George C. Soulas

Glenn Research Center, Cleveland, Ohio

The Impact of Back-Sputtered Carbon on the

Accelerator Grid Wear Rates of the NEXT

and NSTAR Ion Thrusters

NASA/TM—2013-216605

December 2013

IEPC–2013–157
NASA STI Program . . . in Pro¿ le

Since its founding, NASA has been dedicated to the

advancement of aeronautics and space science. The

NASA Scienti¿ c and Technical Information (STI)

program plays a key part in helping NASA maintain

this important role.

The NASA STI Program operates under the auspices

of the Agency Chief Information Of¿ cer. It collects,

organizes, provides for archiving, and disseminates

NASA’s STI. The NASA STI program provides access

to the NASA Aeronautics and Space Database and

its public interface, the NASA Technical Reports

Server, thus providing one of the largest collections

of aeronautical and space science STI in the world.

Results are published in both non-NASA channels

and by NASA in the NASA STI Report Series, which

includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major signi¿ cant phase

of research that present the results of NASA

programs and include extensive data or theoretical

analysis. Includes compilations of signi¿ cant

scienti¿ c and technical data and information

deemed to be of continuing reference value.

NASA counterpart of peer-reviewed formal

professional papers but has less stringent

limitations on manuscript length and extent of

graphic presentations.

• TECHNICAL MEMORANDUM. Scienti¿ c

and technical ¿ ndings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies that

contain minimal annotation. Does not contain

extensive analysis.

• CONTRACTOR REPORT. Scienti¿ c and

technical ¿ ndings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scienti¿ c and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scienti¿ c,

technical, or historical information from

NASA programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scienti¿ c and

technical material pertinent to NASA’s mission.

Specialized services also include creating custom

thesauri, building customized databases, organizing

and publishing research results.

For more information about the NASA STI

program, see the following:

• Access the NASA STI program home page at

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

 443–757–5802

• Write to:

 STI Information Desk

NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
George C. Soulas

Glenn Research Center, Cleveland, Ohio

The Impact of Back-Sputtered Carbon on the

Accelerator Grid Wear Rates of the NEXT

and NSTAR Ion Thrusters

NASA/TM—2013-216605

December 2013

IEPC–2013–157

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

33rd International Electric Propulsion Conference (IEPC2013)

sponsored by the Electric Rocket Propulsion Society

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

The author thanks Dr. James E. Polk for his invaluable help, comments, and suggestions. This work was funded by the NASA

Science Mission Directorate’s In Space Propulsion Technology Program Of¿ ce at the NASA Glenn Research Center.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

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

Level of Review: This material has been technically reviewed by technical management.

This report contains preliminary ¿ ndings,

subject to revision as analysis proceeds.
NASA/TM22013-216605 1

The Impact of Back-Sputtered Carbon on the Accelerator Grid

Wear Rates of the NEXT and NSTAR Ion Thrusters

George C. Soulas

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

A study was conducted to quantify the impact of back-sputtered carbon on the downstream

accelerator grid erosion rates of the NASA¶s Evolutionary Xenon Thruster (NEXT) Long Duration Test.

A similar analysis that was conducted for the NASA¶s Solar Electric Propulsion Technology Applications

Readiness Program (NSTAR) Life Demonstration Test was used as a foundation for the analysis

developed herein. A new carbon surface coverage model was developed that accounted for multiple

carbon adlayers before complete surface coverage is achieved. The resulting model requires knowledge of

more model inputs, so they were conservatively estimated using the results of past thin film sputtering

studies and particle reflection predictions. In addition, accelerator current densities across the grid were

rigorously determined using an ion optics code to determine accelerator current distributions and an

algorithm to determine beam current densities along a grid using downstream measurements. The

improved analysis was applied to the NSTAR test results for evaluation. The improved analysis

demonstrated that the impact of back-sputtered carbon on pit and groove wear rate for the NSTAR LDT

was negligible throughout most of eroded grid radius. The improved analysis also predicted the

accelerator current density for transition from net erosion to net deposition considerably more accurately

than the original analysis. The improved analysis was used to estimate the impact of back-sputtered

carbon on the accelerator grid pit and groove wear rate of the NEXT Long Duration Test. Unlike the

NSTAR analysis, the NEXT analysis was more challenging because the thruster was operated for

extended durations at various operating conditions and was unavailable for measurements because the test

is ongoing. As a result, the NEXT LDT estimates presented herein are considered preliminary until the

results of future post-test analyses are incorporated. The worst-case impact of carbon back-sputtering was

determined to be the full power operating condition, but the maximum impact of back-sputtered carbon

was only a 4 percent reduction in wear rate. As a result, back-sputtered carbon is estimated to have an

insignificant impact on the first failure mode of the NEXT LDT at all operating conditions.

Nomenclature

dAerode/dAo Ratio of pit and groove eroded area to the hexagon area surrounding a single aperture

(dE/dx)e Electronic stopping power

(dE/dx)n Nuclear stopping power

e Electron charge

i Adsorbate adlayer (i = 0 denotes the substrate surface)

ja Average accelerator current density in the pit and groove erosion pattern

Ja Accelerator current

ja-trans Average accelerator current density at transition from net erosion to net deposition

Jaw Accelerator current collected by the accelerator aperture barrel walls

jb Beam current density along the accelerator grid

Jb Beam current
NASA/TM22013-216605 2

Nc Surface density of substrate adsorption sites occupied by adatoms

NEXT NASA¶s Evolutionary Xenon Thruster

NEXT LDT NEXT Long Duration Test

No Surface density of substrate adsorption sites

NSTAR NASA¶s Solar Electric Propulsion Technology Applications Readiness Program

NSTAR LDT NSTAR Life Demonstration Test

Ri Particle projectile range

RN Particle reflection coefficient (the ratio of reflected-to-total particles incident on a

surface)

s Adsorbate sticking coefficient

Va Accelerator power supply output voltage

Vbeam Beam plasma potential

Vcex Charge exchange ion energy

Vg Coupling voltage

Y Sputter yield

C Carbon back-sputter flux

i Fractional surface coverage of adlayer i

c Total fractional surface coverage of substrate adsorption sites by adsorbate

Subscripts and Superscripts:

C Carbon adsorbate

C-Mo Single carbon adsorbate adlayer on a molybdenum substrate

i Adsorbate adlayer (i = 0 denotes the substrate surface)

max Maximum value

Mo Molybdenum substrate

net Net value

trans Transition from net erosion to net deposition

I. Introduction

The NASA Glenn Research Center is responsible for the development of NASA¶s Evolutionary

Xenon Thruster (NEXT) ion propulsion system (Ref. 1). The NEXT system is a next generation ion

propulsion system to follow the successful NASA¶s Solar Electric Propulsion Technology Applications

Readiness Program (NSTAR) ion propulsion system that propelled NASA¶s Deep Space 1 spacecraft and

is presently propelling the Dawn spacecraft (Refs. 2 and 3). The objective of the NEXT project is to

advance this propulsion technology to NASA Technology Readiness Level 5, with significant progress

towards level 6, to support NASA Science Mission Directorate missions (Ref. 4). Propulsion system

elements under development by the NEXT program include a high performance, 7 kW ion thruster; a

modular, high-efficiency 7 kW power processor unit; a highly flexible advanced xenon propellant

management system; and a compact, light-weight thruster gimbal. This design approach was selected to

provide future NASA science missions with the greatest value in mission performance benefit at a low

total development cost (Ref. 1).

