevated

background pressure due to a CEX ion current, and therefore

operation at these elevated pressures is often impractical well before

ingestion effects become a significant factor. This is further discussed

in Sec. IV.E.

Multiple studies have evaluated Faraday probe design modifications

to minimize facility effects associated with probe collection of low-

energy CEX ions and ions generated from ingested propellant,

including probe filtering mechanisms and collimators [1,30–32].

Although these techniques successfully mitigate the collection of low-

energy ions generated through facility interactions, they introduce

additional error that is not representative of thruster plumes in the space

environment. The impact of these facility interactions on Faraday

probe measurements will be discussed, and guidelines to mitigate and

account for the effects will be recommended.

In theory, computational simulations of the EP plume allow

isolation and elimination of facility pressure effects to predict the

on-orbit ion beam. However, this predictive capability relies on

accurate plasma input source models, understanding of facility

interactions, and validation with flight measurements and ground

testing. To date, comparisons of plume profiles between ground

testing, flight data, and/or simulations demonstrate inconsistent

agreement [33–37].

III. Experimental Apparatus

The test hardware and configuration requirements for plume

measurements of ion current density include the Faraday probe,

motion control system, power electronics, and data acquisition

(DAQ) system to monitor collected current. The power electronics,

experimental configuration, and probe calibration considerations are

described in the following sections.

0 0.1 0.2 0.3 0.4

Distance Downstream of Thruster Exit Plane (m)

Neutral Particle Density (m

-3

)

4.0x10

2.0x10

Total

Facility

Hall Thruster

Hollow Cathode

Fig. 5 Neutral particle density on thruster centerline, recreated from [22].

0.0

1.0

2.0

3.0

4.0

5.0

Neutral Particle Density (m

-3

)

Ion-Neutral Mean Free Path (m)

4.0x10

3.0x10

2.0x10

1.0x10

0.0

Fig. 6 Xenon ion-neutral CEX mean free path for expected neutral

particle density in the near-field plume, for σ  6 × 10

−19

Thruster

Centerline

+, +2,…

Accelerated

Background Ions

CEX Collision

Slow Xe

Fast Xe

Ingested

Background

Neutralizer

Cathode with

Gas Feed

Ion Optics

Anode

Plasma

Generator

Propellant

Gas Feed

Discharge

Cathode

with Gas

Feed

Electrostatic Ion

Acceleration

↔Xe

Fig. 4 Diagram of GIT plasma interactions of facility background

neutrals.

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A. Hemispherical Coordinate System and Test Configuration

Faraday probe measurements in a hemispherical coordinate system

are shown in Fig. 7 with respect to Cartesian coordinates, where θ is the

angular position from thruster centerline, Φ is the azimuthal angle, R is

the measurement distance, and D

is the thruster diameter. In this

paper, D

is defined as the outer grid diameter for GITs or outer

channel diameter for HETs. Different definitions, such as the

midchannel diameter of HETs, may necessitate minor modification to

equations and will be identified in the text. The plume is assumed

axisymmetric about the z axis,and the probe axis of rotation is typically

the y axis at the intersection of the thruster exit plane and the thruster

centerline axis in Fig. 7. The Faraday probe is swept in an arc at

constant R, and the collector face is pointed toward the rotation axis at

all angular locations of the measurement.

Note that, in a true hemispherical coordinate system, the angular

coordinate θ cannot be negative with respect to the thruster centerline

axis. However, for EP thruster testing, probes are generally swept

from one side of the thruster to the other. Plasma measurements are

collected during the entire sweep, thereby providing data from two

opposing azimuthal angles (i.e., Φ  0 and 180 deg). Common

convention within the EP test community is to refer to these two

datasets as the positive θ and negative θ datasets, where −θ refers to

data collected at Φ  180 deg since cos180 deg is −1. Collecting

data in this fashion has the advantage of allowing researchers to

determine the symmetry of the plasma plume in the swept plane. For

the purpose of this paper, −θ positions represent the left side of the

plume where Φ  180 deg and is understood to represent angular

positions opposite of the azimuthal plane at Φ  0 deg.

The hemispherical coordinate geometry should be used for

measurements of the far-field HET and GIT plume, which is defined

as the region where R is greater than four thruster diameters

downstream (TDD) of the exit plane, such that R∕D

is greater

than 4. Measurements where R∕D

is less than 4 have been shown

to introduce systematic error, since the hemispherical coordinate

system assumes a point ion source [18]. This issue is further

discussed in Sec. V.B. In addition, multiple HET investigations have

shown a nonnegligible population of beam ions on the periphery of

the plume beyond θ  50 deg for different thruster designs and over

a wide range of operating conditions [38,39]; the hemispherical

coordinate system is well-suited to evaluate these divergent plume

structures.

If an external cathode is used for beam neutralization and the

Faraday probe measurement sweep is conducted in the Φ  0 deg

plane, the cathode should be positioned in the Φ  90 deg or

270 deg plane (i.e., y-axis). Faraday probe sweeps in the cathode

plane may measure localized plume asymmetry near the cathode.

B. Cylindrical Coordinate System and Test Configuration

The cylindrical coordinate system is defined in Fig. 8 with respect

to Cartesian coordinates, where r is the radial coordinate, z is the axial

coordinate, and Φ is the azimuthal angle [40]. The plume is assumed

to be axisymmetric about the z-axis and the axial measurement

distance Z is defined with respect to the thruster exit plane, where

z  0. Beam ions are assumed to be aligned in the axial direction, and

therefore the probe face is oriented normal to the z-axis. The probe is

typically swept in the radial direction at a fixed axial distance Z, with

Φ  0 deg and/or 180 deg.

In a true cylindrical coordinate system, r cannot be negative with

respect to the thruster centerline axis. Similar to discussions of −θ in

the hemispherical coordinate system, near-field Faraday probe

measurements are typically swept across the plume. Thus, a single

Fig. 7 Diagram of a) hemispherical coordinate system for far-field

Faraday probe measurements and b) measurement geometry in x-z plane

where Φ  0 and 180 deg.

Fig. 8 Diagram of a) cylindrical coordinate system for Faraday probe

measurements and b) measurement geometry in x-z plane where

Φ  0 deg.

586

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dataset includes opposing azimuthal angles (i.e., Φ  0 and

180 deg). Common convention within the EP test community is to

refer to these two datasets as the positive r and negative r datasets,

where −r refers to data collected at Φ  180 deg because

cos180 deg is −1. Collecting data in this fashion has the advantage

of allowing researchers to assess plume symmetry. For the purpose of

this paper, −r positions represent the right side of the plume where

Φ  180 deg and are understood to represent angular positions

opposite of the azimuthal plane at Φ  0 deg.

A cylindrical coordinate system should be used in the near-field

plume extending from the thruster exit plane to Z∕D

less than four,

which is equivalent to R∕D

less than four on the thruster centerline

in the hemispherical coordinate system. If an external cathode is used

for beam neutralization and the Faraday probe measurement sweep is

conducted in the Φ  0 deg and/or 180 deg plane, the cathode

should be positioned in the Φ  90 or 270 deg plane (i.e., y axis).

Faraday probe sweeps in the cathode plane may measure localized

plume asymmetry and plasma gradients near the cathode, which

complicate data analysis [41].

A limitation of the cylindrical coordinate system is the inability to

measure high-energy beam ion flux at high angles from the thruster

centerline approaching Ψ  90 deg (in Fig. 8) because the probe is

oriented perpendicular to the thrust axis. HETs in particular exhibit a

nonnegligible fraction of beam ions on the plume periphery [38,42];

thus, the cylindrical coordinate system may not be practical for

quantitative evaluation of the near-field HET plume for 1 < Z∕D

< 4.

C. Probe Positioning Techniques

Faraday probe measurement positioning may be performed with

two methods, either 1) maintain continuous motion and data

acquisition, or 2) stop at a specific measurement position, record data,

and then move to the next position. Probe acceleration and translation

speed impacts spatial accuracy, resolution, and scan duration. Large

acceleration and deceleration magnitude may induce probe vibration,

and thus it is critical to characterize the effect on resolution if the probe

is stopped at each measurement location. For continuous motion, the

probe translation speed will limit spatial measurement resolution.

Limiting factors for slow translation speeds include long duration of

the measurement sweep, probe heating, and survivability. High-speed

motion stages should be employed if excessive probe heating and

survivability are an issue, which imposes additional demands on the

mechanical setup. For example, the supporting structure for Faraday

probe armature and the high-speed motion stage must be secure, and

they should be attached to the test facility in a way that also braces

against possible torsional modes. Additional information on high-

speed probe positioning may be found in [43,44].

There is currently no simple formula for determining a minimum

motion stage speed necessary to pass through the thruster plasma.

The probe area and the residence time in the plasma are proportional

to the total energy transferred to the probe as heat. Past near-field

studies of a 20 kW HET plasma demonstrated a probe residence time

in the plasma of ∼1swas acceptable for a probe with frontal area of

∼10 mm

at 0.05 TDD from the exit plane [45]. During these studies,

the probe translation speed ranged from 150 to 500 mm∕s.

D. Power Electronics and Data Acquisition

Power electronics serve two functions: to source electrode bias

voltage, and to measure ion current collected by the electrode. The

probe bias repels electrons such that the probe is in ion saturation.

Probe electrode biasing is accomplished through the use of one or

more dc power supplies, typically −15 to −30 V with respect to

facility ground in far-field measurements and approaching −100 V

with respect to facility ground in near-field measurements. A single

power supply can bias the collector and guard ring electrodes to the

same bias potential V

bias

, assuming equivalent electrical wiring

lengths are used to both electrodes. Additional power supplies may be

necessary if a filtering or collimating technique is used that requires

different voltages than that applied to the collector. The electrical

diagram of a recommended probe circuit is shown in Fig. 9, where the

ion current to the collector I

may be read as a voltage V

across the

resistor R

. The resistance of R

is typically between 10 and

1000 Ω. Larger R

resistance values may influence measurements

in several ways, including generation of a low-pass filter, creating a

voltage divider effect with measurement equipment, or Johnson–

Nyquist noise [46]. Avoltmeter may be used to measure V

. Often, a

DAQ system or digital multimeter with high impedance (greater than

gigaohms) is required to further reduce leakage current. (Leakage

current is equivalent to probe voltage divided by input impedance.

For megaohm input impedance, the leakage current may exceed a

nonnegligible fraction of the probe signal strength in the far-field

plume (∼10–100 μA∕cm

), thereby limiting resolution and increas-

ing measurement uncertainty. For example, a probe bias of −20 V

and 1MΩ input impedance generates leakage current of ∼20 μA,

whereas 1GΩ input impedance corresponds to ∼20 nA.)

Resistance between the collector and guard ring, identified as

C-GR

in Fig. 9, and between the collector to ground should be large,

such that stray current does not exceed the ion current measurement

resolution. For ion current measurement resolution of 1 nA and

typical electrode bias voltage ranging from −10 to −100 V, the

resistance R

C-GR

from the collector to the guard ring should exceed

100 MΩ 10 V∕1nA). An isolation amplifier may be imple-

mented to prevent arc events from damaging the DAQ system.

The measurement DAQ rate is typically determined by the desired

spatial resolution and probe speed. High-speed probe positioning may

require an encoder. If an encoder is not used, the repeatability of probe

positioning should be characterized to evaluate precision and estimate

positioning error. During measurements with low data acquisition

rates, the probe location may be monitored through encoders, through

the motion controller, or through the controlling program.

E. Probe Calibration, Alignment, and Periodic Maintenance

The methods described in this section are suitable to minimize

systematic error in key aspects of the measurement system and

experimental configuration in a ground test environment. The F araday

probe, probe positioning, and D AQ system may be characterized and/or

calibrated according to manufacturer recommendations before Faraday

probe measurements. Ideally , before testing the probe, an experimental

measurement system would be ev aluated with an ion source that could

provide a uniform, monoenergetic ion beam with the ion energy per

charge ranging from 0 V to greater than the maximum thruster

acceleration voltage. Although this approach may be ideal in an

inv estigation with unlimited resources, there are significant limitations in

applying the characterization of an ideal ion beam to measurements of EP

thruster plumes and mitigating systematic error associated with facility

pressure effects. First, the thruster ion beam will vary spatially (and

temporally in the case of HETs) throughout the plume, including ion

energy distribution and ion charge states. Second, the thruster ion beam

will be influenced by facility effects and vary with thruster operating

condition. Thus, the complexities of EP plumes and resources required to

characterize the experiment with an ion source make it impractical for

most investigations. In practice, the errors may be characterized and/or

mitigated with careful probe design, using correction factors, and

implementing the test and analysis methods described in Secs. IVand V.

The manufacturer uncertainty in DAQ system components should

account for many drift errors or offsets. It is important to account for

Guard Ring

bias

C-GR

Collector

Fig. 9 Electrical schematic of a typical Faraday probe showing the

collector and guard ring.

BROWN ET AL. 587

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DAQ system error for the measurement range and DAQ thermal

environment specified by the manufacturer. In addition, a null

measurement of the DAQ system without plasma may be used to

assess DAQ system uncertainties.

Resistance of the collector to ground and R

C-GR

should be

measured before testing; both should exceed 100 MΩ. If the

resistance is below this threshold, the exposed surfaces within the gap

between the collector and guard ring should be evaluated for surface

deposition. Faraday probe contaminants may include materials used

in the thruster, cathode, spacecraft or facility, Faraday probe

materials, and experimental mounting hardware. Common sputtering

contaminants may include iron, tungsten, molybdenum, stainless

steel, ceramics (i.e., boron nitride, alumina, etc.), graphite, and

Kapton. Sputtering of dielectric or conductive materials may impact

probe ion collection in different ways, such as leakage current from

the collector, collector thermionic emission, or collector secondary

electron emission (SEE) [47–50]. Contamination effects will likely

manifest in multiple ways and may affect the data in a competing

manner. In this case, the probe should undergo a cleaning process to

reduce contamination and remove buildup of sputtered material

through exposure to high-energy ions in the beam [51,52], or it may

be cleaned periodically, such as with 40% isopropyl alcohol.

Although it is possible to remove surface material buildup, and even

achieve a polished finish by sanding the probe surfaces, this should be

done with caution to avoid altering probe dimensions and tolerances;

reassessment of probe dimensions and evaluation of the collection

area are recommended if sanding is implemented.

Probe alignment and orientation with respect to the thruster should

be conducted before evacuating the facility. For evaluation of the

axisymmetric plume, the collector face should be aligned parallel to

the thruster exit plane to within 1 deg when the probe is located on the

thruster centerline. The downstream distance R (or Z)shouldbe

measured along the thruster centerline from the centerpoint of the

probe collector surface to the intersection with the thruster exitplane, as

shown in Figs. 7 and 8. The definition of the thruster exit plane is

thruster design dependent, and it is left to the user. The probe axial and

radial position accuracy should be within 1 mm or 0.5% of R (or Z)at

the furthest measurement distance (i.e., 5 mm at R  1m): whichever

is greater. Alignment may be repeated at multiple distances and angles

from the thruster centerline. These alignment tolerances are less than

the measurement resolution, and they are intended to minimize spatial

error in measurements to provide sufficient resolution for plume

regions with steep gradients in plasma properties and for validation of

high-fidelity modeling and simulation[53,54]. Due to the possibility of

damage to the probe or thruster with misalignment, a device for

alignment while under vacuum may be used, such as a contact probe

and a reference with a fixed, known position relative to the thruster.

During plasma plume mapping, there should be no obstructions in

the line of sight of the Faraday probe to any point of the thruster

plasma discharge. Diagnostic wiring should be a coaxial cable or

twisted shielded pair, and electrical connections should not be

exposed to the plasma. Cable shielding should be grounded to the

facility walls in ground testing. All probe mounting structure and

cables near the probe should be downstream of the probe collection

surface. Any mounting structure that experiences direct beam ion

impingement should be shielded with low-sputter materials, such as

Kapton or graphite [48,55].