The service life capabilities of NEXT and NSTAR ion thrusters were assessed via analyses (e.g., see

Refs. 5 and 6) and long duration tests (e.g., see Refs. 7 to 11). During the operation of any long duration

test, accelerator grid wear rates are affected by two competing, facility-induced effects. The facility
NASA/TM22013-216605 3

background pressures are higher than that in space due to pumping speed limitations. This leads to a

higher neutral density near the accelerator grid and therefore the creation of more charge-exchange ions at

the accelerator grid region, which subsequently enhances accelerator grid wear rates. However, energetic

ions from the thruster¶s exhaust plume will also sputter-erode downstream vacuum facility surfaces. This

sputter-eroded facility material is ejected in all directions, including upstream towards the ion thruster and

its exposed accelerator grid. The phenomenon of depositing this sputter-eroded vacuum facility material

back onto a thruster is commonly referred to as back-sputtering. The back-sputtering of eroded facility

material onto the thruster¶s accelerator downstream grid can potentially introduce an unwanted effect

where the accelerator grid downstream surface erosion rate is masked by the arrival rate of back-sputtered

facility material. To mitigate this effect, sputter-eroded facility walls are lined with a low sputter yield

material, typically carbon in the form of graphite. Unfortunately, there is a concern that carbon deposition

on critical accelerator grid erosion sites can significantly reduce their erosion rates compared to that in

space (Ref. 12).

The NEXT ion thruster service life capability is being assessed, in part, via a long duration test

(NEXT LDT) that was initiated in June 2005 and is still operational today (Ref. 7). The objectives of this

test are to demonstrate the initial project qualification propellant throughput requirement of 450 kg,

validate thruster service life modeling predictions, quantify thruster performance and erosion as a function

of engine wear and throttle level, and identify unknown life-limiting mechanisms. After demonstration of

the qualification propellant throughput of 450 kg of xenon, the first objective was redefined to test to

failure or as long as project funding permits. In September of 2013, the thruster exceeded 50,000 h of

accumulated operation and 900 kg of propellant throughput with a demonstrated total impulse of

 34.8 MN·s over a range of power-throttled operating conditions. The NEXT LDT has set electric

propulsion records for the most hours of operation, highest propellant throughput processed, greatest total

impulse demonstrated, and longest hollow cathode operation (Ref. 7).

A detailed service life assessment was also conducted in parallel with the NEXT LDT (Ref. 5). All

credible thruster failure modes were assessed over the full power throttling range of the NEXT ion

thruster. The first failure mode of the NEXT thruster over the entire power throttling range was predicted

to be structural failure of the accelerator grid. This failure mode is due to sputter erosion of the

downstream accelerator grid surface by charge-exchange ions created in this region. These eroding ions

create a hexagonal 3pit and groove ́ erosion pattern that surrounds each aperture as shown in Figure 1.

Because the NEXT LDT ion thruster is operated in a vacuum facility that is lined with graphite panels

(Ref. 7), this thruster wear is subject to carbon back-sputtering. As a result, the impact of back-sputtered

carbon on accelerator grid pit and groove wear rate must be assessed to verify that the objectives of the

test are being met.

Pit

Groove

Figure 1.2The NEXT LDT accelerator

grid center aperture at 19,520 h

showing the pit and groove erosion

pattern. Darker regions are net carbon

deposition while lighter regions are net

molybdenum erosion.
NASA/TM22013-216605 4

Following the NSTAR Life Demonstration Test (NSTAR LDT), a detailed analysis was conducted to

assess the effects of carbon deposition on accelerator grid pit and groove wear rate (Refs. 11 and 12). A

surface coverage time rate of change model was developed to assess the impact of back-sputtered carbon

on the sputter yield of the molybdenum accelerator grid surface. Sputter yields of a single carbon

monolayer adsorbed onto a molybdenum surface were both measured and determined theoretically based

on a model by Sigmund and Winters (Ref. 13). Both measured and theoretically-determined sputter yields

for a single carbon monolayer were found to be much higher than that of bulk carbon. Unfortunately, the

surface coverage model was unable to correctly predict the measured location of the transition from net

grid erosion to net carbon deposition using these higher yields. This ultimately brought into question the

efficacy of the analysis.

The objective of this paper is to quantify the impact of back-sputtered carbon on the downstream

accelerator grid erosion rates for the NEXT LDT. The NSTAR analysis of Reference 12 provides an

excellent foundation for the analysis of the NEXT LDT. However, the NSTAR analysis must first be

improved to more accurately predict this transition from net erosion to net deposition. This paper is

therefore divided into four sections. The analysis for this study is first presented. It includes a description

of the original NSTAR analysis with improvements developed for this study. Afterwards, these analysis

improvements are evaluated and sensitivities to the model inputs are determined using the NSTAR LDT

results. The improved analysis is then applied to the NEXT LDT to determine the impact of backsputtered carbon on the accelerator grid pit and groove wear rates. Finally, conclusions from this study are

presented.

II. Analysis Approach

The NSTAR analysis approach and improvements for this study are described in the following

sections. The general model for determining the impact of back-sputtered carbon on accelerator grid wear

is initially described. A more rigorous carbon surface coverage model is then presented, which is the

primary input to the aforementioned general model. Finally, the various model inputs for this study are

determined.

A. Impact of Back-Sputtered Carbon on Accelerator Grid Wear

The following general model for the impact of back-sputtered carbon on accelerator grid pit and

groove wear rate is the same as that developed for the NSTAR LDT analysis in Reference 12 and is

presented here for completeness. There are three particles involved in the sputter erosion process at the

accelerator grid surface in the presence of carbon back-sputtering: the xenon ion, the molybdenum grid

substrate, and the carbon adsorbate. Molybdenum has a body-center cubic lattice with a total carbon

adsorption site surface density, No, of 1.0 1015 cm±2

. If Nc is the number density of adsorbed carbon atoms

(or adatoms) occupying those potential adsorption sites, then the fractional substrate surface coverage by

adsorbate adatoms, c

, is given by:

o

c

c

N

N

. (1)

The fractional surface coverage will later be shown to be a function of parameters that can vary across a

grid (e.g., accelerator current density), so c represents the fractional surface coverage of a differential

area along the grid.
NASA/TM22013-216605 5

For the moment, adsorbed carbon is assumed to form no more than a single monolayer on the

molybdenum substrate and that the fractional substrate surface coverage is small (i.e., c

 1). According

to Sigmund and Winters, there are three potential interactions that can occur when a xenon ion bombards

the surface of the molybdenum accelerator grid and these are depicted in Figure 2 (Ref. 13). For the first

interaction, the xenon ion collides with a carbon adatom, elastically transferring a portion of its kinetic

energy to the adatom, which subsequently reflects from the substrate surface. For the second interaction,

the xenon ion reflects from the molybdenum substrate and collides with a carbon adatom. For the third

interaction, the xenon ion collides with the molybdenum substrate, initiating a collisional cascade that

causes a molybdenum substrate atom(s) to collide with a carbon adatom, transferring a portion of its

kinetic energy to the adatom. For all three interactions, the adatom escapes the surface only if its energy

normal to the surface is greater than the adsorbate surface binding energy. Finally, there is an increased

probability that a single xenon ion can cause more than one interaction as the fractional substrate surface

coverage approaches complete coverage (i.e., c 1).

The ion and substrate atoms colliding with adsorbate adatoms for the first and third interactions only

transfer a portion of their kinetic energy, so some substrate sputtering still occurs even in the presence of

single carbon monolayer surface coverage. However, substrate sputtering can be eliminated in the

presence multiple carbon adsorbed monolayers, or adlayers. Multiple adlayers of carbon adsorbate result

in xenon ion energy dissipation as it penetrates the adsorbate surface. If the number of adlayers is large

enough, no substrate sputtering occurs. Because multiple adlayers of carbon adsorbate will be shown to

exist for c 1, it can be assumed that the net sputter yield of the molybdenum substrate, net YMo , is given

by (Ref. 12):

Mo c

net YMo Y 1 . (2)

Mo Substrate

C Adsorbate

Xe Ion Interaction 1

Mo Substrate

C Adsorbate

Xe Ion Interaction 2

Mo Substrate

C Adsorbate

Xe Ion Interaction 3

Figure 2.2Collisional interactions between ion,

adsorbate, and substrate atoms.
NASA/TM22013-216605 6

Here, YMo is the sputter yield of the bulk molybdenum substrate. The above equation conservatively

assumes that any carbon surface coverage results in the elimination of molybdenum substrate sputtering at

that site. This equation defines an average sputter yield of a molybdenum substrate covered with carbon

adatoms, and therefore represents a macroscopic quantity. Rearranging this equation yields:

c

Mo

net

Mo

Y

Y

1 . (3)

The above ratio represents a correction factor for the accelerator grid wear rate in the presence of carbon

back-sputtering. Because 0 c

 1 in the presence of back-sputtering, back-sputtered carbon acts to

reduce the accelerator grid wear rate demonstrated in ground test facilities. And because this net to bulk

molybdenum sputter yield ratio is a function of c, this ratio can vary along the surface of the grid. All

that remains is to determine c

, which is the topic of the next section.

B. Carbon Surface Coverage Model

Development of a carbon surface coverage model requires an understanding of the thin film growth

processes. During a sputter deposition process, sputtered adsorbate collides with the substrate surface

atoms. If the subsequent elastic collisions are sufficient to dissipate the adsorbate kinetic energy normal to

the surface, the adsorbate can be physisorbed onto the substrate surface to create an adatom. While

physisorbed on the surface, these adatoms can diffuse along the surface to form and grow clusters.

Clusters can also form and grow due to direct adatom collision. After reaching a certain critical size, the

clusters become stable nuclei and are chemisorbed onto the surface, marking the start of the nucleation

stage. During this stage, these nuclei grow in number and size until a saturation nucleation density is

achieved. During this growth process, the nuclei exhibit one of three growth modes (Refs. 14 and 15):

1. Island-type growth (or Volmer-Weber growth), where the nucleus grows both normal and parallel

to the substrate surface;

2. Layer-type growth (or Frank van der Merwe growth), where the nucleus grows parallel to the

substrate surface layer by layer; and

3. Mixed-type growth (or Stranski-Krastanov growth), where the nucleus typically exhibits a layeredtype growth, followed by island-type growth.

The nuclei will eventually coalesce, forming bigger islands in a process called agglomeration. These

larger islands eventually merge leaving channels and holes of uncovered substrate surface, which are

eventually filled by secondary nucleation and growth (Ref. 14).

In most practical sputter deposition applications, island-type growth occurs (Ref. 14). Layer-type

growth requires a lower binding energy between carbon adatoms than that between carbon adatoms and

the molybdenum substrate (Ref. 15). Because the primary desorption mechanism in this study is

sputtering, this layer-type growth requires the sputter yield of a single carbon monolayer on a

molybdenum substrate to be less than that of bulk carbon, a condition that was shown to be violated in

Reference 12. As a result, layer- and mixed-type growths are not occurring during back-sputtered carbon

adsorption on the accelerator grid.

Another growth mode type can also occur and is called columnar growth. This surface layer growth

mode is characterized by ballistic aggregation of adsorbate due to very low adatom surface mobility

(Ref. 15). The resulting columnar-like film structure is quite porous and exhibits poor mechanical

properties.

Whether island-type or columnar growth is occurring during back-sputtered carbon adsorption on the

molybdenum accelerator grid, both growth modes have a common attribute: there are multiple adlayers

before complete surface coverage is achieved. As a result, the carbon surface coverage model must

account for these multiple carbon adlayers.
NASA/TM22013-216605 7

For the original NSTAR analysis, the surface coverage time rate of change was described with the

model below:

C Mo c

a

C

c

o Y

e

j

dt

d

N . (4)

Here, C is the back-sputter flux of carbon adsorbate, ja is the accelerator ion current density in the pit and

groove erosion pattern, e is the electron charge, and YC-Mo is the sputter yield of a single carbon adlayer on

a molybdenum substrate. To determine equilibrium surface coverage, d c/dt is set equal to zero and the

result is solved for c:

a C Mo

c

c

j Y

e

. (5)

However, this equation lacks adequate rigor because it fails to account for the growth of multiple carbon

adlayers before complete surface coverage is achieved. In addition, it fails to distinguish between

adsorption onto substrate versus existing adsorbate surface coverage.

So, for this study, a more rigorous carbon surface coverage model was developed. The basis for this is

a model developed by Brunauer, Emmitt, and Teller that was originally used to describe the physisorption

of additional gas adlayers on a chemisorbed adlayer (Ref. 16). For the development of this model, the

following assumptions were made:

1. Back-sputtered carbon adsorbate can be adsorbed both onto a molybdenum substrate and existing

carbon adatoms, allowing for a range of adlayers before complete surface coverage is achieved.

2. Carbon adatom surface diffusion is neglected. Although some surface diffusion is likely occurring,

surface diffusion is likely limited by ion bombardment. The evidence for this is shown in Figure 3

for the NSTAR LDT accelerator grid surface at the transition from net erosion to net deposition.

The image shows carbon deposition throughout most of the surface. However, the carbon film in

the pit and grove erosion pattern is significantly porous compared to the films next to it. And the

only difference between these sites is the degree of ion bombardment. Significant ion

bombardment is speculated to have caused sputter-induced desorption of the weakly-bonded

physisorbed carbon, limiting its mobility on the film and substrate surfaces.

3. Carbon adsorbate bulk diffusion is neglected. Thermally-induced bulk diffusion is limited by the low

anticipated molybdenum substrate temperature (i.e., an anticipated grid temperature of

approximately 200 C versus the 3650 C sublimation temperature for graphite) (Ref. 17). However

there can be sputter-induced redistribution of adsorbate particles, which is neglected here.

4. Carbon adatoms only stack one on top of another, so No is constant for all adlayers. Graphite,

which has a stacked hexagonal lattice, has surface densities of 3.8 1015 cm±2

 along the hexagonal

plane and 1.4 1015 cm±2

 perpendicular to it. Although this varying No is not captured by the

model, the carbon film in the pit and groove pattern was shown to be porous with a density

 60 percent of maximum theoretical density of graphite (Ref. 12).

5. The only carbon desorption mechanism is sputter erosion. Ho et al. showed that thermal

desorption for a single carbon adlayer on a molybdenum substrate is negligible for temperatures

 300 C (Ref. 18). And sublimation of bulk carbon in the form of graphite requires significantly

higher temperatures.

6. Sputter erosion can only remove a surface carbon adatom and not underlying atoms.

7. Carbon adsorption onto either the molybdenum substrate or carbon adsorbate includes a sticking

coefficient.
NASA/TM22013-216605 8

Figure 4.2Illustration of the surface coverage model developed for this study.

The assumptions are appropriate for column-like growth, with the only shortcomings being the lack of the

adatom self-shadowing that leads to the columnar structures in the thin film and that the redistribution due

to adsorbate layer sputtering was neglected (Ref. 15). If island-type growth is occurring, the impacts of

limited surface diffusivity and the redistribution due to adsorbate sputtering are not included in this

model. At present, the exact growth mode is unknown.

The surface coverage model developed for this study is illustrated in Figure 4. Because the adsorption

of multiple carbon adlayers must be considered, total surface coverage is given by summing the fractional

surface coverages of the various adlayers of carbon adatoms, i:

i 1

c i

. (6)

And surface area fraction not covered by carbon adatoms, 0, is given by:

c

1 0

. (7)

Figure 3.2Scanning electron photomicrograph of the

downstream NSTAR accelerator grid at 11.8 cm from

the center of the grid (Ref. 12). White areas are

molybdenum and gray areas are carbon.

Mo Substrate

Carbon

Adatom ---- i = 9

---- i = 8

---- i = 7

---- i = 6

---- i = 5

---- i = 4

---- i = 3

---- i = 2

---- i = 1
NASA/TM22013-216605 9

The time rate of change of i

 is the creation rate of i per unit area minus the removal rate of i per unit

area which is given by:

dt

d

N

i

o = Creation rate of i

 per unit area2Removal rate of i per unit area.