The user should consider Faraday probe distance from the facility

walls or other grounded surfaces. One possibility is maintaining a

probe distance greater than one mean free path from the facility walls.

In this case, using Eq. (1) for a thruster operating at 1.3 ×

−5

torr-Xe and a local electron temperature of 2 eV (electron-

neutral elastic collision cross section of 1.6 × 10

−19

) results in an

electron-neutral MFP of 12.3 m [56]. Thus, this approach is likely not

practical. An alternative approach is based on the Debye length λ

Eq. (2), which is the length scale that the bulk plasma shields the

effect of the perturbing electrode:





(2)

Electron number densities typically vary over more orders of

magnitude than electron temperature in the EP plume; therefore, the

electron Debye length is primarily dictated by the plasma density. For

a typical thruster plasma with an electron temperature of 2 eV and an

electron number density of 10

−3

, the electron Debye length

is 3.3 mm.

IV. Test Methodology

A. Test Conditions and Plasma Regimes

Spatial variations of plasma properties in EP plumes span orders of

magnitude, and they necessitate consideration of the facility

interactions with the thruster plasma and probe ion collection. The

time-averaged ion current density in the plume of HETs and GITs

typically ranges from 1 to 100 mA∕cm

in the near-field to less than

0.001 mA∕cm

in they periphery of the far-field plume [21,45]. Over

this region, the time-averaged electron temperature and ion density

range from approximately 10 eV and greater than 10

−3

in the

near-field (Z > 0.2D

) to less than 1 eVand 10

−3

in the far-field

plume periphery.

Analyses of collisional processes in the plasma plume indicate

CEX collisions between beam ions and facility neutrals dominate

over ion-neutral momentum collisions or Coulomb interactions [39].

There is an important distinction in CEX collisions between beam

ions with facility neutrals or beam ions with non-ionized propellant

from the thruster and cathode. The former are a leading source of

facility effects that should be evaluated and corrected for. The latter

CEX collisional processes exist on orbit and should not be filtered

from Faraday probe measurements. Differentiating these CEX

processes and characterizing the facility influence on ion beam

properties requires the lowest facility pressure achievable and

execution of the methodologies described in this paper.

Facility pressure during Faraday probe measurements should be as

low as possible to better replicate the space environment. Modern

vacuum facilities may achieve background pressure less than

−5

torr-Xe. Lower pressure will give more accurate results, and

therefore it is highly recommended for model validation data and

predictions of the in-space plume properties. The pressure should be

monitored near the thruster and adhere to recommendations in [57].

The thruster discharge should reach operational steady state before

conducting Faraday probe measurements. Thruster input parameters

are typically fixed, such as applied magnetic fields and voltage applied

to electrodes. In addition, the thruster should be monitored for possible

perturbation during a sweep, which may be associated with plasma

interaction with the probe mounting structure or the influence of probe

bias and local sheath effects. The definition of steady state and

perturbation should be identified by the user. It is recommended that

the thruster discharge telemetry be monitored throughout plume

characterization. Monitoring may include time-resolved and time-

averaged thruster telemetry such as discharge voltage(s) and current(s),

mass flow rate, cathode to ground potential, and thrust.

Facility background pressure may influence the ratio of thruster

discharge current to the anode propellant flow rate. If Faraday probes

are used to measure the ion current density of the HET plume at

multiple background pressures, either the thruster discharge current

or anode mass flow rate should be held constant; this may require

adjustment of the unfixed parameter and should be reported.

B. Probe Operating Characteristics

The bias potential to the collector and guard ring should be equal,

and it must be sufficient for collector ion current saturation

throughout the plume measurement region. The probe ion saturation

should be characterized at multiple locations in the plume to span the

maximum and minimum plasma densities and electron temperature.

In far-field measurements, this typically corresponds to the minimum

R at θ  0 deg and the maximum R at θ  90 deg. In cylindrical

coordinates, this typically corresponds to the minimum Z down-

stream of the plasma discharge (e.g., channel centerline for HET) and

at maximum distance on the plume periphery (i.e., maximum Z and/

or r). At each location, the collector ion current should be assessed,

starting from 0 V to a negative bias voltage where the collected

588 BROWN ET AL.

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current asymptotes. This negative bias voltage indicates ion

saturation. Characterization of ion saturation is demonstrated in

Fig. 10 at R  50 cm for the nested Faraday probe described in [18],

where the measured collector current is peak normalized at each

angular location. There is not a quantified value for the degree of ion

saturation necessary for Faraday probes in an EP plasma. Thus, it is

suggested that ion saturation is achieved when the change in

measured collector current is less than approximately 1% per volt of

collector bias. Applying this criterion to data in Fig. 10, ion saturation

is achieved for an approximately −20 V bias on the collector and

guard ring with respect to test facility ground. This value is consistent

with bias voltage typically used in far-field measurements, which

range from −10 to −30 V. Typically, the least negative bias voltage

necessary to achieve ion saturation throughout the far-field plume

should be used. In near-field measurements, there can be a large

variation in bias voltage required for ion saturation, and interactions

between the plasma and thruster surfaces can introduce large

variations in floating potential. A Faraday probe bias voltage as low

as −100 V may be necessary to enter the ion saturation regime at the

closest approach to the thruster [45]. Since the bias voltage can vary

greatly depending on distance from the thruster and thruster

operating condition, a variable bias voltage may be used. If a fixed

Faraday probe bias voltage is used at all locations, local Langmuir

probe plasma measurements may inform whether collector sheath

expansion is impacting Faraday probe measured current.

The wide range of plasma conditions in the EP plume necessitate

careful e v aluation of collected ion current due to ambient plasma and the

collector plasma sheath. The Bohm sheath criterion is used to calculate

the probe ion current (also called the Bohm current [6]) in Eq. (3), where

the thin-sheath assessment is applicable (R

> 10λ

)[58]:

Bohm

 e

−1



(3)

The Bohm current density j

Bohm

is evaluated for n and T

at the edge

of the presheath. It is expected to increase for elev ated background

pressure; thus, the Faraday probe would measure an artificially high ion

current density. If the ratio of R

∕λ

is less than 50, the collector sheath

will expand as an oblate ellipsoid and increase the effective ion

collection area [59,60]. Note that the ou ter diameter of the biased

surface is suitable for e v aluation of sheath expansion; thus, probe radius

is equal to the guard ring outer radius or else R

is equivalent to R

no guard ring is used. Probe sheath expansion is most likely to arise for a

small probe radius on the plume periphery at low background pressure,

where the plasma density is lowest. T rends in j

Bohm

and R

∕λ

are

ev aluated in Fig. 11 over a range of typical plasma properties, where

 20 mm.InFig.11,j

Bohm

shows significant va riation over the

range of plasma density from 10

to 10

−3

but minor sensitivity to

electron temperature from 0.5 to 3 eV. For a typical Faraday probe radius

of 20 mm in 3 eV plasma conditions, the thin-sheath assessment is not

applicable (i.e., R

∕λ

< 50) at pressure less than approximately

−3

(in Fig. 11); thus, collector sheath expansion may be an issue

at these local plasma conditions. In cases where R

∕λ

is less than 50,

the trends in ion Bohm current may deviate from Eq. (3), as identified

with the black circles on lines of j

Bohm

in Fig. 11 for R

 20 mm .The

other issue identified in Fig. 11 is ele v ated ion Bohm current density at

high plasma density, which may be a nonnegligible fraction of the ion

beam current. Ideally, j

Bohm

should be less than 1% of the measured ion

current density. Issues associated with probe sheath expansion and

Bohm current collection may have impacted data in Secs. V.B and V.E,

and they will be identified. To evaluate these issues and reduce

measurement error, Langmuir probe measurements of local plasma

density and electron temperature near the Faraday probe may be used to

quantify the effects.

In general, the high-energy flux of EP plasma plumes generates a

harsh environment for plasma diagnostics, the thruster, and other

exposed surfaces in the test or operational space environment. Probe

surfaces with long-duration exposure to beam ions may undergo

degradation through sputtering and subsequent deposition of nearby

materials. This could impact the probe collection area, collector

surface properties, or electrical characteristics of the probe. Thus, it is

recommended to conduct visual inspection and electrical verification

of the Faraday probe at the beginning and end of a test campaign, or if

there is a change in measurement repeatability over time.

In addition to surface degradation, ions transfer a significant

fraction of their energy upon probe impact, leading to elevated

temperatures of the probe, associated support structure, and wiring.

For modern HET and GIT designs of moderate power (less than

5 kW), the maximum ion current density in the near-field is typically

less than 250 mA∕cm

for HETs and less than 10 mA∕cm

for GITs

[21,44,54,61]. For a beam where each ion deposits 400 eV, the

corresponding maximum energy flux is typically less than

100 W∕cm

for HETs and less than 4W∕cm

for GITs. Since

plasma diagnostics for EP plumes rarely have active cooling, the

principal means of heat rejection is radiation and passive thermal

conduction through the probe support structure. In the worst-case

estimate of heating with no thermal conduction, the collector radiated

power per unit area is calculated with the Stefan–Boltzmann relation

as εσ

, where T

is surface temperature [62]. For a molybdenum

collector at 1000 K, the radiated power is approximately 0.6 to

1.8 W∕cm

for a polished surface (ε  0.10) or roughened surface

(ε  0.31), respectively [62]. This is significantly lower than the

high-energy flux conditions of HETs (less than 100 W∕cm

) and

GITs (less than 40 W∕cm

) described previously; therefore, probe

heating is expected unless there is sufficient thermal conduction in

the probe apparatus. This will be further considered for higher-energy

density devices discussed in Sec. IX, including electromagnetic

propulsion concepts.

In plume regions with high-energy flux, probe heating may

introduce additional measurement error. Thermionic emission

current density may be estimated with the Richardson–Dushman

0.0

0.2

0.4

0.6

0.8

1.0

-25-20-15-10-50

Normalized Colllected Current (-)

Bias Voltage to Chamber Ground (V)

90 deg

60 deg

30 deg

0 deg

Fig. 10 Normalized Faraday probe collector current in the plume of a

200 W HET at R  50 cm.

100

Plasma Density (m

-3

)

Ion Bohm Current Density (mA/cm

)

-1

Probe Radius / Debye Length (-)

Thin

Sheath

-2

-3

-4

-5

Bohm

0.5 eV

1 eV

3 eV

/ λ

0.5 eV

1 eV

3 eV

Fig. 11 Trends in ion Bohm current density and ratio of probe radius

 20 mm) to Debye length.

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equation in Eq. (4), where φ is the material work function and the

parameter A

is specific to material and surface properties (based on

the theoretical Richardson constant) [63]:

 A

−φ

(4)

The Richardson–Dushman equation is valid for surfaces in zero or

weak electric fields. Past measurements of the region surrounding a

nude Faraday probe in the far-field HET plume revealed local electric

fields were less than approximately 100 V∕m [19], and Eq. (4) is

suitable in these plasma conditions. Measurements in regions of high

electric field strength may be susceptible to field enhanced thermionic

emission, also known as the Schottky effect, and may require a

modified version of the Richardson–Dushman equation [64]. A

thermionic emission current less than 1% of the Faraday probe

collected current is recommended, and the maximum collector

temperature may be estimated accordingly for each experiment. For

example, a far-field measurement with an ion current density of

0.01 mA∕cm

on the plume periphery would correspond to a

maximum collector temperature of ∼1500 K for thermionic emission

less than 10

−4

mA∕cm

, based on Eq. (4) for a pure tungsten surface

where A

 60 A∕cm

· K

 and φ  4.52 eV [65,66]. Note that

Eq. (4) is sensitive to φ, which may have a significant error due surface

characteristics, such as adsorption of contaminants on the surface [67].

Since the collector surface material properties are typically not well

defined, the collector temperature may be monitored with a

thermocouple to enable qualitative analysis of thermionic emission.

This may also set allowable limits for collector temperature and inform

probe positioning speed through the plume. For example, a collector

temperature less than 700 K would maintain thermionic emission

below 10

−4

mA∕cm

, even if surface contamination was suspected of

lowering the work function to φ  2eV.

In the absence of collector temperature measurements, the effects

of probe heating and measurement drift are often considered by

consecutive measurements in opposite sweep directions. The user

may determine whether discrepancies between scans are acceptable.

For example, a past study showed Faraday probe measurements

unaffected by probe heating yielded repeatable profiles of collected

current density to within 2% [18]. In the event ion current density

profiles are not repeatable, experience measurement drift, or the

measurement exhibits sensitivity to sweep direction, further

assessment of the cause is necessary, as this could be associated

with effects not related to the Faraday probe, such as thruster

construction, experimental misalignment, and plasma dynamics or

perturbations.

C. Far-Field Spatial Range and Resolution

When using the hemispherical coordinate system for far-field

plume measurements, the angular sweep should be performed in a

single plane from θ  0 to 90 deg at constant R and fixed Φ (i.e.,

Φ  0 deg), according to Fig. 7a. Faraday probe sweeps should also

be conducted from θ  0 to 90 deg at fixed Φ for the opposite side of

the plume (i.e., Φ  180 deg), such that a continuous measurement

is taken from θ 90 deg at fixed R, as shown in Fig. 7b, to assess

plume symmetry. Asymmetry in the plume may arise due to thruster

misalignment with respect to the coordinate geometry, probe

positioning misalignment, or an asymmetric feature of the thruster,

such as external cathode placement or a mechanical misalignment in

thruster assembly. If significant asymmetry in the plume is observed,

the cause and the impact on measurement uncertainty should be

evaluated.

The plume periphery beyond θ  90 deg may be evaluated to

characterize particle scattering, although data are more susceptible to

facility effects and may influence calculations of total ion beam

current and divergence. Angular measurement resolution should be

less than or equal to 2 deg, and less than 1 deg is recommended. In

addition, the Faraday probe should be sized such that the ratio of

probe collector diameter to measurement radius is less than the

angular resolution (i.e., 2R

∕R ≤ dθ ≤ 2 deg). Thus, for a

measurement resolution of 1 deg at a measurement distance of

100 cm, the probe collector diameter should be less than 1.7 cm.

A distance greater than four TDD should be used for far-field

Faraday probe measurements employing the hemispherical coor-

dinate system. This is necessary based on the assumption of an

axisymmetric hemispherical coordinate system with a point source

origin, where approximating the plasma discharge as a point source is

a poor assumption for measurement distances closer than four TDD

[18]. Further discussion on the systematic spatial measurement error

and analytical corrections are provided in Sec. V.B.

D. Near-Field Spatial Range and Resolution

When using the cylindrical coordinate system for near-field

measurements, the Faraday probe radial sweep should be performed

at constant axial distance Z and fixed Φ (e.g., Φ  0 deg), as shown

in Fig. 8. The radial measurement range should extend to the location

where measured ion current density is less than 0.2% of the maximum

current density along the radial profile at fixed Z. This range enables a

0.2% threshold-based integration limit, and it is recommended based

on past experiments [45]. Faraday probe sweeps should also be

conducted at fixed Φ for the opposite side of the plume (i.e.,

Φ  180 deg), such that a continuous radial sweep is taken to less

than 0.2% of the maximum current density value for the left side

(r>0) and right side (r < 0), as shown in Fig. 8b, in order to assess

plume symmetry. Multiple axial measurement distances may be

evaluated for near-field plume asymmetry. Measurement resolution

in the radial coordinate should be less than 0.01D

between

measurement locations, where the best resolution is limited by the

probe collector diameter 2R

. In the event this criterion is not

practical for small thruster designs or for suitable probe signal

strength, the probe collector diameter may be minimized to approach

the 0.01D

criteria and the radial distance between measurements

may be less than 1 mm (i.e., 2R

≤ dr ≤ 0.01D

or ≤ 1mm,

whichever is greater).

The near-field HET plume should be analyzed at axial distances

upstream of the plume merging region, termed the “transitional

region” in [54], where ion beams from opposing sides of the channel

merge. Past near-field studies of multiple HET designs found this

transitional region was approximately 0.5 to 1.0 TDD [44,45,54].