The fractional coverage of adlayer i can be increased by either carbon adsorption onto i-1 or desorption

via sputtering of i+1:

C i 1 i 1

s Carbon adatom adsorbed onto layer i±1

i 1 i 1

a Y

e

j

Carbon adatom desorbed from layer i+1

Here, si is the adsorbate sticking coefficient on adlayer i and Yi is the sputter yield of carbon adlayer i. The

fractional coverage of adlayer i

 can be decreased by either carbon adsorption onto i or desorption via

sputtering of i:

C i i

s Carbon adatom adsorbed onto layer i

i i

a Y

e

j

Carbon adatom desorbed from layer i

Substituting the creation and removal rates per unit area above into the time rate of change of i

 yields for

i 1:

i i i i

a

C i i i i

i

o Y Y

e

j

s s

dt

d

N 1 1 1 1

 (8)

and for i = 0 (i.e., along the molybdenum substrate surface):

0 0 1 1

0 Y

e

j

s

dt

d

N

a

o C . (9)

At equilibrium surface coverage, the fractional surface coverage time rate of change is equal to zero,

so:

0

i 1

c i

dt

d

dt

d

. (10)

After substituting the equations for d i

/dt into the above equation and rearranging, it can be shown that

the fractional surface coverage of carbon adsorbate is given by:

1 1

1

1 1

1

1

i

i

k

k

k

i

a

C

i

i

k

k

k

i

a

C

c

Y

S

j

e

Y

S

j

e

. (11)

.
NASA/TM22013-216605 10

This equation includes a series summation to infinity, which complicates numerical evaluation. However,

this summation to infinity can be eliminated by noting that for i imax adlayers, carbon adlayer sputter

yield and sticking are equivalent to that of bulk carbon and are, therefore, constant (i.e., Yi = YC and si =

sC, respectively, for i imax). It can, therefore, be shown that the fractional surface coverage of carbon

adsorbate is given by:

1 max 1 max 1 max

1 max1 max1 max

1 1

1

1 0

1

1 0 1 1

1

1

1

1

1

1

1

i

i

i

k

k

k

i

a

C

i

i

i

a C

C C

a C

C C

i

k

C k

C k

i

i

i

k

k

k

i

a

C

i

i

i

a C

C C

a C

C C

i

k

C k

C k

c

Y

S

j

e

j Y

e S

j Y

S Y e S

Y S

Y

S

j

e

j Y

e S

j Y

S Y e S

Y S

 (12)

for a

j

C

C C

Y

e S

 and:

1 c

 (13)

for aj

C

C C

Y

e S

. Here, the series summation to infinity was eliminated with the use of a power series

expansion.

A value of interest from the above equations is the accelerator current density at the transition from

net erosion to net carbon deposition. At this transition, there is complete carbon adsorbate surface

coverage, so c = 1. It can be shown that c 1 as:

a C

C C

j Y

e S

1 0. (14)

The resulting ion current density is given by:

C

C C

a trans Y

e S

j . (15)

Here, ja-trans is the accelerator ion current density where transition from net erosion to net deposition

occurs. This equation shows that the transition is a function of bulk carbon sputter yield and adsorbate

sticking coefficient, indicating that the surface is made up of multiple carbon adlayers at complete surface

coverage.

The fractional surface coverage from Equation (12) is the more rigorous model used in this study. It

accounts for the multiple carbon adlayers prior to complete substrate surface coverage with the

aforementioned assumptions. However, this more rigorous model requires knowledge of more terms than

that of the original NSTAR analysis. While the NSTAR analysis model required knowledge of C, ja, and

YC-Mo, this new model also requires knowledge of:

1. adlayer sputter yields Yi between Y1 (= YC-Mo) and Yi imax (= YC);

2. carbon adsorbate sticking coefficients sMo and sC;

3. carbon adlayer sticking coefficients si between s0 (= sMo) and si imax (= sC); and

4. imax for both sputter yield and sticking coefficient.

The next section will define these model inputs.
NASA/TM22013-216605 11

C. Model Inputs

The following sections will discuss how some carbon surface coverage model inputs were

determined. This includes the determination of adsorbate sputter yields, adsorbate sticking coefficients,

and accelerator ion current densities in the pit and groove erosion pattern.

1. Adsorbate Sputter Yields

Reference 12 included measurements of sputter yields of a single monolayer of carbon adsorbate on a

molybdenum substrate with xenon ions (i.e., Y1 = YC-Mo). As discussed by Polk et al., there was some

concern that their study¶s measured sputter yields with xenon required a surface binding energy to match

their theoretical predictions that was too low (Ref. 12). Since that study, these sputter yields were remeasured by Ho et al. with the results being nearly identical to those of the original study (Refs. 12 and

18). In addition, the Sigmund and Winters theoretical model used in Reference 12 was reviewed by this

author and updated with more recent sputter yields, reflection coefficients, and screening potentials for

elastic collisions. The resulting theoretical predictions required unrealistically high surface binding

energies for favorable comparisons with measurements, indicating that this theoretical model should not

be used to draw conclusions about surface binding energy magnitudes. So, for this study, sputter yields of

a single monolayer of carbon adsorbate on a molybdenum substrate with xenon ions were those measured

by Ho et al. and extrapolated to the lower xenon ion energies of interest in this study (Ref. 18).

The sputter yield of bulk carbon graphite (i.e., YC) was used to define the carbon adlayer sputter

yields (i.e., Yi) for i imax. These sputter yields were determined by curve-fitting the carbon sputter yield

measurements of Ref. 19 as a function of xenon ion energy.

Thin film sputter yield measurements were used to estimate the number of adlayers required for the

carbon adsorbate sputter yield to equal that of bulk carbon (i.e., imax). Anderson and Bay found that

reliable bulk sputter yields could be measured when film thicknesses were 1/2 of the projectile range

(Ref. 20). The projectile range, Ri, is the total path length of a bombarding ion in a solid material and is

given by (Ref. 21):

0

Vcex

n e

i

dx

dE

dx

dE

dE R . (16)

Here, Vcex is the ion energy and (dE/dx)n and (dE/dx)e are the nuclear (or elastic) and electronic (or

inelastic) stopping powers of a xenon projectile in a carbon target. These stopping powers are defined in

Reference 21 using a Ziegler, Biersack, and Littmark screening potential. The stopping powers also

require a density for the carbon adsorbate. The density of graphite is 2.25 gm/cm3, and this density was

found to be consistent with the quartz crystal microbalance mass and post-test thickness measurements for

the NSTAR LDT (Ref. 12). However, carbon films from the accelerator grid downstream surface were

thicker due to enhanced porosity with a corresponding density of 1.35 gm/cm3 (Ref. 12). This latter

carbon density was used to determine adsorbate stopping powers. The number of adlayers required for the

carbon adsorbate sputter yield to equal that of bulk carbon, imax, is given by:

3 3

3 3

10

max

1.35 10 /

2.25 10 /

2 3.35 10

kg m

kg m

m

R

i

i

. (17)

Here, an average adlayer thickness of half of the lattice parameter perpendicular to hexagonal plane of a

graphite lattice (i.e., 3.35 10±10 m) was conservatively assumed and this dimension is further modified
NASA/TM22013-216605 12

with the lower carbon density deposited on the NSTAR grid. For the range of xenon ion energies

investigated in this study, the number of adlayers required for the carbon adsorbate sputter yield to equal

that of bulk carbon was estimated to be about 3 (i.e., imax 3).

Thin film sputter yield measurements were also used to estimate how sputter yields vary as a function

of adlayer number for 1 i imax (i.e., Yi

 between YC-Mo and YC). Anderson and Bay measured sputter

yield variations of thin gold films on a beryllium substrate as a function of film thickness for thicknesses

less than 1⁄2 the projectile range (Ref. 20). Their results showed that the sputter yield varies

approximately linearly as a function of adsorbate thickness. Therefore, Yi was assumed to vary linearly

from YC-Mo to YC for 1 i imax for this study.

2. Sticking Coefficient

Sputtered particles are known to be eroded with kinetic energies that follow a Sigmund-Thompson

energy distribution function (Ref. 21). For a carbon target eroded by xenon ions, eroded particle energies

range from zero to 31 percent of the bombarding ioQ¶s kinetic energy with the most probable energy

being half of the carbon surface binding energy (i.e., about 3.7 eV) (Refs. 21 and 22). For back-sputtered

carbon to be either physisorbed or chemisorbed onto the molybdenum substrate or a carbon adlayer, the

back-sputtered carbon¶s energy normal to surface must first be dissipated via elastic collisions with

surface atoms. If the back-sputtered carbon collides with carbon adlayers, the full kinetic energy of the

eroded carbon projectile can be elastically transferred in a single collision. However, if back-sputtered

carbon collides with the molybdenum substrate, a maximum of only 40 percent of the carbon projectile¶s

kinetic energy can be elastically transferred in a single collision. Because the back-sputtered carbon

particle¶s energy can be large, and in the case of the molybdenum substrate, its energy transfer via

collisions is inefficient, back-sputtered carbon reflection can be significant. The fractional number of

reflected carbon particles is given by RN, and therefore, the sticking coefficient is given by s = 1 ± RN.

Modeling results from Joh, et al. were used to determine the reflection coefficients for a carbon

projectile on molybdenum and carbon targets (Ref. 23). That study yielded reflection coefficients of ~0.4

and 0.07 for a carbon projectile on molybdenum and carbon targets, respectively, for the energy range

of interest in this study. But that study assumed that reflected particles with a reflected energy of 1 eV

were adsorbed by the surface (Ref. 23). A more appropriate energy would have been the anticipated

chemisorption energy, which would have resulted in a lower reflection coefficient. In an attempt to

correct these results for this higher chemisorption energy, the reflection coefficients were integrated over

the full Sigmund-Thompson energy distribution range so that projectiles with an energy less than or equal

to a conservatively assumed energy of 7.4 eV (i.e., the surface binding energy of carbon) (Ref. 22) were

not reflected, but those with a higher energy retained the aforementioned reflection coefficients. The

resulting sticking coefficients for a carbon projectile were estimated to be sMo 0.7 for a molybdenum

target and sC 1.0 for a carbon target for the full range of energies examined in this study.

Finally, the sticking coefficient at the accelerator grid surface was conservatively assumed to

immediately transition from sMo to sC with the first adlayer of carbon (i.e., s0 = sMo and si 1 = sC for carbon

sticking) for this study.

3. Average Accelerator Current Density

In this study, an average accelerator current density in the pit and groove erosion pattern was

estimated using the equation below, which is similar to that used in Reference 12:

erode

o

b

a aw

a b

dA

dA

J

J J

j j . (18)
NASA/TM22013-216605 13

Here, jb is the beam current density along the grid surface, Ja is the accelerator current, Jaw is the

accelerator current collected at the accelerator aperture walls, Jb is the beam current, and dAerode/dAo is

ratio of the pit and groove eroded area to the hexagon area surrounding single aperture. Note that Ja± Jaw

represents the total grid current collected at the pit and groove erosion site and that the area surrounding a

single aperture is a hexagon because of the hexagonal aperture pattern used for the grids.

For this study, Ja and Jb were averages of the measured values during operation at a particular

operating condition. The current Jaw was determined using the ion optics code developed in Reference 24.

The ratio dAerode/dAo was determined from pit and groove erosion measurements.

Finally, the beam current density along the grids (i.e., jb) was rigorously determined using measured

downstream beam current densities and an algorithm developed by this author that is similar to that of

References 6 and 24. For this algorithm, the ion optics code of Reference 24 is used to develop an

empirical equation for the emitted beam current density per steradian as a function of beamlet current

along the grid for a given set of grid potentials. Equations were developed for predicting the radial

downstream beam current density profile from the spherically-domed grid surface. These equations treat

individual beamlets as point sources and assume a direct line-of-sight transmission (i.e., beam ion

deflection by downstream potential gradients is neglected). These equations also account for the current

emitted by every aperture and for probe area effects, which are important for beam current density

measurements close to the thruster grid. The beamlet current distribution along the spherically-domed

grid must be integrated to predict the downstream beam current density. However, the downstream beam

current density is an algorithm input, so a program was developed to iteratively determine the beamlet

current distribution along the grid surface. The beam current density along the grid is just the beamlet

current divided by the hexagonal area surrounding an aperture.

A sample output of the aforementioned algorithm is shown in Figure 5 for the NEXT LDT thruster

operating at full power. As shown in the figure, the planar probe measurement 2.0 cm downstream of the

grids was used to predict the beam current density along the grid surface. Because the NEXT LDT is also

equipped with planar probes located 17.3 and 23.8 cm downstream, these can be used to check the

algorithm. The results, shown in Figure 6, demonstrate the algorithm¶s ability to predict these

downstream beam current density profiles.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

30 20 10 0 10 20 30

Radius, cm

Algorithm Result Along Grid

Measured 2.0 cm Downstream

Figure 5.2Measured and predicted beam current densities for the

NEXT LDT thruster at full power.
NASA/TM22013-216605 14

III. Evaluation of Analysis Improvements Using the NSTAR LDT

The objective of this section is to evaluate the improvements made to the analysis and determine

sensitivities to the model inputs. This is done by applying the improved analysis approach to the NSTAR

LDT. The first section describes test-specific inputs to the analysis. The section thereafter presents and

discusses the results of the analysis.

A. NSTAR LDT Analysis Inputs

Test-specific model inputs have to be determined to apply the improved analysis to the NSTAR LDT.

During this test, a NSTAR ion thruster was operated at full power throughout the 8,192 h test

(Refs. 11 and 12). The NSTAR LDT vacuum facility was internally lined with graphite panels to reduce

facility material back-sputtering. The back-sputter rate was measured with a quartz crystal microbalance

located next to the thruster and confirmed with post-test film thickness measurements. The back-sputter

rate of carbon was determined to be 0.7 m/kh, which corresponded to a carbon flux of 2.19 1012 atoms/

cm2·s (Ref. 12).

The average beam and accelerator currents were 1.76 A and 6.78 mA, respectively (Ref. 12). An ion

optics code was used to determine that only 0.96 mA of accelerator current was collected on the

accelerator aperture barrels (Ref. 24), which is significantly less than the 3.7 mA estimate in the original

NSTAR analysis (Ref. 12). The original NSTAR analysis determined this accelerator current split by

using a simple ratio of the measured mass losses from the accelerator grid erosion sites. However, this

incorrectly assumes that charge exchange ions that impact aperture barrel walls have the same average

energy and sputtering angle of incidence as those of the pit and groove sites. Charge exchange ions that

impact the accelerator barrels are created within inter-grid region and have higher average energies and

sputter the barrel walls at higher angles of incidence than those of the pit and groove erosion sites

(Refs. 25 and 26). Finally, the ratio dAerode/dAo was inferred from Reference 12 to be 0.312, and this was

constant across the accelerator grid.

The beam current density, shown in Figure 7, was measured with a planar probe located 2.5 cm

downstream of the grid. Also shown in the figure is the current density along the grid, which was

determined by the algorithm of this study. The average accelerator grid current density in the pit and

groove erosion pattern from Equation (18) is shown in Figure 8. Note that these current densities are

nearly twice those of Reference 12, and this is primarily due to that study¶s inaccurate accelerator current

split. The maximum accelerator current density, ja-max, was 64 A/cm2

 at the center of the grid.