Axial distances less than 0.2 TDD are not recommended due to

ionization and acceleration processes that may occur downstream of

the HET exit plane, and they have been shown to be influenced by

background pressure [68]. In addition, distances within 0.2 TDD of

the HET body may perturb discharge plasma behavior or encounter

plasma floating potentials on the order of the Faraday probe bias

potential, such that the probe is not electron repelling and may be

susceptible to sheath effects [54]. It should be noted that regions of

plume merging, probe perturbation, and issues due to collector sheaths

or ion Bohm current may vary with thruster design, operating condi-

tions, and background environment. Thus, the spatial measurement

and analysis range should be evaluated for each experiment, and this

will be further discussed in Secs. V.C and V.E. In many cases, these

issues are mitigated by avoiding plume regions where the issues are

present (i.e., plume merging, probe perturbation) or addressed by

monitoring thruster discharge telemetry, described in Sec. IV.A.

Near-field measurements of GIT plumes can be made at distances

as close as a few millimeters downstream of the ion optics. Such

measurements can be used to study individual beamlets. Near-field

measurements of the NASA Evolutionary Xenon Thruster (NEXT)

plume revealed beamlets merged within 0.1D

downstream of the

exit [21]. In NEXT investigations, the very near-field Faraday probe

measurements revealed beamlet merging was a viable indicator of

far-field plume divergence. However, the actual location of beamlet

merging is in large part a function of the ion optics geometry. For

example, investigations of the High Power Electric Propulsion

(HiPEP) ion thruster, which has flat rectangular ion optics apertures

(40 by 90 cm), measured individual beamlets as far as 13 cm

downstream of the grids, which was approximately 36% of the grid

width (analogous to 0.36 D

) [69]. To accurately interrogate the

region upstream of beamlet merging in GITs, a small Faraday probe

590 BROWN ET AL.

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collector diameter less than the grid aperture spacing is required and a

high radial measurement resolution is necessary to resolve beamlet

ion current density profiles. Systematic evaluation of different

thrusters and examination of facility interactions in the very near-field

of GITs is recommended to establish a minimum measurement

distance. The maximum near-field distance for GITs is likely limited

by the radial measurement range required to capture a significant

fraction of beam ions, where proximity to facility walls may be a

factor. Thus, the spatial measurement range should be evaluated for

each GIT experiment.

E. Characterization of Facility Effects

Facility pressure effects associated with background neutral

particles are inherent in ground-based EP plumes, and they are

unavoidable in both near-field and far-field plume measurements.

The following guidelines are based on experiments with multiple

thrusters at multiple facilities. Although understanding of facility

effects on the near-field plume region is limited, many of the same

plasma interactions known to impact far-field measurements are

expected, as described in Sec. II.B. Thus, recommendations for near-

field measurements are primarily derived from the current state of

knowledge for far-field Faraday probe measurements.

Faraday probe measurements of the far-field and near-field plumes

should be conducted at a minimum of four distances. Further, plume

measurements at each distance should be conducted at a minimum of

four background pressures to enable the extrapolation to spacelike

conditions from ground testing, and they should adhere to

recommendations in [57]. One of the four background pressures

should be the lowest achievable facility pressure during thruster

operation. Background pressure variation is often achieved by

injecting additional propellant gas into the ground test facility or

varying the facility pumping. The maximum background pressure is

typically less than 5.0 × 10

−5

torr-Xe; however, this value may vary

with thruster technology, operating condition, and facility pumping

capability. In HETs, the facility background pressure may influence

thruster operating mode and stability, which is caused by the

additional neutral density near the thruster plasma that is not present

on orbit [70,71]. This behavior has been observed in HETs and may

be identified by a large change in discharge oscillation behavior or

time-averaged discharge current, voltage, or mass flow rate [72,73].

Significant changes in HET operation may invalidate the pressure

characterization for Faraday probe measurements; therefore, the

thruster should be monitored for large changes in operation, as

described in Sec. IV.A.

In GITs, the influence of background pressure is evident from the

accelerator grid current. In the space environment, the accelerator

grid current is primarily associated with collection of low-energy ions

generated from CEX collisions between beam ions and the non-

ionized thruster neutrals that escape through the ion optic grids [23].

The elevated pressure in ground testing introduces additional CEX

collisions, and thereby increases GIT accelerator grid current that is

not present in flight conditions; the increased GIT accelerator grid

current indicates increased CEX ions impinging the grid, which

cause significant erosion and eventually form holes through the

accelerator grid webbing. At high propellant utilization of ∼90%, the

space equivalent accelerator grid current ranges between 0.25 to

0.5% of the total beam current over a range of operating conditions, as

shown in Fig. 12 for the NASA Solar Technology Application

Readiness (NSTAR) ion thruster on the Deep Space One (DS1)

Mission and in ground test facilities [74,75]. In general, the ratio of

accelerator grid current relative to thruster beam current decreases

with decreasing chamber pressure, as shown in Fig. 13 for a 30 cm

GIT at 3.2 A beam current in ground tests at NASA Glenn Research

Center (GRC) and Jet Propulsion Laboratory (JPL) [76]. This

variation can be used as guidance to determine the maximum facility

background pressure used in pressure characterization of GIT

plumes. Although a maximum allowable ratio of accelerator grid

current to total beam current has not been determined, it is expected to

be less than a few percent and may be determined by the user.

Without predictive capability of facility pressure effects on the

thruster and on the Faraday probe, the systematic error cannot be

determined a priori. Different facility interactions may dominate in

different regions of the plume; thus, plume characterization with

distance and pressure is considered the best approach to quantify

spatial variation in plume properties and probe behavior; systematic

errors are not easily quantified through data postprocessing or

generalized analysis. Plume characterizations over a range of

measurement distances and background pressures are recommended

to resolve nonlinear trends, as will be shown for experiments with a

200 W HET in Sec. V.E. Additional measurement distances, lower

facility background pressure, and characterizations at additional

pressures will improve corrections for facility interactions and

predictions of the space environment.

Qualitative assessment of the plasma profile may be conducted at a

single measurement distance or pressure, which limits the application

to thruster-to-thruster comparisons of the same model (i.e., acceptance

testing) or over the course of an extended firing (i.e., life test). A single

Faraday probe measurement should not be used to quantify ion beam

current or plume divergence losses in performance. Further, using a

single Faraday probe measurement should be avoided for plume

predictions of the space environment, comparisons between facilities,

or validation data for computational simulations.

V. Data Analysis

A. Ion Current Density

For a Faraday probe collector in ion saturation, the ion charge flux

or ion current density j is calculated as

j 

e 

 κ

SEE

(5)

where Γ is the local ion flux of the k th species, Z

is the ion charge

state, A

is the cross-sectional geometric area of the collector face

0.0

1.0

2.0

3.0

4.0

5.0

0.4 0.6 0.8 1.0 1.2 1.4 1.6

Beam Current (A)

Accelerator Grid Current (mA)

Ground Test, VF 5 at NASA GRC

Ground Test, 10 ft Chamber at JPL

DS1 Flight, 0-432 h

DS1 Flight, 432-14200 h

Markers = Data

Lines = Best Fit

Fig. 12 Accelerator grid current of the NSTAR GIT, recreated from [74].

0.0

0.5

1.0

1.5

2.0

Background Pressure (torr-Xe)

Accelerator Grid Current (mA)

-4

-5

-6

Accelerator Grid Current / Beam Current (%)

GRC 890 h

life test

Curve-Fit to

GRC Data

JPL Data

Fig. 13 Accelerator grid current of a 30 cm GIT, recreated from [76].

BROWN ET AL. 591

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 πR

), κ

is a correction for ions collected in the gap between

collector and guard ring, and κ

SEE

is a correction for SEE at the

collector surface. The collected ion current I

is a point

measurement by the Faraday probe at (θ, R) for hemispherical

coordinates as shown in Fig. 7 or at (r, Z) for cylindrical coordinates

in Fig. 8. The correction factors are calculated as

 πR

-R





2πR

 2πR



(6)

SEE



1 

(7)

where γ

is the SEE yield from the kth ion species; Ω

is the ion

current fraction of the kth species; and the parameters R

, R

, h

and h

are collector and guard ring dimensions for a typical nude

Faraday probe configuration, as shown in Fig. 14.

Past experiments demonstrated ions entering the gap between the

Faraday probe collector and guard ring are a nonnegligible fraction of

the measured collector current [77]. The effect is illustrated in Fig. 14,

where the effective cross-sectional ion collection area is the sum of A

and κ

. The correction κ

in Eq. (6) is formulated based on the

assumption that ions entering the gap volume will be collected by

exposed, conductive walls and distributed between the collector and

guard ring based on relative wall surface areas. Laboratory studies have

shown the assumption is suitable for probes with a nonconducting

material at the base of the gap, such as ceramic. Ions entering the gap in

probes with a conductiv e base are preferentially collected by this line-

of-sight surface, and the current collected on the sidewalls becomes

sensitive to changes in background pressure [77]. The conductive gap

base raises issues for facility characterizations, and it is discussed with

respect to probe design considerations in Sec. VII.

Although the Faraday probe collector is typically made of low SEE

yield material, such as molybdenum or tungsten, SEE has a

nonnegligible effect on measured ion current. Secondary electrons

born on the negatively biased collector surface will accelerate away

from the probe, which artificially increases measured current. The

correction κ

SEE

formulated in Eq. (7) accounts for the effect, and it

may be calculated using the SEE yield values in Table 1 [78–80].

Tungsten and molybdenum SEE yields in Table 1 were averaged for

xenon ion bombardment over the energy range of 100–1000 V, where

measured yields varied by less than 20% for Xe



bombardment and

less than 10% for Xe

2

and Xe

3

bombardment. Note the

molybdenum SEE yield for Xe

3

ion bombardment is unavailable in

the literature, and it is estimated in Table 1 based on trends observed

for tungsten. Calculation of κ

SEE

in Eq. (7) requires knowledge of the

ion species composition, which may be measured using analysis

techniques for ExB probes (also known as Wien filters) developed in

[81]. The effect of κ

SEE

is small but nonnegligible for the ion species

compositions of typical HET and GIT plumes; the value of κ

SEE

greater than 0.95 for typical EP plumes and greater than 0.90 if the



ion current fraction is reduced to 60%. Thus, not correcting

measurements with κ

SEE

may lead to overprediction of local ion

current density by 5 to 10%, and it should be accounted for in the data

analysis and/or error assessment. However, the spatial variation of

ion species composition in the central plume is not expected to have

a significant effect on the value of κ

SEE

; therefore, a single

measurement of ion species current fraction in the central core is

sufficient to calculate κ

SEE

[82] for evaluation of ion beam current and

divergence. The population of multiply charged ions may increase

beyond the central core; thus, it is advised to incorporate local values

of ion species current composition in evaluations of local spacecraft

plume interactions on the plume periphery.

B. Far-Field Plume

Far-field test methodologies described in Sec. IV.C provide the

necessary characterization to isolate pressure effects and predict

time-averaged ion current density properties in the space vacuum

environment. This is achieved by simple linear regression [83] of ion

current density as a function of pressure at each location in the plume,

as exemplified by far-field measurements of the H6 HET plume in

Fig. 15. The linear extrapolations of ion current density to vacuum

conditions in Fig. 15 reveal regions where the linear regression slope

is positive, negative, and near zero. In this paper, a positive slope

refers to an increase of ion current density with increasing pressure,

such as θ  0, 30, 40, and 90 deg in Fig. 15. A negative slope refers to

a decrease of ion current density with increasing pressure, such as

θ  3 and 15 deg. A linear regression slope near zero, such as θ  1

and 24 deg, occurs in regions when the extrapolation to zero pressure

transitions between positive and negative linear regression slope. The

coefficient of determination, termed R-squared (no relation to radial

measurement distance R), for each linear extrapolation is calculated

as the square of the Pearson product moment correlation coefficient,

and it can be interpreted as a metric for how well the linear regression

fits the data [83]. The R-squared term ranges from zero to one, where

a value of unity indicates a perfect fit. Although the linear regression

slope is near zero in the transition region and is associated with low

coefficient of determination, there is minimal change in ion current

density as a function of background pressure, and thus the correction

is small. The method of extrapolating ion current density to zero

pressure conditions has been conducted with multiple HETs at

different facilities [18,70,84–86]. Based on the far-field plume

processes involved, GIT plumes are expected to follow similar trends.

Collector

Ceramic

Guard

ring

Ions to collector face

= Cross-Sectional area

Ions to guard ring face

Ions to guard ring Sidewall

Ions to collector Sidewall

= effective Cross-Sectional collection area

Fig. 14 Illustration of ions collected by the sidewalls of the Faraday

probe and the effective increase in cross-sectional ion collection area.

Table 1 Summary of SEE yield for xenon ion

bombardment of Faraday probe collector materials [78–80]

Bombarding particle ion

charge state Z

SEE yield of

molybdenum γ

SEE yield of

tungsten γ

1 0.022 0.016

2 0.20 0.20

3 0.70

0.71

SEE yield unavailable in literature; value estimated based on measured

yield for tungsten.

592 BROWN ET AL.

Downloaded by GEORGIA INST OF TECHNOLOGY on January 19, 2018 | http://arc.aiaa.org | DOI: 10.2514/1.B35696

In Fig. 16, angular profiles of far-field ion current density in the H6

HET plume reveal background pressure effects and show the ion

current density linear regression to vacuum conditions at each

angular location, based on the method shown in Fig. 15. At the plume

periphery in Fig. 16, a difference in ion current density greater than

one order of magnitude between low-pressure measurements and

extrapolated vacuum conditions is consistent with comparison of

flight and ground data for the SPT-100 on the Express Satellite

[33,34,42]. It should be noted that the linear regression to zero

pressure does not arbitrarily force the extrapolated ion current density

to zero at θ  90 deg. The primary sources of error, unrelated to

facility effects, in H6 HET results in Figs. 15 and 16 were accounted

for, including the effective probe collection area and collector SEE.

The effective collection area was determined using Eq. (6), where κ

increased the collection area by 13%. The thruster plume was

approximately 90% Xe



and κ

SEE

 0.97 as calculated from Eq. (7).

Thus, facility effects were the principal source of error, which is the

motivation for facility pressure characterization. Remaining errors

were expected to be minimal with respect to the trends in Figs. 15

and 16.

Figure 17 displays the angular distribution of the linear regression

slope and coefficient of determination of the H6 thruster operating at

120, 150, and 300 V with 10 mg/s anode flow and 7% cathode flow.

The linear regression slope at thruster centerline decreased from

15 A∕torr · cm

 at 150 V H6 HET operation to less than

3A∕torr · cm

 at 120 and 300 Voperation. All H6 HET operating

conditions showed reduction in ion current density with increasing

facility pressure within the central plume core at θ 25 deg,

where the linear regression slope approached −30 A∕torr · cm

 for

y = 7197.4x + 3.39

R² = 0.8723

y = -222.9x + 3.72

R² = 0.0033

y = -34082x + 4.38

R² = 0.9857

θ = 0°

θ = 1°

θ = 3°

Ion Current Density (mA/cm

)

4.5

4.2

3.9

3.6

3.3

3.0

Pressure (torr-xenon)

01x10

-5

2x10

-5

3x10

-5

4x10

-5

5x10

-5

y = 7197.4x + 3.39

R-Squared = 0.8723

y = -34,082x + 4.38

R-Squared = 0.9857

y = -222.9x + 3.72

R-Squared = 0.0033

y = 93.7x + 0.30

R² = 0.0582

y = 1925.1x + 0.12

R² = 0.9933

Ion Current Density (mA/cm

)

1.0

0.8

0.6

0.4

0.2

Pressure (torr-xenon)

01x10

-5

2x10

-5

3x10

-5

4x10

-5

5x10

-5

θ = 15°

θ = 24°

θ = 30°

y = -5535.6x + 0.89

R-Squared = 0.9560

y = 93.7x + 0.30

R-Squared = 0.0582

y = 1925.1x + 0.12

R-Squared = 0.9933

y = 1525.9x 0.0002

R² = 0.9981

y = 2949.8x + 0.04

R² = 0.9989

θ = 40°

θ = 90°

Ion Current Density (mA/cm

)

0.20

0.16

0.12

0.08

0.04

Pressure (torr-xenon)

01x10

-5

2x10

-5

3x10

-5

4x10

-5

5x10

-5

y = 2949.8x + 0.04

R-Squared = 0.9989

y = 1525.9x - 0.0002

R-Squared = 0.9981

Fig. 15 Ion current density at six TDD as a function of pressure for the

H6 HET at 300 V, 10 mg∕s anode flow, and 7% cathode flow.