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 5 10 15 20 25 30 35 40

Radius, cm

2.0 cm Measured

2.0 cm Modeled

17.3 cm Measured

17.3 cm Modeled

23.8 cm Measured

23.8 cm Modeled

Figure 6.2Measured and predicted beam current densities for the

NEXT LDT thruster at full power at various axial locations.
NASA/TM22013-216605 15

The maximum accelerator current density is important because its corresponding location on the grid is

where failure due to pit and groove erosion would be expected to occur.

The charge exchange ions that erode the pit and groove erosion site are assumed to be created downstream

of the accelerator grid sheath, so that they impact this erosion site with a potential, Vcex given by:

Vcex Va Vg Vbeam . (19)

Here, Va is the accelerator power supply voltage (i.e., ±180 V for the NSTAR LDT), Vg is the coupling

voltage (i.e. ±15 V for the NSTAR LDT), and Vbeam is the beam plasma potential, which is assumed to be

5 V throughout this study. So, charge change ions are assumed to erode the pit and groove erosion site

with a 200 V potential for the NSTAR LDT. The resulting sputter yields for a single carbon monolayer on

molybdenum (i.e., YC-Mo) and bulk carbon (i.e., YC) were 0.99 and 0.040, respectively.

The transition from net erosion to net deposition was measured post-test to be at a radial location of

11.8 cm (Ref. 12). This corresponded to a transition accelerator current density of 17 A/cm2

. As will be

shown in the next section, this transition current density can be used, in part, to check the analysis.

0

1

2

3

4

5

6

7

0 2 4 6 8 10 12 14 16

Radius, cm

Algorithm Result Along Grid

Measured 2.5 cm Downstream

Figure 7.2Measured and predicted beam current densities for

the NSTAR LDT thruster at full power.

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12 14 16

Radius, cm

Figure 8.2Estimated average accelerator current density in the

pit and groove erosion pattern for the NSTAR LDT thruster at

full power.
NASA/TM22013-216605 16

B. NSTAR LDT Results and Discussions

Results from the improved analysis are shown in Figure 9 along with NSTAR analysis results for

comparison. Note that the only difference between the analyses in this figure is the surface coverage

model. The improved analysis utilizes Equations (12) and (13) while the NSTAR analysis utilizes

Equation (5). The figure also includes the maximum and transition accelerator current densities

determined in the prior section. Figure 9 illustrates that the improved analysis net-to-bulk molybdenum

sputtering ratio exhibits a steep drop with decreasing current density near the predicted transition. The

NSTAR analysis exhibited a more gradual decrease with decreasing current density. The improved

analysis shows that for current densities greater than the transition current density, the impact of backsputtered carbon on the pit and groove wear rate is insignificant. Or, put differently, the impact of backsputtered carbon on the pit and groove wear rate is insignificant at the net erosion sites.

Figure 9 also illustrates that the improved analysis predicts the transition current density considerably

more accurately than the NSTAR analysis. The measured transition current density is 1.9 times the

improved analysis prediction, but is 47 times the NSTAR analysis prediction. Possible causes for the

remaining discrepancy between improved analysis¶ prediction and the measured transition current density

include the following:

1. The bombarding ion potential determined by Equation (19) is too high, leading to a high sputter

yield. Charge-exchange ions that bombard the pit and groove erosion site have an energy

distribution with a maximum of Vcex. Though an ion optics code confirmed this (Ref. 24), code

results showed that this error only accounts for about a tenth of the discrepancy.

2. The bulk carbon sputter yield used in this study may be incorrect. Bulk carbon sputter yield

measurements for xenon at 200 V range from 0.024 to 0.090 (Ref. 27). This study used a yield of

0.040, and this may have been too high (Ref. 19). In addition, the porous surface may be affecting

this yield. This porous surface could have led to increased re-deposition, leading to an overall

reduction in sputter yield (Ref. 20).

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100

Accelerator Current Density, A/cm2

NSTAR Analysis

Improved Analysis

Transition Current Density

Maximum Current Density

Figure 9.2The ratio of net-to-bulk molybdenum sputter yield as a function

of accelerator current density in the pits and grooves for the improved

and NSTAR analyses. The input values for the improved analysis were:

YC-Mo = 0.99, YC = 0.040, imax = 3, and sMo = 0.7.
NASA/TM22013-216605 17

3. A poor assumption or error in the determination of the transition accelerator current density may

be contributing to the discrepancy. For example, Figure 8 shows that the radial location for this

transition (i.e., 11.8 cm) occurs where the accelerator current density was changing significantly

as a function of radius. This could have introduced error in the measured transition accelerator

current density.

4. A poor assumption used for the carbon surface coverage model may be contributing to the

discrepancy. For example, the surface coverage model is a simple one-dimensional model.

However, there may be two- and three-dimensional effects, such as buildup of carbon deposition

surrounding the pits and grooves, that are leading to a local increase in carbon flux to the erosion

site. This would lead to a higher transition current density.

Figure 10 illustrates the sensitivity of the new carbon surface coverage model of Equations (12) and

(13) to the model inputs Y1, imax, and s0. Figure 10 shows that increasing Y1 from an unrealistically low

value of YC (i.e., 0.040) to YC-Mo (i.e., 0.99) and imax from 2 to 3 causes the ratio of net-to-bulk

molybdenum to exhibit a significantly steeper drop with decreasing current density. Decreasing s0 from

1 to sMo (i.e., 0.7) had a similar effect, but it was not as pronounced as that from the other inputs. This is

an indication that the first carbon adlayer (i.e., 1) is dictating the shape of the curve. This is further

demonstrated in Figure 11 for the fractional surface coverages of the various adlayers as a function of

accelerator current density. The first adlayer dominates the total carbon surface coverage for much of the

current density range. It is only near the transition current density that the surface coverages of the

subsequent adlayers impact the shape of the total surface coverage profile. Figure 11 shows that at the

transition current density, the surface coverage of the adlayers displayed decrease abruptly because of

rapid adlayer buildup due to decreased desorption via sputtering.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 10 100

Accelerator Current Density, A/cm2

Y1 = 0.99, imax = 3, s0 = 0.7

Y1 = 0.99, imax = 3, s0 = 1

Y1 = 0.99, imax = 2, s0 = 1

Y1 = 0.04, imax = 2, s0 = 1

Transition Current Density

Maximum Current Density

Figure 10.2The ratio of net-to-bulk molybdenum sputter yield as a function

of accelerator current density in the pits and grooves for various values

of Y1, imax, and s0.
NASA/TM22013-216605 18

Figure 12 shows the ratio of net-to-bulk molybdenum sputtering from Figure 9 at the transition

current density more clearly. The figure shows two solutions. The 3unlatched ́ solution uses

Equation (19) to determine Vcex (i.e., 200 V). The 3latched ́ solution uses the measured transition current

density to determine Vcex (i.e., 149 V) and represents a conservative estimate because the reduced ion

energy decreases YC-Mo, which may not be occurring here. For either solution, however, Figure 12 shows

that the impact of back-sputtered carbon on pit and groove erosion for the NSTAR LDT was negligible

throughout most of eroded grid radius.

0.0001

0.001

0.01

0.1

1

8 10 12 14 16 18 20

Accelerator Current Density, A/cm2

Total Surface Coverage

i = 1 Surface Coverage

i = 2 Surface Coverage

i = 3 Surface Coverage

i = 4 Surface Coverage

i = 5 Surface Coverage

i = 10 Surface Coverage

Figure 11.2The fractional surface coverage of various adlayers (i.e., i)

and the total carbon surface coverage (i.e., c) as a function of

accelerator current density in the pits and grooves. The input values

were: YC-Mo = 0.99, YC = 0.040, imax = 3, and sMo = 0.7.