0.0001

0.001

0.01

0.1

Ion Current Density, mA/cm

-90 -60 -30 0 30 60 90

Angular Position, deg

Extrapolation to Vacuum

9.1x10 torr

1.5x10 torr

1.9x10 torr

2.5x10 torr

3.0x10 torr

-6

-5

Ion Current Density (mA/cm

)

Angular Position (deg)

Fig. 16 Ion current density at six TDD as a function of angular position

for the H6 HET at 300 V, 10 mg∕s anode flow, and 7% cathode flow.

-50

-40

-30

-20

-10

Slope, A/torr-cm

-90 -60 -30 0 30 60 90

Angular Position, deg

0.0001

0.001

0.01

0.1

Residuals

Line Style Line Color

300V Slope

150V Residuals

120V

Slope (A/torr-cm

)

Angular Position (deg)

R-Squared (-)

R-Squared

Slope

Fig. 17 Linear regression slope and coefficient of determination of the

H6 HET ion current density at six TDD.

BROWN ET AL. 593

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the 300 V condition. The ion current density ranged from

approximately 1 to 3A∕torr · cm

 beyond θ 25 deg, which is

attributed to the net migration of scattered beam ions from the

primary ion beam. Although the angular features of the linear

regression slope in Fig. 17 are consistent across operating conditions

(i.e., positive on thruster centerline, negative in the central core, and

positive on the wings), the magnitude and shape are significantly

different, thereby revealing the importance of characterizing

background pressure interactions.

The linear regression of ion current density and extrapolation to zero

pressure are further demonstrated in Figs. 18 and 19 for a 200 W HET

[18]. In Fig. 18, ion current density profiles at 8 and 20 TDD show the

influence of background pressure varies with downstream distance and

pressure, where ion current density is normalized to the centerlinevalue

at eight TDD and 3.1 × 10

−6

torr-Xe. The effects are also evident in

Fig. 19, where a positive linear regression slope on the thruster

centerline is attributed to ingestion, ionization, and acceleration of

facility neutral particles within 10 deg. The region from 10 to

40 deg in Fig. 19 shows a negative linear regression slope. This

feature may be attributed to ion scattering when a slow ion, resulting

from a CEX collision event, is accelerated by radial electric fields in the

plume. The process leads to increased ion scattering to the plume

periphery beyond 40 deg from centerline and increased overall

divergence of the plasma plume.

The angular profiles of linear regression slope were decomposed

into contributions from facility neutral ingestion and ion scattering in

[18], and they enabled examination of the magnitude and angular

range of each effect to enhance evaluations of EP plume structure

with variation in pressure, downstream distance, or operating

condition. The consistent angular features in the linear regression

slope between different thrusters in Figs. 17 and 19 at multiple

operating conditions and at multiple downstream measurement

distances is evidence that the dominant facility effects are common

between the two thruster plumes. Note that ion scattering may be the

dominant effect on thruster centerline rather than facility neutral

ingestion effects, resulting in a net negative linear regression slope.

These results increase confidence that facility effects on the HET ion

beam can be effectively characterized and extrapolation of ion current

density to vacuum is suitable, given the thruster operation and

oscillations are not significantly altered with variation in facility

background pressure.

The far-field GIT beam also shows complex plume structure on the

periphery, as shown for the T5 GIT in Fig. 20 [87] at 11.8 m

downstream (

11.8 TDD) and 2 × 10

−6

torr-Xe. Similar structures

were observed on the NEXT thruster [21]. As discussed in Sec. V.D,

the integrated ion beam current from GIT Faraday probe

measurements is often greater than beam current measured by the

ion optics. This may be associated with not using corrections

described in Sec. V.A, such as κ

for the effective probe collection

area. To remedy this discrepancy and improve evaluation of GIT

beam divergence, a systematic investigation of the GIT far-field

plume and characterization with background pressure is warranted,

similar to investigations of the 200 W HET plume in Figs. 18 and 19.

The ion beam current of GITs and HETs is calculated from far-field

plume measurements of ion current density in Eq. (5) integrated over

the axisymmetric, hemispherical surface for the fixed sweep radius R:

Beam

 2πR

π∕2

jθ

sinθ dθ (8)

0.001

0.01

0.1

Normalized Current Density

Extrapolation to Vacuum

3.1x10 torr

1.0x10 torr

3.4x10 torr

-6

-5

8 TDD

20 TDD

-90 -60 -30 0 30 60 90

Normalized Ion Current Density (-)

Angular Position (deg)

Fig. 18 Normalized ion current density of a 200 W HET.

-5

-10 0.0001

0.001

0.01

0.1

Line Style Line Color

8 TDD Slope

12 TDD

16 TDD

20 TDD

-90 -60 -30 0 30 60 90

Slope (A/torr)

Angular Position (deg)

R-Squared (-)

R-Squared

Slope

Fig. 19 Linear regression slope and coefficient of determination of ion

current for a 200W HET.

-40-30-20-100 102030405060

-1

-2

-3

-4

-5

-6

-7

Angular Position (deg)

Ion Current Density (mA/cm

)

Fig. 20 Ion current density of the T5 GIT at 1.18 m downstream,

recreated from [87].

594

BROWN ET AL.

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Since Faraday probe plume measurements using hemispherical

coordinates are often conducted from θ  0 to 90 deg on both the left

and right sides of the plume in Fig. 7, the ion beam current in Eq. (8)

may be calculated for each side of the plume and averaged. Two

spatial correction factors, κ

and κ

, are introduced to account for

systematic error associated with the hemispherical coordinate

system, where measurements are with respect to a point source as

opposed to the thruster discharge geometry. The angular correction

factor κ

and the distance correction factor κ

are formulated by

approximating the thruster ions as originating from two point

sources, as shown in Fig. 21. These point sources are located on the

channel centerline at the exit plane of an annular HET in Fig. 21a. For

GIT geometry, the point sources may be located at the midpoint

between the GIT centerline and the outer diameter of the acceleration

grid, as shown in Fig. 21b. Although the spatial correction factors κ

and κ

will not eliminate the systematic error introduced with the

hemispherical coordinate system, the approximations serve to

quantify the effect and reduce measurement error.

The correction factor κ

accounts for variations in probe angle with

respect to the point sources, which affects the ion angle of incidence

to the probe face and changes with angular position and distance. In

addition, the ion angle of incidence is different for each point source.

An average cosine loss in probe collection area is defined in Eq. (9),

where the ion angles of incidence from the near- and far-point sources

are calculated in Eq. (10) as α

and α

, respectively. As shown in

Fig. 21, the angle α

refers to the ion angle of incidence from the near

source and will alternate from the left to right sides of the diagram in

Fig. 21 as the probe crosses thruster centerline. The width of the

plasma discharge is denoted w, which is the width of the channel in an

annular HET or w  D

∕2 in a GIT:

 cos



 α



(9)

N;F

θ;R;D





θ − tan

−1



sinθ∓

−w

cosθ



(10)

The correction κ

accounts for differences in path length from the

near- and far-point sources to the probe, which would introduce a

systematic error in the R

term in Eq. (8). Probe collector distances

from the near- and far-point sources are characterized as R

and R

respectively. Similar to the analysis of ion angle of incidence, the path

length will vary with probe angular position, and R

and R

will

alternate from the left to right sides of the diagram in Fig. 21 as the

probe crosses thruster centerline. The exception is on the thruster

centerline, where the distance from the probe to each point source is

equal and greater than R . Using the geometry in Fig. 21, κ

is defined

in Eq. (11) based on the lengths R

and R

, shown in Eq. (12):







(11)

N;F

θ;R;D







cosθ





sinθ∓

− w



(12)

The ratio of spatial correction factors (κ

∕κ

) is displayed for GITs

(w  0.5D

) and HETs (w  0.15D

) as a function of probe

angular position in Fig. 22 in terms TDD, calculated as R∕D

. The

value of w  0.15D

is a representative value for the HET channel

width; however, a smaller channel will further increase the ratio

(κ

∕κ

). The overall effect of κ

∕κ

is to increase current density in

the plume central core, where ion current density is greatest, and thus

the spatial corrections increase the calculated ion beam current in

Eq. (8). The variation in κ

∕κ

decreases rapidly with downstream

distance in the far-field, where the approximation of a point source

measurement improves for hemispherical coordinate system. In

Fig. 23, the correction on the thruster centerline shows the ratio of

∕κ

rapidly approaches unity with the downstream measurement

distance, and it is less than 1.02 for distances greater than four TDD.

The spatial corrections are valid for beam ions originating near the

exit plane. In addition, the correction only increases the ion source

model from one to two, and it does not directly account for the

accelerated ions across the full grid diameter or the channel width.

This is expected to have a small effect on far-field measurements

taken beyond four TDD, as evidenced by the comparison of w 

0.15D

and 0.50D

in Fig. 23. Although the corrections are

formulated assuming equal contribution of beam ions from each side

of the channel or grid, this should also not be a significant source of

error in the far-field plume.

The axial component of ion beam current is necessary for

calculations of beam divergence, as discussed in Sec. V.E, and is

formulated as

Axial

 2πR

π∕2

jθ

cosα

 sinθ dθ (13)

where the angle α

is introduced to calculate plume divergence with

respect to the channel centerline in HETs or the grid radius midpoint

in GITs as opposed to thruster centerline, as shown in Fig. 24 for HET

geometry. Although this approach has not been applied to GIT

plumes, the geometry will be equivalent to the grid radius midpoint of

w  0.5D

. If the GIT outer grid diameter or the HET outer channel

Probe

Channel Centerline

R cos(θ)

R sin(θ)

θ=90°

Φ=180°

θ=90°

Φ=0°

Thruster Centerline, θ = 0°

Probe

Outer Grid Diameter

R cos(θ)

R sin(θ)

θ=90°

Φ=180°

θ=90°

Φ=0°

Thruster Centerline, θ = 0°

Fig. 21 Measurement coordinate geometry showing probe distance

and angular location in a two-point source model for a) annular HET

geometry or b) GIT geometry.

BROWN ET AL. 595

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diameter is the preferred, then w  0. The parameter α

is calculated

as a piecewise function in Eq. (14):

θ;R;D





θ −α

 tan

−1



sinθ∓

−w

cosθ



for sin

−1



−w



≤ θ ≤ 90 deg

0 for 0 ≤ θ ≤ sin

−1



−w



(14)

With the axial and total ion beam current, the charge flux weighted

average cosine hcosθi

is calculated to determine an effective far-

field divergence angle λ [88].

λ  cos

−1

hcos θi

cos

−1



Axial

Beam



(15)

For Faraday probe plume measurements of the H6 HET in Figs. 16

and 17, the variation in thruster discharge current I

, I

Beam

, and I

Axial

are shown in Fig. 25. The pressure characterizations indicate these

plume properties increased by 10–20% compared to extrapolated

vacuum conditions and, if unaccounted for, would represent a

significant error in analysis of thruster divergence and utilization

efficiencies. The linear increase in I

and I

Axial

with increasing

background pressure is comparable in magnitude for all conditions,

and it is consistent with increasing facility neutral ingestion,

ionization, and acceleration. However, I

Beam

increased at a higher

rate than thruster discharge current with increasing pressure,

indicating I

Beam

was influenced by a facility interaction not related to

the thruster discharge. The I

Beam

trend in Fig. 25 may be influenced

by ionization of facility neutrals far downstream of the thruster

discharge, which would not increase I

. However, this is unlikely

because the electron-neutral ionization MFP is greater than 10

(for n>10

−3

, σ ∼ 10

−20

A more probable cause of the increased I

Beam

is associated with

Faraday probe collection of the Bohm current on the plume periphery,

described in Sec. IV.B. The Bohm current would have the greatest

influence in regions of low beam ion current density, which is

expected on the plume periphery. Although local plasma densities

and electron temperatures in the H6 HET plume are not known for

these Faraday probe measurements, plasma properties and variation

with pressure may be estimated based on models of a 4.5-kW-class

HET at 300 V discharge [89]. The model indicates local plasma

conditions at R  1m(approximately six TDD in the H6 HET) are

b)a)

1.00

1.02

1.04

1.06

1.08

1.10

0 153045607590

2 TDD

4 TDD

6 TDD

10 TDD

20 TDD

Ratio of Correction Factors,

(-)

Angular Position (deg)

1.00

1.02

1.04

1.06

1.08

1.10

0 153045607590

2 TDD

4 TDD

6 TDD

10 TDD

20 TDD

Ratio of Correction Factors,

(-)

Angular Position (deg)

Fig. 22 Combined correction factors (κ

∕κ

) for a) GIT with w  0.5D

and b) HET with w  0.15D

a) b)

1.00

1.05

1.10

1.15

0 3 6 9 12 15 18

Axial Position (TDD)

Ratio of Correction Factors,

(-)

1.00

1.05

1.10

1.15

0369121518

Axial Position (TDD)

Ratio of Correction Factors,

(-)

Fig. 23 Combined correction factors (κ

∕κ

) on thruster centerline for a) GIT with w  0.5D

and b) HET with w  0.15D

Probe

R cos(

)

R sin(

)

=90°

=0°

=90°

Φ=180°

Thruster Centerline,

= 0°

Channel Centerline (HET) or

Grid Radius Midpoint (GIT),

= sin

-1

((D

- w)/2R)

Fig. 24 Diagram of plume divergence with respect to channel centerline

for a two-point source model.

596

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approximately 1.2 to 1.6 eV and 10

to 10

−3

on the plume

periphery over a range of high background pressure conditions

comparable to the H6 HET measurements in Figs. 16 and 17. Based

on Eq. (3), j

Bohm

would be 0.001 − 0.1 mA∕cm

, which may be a

significant fraction of the measured ion current density on the plume

periphery beyond approximately 30 deg from centerline in

Fig. 16. Confirming this cause for increased I

Beam

with increasing

background pressure requires experimental data, such as local

Langmuir probe measurements of plasma density and electron

temperature to subtract j

Bohm

from Faraday probe measurements.

These trends are further examined in Sec. V.E with respect to the

beam divergence and thruster utilization efficiencies.

C. Near-Field Hall Thruster Plume

A systematic investigation of facility interactions on the near-field

HET ion current density has not been conducted, though there are

several Faraday probe studies on the spatial variation of ion current

density in this region for multiple HET technologies [7,41,44,45,90].

Characterization of the near-field HET plume at multiple background

pressures is recommended to enable extrapolation of ion current

density to zero pressure, similar to the linear regression of far-field

ion current density in Sec. V.B.

The near-field ion current density measurements from four HET

designs are shown in Fig. 26, with thruster operation ranging from 2

to 50 kW. This includes the NASA-457Mv2 at 500 V∕50 kW [54] in

Fig. 26a, the NASA-300M at 500 V∕20 kW [54] in Fig. 26b, the H6

at 300 V∕6kW [44] in Fig. 26c, and the NASA-173Mv2 at

500 V∕2.2 kW [41] in Fig. 26d. These near-field measurements

illustrate features common to the annular HET designs, and they

range from less than 0.1 TDD to beyond two TDD. For all four

thruster designs, the plume merges at approximately 0.5–1.0 TDD.