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1

1 10 100

Accelerator Current Density, A/cm2

Unlatched (200 V)

Latched (149 V)

Transition Current Density

Maximum Current Density

Figure 12.2The NSTAR LDT ratio of net-to-bulk molybdenum sputter yield

as a function of accelerator current density in the pits and grooves using

the improved analysis for latched and unlatched ion energies.
NASA/TM22013-216605 19

IV. Application of the Improved Analysis to the NEXT LDT

The improved analysis was used to estimate the impact of back-sputtered carbon on the accelerator

grid pit and groove wear rate of the NEXT LDT. The first section describes test-specific inputs to the

analysis. The section thereafter presents and discusses the results of the analysis.

Unlike the NSTAR analysis, the NEXT LDT analysis is more challenging because the thruster was

operated for extended durations at various operating conditions as shown in Table 1. In addition, the test is

ongoing, so direct measurements of back-sputtered carbon film thicknesses and grid wear cannot be made.

As a result, the NEXT LDT estimates presented herein are considered preliminary until the results of future

post-test measurements are incorporated. The following analyses will estimate the impact of back-sputtered

carbon on the accelerator grid wear for all extended operating conditions during the NEXT LDT.

A. NEXT LDT Analysis Inputs

The NEXT LDT vacuum facility was internally lined with graphite panels to reduce facility material

back-sputtering, and the back-sputter rate was measured with a quartz crystal microbalance located next

to the thruster (Refs. 28 and 29). Although the quartz crystal microbalance failed during the first full

power test segment, measurements made during regularly scheduled performance tests were used to

determine the back-sputter rates for the operating conditions of Table 1. The resulting estimated carbon

back-sputter rates are shown in Table 2.

TABLE 1.2THRUSTER OPERATING CONDITIONS, DURATIONS, AND PROPELLANT

THROUGHPUT DURING THE NEXT LDT IN CHRONOLOGICAL ORDER

Operating

conditiona

Segment duration,

h

Post-segment

duration,

h

Segment

throughput,b

kg

Post-segment

throughput,b

kg

3.52 A, 1800 V 13,042 13,042 264.7 264.7

3.52 A, 1179 V 6,478 19,520 132.6 397.3

1.20 A, 679 V 3,411 22,931 26.7 424.0

1.00 A, 275 V 3,198 26,129 23.4 447.4

1.20 A, 1800 V 3,111 29,240 24.5 471.9

3.52 A, 1800 V c20,265 c49,505 c415.9 c887.8

aBeam current and beam power supply voltage.

bXenon propellant.

cAs of August 8, 2013.

TABLE 2.2NEXT LDT BACK-SPUTTER RATES, AVERAGE MEASURED ACCELERATOR

CURRENTS, MODELED APERTURE WALL CURRENTS, AND ERODED AREA RATIOS

FOR ALL OPERATING CONDITIONS

Operating

conditiona

Back-sputter rate,

m/khb

Average accelerator

current (Ja),

mA

Accelerator barrel

current (Jaw),c

mA

Eroded area ratio

(dAerode/dAo)

d

3.52 A, 1800 V 3.00 14.0 0.92 0.278

3.52 A, 1179 V 1.70 14.4 3.51 0.233

1.20 A, 679 V 0.35 2.35 0.30 0.205

1.00 A, 275 V 0.38 2.21 0.50 0.223

1.20 A, 1800 V 1.28 2.47 0.07 0.174

3.52 A, 1800 V 3.00 13.4 0.92 0.278

aBeam current and beam power supply voltage.

bAssumes a carbon density of 2.25 gm/cm3

.

cUsing the ion optics code of Reference 24.

dAssumed constant throughout the grid.
NASA/TM22013-216605 20

Also shown in Table 2 are the average measured accelerator currents and the modeled current

collected at the aperture barrel walls at each operating condition. The eroded area ratio, dAerode/dAo, was

determined with images of the center accelerator aperture, a sample of which is shown in Figure 1. Net

erosion site areas were measured from the images taken at the end of each test segment. This eroded area

was assumed to be constant throughout the grid. The resulting eroded area ratios are also listed in Table 2.

For the NEXT LDT, beam current densities were measured, in part, with a planar probe located 2.0

cm downstream of the accelerator grid. An example of a beam current density profile at full power is

shown in Figure 5. These measurements were used to determine the beam current density along the grid

using the algorithm discussed earlier. The resulting profiles were then used with the results of Table 2 to

determine the average accelerator current density in the pits and grooves along the grid using

Equation (18). The resulting accelerator current density profiles are shown in Figure 13 for the different

operating conditions. The slight difference for the two full power profiles is due to the accelerator current

difference in Table 2. Figure 13 shows that the maximum accelerator current density was off-center and

typically located at a radial location of about ±7 cm. The maximum accelerator current density for each

operating condition is listed in Table 3.

The transition from net erosion to net deposition for each operating condition was determined from

far-field thruster images taken with a high magnification zoom lens. A sample image taken at the end of

the first full power test segment is shown in Figure 14. The resolution of these images was sufficient to

discern individual apertures and their surrounding erosion pattern. The radial location for transition from

net erosion to net deposition was determined from images taken at the end of each operating condition,

and the corresponding transition accelerator current density determined with the results of Figure 13. The

transition radial location and current density for each operating condition are listed in Table 3.

The charge exchange ion energy, Vcex, was determined using two methods. For the first method, the

energy was determined with Equation (19) using accelerator voltage settings and average coupling

voltages measured during each operating condition. The resulting values using this energy are termed

3unlatched. ́ For the second method, the measured transition current densities listed in Table 3 were used

to determine Vcex using Equation (15). The resulting values from this method are termed 3latched ́ and

represent a conservative result. The unlatched and latched ion energies and the resulting sputter yields are

listed in Table 4 for all operating conditions.

0

10

20

30

40

50

60

20 15 10 5 0 5 10 15 20

Radius, cm

3.52 A, 1800 V 1st Seg.

3.52 A, 1179 V

3.52 A, 1800 V 2nd Seg.

1.20 A, 1800 V

1.20 A, 679 V

1.00 A, 275 V

Figure 13.2Average accelerator current density in the pits and grooves as a

function of radius for all NEXT LDT operating conditions.
NASA/TM22013-216605 21

TABLE 3.2NEXT LDT NET EROSION TO NET DEPOSITION TRANSITION RADIAL

LOCATIONS AND ACCELERATOR CURRENT DENSITIES, AND MAXIMUM

ACCELERATOR CURRENT DENSITIES FOR ALL OPERATING CONDITIONS

Operating conditiona Transition radius,

cmb

Transition

accelerator current

density (ja-trans),

A/cm2

Maximum

accelerator current

density (ja-max),

A/cm2

3.52 A, 1800 V 10.4 47.4 51.2

3.52 A, 1179 V 11.1 47.0 51.0

1.20 A, 679 V 9.5 12.1 13.8

1.00 A, 275 V 11.1 8.88 10.5

1.20 A, 1800 V 6.8 16.5 19.0

3.52 A, 1800 V 11.9 44.9 49.2

aBeam current and beam power supply voltage.

b

Positive radial locations only.

TABLE 4.2NEXT LDT UNLATCHED AND LATCHED ION ENERGIES AND THE

RESULTING SPUTTER YIELDS FOR ALL OPERATING CONDITIONS

Operating

conditiona

Unlatched values Latched values

Ion energy,

eV

YC-Mo

b

YC

c

Ion energy,

eV

YC-Mo

b

YC

c

3.52 A, 1800 V 225 1.09 0.050 177 0.91 0.032

3.52 A, 1179 V 215 1.05 0.046 141 0.79 0.018

1.20 A, 679 V 129 0.75 0.014 131 0.76 0.015

1.00 A, 275 V 364 1.88 0.11 142 0.79 0.019

1.20 A, 1800 V 225 1.09 0.050 196 0.98 0.039

3.52 A, 1800 V 226 1.10 0.050 182 0.93 0.034

aBeam current and beam power supply voltage.

bExtrapolated sputter yields from Reference 18.

c

Interpolated and extrapolated sputter yields from Reference 19.