Downstream of the transitional region of plume merging, the plume

interactions are complex and complicate data analysis. Negative

collected current near the thruster was observed in Fig. 26d near

100 mm radial distance and 25 mm downstream of the exit. The

negative current was attributed to a region of reduced plasma

potential where the electrons were 5–10 eV; thus, the probe bias

potential was insufficient to achieve ion saturation [41]. Although a

more negative bias may mitigate the effect, it may also affect probe

sheath expansion and induce thruster perturbations. These issues

were minimal at greater than 0.2 TDD in Figs. 26b and 26d. In these

studies, the recommended near-field measurement range would

extend from 0.2 to 0.5 TDD downstream of the thruster exit. Near-

field HET plume measurements outside of this range may be

desirable for model validation and investigation of ion acceleration

processes or the transition region; however, the probe perturbations,

sheath effects, and plume merging effects should be addressed.

A common HET feature is the region of high ion current density on

thruster centerline, which is often visually observed and described as

the “center spike” or “dovetail” [72]. This is evident in Fig. 26 for all

thrusters upstream of the region of beam merging, including those

with a centrally mounted cathode or external cathode configuration.

The center spike contains beam ions, whereas the cathode plume does

not. As stated in Sec. III.B, in the case of an externally mounted

cathode, the recommended approach is to sweep the Faraday probe in

a plane orthogonal to the plane containing the cathode. In the case of a

centrally mounted cathode, the recommended approach is to remove

the contributions of the cathode plume from the Faraday probe

results, as shown in Appendix B.

The total ion beam current from near-field plume measurements of

ion current density is calculated with Eq. (5) for a fixed downstream

distance Z, written as

Beam

 2π

∞

jrr dr (16)

Note the measured ion current density jr in near-field

measurements is simply the axial component of current density;

therefore, I

Beam

 I

Axial

as the radial integration limit approaches

infinity. In contrast to Eq. (8) used for the hemispherical coordinate

system, no correction factors associated with coordinate system

geometry are necessary in Eq. (16). Since near-field Faraday

probe measurements are t ypically conducted across the entire

thruster, the ion beam current in Eq. (16) may be calculated for each

side of the plume and averaged. The radial integra tion in Eq. (16) is

limited in practice by low signal strength and probe proximity to the

facility walls. A 0.2% t hreshold-based integration limit may be

used, as described in Sec. IV.D. The integrated ion beam current is

sensitive to integration limit; therefore, it is recommended to

characterize I

Beam

as a function of the integration limit [45] and

correlate the results to far-fiel d Faraday probe results or assess with

a thruster efficiency analysis [45,88], if resources allow. The

recommended radial span of 1.5D

from thruster centerline was

sufficient for the 0.2% threshold- based limit from 0.2 to 0.5 TDD in

Fig. 26b.

Evaluation of HET beam divergence from near-field Faraday

probe data is complicated by the proximity to the thruster exit plane,

since the ion current point of origin cannot be assumed at the channel

midpoint or outer channel diameter, nor emanating from the exit

plane. Although the bulk HET plasma is directed along the firing axis,

the local plasma jet from the annular channel may be traveling toward

or away from the thruster centerline. The iterative path-finding

method may be used to determine the effective origin of the plasma

plume within the channel, and thereby used as a reference for ion

beam divergence. The points of origin from each side of the HET

channel are illustrated as a two-dimensional channel cross section in

Fig. 27, where the variables θ

and δ

are the travel angle and

divergence angle of the jet, and r

and z

are the radial and axial

coordinates of the jet point of origin, respectively.

The iterative path-finding method starts with the assumption that

the near-field annular HET plasma plume can be treated as a free-

expanding jet, such that the travel and divergence angles do not

change as a function of axial distance downstream. Based on past

experiments, this assumption was only valid downstream of the

evolving jet structure (greater than 0.2 TDD) and the region upstream

of merging beams from opposite sides of the annular channel (less

than 0.5 TDD) [45].

The iterative path-finding method iterates between two calculation

steps. In the first step, an initial estimate of the point of origin is

applied to expressions of the travel angle in Eq. (17) and the

divergence angle in Eq. (18):

tanθ



2π

∞

jr; z

r−r

z−z

r dr

2π

∞

jr; zr dr

(17)

Current (A)

Pressure (torr-xenon)

0 1 2 3x10

-5

Beam

Axial

300 V 300 V 300 V

150 V 150 V 150 V

120 V 120 V 120 V

Fig. 25 Plume properties of the H6 HET at six TDD.

BROWN ET AL. 597

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cosδ



2π

∞

jr; z cos



tan

−1



r−r

z−z



− θ

r dr



2π

∞

jr; zr dr

(18)

In contrast to the expression for ion beam current in Eq. (16), the

iterative path-finding method in Eqs. (17) and (18) is generally

insensitive to changes in the choice of integration limit.

In the second step, variations in the travel and divergence angles

with axial distance are used to compute the error metrics and update

the point of origin location on each side of the plume. Equations (19)

and (20) are feedback equations that are used to update the point of

origin and may be reinserted into Eqs. (17) and (18). Equations (21)

and (22) are the error metrics for radial and axial coordinates,

respectively:

0;m1

 r

0;m

− β

sin



0;m−1

− r

0;m

θ;m−1

− E

θ;m



θ;m

(19)

0;m1

 z

0;m

− β

sin



0;m−1

− z

0;m

δ;m−1

− E

δ;m



δ;m

(20)





θ

−







1∕4

(21)





δ

−







1∕4

(22)

Point of Origin

Thruster Centerline, r=0

Fig. 27 Illustration of free-expanding jet emanating from the

axisymmetric annular HET channel.

b)a)

d)c)

-1.0

-0.5

0.0

0.5

1.0

00.511.52

Radial Distance from Centerline (r/D

)

Axial Distance from Exit Plane (z/D

)

Ion Current Density, mA/cm

150

100

-1.0

-0.5

0.0

0.5

1.0

00.511.52

Radial Distance from Centerline (r/D

)

Axial Distance from Exit Plane (z/D

)

Ion Current Density, mA/cm

150

100

0.0

0.5

1.0

1.5

2.0

012345

Ion Current Density, mA/cm

200

2052

Radial Distance from Centerline (

r/D

)

Axial Distance from Exit Plane (

z/D

)

20 mg/s

Fig. 26 Ion current density measurements of the a) NASA-457Mv2 [54], b) NASA-300M [54], c) H6 [44], and d) NASA-173Mv2 [41] HETs.

598

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where the subscript m indicates the mth iteration, β

and β

are tuning

parameters to control the speed of convergence, E

θ;m

is the error

metric of the travel angle, E

δ;m

is the error metric of the divergence

angle,



is the mean travel angle,



is the mean divergence angle,

and N is the number of axial positions over which the angles were

calculated. This process is typically repeated on both sides of the

measurement sweep, for r greater than zero and r less than zero.

Convergence of the iterative path-finding method for the point of

origin within the channel is shown for the NASA-300M operating at

500 V, 20 kW in Fig. 28 [45], where the black lines represent the

origin for the jet in the channel for r greater than zero and the red lines

represent the opposite channel where r is less than zero [45]. The

corresponding integrated total ion beam current, travel angles, and

divergence angles are shown in Fig. 29, where dashed vertical lines

indicate the boundaries of the jet analysis zone for near-field plume

[45]. Although this dataset extends beyond the defined near-field

plume, the expansive range shows the variation in parameters outside

of the 0.2–0.5 TDD region. The trends were consistent for near-

field Faraday probe measurements over a wide range of operating

conditions for the both NASA-300M and NASA-457Mv2

HETs [45].

To calculate the overall beam divergence angle as a global plume

parameter of annular HETs, the jet momentum is assumed to be

decomposed into the momenta of two collimated beams from the

channel. The beams each carry half of the momentum of the

associated jet and radiate outward from the jet travel angle at plus/

minus the jet divergence angle, as shown in Fig. 27. This approach is

represented mathematically in Eq. (23):

δ 

jθ

 δ

jjθ

− δ

(23)

For Faraday probe sweeps across the channel, the divergence angle

should be averaged from each side of the thruster, where r is greater

than zero and r is less than zero. The near-field HET divergence half-

angle δ is suitable for evaluation of thrust loss, and ideally is

equivalent to the effective far-field divergence angle λ. The HET

beam divergence using the iterative path-finding method was

compared to evaluations of the outer beam threshold limit and to

far-field Faraday probe measurements [45,54]. The iterative

path-finding method generally provided good agreement with far-

field measurements and expected divergence based on thruster

performance, whereas the outer beam threshold limits consistently

underpredicted divergence.

D. Near-Field Gridded Ion Thruster Plume

As with the near-field HET plume, a systematic investigation of

facility interactions on the near-field GIT ion current density has not

been conducted. Facility effects associated with background

pressure, such as CEX collisions and propellant ingestion, on the GIT

plume may be characterized similar to far-field characterizations.

However, there are unique considerations for GITs. Near-field test

recommendations described in Secs. IV.D and IV.E are expected to

provide the necessary data to predict time-averaged ion current

density properties in the space vacuum environment.

In the near-field GIT plume, a Faraday probe can be used to

evaluate ion plume properties, infer plasma uniformity, and resolve

features of the ion beamlet structure in the very near-field. Ion plume

profiles may be integrated according to Eq. (16) to estimate the actual

extracted beam current and compare to the beam current measured

by the ion optics. In many cases, the integrated ion beam current

measured by Faraday probes is greater than 10% larger than

measured by ion optics [61,91–93], which may be associated with not

using corrections described in Sec. V.A, such as κ

for the effective

probe collection area. However, the integration is also complicated by

asymmetry in the near-field ion current density beam profile,

specifically near the thruster centerline axis [94]. The location of peak

ion current density is often specific to a particular engine. The

physical origin of this effect is not well understood, although it has

been speculated to be associated with peculiarities in cathode

operation and coupling to the anode. Figure 30 illustrates typical ion

current measurements of a nude Faraday probe ranging from

approximately 0.16 to 1.7 TDD (∼5 to 50 cm) downstream of the ion

optics of an NSTAR thruster at 1.76 A beam current and 2.3 kW input

power [92,95]. In these measurements, the peak ion current density

profile is left of the thrust axis, and the left and right plume profiles

show slight asymmetry about the peak. Similar behaviors were

observed in the NEXT near-field ion current density profiles [21,93].

In cases of plume asymmetry, past studies have calculated differences

in integrated ion beam current exceeding 20% on the left or right side

of the plume [92]. To mitigate the asymmetry, the ion current density

Fig. 28 Convergence of the iterative path-finding method of the NASA-

300M plume [45].

Fig. 29 Calculated parameters for the NASA-300M plume using the

iterative path-finding method [45].

BROWN ET AL. 599

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profile was shifted radially to align the peak to thruster centerline. The

plume divergence and ion beam current were then averaged from

each side of the redefined profile [61,92]. This approach can lead to

large error, and it should be included in error analysis if it is

implemented.

Similar to Faraday probe measurements of the near-field HET

plume in Sec. V.C, the radial extent of integration limits for GIT

plumes using Eq. (16) is uncertain. Additional studies are necessary

to determine the suitable limits of integration. However, since the GIT

beam current is known based on ion optics, the integrated ion beam

current from near-field plume measurements is often scaled and, in

many cases, the radial measurement range is limited to the central

beam. Traditionally, the primary use of Faraday probe measurements

of GIT plumes has been to determine the plume divergence for

calculations of thrust. To this end, near-field Faraday probe measure-

ments at fixed axial location are used to calculate the fraction of total

ion beam current enclosed within a given radius, shown in Eq. (24)

for the 95% fraction:

0.95I

Beam

 2π

jrr dr (24)

Note that the value of I

Beam

in Eq. (24) is typically the beam current

measured by ion optics, but it could also be the integrated ion beam

current from Faraday probe measurements. If the integrated ion beam

current is used, the radial integration limits will impact the radius

enclosing a given fraction of the beam.

In Fig. 31, the enclosed current fractions from 20 to 99% are shown

for the ion current density profiles in Fig. 30, where I

Beam

determined by GIT ion optics. This GIT dataset reveals the spatial

distribution of calculated enclosed current fractions yields a linear

relationship in the near-field plume, where the arctangent of the

best-fit linear regression slope S

of each enclosed current fraction

may be used to determine an effective divergence half-angle β of the

GIT near-field plume as defined in Eq. (25):

β  tan

−1





(25)

For this method to be meaningful, the Faraday probe radial

measurement sweeps must extend beyond the beam central core and

multiple axial distances are required. Figure 32 shows is the enclosed

current fractions from Fig. 31 relative to thruster beam current and

corresponding β. The relevant enclosed current fractions used for

evaluation of thrust loss parameter are often 90, 95, or 99%. Ideally,

the near-field GIT divergence β should be equal to the effective far-

field divergence half-angle λ if facility pressure interactions are

suitably isolated and mitigated in data analysis.

This approach was used for the 30 cm GITs on the Dawn ion

propulsion system and demonstrated good agreement between flight

thrust levels and predictions using the 90% beam divergence half-

angles from ground measurements [75]. Nevertheless, the method

requires further analysis and the assumptions should be evaluated for

future systems. For example, it is not clear that the 90% enclosed

current fraction is the most suitable nor whether the integrated total

ion beam current should be used instead of the beam current from ion

optics for this calculation. In addition, the results may benefit from

plume characterization at multiple background pressures to improve

consistency between the total ion beam current calculated with

Faraday probe plume measurements and the values determined from

the ion optics. Unlike far-field Faraday probe measurements, Faraday

probe measurements of the near-field GIT plume are not significantly

affected by CEX collisions due to the large mean free path relative

to the plume region of interest. Instead, background pressure

characterizations of the near-field GIT plume may enable evaluation

of processes associated with facility neutral ingestion and features

associated with the beamlets. For example, Faraday probe studies of

the very near-field plume region of the NEXT indicated beamlet

focusing was a better indicator of far-field GIT beam divergence than

the near-field region downstream of beamlet merging. Alternative

approaches should also be considered, such as the iterative path-

finding method described for near-field HET plumes in Sec. V.D. Thus,

a systematic evaluation of background pressure effects on the GIT

near-field plume and the advantages, or limitations, of the different

analysis techniques should be conducted to establish standard test

practices for Faraday probe measurements of near-field GIT plumes.

E. Global Plume Properties

Thruster plume properties calculated with Faraday probe

measurements may be used to quantify thruster performance loss

mechanisms and determine utilization efficiencies. The development

and derivation of these parameters may be found elsewhere in the

literature [6,88].

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

-400 -300 -200 -100 0 100 200 300 400

Radial Position (mm)

Ion Current Density (mA/cm

)

49 mm

199 mm

274 mm

349 mm

499 mm

Fig. 30 Ion current density profiles of the 30 cm NSTAR thruster,

recreated from [92].

100

200

300

400

500

600

0 100 200 300 400 500 600

Radial Position (mm)

Axial Location (mm)

0.20

0.40

0.60

0.80

0.90

0.95

0.98

0.99

Fig. 31 Fractions of total integrated beam current of the 30 cm NSTAR

thruster, recreated from [92].

100

0 5 10 15 20 25 30 35 40

Diver

ence Half An

le (de

)

Fraction of Enclosed Beam Current (%)

Fig. 32 Fraction of enclosed ion beam current and corresponding

divergence half-angle of the 30 cm NSTAR thruster, recreated from [92].

600

BROWN ET AL.

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Current utilization is defined by the ratio of ion beam current to

input discharge current as

Current



Beam

(26)

The thruster mass utilization may be calculated with Eq. (27) as the

ratio of the ion mass flow rate to the total thruster mass flow rate,

which includes both anode and cathode propellant flows. The ion

mass flow rate is calculated using ion beam current and the average

ion charge Q from measurements of ion species charge fractions in

the plume in Eq. (28):

Mass



Beam

(27)

where

Q 



k1



−1

(28)

The beam utilization, also known as divergence utilization, is a

measure of momentum losses in axial thrust due to plume divergence.

Losses in directed thrust may be estimated using divergence of ion

beam current. A past analysis indicated the differences in divergence

in momentum and divergence of ion current are primarily affected by

spatial variation in ion charge species fractions within the central core

of the plume [88]. Variation in the ion charge state within the ion

beam is small and, typically, Q may vary less than 5% [96]; thus, the

assumption that divergence in ion current is representative of

divergence in momentum is suitable. The beam utilization may be

expressed in Eq. (29) with λ for far-field plume measurements.

Replacing divergence half-angle λ with δ or β enables calculation of

beam utilization for near-field HET measurements or near-field GIT

measurements, respectively:

Beam

 cos

λ



(29)

The thrust loss parameter F

in Eq. (29) is often used to calculate

thrust in Eq. (30), where α represents thrust reduction due to multiply

charged ions, M

is the ion mass, and V

Beam

is the average ion

acceleration voltage [6]. In practice, the uncertainty in measured

global plume parameters has higher uncertainty than direct

measurements of thrust. This approach is used more often for GITs,

since I

Beam

and V

Beam

are known from the ion optics:

T  αF

Beam



Beam

(30)

Calculated values of η

Current

, η

Mass

, and η

Beam

are shown in Fig. 33

for H6 HET operation at 10 mg∕s anode flow and 7% cathode flow,

based on plume properties in Fig. 25. The mass utilization was

calculated with Eq. (27), using measurements of ion species current

fractions measured at 1 m on the H6 HET channel centerline [88].

The trends in Fig. 33 over the range of 1 × 10

−5

to 3 × 10

−5

torr-Xe

were primarily associated with increased I

Beam

in Fig. 25, and they

revealed η

Current

increased by 0.1, η

Mass

increased by 0.16–0.21, and

Beam

decreased by 0.09–0.16. The extrapolations of η

Current

, η

Mass

and η

Beam

to zero pressure provided R-squared greater than 0.99 for

all operating conditions. In addition, these values at zero pressure

were consistent with analysis of H6 HET utilization efficiencies in

[88], which were calculated with a combination of ion energy

diagnostics in the plume and performance measurements. Thus, the

extrapolation of Faraday probe ion current density to zero pressure

may be partially mitigating the effect of the Bohm current, and this

increases confidence in the approach to estimate global properties in

the space environment.

The global far-field plume properties of a 200 W HETwith variation

in facility pressure and downstream distance are shown in Figs. 34–36,

based on plume measurements in Figs. 18 and 19. This unique dataset

included all corrections in Secs. V.A and V.B, and it was conducted

with a nested Faraday probe that enabled simultaneous measurements

of the HET plume with four probe collector and guard ring geometries

[18]. The precision in measured ion current density profiles, calculated

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Utilization Efficiency (-)

Pressure (torr-xenon)

0 1 2 3x10

-5

Current

Beam

Mass

300 V 300 V 300 V

150 V 150 V 150 V

120 V 120 V 120 V

Fig. 33 Current utilization, beam utilization, and mass utilization of the

H6 HET at six TDD.

Divergence, deg

4x10

-5

3210

Chamber Pressure, torr

8 TDD

12 TDD

16 TDD

20 TDD

Pressure (torr-xenon)

Divergence (deg)

Divergence, deg

20181614121086420

Measurement Distance, TDDs

Vacuum Extrapolation

3.1x10 torr

1.0x10 torr

3.4x10 torr

-6

-5

Axial Distance (TDD)

Divergence (deg)

Fig. 34 Beam divergence of a 200 W HET as a function of a) facility

pressure and b) measurement distance.

BROWN ET AL. 601

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global plume properties, and extrapolations to zero pressure between

four probe geometries and over a wide range of background pressure

and regions of the far-field plume in [18] increased confidence in the

results and test methodologies. No such dataset is known for GITs or

near-field HET plumes.

The data in Figs. 34–36 reveal several key considerations for

Faraday probe measurements of a far-field HET plume. First, the

variations in global plume properties with pressure show the impact of

facility background particles are nonnegligible at all far-field distances

and angular locations. Second, the extrapolations to zero pressure in

Figs. 34a, 35a, and 36a yielded different results at fixed R. These trends

suggest a natural evolution of the plume unrelated to facility effects,

which may be associated with HET plume merging or CEX collisional

processes between beam ions and neutral propellant from the thruster

and cathode. This outcome is in agreement with results in Figs. 34b,

35b, and 36b, where the global plume properties (at fixed pressure)

extrapolated to the thruster exit plane at zero TDD yielded consistent

values of λ, η

Current

,andη

Beam

; this was true for the three background

pressures characterized and the values extrapolated to zero pressure.

The reduction in η

Beam

with increasing pressure for the 200 W HET

in Fig. 35a was associated with ion scattering, and it was consistent

with the reduction shown for the H6 HET in Fig. 33, and it was

associated with ion scattering. However, the extrapolation of 200 W

HET η

Beam

to zero TDD in Fig. 35b reveals the beam utilization

increases near the thruster exit plane, ranging from 0.81 at eight TDD to

0.89 at zero TDD for the lowest pressure condition 3.1 × 10

−6

torr-Xe.

The value η

Beam

extrapolated to zero TDD ranged from 0.88 to 0.89 for

all facility pressure conditions in Fig. 35a, and the corresponding

divergence half-angle λ at zero TDD ranged from 20 to 21 deg for

all facility pressure conditions in Fig. 34a. The consistent estimates of

Beam

and λ at zero TDD from Faraday probe measurements

demonstrate the value of characterizing the HET plume across a wide

range of facility pressures and measurement distances. Based on this

result, the values of η

Beam

for H6 HET in Fig. 33 at a single distance are

likely underestimating the true plume divergence as a thruster

performance loss mechanism [88].

The reduction in 200 W HET η

Current

with increasing pressure in

Fig. 36a is opposite to the H6 trends in Fig. 33. However, the 200 W

HET trend has been observed in other thrusters [97], and different

HET behaviors have been observed with increasing facility pressure

in multiple past studies [73,98,99]. These inconsistent trends indicate

complex physics between the facility neutrals with thruster plasma or

the Faraday probe that are not fully understood. Although the effect

may be related to additional electron current fraction in the HET

discharge, another possibility is related to probe sheath expansion

when R

∕λ

is less than 50, as discussed in Sec. IV.B and in [59,60].

The ratio of R

∕λ

(where R

is the biased guard ring outer diameter)

in Faraday probe measurements of the 200 W HET plume were

estimated based on past studies [100]. The estimated ratio R

∕λ

varied from 21 at eight TDD to 15 at 20 TDD at 3 × 10

−6

torr-Xe,

and it increased to 64 at eight TDD and to 49 at 20 TDD at

3 × 10

−5

torr-Xe. Although this is still in the thin-sheath regime, it is

possible that sheath expansion artificially increased Faraday probe

measured ion current density at low pressure by several percent on the

plume periphery; thus, the value of η

Current

extrapolated to zero

pressure in Fig. 36a is overestimating the true current utilization as a

thruster performance loss mechanism. It is noteworthy that the

extrapolation of η

Current

to zero TDD in Fig. 36b resulted in consistent

0.9

0.8

0.7

0.6

Beam Utilization Efficiency

4x10

-5

3210

Chamber Pressure, torr

8 TDD

12 TDD

16 TDD

20 TDD

Pressure (torr-xenon)

Beam Utilization Efficiency (-)

0.9

0.8

0.7

0.6

Beam Utilization Efficiency

20181614121086420

Measurement Distance, TDDs

Vacuum Extrapolation

3.1x10 torr

1.0x10 torr

3.4x10 torr

-6

-5

Axial Distance (TDD)

Beam Utilization Efficiency (-)

Fig. 35 Beam utilization efficiency of a 200 W HET as a function of

a) facility pressure and b) measurement distance.

0.88

0.86

0.84

0.82

0.80

Current Utilization Efficiency

4x10

-5

3210

Chamber Pressure, torr

8 TDD

12 TDD

16 TDD

20 TDD

Pressure (torr-xenon)

Current Utilization Efficiency (-)

0.88

0.86

0.84

0.82

0.80

Current Utilization Efficiency

20181614121086420

Measurement Distance, TDDs

Vacuum Extrapolation

3.1x10 torr

1.0x10 torr

3.4x10 torr

-6

-5

Axial Distance (TDD)

Current Utilization Efficiency (-)

Fig. 36 Current utilization efficiency of a 200 W HET as a function of

a) facility pressure and b) measurement distance.

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values for all background pressures, and it is further indication that

the Faraday probe plume characterization with distance is necessary

to determine global plume properties.

Based on the nature of facility effects on the plasma plume (i.e., ion

scattering, ingestion) and Faraday probe (i.e., Bohm current, sheath

expansion) measurements of far-field HET plume properties, the issues

are expected to apply generally to the near-field and far-field of the

HET and GIT plumes. Hence, the guidelines and recommendations in

Secs. IV and V were aimed to characterize and correct for the overall

facility pressure effects, including Faraday probe collection of Bohm

current, ingested and ionized facility neutrals, ion scattering, and probe

collector sheath expansion. If Faraday probe plume characterization

with distance and facility pressure is a valid approach to correct and/or

mitigate the overall facility effects, then a complete understanding of

the individual processes may not be necessary. This result warrants

further investigation, including different thruster technologies and

thruster models, different facilities, and measurement region.

VI. Measurement Error and Uncertainty

The total measurement error is the difference between a measured

value and the true value, and it may be separated into a random error

and a systematic error . Random error is stochastic or unpredictable in

nature and may be associated with equipment sensitivity or signal

noise; it may be reduced through repeated measurement, but not

eliminated. The systematic error, or statistical bias, may be predictable

and is typically constant or proportional to the true value. The

systematic error may be known or unknown, and it may be associated

with imperfect calibration, imperfect observation, or interference of the

measurement process by the environment (i.e., facility effects). If the

known systematic error is significant relative to the required mea-

surement accuracy, a correction factor is appropriate to minimize the

impact. Ideally, the systematic error is zero after correction factors are

implemented; however, errors arising from imperfect corrections

cannot be exactly quantified. Thus, there will be inherent errors in the

correction factors, such as κ

, κ

SEE

, κ

,andκ

.Theerrorinthese

corrections contributes to overall measurement uncertainty. A detailed

description of measurement error, uncertainty, and definition of terms

and concepts may be found in [101,102].

In Faraday probe measurements of ion current density in EP

plumes, the random error is typically minimal compared to sys-

tematic error. The exception is on the plume periphery where the ion

current density is orders of magnitude less than the central core and

random error may be nonnegligible. The correction factors, test

methodologies, and recommended analytical techniques in this guide

have been established to allow characterizations and corrections that

minimize systematic error and improve estimates of local charge flux

and global EP plume properties in the space environment. A list of the

primary systematic errors is provided in Table 2, along with the

location of discussion. The magnitude of systematic measurement

errors may vary for different experiments due to thruster technology,

operating condition, experimental setup, and/or facility test condi-

tions. In addition, there are limited flight comparisons with ground

data and insufficient Faraday probe plume measurement in the space

environment to rigorously determine the fidelity of linear regression

to vacuum conditions or to zero TDD.

Based on this knowledge, experiments that follow the guidelines in

Secs. III–V, as well as Appendix A, are expected to have less than

approximately 5% uncertainty in far-field measurements and

10% uncertainty in near-field measurements. Local Langmuir

probe measurements at the Faraday probe location enable direct

calculation of the Bohm current and evaluation of the probe sheath,

and they may be used to reduce measurement uncertainty. Comparing

calculated global plume properties from Faraday probe measure-

ments with other plasma diagnostics and evaluation with a thruster

performance analysis may further increase confidence in results. For

example, the GIT ion beam current measured by ion optics may be

used to evaluate the Faraday probe integrated ion current density

results. For a HET, the total ion beam current measured by a Faraday

probe may be bounded by the thruster discharge current (maximum)

and the lower limit based on evaluation of total thruster efficiency

and utilization efficiencies [88]; this approach necessitates thrust

measurements and other plasma diagnostics, such as electrostatic

analyzers [103] or ExB probes [81].

VII. Probe Design Considerations

A. Design Guidelines

Numerous investigations have evaluated Faraday probe designs

and modifications aimed to form a uniform collector sheath and to

prevent collection of low-energy ions generated through facility

effects, such as CEX ions and ingested neutral particles [1,30,32].

These ion filtering mechanisms include collimators, electrically

biased grids, or magnetic fields. Although these filtering approaches

will successfully attenuate low-energy ions, they do not selectively

isolate facility effects from the ionization of thruster and cathode

neutrals downstream of the primary acceleration zone. For example, a

collimated Faraday probe collects the low-energy thruster beam ion

population, CEX ions, and ingested facility neutrals that are ionized

and accelerated near the thruster exit. In contrast, the magnetically

filtered Faraday probe or gridded Faraday probe eliminates all low-energy

ion populations. T hus, the filtering mechanisms may no t accurately

determine the on-orbit plume characteristics. The recommended design is

a nude Faraday probe with a guard ring, based on design simplicity and

past systematic experiments that increase confidence in the ability to

characterize systematic measurement errors.

A typical nude Faraday probe consists of a collector, guard ring,

ceramic isolator, probe housing, and necessary fasteners and

electrical wiring. The collector and guard ring are often made of metal

with low sputter yield and low SEE, such as molybdenum, tungsten, or

graphite [49,78,79,104,105]. Although materialsspray coated with 2%

thoriated tungsten have been used, it is not recommended due to a

lower work function that leads to increased thermionic emission at a

given temperature [65]. High-purity (≥99%) collector and guard ring

materials should be used due to availability of literature on material

properties. The collector and guard ring should be the same material to

minimize differences associated with material properties, such as SEE

and thermionic emission. The collector and/or guard ring electrical

connections internal to the probe housing may be a suitable location to

monitor a representative probe temperature for evaluation of effects

associated with heating, such as thermionic emission.

The collector diameter is determined based on the expected range

of ion current density, which may span microamperes per square

centimeter in the far-field plume to milliamperes per square

centimeter in the near-field plume of HETs and GITs; ion current

density may exceed amperes per square centimeter in the far-field

plume of pulsed electromagnetic thruster concepts, as discussed in

Sec. VIII.C. Thus, the collector diameter should be scaled to achieve

the necessary signal strength over the measured ion current density

range in the near-field and far-field plumes for the experiment DAQ

system capabilities, or voltage should be measured across a shunt

resistor as described in Sec. III.D. In addition, the lowest achievable

Table 2 Systematic errors in Faraday probe measurements

Parameter Section

Probe positioning and alignment III.C

Probe leakage current III.D

DAQ system and electrical configuration III.D, III.E

Collector surface contamination III.E

Thermionic emission IV.B

Bias voltage and ion saturation IV.B

Sheath expansion IV.B, V.E

Bohm current collection IV.B, V.B

Ion collection in collector–guard ring gap V.A

Collector secondary electron emission V.A

Hemispherical coordinate system V.B

CEX collisions with facility neutrals V.B

Facility neutral ingestion V.B

Divergence angle reference V.B,V.C,V.D

Linear regression (to zero pressure, zero TDD) V.B, V.E

Cathode plume Appendix B

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measurement resolution is set by the collector diameter 2R

; thus, the

collector diameter should be scaled to satisfy the experimental

guidelines in Secs. IV.C and IV.D.

The gap width between the collector and guard ring may be less than

5to10λ

to create a flat, uniform sheath over the collector surf ace. Past

experiments demonstrated that ions entering the gap between the nude

Farada y probe collector and guard ring were collected by the walls, and

they were a nonnegligible fraction of the measured collector current

[77]. Although the ef fectiv e ion collection area of nude Faraday probes

is larger than cross-sectional geometric area of the collector , the area

correction factor κ

, as defined in Sec. V.B, has demonstrated consistent

results for different nude probe configu ratio ns ov er a range of

measurement distances and background pressures, where the isolator

base of the gap between collector and guard ring was ceramic [18].

The ratio R

∕λ

is an important consideration in determining the

range of plasma conditions where the thin-sheath assessment is valid.

In a nude Faraday probe, the probe radius R

is equal to the guard ring

outer diameter. The ratio R

∕λ

 50 in Fig. 37 for R

from 0 to

100 mm over a wide range of plasma densities and electron

temperatures is based on Eq. (2), showing the conditions where

sheath expansion is negligible. Large R

enables Faraday probe

measurements at larger λ

while satisfying R

∕λ

greater than 50,

thereby enabling studies of lower plasma density at a given T

.For

example, R

of 40 mm enables Faraday probe measurements of 1 eV

plasma at density 10

−3

, and R

of 100 mm is insufficient to

measure a 1 eV plasma at density of 10

−3

There are two circumstances when a guard ring may not be viable. In

regions of high plasma density , such as near-field measurements close to

the plasma discharge, the gap between the collector and guard ring may

be less than 5 to 10λ

andthegapdesigncriteriaisnotsatisfied.For

instance, plasma density in the very near-field of HETs and GITs is 10

to 10

−3

, and the corresponding λ

is 17–50 μm in a 5 eV plasma

based on Eq. (2). Thus, the gap between the collector and guard ring

must be less than 0.1 to 0.5 mm to satisfy the 5 to 10λ

gap criteria.

Under these conditions, there may be practical limits to the minimum

gap width and significant challenges associated with probe fabrication,

construction, assembly, alignment, and/or tolerance. A second situation

where a guard ring may not be pra ctical is one in which the physical

probe diameter is large with respect to the region of interest, such as the

near-field of a very small thruster, within or very near a HET discharge

channel, or directly downst ream of GIT grids before beamlet merging.

Evaluation of gap widths larger than 5 to 10λ

was conducted in [77].

These experimental results indicated the 5 to 10λ

design criterion may

be relaxed if the gap correction factor κ

was applied. It is

recommended to evaluate these challenges and errors, as well as to

compare to errors associated with collector sheath expansion if no guard

ring is implemented. In the absence of plasma properties to estimate the

range of λ

, it is recommende d to use a guard ring. Both approaches

necessitate careful analysis and should be accounted for in the error

analysis.

The isolator is intended to electrically isolate the collector and

guard ring, and it is typically a dielectric, such as boron nitride (BN),

Macor®, or aluminum oxide (Al

). A comparison of dielectric

materials used in probe construction for use in an EP plasma was

provided elsewhere in the literature [106,107]. Boron nitride is

available in multiple grades with high thermal conductivity, a

temperature limit exceeding 3000 K (for XP grade BN), and excellent

thermal shock resistance [108,109]. Aluminum oxide, also known as

alumina, has sufficient thermal conductivity and maximum temper-

ature for most EP plasma plume environments, and it has a higher

elastic modulus that is advantageous for applications with high

mechanical and vibrational loads [110]. Macor is an easily machin-

able glass ceramic with the low thermal conductivity, no porosity, and

no outgassing [111]. In general, the ceramic isolator SEE and sputter

yields should be minimized; these properties may be found in the

literature [48,50,107,112]. However, other test considerations may

drive material selection. For example, BN may have advantages

associated with thermal properties and alumina may have beneficial

mechanical properties for rapid probe positioning.

The probe housing should be capable of withstanding the plasma

environment, and thus it is made from a material with a low sputter

yield, such as graphite [55,105]. Alternative materials such as alumi-

num may have advantages for probe construction; however, the

aluminum sputter yield due to xenon bombardment is approximately

five times higher than graphite [105]. Kapton [48] may be used to

cover the housing material, but it will undergo degradation in the

plasma environment. As stated in Sec. III.E, Faraday probe electrical

wiring and fasteners should not be exposed to the plasma in order to

minimize sputtering, deposition, and degradation. A shield may be

implemented to limit direct ion beam impingement.

B. Recommended Probe Design

Based on the design guidelines in Sec. VII.A, a recommended

nude Faraday probe design is shown in Fig. 38. The diagram shows

major components of the probe design and includes key features

based on past test campaigns. It should be noted that this design is

notional, and it has not been fabricated or evaluated with thruster

plasma in a ground test environment. The collector, guard ring,

isolator, and probe housing are shown in Fig. 38a. Probe materials

discussed in Sec. VII.A would suffice for the design. However, for

consistency in results associated with material properties (i.e., SEE,

sputter yield, work function), it is advised to use tungsten due to an

extensive knowledge of material properties and plasma interactions.

The recommended isolator material in Fig. 38 is BN due to thermal

characteristics and knowledge of material properties based on past

studies [48,50,108,109]. Alternative isolator ceramics may be used

for specific advantages, such as mechanical properties.

Probe manufacturability has been considered, including separating

the isolator into two components for alignment and the notched isolator

base as shown in Fig. 38b. The notched isolator base is to reduce the

buildup of deposited material, and thereby reduce the possibility of

electrical leakage current caused by a conductive path between the

collector and guard ring. In addition, there are through holes in the

isolator and tapped holes in the collector and guard ring, which enable

options for probe assembly and electrical connections at fasteners

internal to the probe housing. This configuration is also expected to

allow adjustments in component alignment, including concentricity

between the collector and guard ring. The diagram does not specify an

attachment between the isolator and probe housing. Vent holes are

included at the base of the ceramic isolator in Fig. 38a to reduce the

buildup of neutral particles in the gap; however, this may not be

necessary for low particle flux in the far-field plume.

Critical design dimensions for the probe in Fig. 38 are shown in

Fig. 39a with respect to recommendations for near-field and far-field

measurements in Sec. IV, including the collector diameter, the gap

width between the collector and guard ring, and the guard ring outer

diameter. These critical dimensions should be evaluated and satisfied

throughout the plume measurement range. For a given investigation,

0 102030405060708090100

Plasma Density (m

-3

)

-15

-14

-13

-12

Probe Radius (mm)

10 eV

3 eV

1 eV

0.3 eV

0.1 eV

0.03 eV

0.01 eV

Fig. 37 Minimum plasma density measureable for a probe radius

satisfying R

∕λ

greater than 50, with manifolds of fixed electron

temperature.

604

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is typically lowest at the highest thruster discharge current

condition and at the nearest downstream measurement location; this

value should be used for scaling the gap width. The ratio R

∕λ

typically smallest at the lowest thruster discharge current condition

and lowest pressure on the plume periphery; this value should be used

for scaling the guard ring outer diameter.

Dimensions for two recommended probe designs are provided in

Fig. 39b . For 2R

of 17 mm, the far-field measurement resolution is

1degat1mand2degat0.5m.Thegapwidthissetto0.5mm,whichis

suitable for λ

greater than 0.05 mm. Two outer diameter guard rings are

shown in Fig. 39b for different values of R

. A guard ring outer diameter

of 106 mm (R

 53 mm) corresponds to R

∕λ

greater than 50 at

greater than 5 × 10

−3

in a 1 eV plasma. The guard ring outer

diameter of 34 mm (R

 17 mm) corresponds to R

∕λ

greater than

50 at greater than 5 × 10

−3

in a 1 eV plasma, where the smaller

probe cross section may reduce probe heating and thruster perturbations.

The Faraday probe is connected with fasteners that attach the

collector and guard ring to the isolator assembly. In addition, the

fasteners may be used as attachment points for electrical connections

and thermocouples within the probe housing. A thermocouple is

recommended at the guard ring electrical connection to monitor

probe temperature. The probe housing may extend greater than

50 mm from a mounting post or diagnostic array. The isolator extends

upstream of the probe housing in order to reduce deposition and the

possibility of a current path forming across the isolator surface

between the guard ring and conductive probe housing. In general,

these probe dimensions may be modified to improve manufactur-

ability, or as needed, for experimental requirements.

In situations where the probe diameter is minimized or a guard ring

is not used, several design options have been implemented

[7,21,44,54,113]. For simplicity, the planar Faraday probe design

used in [113] is the recommended approach, where the collector is

flush mounted with an isolator jacket. This is due to a known exposed

collection area with no possibility of ion collection on the sidewalls,

as occurs in the probe configuration in Figs. 38 and 39. The sheath

effects should be evaluated as stated in Sec. VII.A with local

Langmuir probe measurements, and probe heating may be monitored

with a thermocouple. Techniques for construction and assembly of

small plasma probes were found elsewhere [45,106,114].

Evaluations of the plume periphery for high-fidelity predictions of

ion flux in the space environment may necessitate a larger collector to

improve the signal-to-noise ratio and a larger guard ring to satisfy

∕λ

greater than 50. The scaling shown in Fig. 39a should be used

to scale this probe design. In addition, local Faraday probe mea-

surements are recommended to evaluate sheath expansion and Bohm

current, as discussed in Sec. IV.B.

Fig. 38 Recommended nude Faraday probe design showing a) key components and b) internal features.

b)a)

<5-10

>50

≤ R

(far-field)

≤ 0.01 D

(near-field)

0.5

>50

34 (>5x10

-3

at 1 eV)

106 (>5x10

-3

at 1 eV)

Fig. 39 Recommended nude Faraday probe design showing a) key design parameters and b) a design dimensions in mm.

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VIII. Considerations for Other EP Technologies

The Faraday probe experimental apparatus, test methodologies, and

analysis techniques presented in Secs. III, IV, and V, respectively, are

applicable to many EP technologies. Multiple criteria in Table A1 of

Appendix A are common to all EP devices. These are primarily related

to probe considerations and experimental apparatus. However, there is

limited information in the literature on Faraday probe measurements

for the EP devices in this section, and it is undetermined if additional

measurement considerations or analysis techniques are warranted. This

is especially true for issues related to thruster interactions and plume

characterizations with distance and pressure. Limitations of the

guidelines in Table A1 and modifications for select EP technologies are

described in the following.

A. Electrospray Thrusters

Electrospray propulsion technologies, which includes fieldemission

electric propulsion and colloid thrusters, typically use a small number

(less than 10) of emission sites and small emission area for low-power

sub-millinewton thrust applications [115,116]. There is limited

information in the literature of Faraday probe measurements for single

emitter experiments or electrospray arrays with a small number of

emitters; thus, it is unclear if additional Faraday probe considerations

will arise in measurements of large electrospray arrays for greater than

microampere-level devices [117].

Plume measurements of the colloid micronewton thruster (CMNT)

system, a nine-emitter array , were conducted for the NASA Space

Technology 7-Disturbance Reduction System (ST7-DRS) flown on the

Laser Interferometer Space Antenna Pathfinder mission. The CMNT

beam was not evaluated with a traditional Faraday probe; however , a

segmented plume target in the far-field plume provided details of the ion

current density profiles approximately 34 cm downstream of the

thruster [115,117]. The plume target consisted of 64 electrometers in a

cross configuration along the x axis and y axis, as shown in Fig. 8 for the

cylindrical coordinate system. There were minimal details on the

experimental apparatus or facility configuration, and the plume

measurements were not consistent with the test methods in this paper.

Howe v er , the reported ion flux and divergence half-angles in Fig. 40

indicate the electrospray ion beam is similar to GIT and HET plumes.

Figure 40b demonstrate the 99.9% diver gen ce half-angles were with in

50 deg from the thruster centerline, and the 95.5% half-angle was no

greater than 24 deg in any operational condition [115]. The integrated

ion beam current was not compared to electrospray emitted current.

Based on the ST7-DRM dataset, Faraday probe guidelines in this

paper should be used as a starting point for measurements of

electrospray plumes. The influence of facility background pressure or

facility electrical environment has not been established for electrospray

thruster technologies. However, the plume characterization with

multiple background pressures and measurement distances are

advised, as listed in Table A1, to isolate facility effects associated with

CEX collisions, Bohm current collection, and probe sheath expansion.

Electrosprays may be operated in several configurations to achieve

beam neutralization, including with a neutralizer cathode, with both

positive and negative emitters, or operated in a bipolar fashion with

alternating positive and negative particles. The latter two approaches

may require additional considerations that are beyond the scope of this

paper. In addition, Faraday probe design should be evaluated for

measurements of the electrospray plasma with charged droplets,

including guidelines for the guard ring and gap spacing. As stated in

Sec. II.A, the effect of propellant on the Faraday probe surfaces should

be considered if an ionic liquid or condensable propellant is used.

B. Arcjet Thrusters

Electrothermal thrusters, such as arcjets and resistojets, use electric

heating to impart energy to the propellant and accelerate through a nozzle

to produce thrust [118,119]. In the arcjet, an arc originating from the

cathode attaches to the anode nozzle to heat the propellant, which can

then be accelerated through the nozzle to produce thrust. The arcjet flow

conditions e volve from nearly fully ionized plasma near the cathode to a

relatively cold plasma near the anode surface, and a weakly ionized

plasma in the exhaust plume. Arc current density near the arcjet cathode

has been estimated at 10

A∕cm

, and peak current density along the

anode surface was measured to be greater than 10 A∕cm

[118,120].

There have been multiple studies of the arcjet exit plane, near -field

plasma, and far-field plasma [121–124]; however , there is a dearth of

information on ion current density in the arcjet plume due to the very low

ionization fraction of less than 10

−3

. Plasma properties in the arcjet plume

are an electron temperature less than 1 eV and electron density ranging

from less than 10

−3

in the near-field plume to less than 10

−3

the far-field plume [118,121]. Thus, the signal-to-noise ratio may be a

challenge and the orbital-motion-limited sheath assessment may be

necessary , as opposed to the thin-sheath assessment, due to the large λ

low plasma density. Neutral propellant temperatures may approach 3000

to 5000 K near the arcjet exit plane, and the exhaust velocity ranges from

hundreds of kilometers per second up to approximately 1000 km∕s on

the thruster centerline, depending on propellant, where the ratio of ion

velocity to neutral exhaust velocity is ∼1.5 [122,125].

The Faraday probe guidelines and recommendations in this paper

may be used as a starting point; however, an examination of the arcjet

near-field and far-field plumes is necessary to determine whether the

guidelines and recommendations are suitable. It is not known to what

extent facility effects influence the arcjet plume; they may be minimal

because most of the acceleration is within the nozzle area and the

ionization fraction is very low in the plume. To establish guidelines for

Faraday probe measurements of arcjet thrusters, examination of ion

current density with characterization of background pressure and

downstream distance is advised. These data should be correlated to

measurements of plasma properties near the exit plane and far-field

plume, and they should be considered with respect to Faraday probe

design requirements and design applicability throughout the plume.

For example, the Debye length may range from 3 × 10

cm [122] near

the arcjet exit planeto the order of 10

−2

cm in the far-field plume [126].

To accommodate these conditions, the gap width of a nude Faraday

probe collector must be less than 0.03 mm and is not practical. Based

on past plasma measurements of the arcjet plume, probe heating must

0.0

10.0

20.0

30.0

40.0

50.0

23456789

Beam Voltage (kV)

Enclosing Half-Angle of Exhaust Beam (°)

Electrodes

Beam Current (µA)

95.5% 99.9%

2.25 2.25

3.0 3.0

4.0 4.0

5.0 5.0

5.4 5.4

ST7 Thruster, 9 Emitters

95.5%

99.9%

Fig. 40 Far-field plume measurements of the ST7-DRS electrospray

thruster a) normalized ion flux recreated from [117] and b) divergence

half-angle recreated from [115].

606

BROWN ET AL.

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also be considered and recommendations for probe operating

characteristics in Sec. IV.B should be implemented.

C. Electromagnetic Thrusters

Faraday probe measurements in the near-field and far-field plumes

of electromagnetic propulsion are challenging due to the severe

plasma plume environment, the wide range of plasma properties, and

the complex transient nature of electromagnetic thrusters. Common

electromagnetic thruster devices include magnetoplasmadynamic

thrusters (MPDTs) and pulsed plasma thrusters (PPTs). Electromag-

netic thruster concepts can range in average power from less than 1 W

up to megawatt levels, and total enthalpies in the plume can reach

5 × 10

J∕kg. Peak pulsed ion current density in these devices may

exceed 10

mA∕cm

near the plasma discharge and be greater than

mA∕cm

in the far-field plume [127–130]. At these extreme

conditions, the probe is likely to experience elevated temperatures

and the recommendations for probe operating characteristics in

Sec. IV.B should be implemented. There have been few compre-

hensive studies of ion current density in the plume of MPDTs or

PPTs. In cases where ion current density is reported, it is typically

measured with Langmuir probes or Hall probes [127–129].

Ion current density measurements using a planar Langmuir probe are

shown i n Fig. 41 from investigations of the Lincoln Experimental

Satellite (LES) 8∕9 PPT plume [128]. These ion current density

measurements were conducted in a hemispherical coordinate system at a

radius of 24 cm with a planar probe rake, which corresponds to

R  9.4 TDD for the 2.54 × 2.54 cm

exit cross section. The planar

probes had copper collectors and a guard ring, both biased to −40 V

with respect to facility ground. In Fig. 41, the relati v ely flat ion beam

profile on the thruster centerline sho ws a peak ion current density of

approximately 2000 mA∕cm

, which is two to three orders of

magnitude lar ger than HETs or GITs at a similar location in the far-field

plume (∼8–10 TDD). Based on the results with a planar Langmuir

probe, a F araday probe designed for the high-energy flux in Fig. 41 may

be viable for examinations of the PPT plume. Howe ver, the proper test

approach, data analysis, and characterization of facility effects on

Faraday probe measurements in the PPT plume has not been established.

For example, several PPT studies with Langmuir probes hav e confirmed

asymmetry in plasma plume properties dow nstream of the exit plane,

which were attributed to the plane parallel or perpendicular to the

rectangular PPT discharge cross section [131]. Thus, the Faraday probe

guidelines and recommendations in this paper should be ev aluated

before adoption and/or modification for the PPT plume.

A representativ e measurement of ion beam current in the very near-

field of an MPDT operating at 60 kW and 1500 A is shown in Fig. 42

[129]. This measurement was conducted with a Hall probe, where the

self-induced magnetic field distribution is related to the enclosed

current. The Hall probe was swept through the plume within ∼50 ms at

fixed 2.7 cm downstream of the exit plane, where the anode outer radius

was ∼2.54 cm, as shown in the diagram within Fig. 42. In this

configuration, the cathode was recessed within the discharge region and

oriented along the thruster centerline (r  0cm). The peak current

within the Hall probe loop was near the anode radius, indicating the

current was attached to the anode face. Multiple studies have reported

that the applied-field MPDT was highly susceptible to facility effects,

such as propellant ingestion and ion scattering in the plume, since

the acceleration region can extend far downstream of the thruster exit

[132–134]. Although facility effects have been evaluated exper-

imentally and computationally, there is not a standard approach to

mitigate the facility effects on MPDT performance or plume ev alua-

tions, and such an analysis is beyond the scope of this paper. A

systematic and comprehensive evaluation of the MPDT near -field and

far-f ield plumes is necessary to determine whether the guidelines and

recommendations in this paper are suitable for the MPDT plume. This

will necessitate Faraday probe measurements of ion current density ,

characterization of background pressure and downstream di stance, and

plume examination of plasma properties throughout the plume (i.e.,

electron density, electron temperature, ion species) to inform Faraday

probe design requirements and design applicability throughout

the plume.

IX. Conclusions

This paper described guidelines and recommended practices for

the use of Faraday probes to measure ion flux in the near-field and

far-field plumes of EP devices: specifically, HETs and GITs. These

measuremen ts were used to quantify thruster performance loss

mechanisms and global beam properties, as well as to evaluate

plasma plume interactions with the host spacecraft. No viable

approach has been demonstrated to quantitatively predict the

influence of facility pressure effects throughout the EP plume a

priori. Rigoro us Faraday pr obe studie s of far-field Hall thrust er

plumes have advanced understanding of the facility effects on

thruster plasma and probe ion collection behavior, and they have

led to t est methods, analysis tec hniques , and c orrection factors to

reduce systematic measurement errors. A measurement un-

certainty l ess than approximately 5% in far-field measu re ments

and 10% in near-field measureme nts was possible, and it may be

improved w ith local Langmuir probe mea surem ents or evalua-

tion with thruster telemetry and efficiency analysis. Further

investigation is warranted to better u nderstand facility effects on

the near- field plume region and dat a analysis a pproach es to

improve plume predictio ns of the spac e environment. The state of

knowledge of Faraday probe measurements for other EP c once pts

is limited, including electrosprays, arcjets, and electromagnetic

thrusters. Thus, the guidelines and recommenda tions describ ed in

this paper should serve as a starting point.

The establishment of recommended test practices for Faraday

probe measurements will enable quantitative evaluation of EP plume

properties and enhance the quality of comparisons between different

EP devices and facilities. This will broaden the acceptance of Faraday

probe results and improve measurement fidelity for on-orbit

predictions and model validation. Standardization and improved

100

1,000

10,000

-100 -75 -50 -25 0 25 50 75 100

Angle from Thrust Axis (deg)

Ion Current Density (A/cm

)

Fig. 41 Far-field ion current density measurements of the LES 8∕9 PPT

with a rake of planar Langmuir probes, recreated from [128].

100

200

300

400

500

600

700

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Radial Distance (cm)

Enclosed Current (A)

Anode Radius

Anode

Hall Probe

Measurement

Centerline

Cathode

Anode Radius

Fig. 42 Enclosed current distribution of the MPDT plume at 2.7 cm

downstream of the exit, recreated from [129].

BROWN ET AL. 607

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predictive capabilities have broad application to laboratory

researchers, satellite designers, and operators, and they ultimately

advance the utilization of EP for flight.

Appendix A: Summary of Recommended Practices

The numerous guidelines and recommendations for Faraday probe

test practices are summarized in Table A1 for HETs and GITs,

including the relevant section where additional information is

provided.

Appendix B: Method o f Cathode Plume Removal

In the case of a centrally mounted cathode, the recommended

approach is to remove the contributions of the cathode plume from the

Faraday probe results. One approach is to evaluate the cathode plume

as an expanding jet into vacuum that does not interact with itself or the

thruster ion beam. The approach will be demonstrated based on

analysis of the NASA-300M at 500 V, 20 kW in Figs. B1–B3 [45]. The

first step is to identify a region near the cathode where the measured ion

current is dominated by the cathode plume. In past studies, the cathode

plume region was defined as Z less than 0.2 TDD in the radial vicinity

Table A1 Summary of Faraday probe guidelines and recommendations for HETs and GITs

Experimental parameter/section Guideline

Coordinate geometry/III.A, III.B 1) Channel or grid outer diameter D

should be used for HETs and GITs, respectively.

2) External cathode should be located at Φ  90 deg (or 270 deg) for measurement in Φ  0 deg, 180 deg plane.

3) Hemispherical coordinate system should be used in far-field.

4) Cylindrical coordinate system should be used in near-field.

Background pressure characterization/

IV.E

1) Measurements should be conducted at a minimum four background pressures.

2) Pressure characterization should include plume measurements at the lowest achievable facility pressure during thruster

operation.

3) Pressure should follow recommendations in [57].

Measurement distance/IV.C, IV.D 1) Far-field measurements should be greater than four TDD.

2) Near-field measurements should be less than four TDD.

3) Near-field HET analysis should be upstream of the transitional region and may be greater than 0.2 TDD.

Spatial characterization/IV.E Measurements should be conducted at a minimum four distances at all background pressures.

Measurement span/IV.C, IV.D 1) Far-field measurements at fixed R should span θ  0 to 90 deg, for fixed Φ and at Φ  180 deg for the opposite side of

the plume (e.g., θ  0 to 90 deg at Φ  0 and 180 deg).

2) Near-field measurements at fixed Z should extend to the location where measured ion current density is less than 0.2%

of the maximum value along the radial profile, for fixed Φ and at Φ  180 deg for the opposite side of the plume (e.g.,

Φ  0 and 180 deg).

Measurement resolution/IV.C, IV.D 1) Far-field angular resolution should be 2R

∕R ≤ dθ ≤ 2 deg.

2) Near-field radial resolution should be 2R

≤ dr ≤ 0.01D

or ≤ 1mm, whichever is greater.

Probe materials/VII.A 1) Probe collector, guard ring, and side surfaces should be ≥99% purity molybdenum, graphite, or tungsten.

2) Isolator materials may be boron nitride, aluminum oxide, or Macor.

Collector bias voltage/IV.B 1) Probe collector and guard ring should be biased voltage relative to ground to achieve ion saturation throughout the

measurement region.

2) Bias voltage to achieve ion saturation should be characterized at multiple locations in the plume to span the maximum

and minimum n and T

(e.g., minimum R at θ  0 deg and the maximum R at θ  90 deg in the far-field).

3) Collector and guard ring bias voltage should be equal.

Probe electrical resistance/III.D, III.E 1) Collector resistance to ground and R

C-GR

should be measured before testing, and they should exceed 100 MΩ.

2) Collector shunt resistor may range from 10 to 1000Ω.

Diagnostic alignment/III.E 1) Probe alignment should be conducted before pumping the facility to vacuum conditions.

2) Collector face should be oriented parallel to the thruster exit plane within 1 deg, when positioned on thruster centerline.

3) Probe position accuracy should be within 1 mm or within 0.5% R (or Z) at the maximum measurement distance (e.g.,

5mmatR  1m), whichever is greater.

Bohm current/IV.B Bohm current density to the collector should be less than 1% of the measured ion current density.

Thermionic emission current/IV.B Collector thermionic emission current should be less than 1% of the measured ion current density.

Probe checkout/III.E, IV.B 1) No obstructions should be in the line of sight of the Faraday probe to any point of the thruster plasma discharge.

2) All probe mounting structures and cables near the probe should be downstream of the probe collection surface.

3) Probe mounting structure that experiences direct beam ion impingement should be shielded with low-sputter materials,

such as Kapton or graphite.

4) May conduct visual inspection and electrical verification of the probe at the beginning and end of a test campaign, or if

there is a change in measurement repeatability over time.

Probe cabling/III.E 1) Probe cabling should be coaxial cable or twisted shielded pair, with no electrical leads or connections exposed to

plasma.

2) Cable shielding should be grounded to the facility walls in ground testing.

Thruster operation/IV.A 1) Thruster discharge should reach operational steady state before conducting measurements (user defined).

2) Thruster telemetry should be monitored for perturbation during measurements.

Probe design dimensions/VII 1) Collector to guard ring gap should be less than 5λ

to 10λ

2) Ratio R

∕λ

should be greater than 50.

3) 2R

should be less than or equal to Rθ in the far-field.

4) 2R

should be less than or equal to 0.01D

in the near-field.

Correction for collector SEE/V.A Measurements should be corrected for collector SEE with κ

SEE

Corrections for hemispherical

coordinate system/V.B

Far-field measurements in a hemispherical coordinate system should be corrected with κ

and κ

Correction for probe collection

area/V.A

Probe ion collection area should be corrected for ions entering gap between the collector and guard ring with κ

Note that alternative definitions of D

may be used, such as midchannel diameter for HETs.

Note that pressure recommendations are the same for all working gases. For increased accuracy, recommend lower background pressure and additional pressure characterizations.

Qualitative assessment of plume profile may be conducted at a single background pressure.

Note that, for increased accuracy, recommend additional distances and additional background pressures. Qualitative assessment of plume may be conducted at a single distance.

Note that, for increased accuracy, recommend 100 deg for far-field measurements.

Note that, for increased accuracy, recommend ≤1 deg resolution for far-field measurements.

Note that recommended probe design lists specific materials for consistency in Sec. VII.B. Alternative materials may be selected for specific applications.

608 BROWN ET AL.

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of the cathode plume [45,54], which is within approximately 0.1D

Fig. B1a, although the range can be modified. The dashed lines in

Fig. B1a are overlaid to show the approximate boundaries of the

cathode plume region in the analysis of [45].

Analyses of the NASA-457Mv2 in Fig. 26a and NASA-300M in

Fig. B1a demonstrated that an exponential decay function of the form

in Eq. (B1) yielded an excellent fit to the radial cathode plume profile

at fixed Z [45]:

frC

−jrj∕C

(B1)

The cathode plume expands as it travels downstream, where the

parameters C

and C

are constant for a given radial plume profile at a

fixed Z but may vary with axial location in the cathode plume region.

The recommended approach is to fit Eq. (B1) at multiple axial

positions within the measured cathode plume region. Past studies

used a method of least squares to determine C

and C

at each axial

measurement location, indicated by markers in Figs. B2a and B2b.

Based on the values of C

and C

for the exponential decay function

in Eq. (B1), the radial cathode current density profiles may be

integrated to calculate the total cathode plume current at each

downstream distance, as indicated by markers in Fig. B2c. This

calculation allows determination of a mean plume current in the

expanding cathode jet, which is assumed constant with downstream

distance in the cathode plume region. The mean cathode plume

current is approximately 0.684 A, as shown in Fig. B2c. To determine

the cathode plume ion current density throughout the Faraday probe

measurement region, it is necessary to develop an expression for

parameters C

and C

as a function of axial location in the cathode

plume. To this end, a second-order polynomial is used to evaluate

variation of C

as a function of Z in Fig. B2b. Using this second-order

polynomial expression for C

and the mean cathode plume current in

Fig. B2c, an expression for C

can be determined as a function of Z

with Eq. (B1), shown as a dashed line in Fig. B2a. The calculated

values of C

for an expanding cathode jet (dashed line) in Fig. B2a are

consistent with the values determined with least-squares analyses

(markers), thereby indicating the approach is suitable to evaluate the

cathode plume ion current density throughout the measurement

domain.

The cathode plume profile developed using Eq. (B1) and Fig. B2

may then be subtracted from the Faraday probe ion current density

measurements. Based on the total cathode plume current in Fig. B2c,

the cathode plume contributed ∼0.68 A current to the integrated

thruster ion beam current, which was ∼2% of the thruster discharge

current. However, removal of the cathode plume has a larger impact

on evaluation of beam divergence, including the iterative path-

finding method described in Sec. V.C. This is due to the elevated

current density outside of the channel, which would alter values of r

and z

in the free-expanding jet in Fig. 27.

The cathode plume model is shown for the NASA-300M HET at

various axial positions in Fig. B3, where solid black lines indicate the

raw trace, and dashed red lines indicate the curve-fit results [45]. The

flooded ion current density plots after cathode plume removal are

shown in Fig. B1b, where dashed lines indicate the limits of integration.

Spurious spikes may be present in the postsubtraction datadue to minor

)

-1.0

-0.5

0.0

0.5

1.0

0 0.5 1 1.5 2

Radial Distance from Centerline (

r/D

)

Axial Distance from Exit Plane (z/D

)

Ion Current Density, mA/cm

150

100

BEFORE

Cathode

Plume

Region

-1.0

-0.5

0.0

0.5

1.0

0 0.5 1 1.5 2

Radial Distance from Centerline (r/D

)

Axial Distance from Exit Plane (z/D

)

Ion Current Density, mA/cm

150

100

AFTER

Fig. B1 Ion current density from a) plume measurements and b) with cathode plume removal, recreated from [45].

500

1,000

1,500

2,000

0.05 0.10 0.15 0.20 0.25

Fit Constant C

Exponential Decay Fit

Expanding Jet (calculated)

Axial Distance (z/D

)

500

1,000

1,500

0.05 0.10 0.15 0.20 0.25

Fit Constant C

Exponential Decay Fit

Expanding Jet (Second-Order Poly)

Axial Distance (z/D

)

500

1,000

1,500

0.05 0.10 0.15 0.20 0.25

0.70

0.68

0.64

0.66

Total Cathode Plume Current (A)

Axial Distance (z/D

)

Fit Constants

Expanding Jet (mean, fixed)

Fig. B2 Curve-fit parameters a) C

,b)C

, and c) the integrated cathode

plume current, recreated from [45].

BROWN ET AL. 609

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misalignment between the measured ion current density and the

cathode plume, as shown in Fig. B1b on the thruster centerline at less

than 0.2 TDD. Removal of the cathode plume is advised, even if the

method generates spurious spikes or does not completely remove the

cathode plume structure, possibly due to a low signal-to-noise ratio.

The cathode plume remnants typically contribute less than a few

percent to the integrated ion beam current due to the small integration

element area. The effects may be included in error analysis. Overall, the

cathode plume removal process is expected to improve analyses of

beam divergence despite limitations of the correction. Additional

details and recommendations are found in [45].

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