Figure 14.2NEXT LDT far-field image showing the

net erosion and net deposition areas along the

accelerator grid. The image was taken at 13,042 h

following the first full power test segment.
NASA/TM22013-216605 22

B. NEXT LDT Results and Discussions

A sample result is plotted in Figure 15 for the first full power test segment. As with the NSTAR LDT

results, the improved analysis under-predicts the transition accelerator current density, so a latched,

conservative solution is shown as well. A comparison of Figures 15 and 12 shows that the net eroded

accelerator current density range (i.e., the current densities between transition and maximum) is smaller

for the NEXT LDT at full power than that for the NSTAR LDT. This occurred for two reasons. First, the

carbon back-sputter rate was much higher in NEXT LDT than that for the NSTAR test. At full power, the

NEXT back-sputter rate was over four times that of the NSTAR test, and this was due to the higher beam

currents and voltages of the NEXT thruster. Second, the NEXT thruster has a much flatter beam current

density profile. As a direct result, the accelerator current density across the grid does not vary as much for

the NEXT thruster (Fig. 13) as it does for the NSTAR thruster (Fig. 8). Regardless, Figure 15 does

illustrate that the impact of carbon back-sputtering for the NEXT LDT is not significant at the maximum

accelerator current density, which is where first failure would be expected to occur.

Table 5 compares the predicted transition accelerator current densities using unlatched ion energies

with those determined from measurements in Table 3. The table shows that the disparities were less than

the 47 percent disparity of the NSTAR LDT comparison except for two cases. But these two larger

disparities had two common attributes. First, operation during that operating condition required the

removal of net carbon deposition. Second, the predicted transition accelerator current density was so low

that net carbon deposition had to be removed from the entire perforated grid. The duration at these

operating conditions was likely insufficient to remove so much net carbon deposition, and this led to the

larger disparities.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10 100

Accelerator Current Density, A/cm2

Unlatched (225 V)

Latched (177 V)

Transition Current Density

Maximum Current Density

Figure 15.2The NEXT LDT ratio of net-to-bulk molybdenum sputter yield

as a function of accelerator current density in the pits and grooves for

unlatched and latched ion energies. Results shown are for the first full

power operating condition.
NASA/TM22013-216605 23

TABLE 5.2NEXT LDT PREDICTED AND MEASURED TRANSITION ACCELERATOR

CURRENT DENSITIES FOR ALL OPERATING CONDITIONS

Operating

conditiona

Transition radius,

cm

Transition accelerator current density

(ja-trans),

A/cm2

Disparity,

percent

Predicted Measured

3.52 A, 1800 V 10.4 30.2 47.4 36

3.52 A, 1179 V 11.1 b18.6 47.0 c

60

1.20 A, 679 V 9.5 12.7 12.1 ±5.2

1.00 A, 275 V 11.1 b1.6 8.88 c

82

1.20 A, 1800 V 6.8 12.9 16.5 21

3.52 A, 1800 V 11.9 30.1 44.9 33

aBeam current and beam power supply voltage.

b

Positive radial locations only.

 cPredicted transition current density requires removal of net carbon deposition from entire perforated grid.

TABLE 6.2NEXT LDT UNLATCHED AND LATCHED NET-TO-BULK

MOLYBDENUM SPUTTER YIELD FOR ALL

OPERATING CONDITIONS

Operating conditionaYMo

net/YMo at ja-max

Unlatched Vcex Latched Vcex

3.52 A, 1800 V 0.979 0.960

3.52 A, 1179 V 0.988 0.978

1.20 A, 679 V 0.984 b0.985

1.00 A, 275 V 0.994 0.983

1.20 A, 1800 V 0.975 0.965

3.52 A, 1800 V 0.978 0.961

aBeam current and beam power supply voltage.

bThe latched ion energy was higher than the unlatched energy, so the latched

result is more conservative for this operating condition.

The impact of back-sputtered carbon on the pit and groove erosion rate of the downstream accelerator

grid is listed in Table 6 for all operating conditions. Shown in the table are the unlatched and the more

conservative latched results. The results are evaluated at the maximum accelerator current densities

because this is where first failure would be expected to occur. The table shows that the worst-case impact

of carbon back-sputtering was the full power operating condition. However, the maximum impact of

back-sputtered carbon was only a four percent reduction in pit and groove erosion rate. As a result, backsputtered carbon is estimated to have an insignificant impact on the first failure mode of the NEXT LDT

at all operating conditions. The results of this analysis will be updated with the results of future post-test

measurements.

Conclusions

Accelerator grid wear rates are affected by two competing facility-induced effects: facility

background pressures that enhance grid wear rates and facility back-sputtered material that reduces grid

wear rates. A study was conducted to quantify the impact of back-sputtered carbon on the downstream

accelerator grid erosion rates of the NEXT LDT. A similar analysis that was conducted for the NSTAR

LDT was used as a foundation for the improved analysis developed herein. The general model for the

impact of back-sputtered carbon on accelerator grid wear rate was the same as that developed for the

NSTAR LDT, where it was conservatively assumed that any carbon surface coverage eliminates

molybdenum substrate sputtering. An investigation of the likely adsorbate growth modes revealed there

are multiple carbon adlayers before complete surface coverage is achieved. As a result, any carbon

surface coverage model must account for these multiple carbon adlayers. A more rigorous carbon surface

coverage model was developed using a model that was originally used to describe the physisorption of

additional gas adlayers on a chemisorbed adlayer. The resulting model requires knowledge of more model

inputs, so they were conservatively estimated using the results of past thin film sputtering studies and
NASA/TM22013-216605 24

particle reflection predictions. In addition, accelerator current densities along the grid were rigorously

determined using an ion optics code to determine accelerator current distributions and an algorithm that

was developed to determine beam current densities along the grid using downstream density

measurements.

The improved analysis was applied to the NSTAR LDT results for evaluation. Model inputs were

rigorously defined. Afterwards, the improved analysis was applied to the NSTAR test. The net-to-bulk

molybdenum sputtering ratio of the improved analysis exhibited a steep drop with decreasing current

density near the predicted transition accelerator current density. The original NSTAR analysis exhibited a

more gradual decrease with decreasing current density. The new analysis shows that the impact of backsputtered carbon on the pit and groove wear rate is insignificant at the net erosion sites throughout most of

the grid. The improved analysis was found to predict the transition current density considerably more

accurately than the original NSTAR analysis. Causes for the remaining discrepancy included incorrect

bombarding ion energies or bulk carbon sputter yields, accelerator current density determination errors,

and a potentially poor surface coverage model assumption. To conservatively account for the transition

current density discrepancy, a 3latched ́ solution was developed that used the measured transition current

density to determine bombarding ion energy. Results showed that the impact of back-sputtered carbon on

pit and groove wear rate of the NSTAR LDT was negligible throughout most of eroded grid radius.

The improved analysis was then used to estimate the impact of back-sputtered carbon on the

accelerator grid pit and groove wear rate of the NEXT LDT. Unlike the NSTAR analysis, the NEXT LDT

analysis was more challenging because the thruster was operated for extended durations at various

operating conditions, and the thruster was unavailable for measurements because the test is ongoing. As a

result, the NEXT LDT estimates presented herein are considered preliminary. Model inputs were defined

for every operating condition, and the improved analysis was then applied to each condition. NEXT LDT

back-sputter rates were higher and accelerator current density variations across the grid were smaller, so

the net eroded accelerator current density range was smaller than that for the NSTAR LDT. Disparities

between predicted and measured accelerator transition current densities were typically less than the

47 percent disparity of the NSTAR LDT comparison. The impact of back-sputtered carbon on pit and

groove wear rate was evaluated at the maximum accelerator current densities because this is where first

failure would be expected to occur. The maximum impact of back-sputtered carbon was only a four

percent reduction in pit and groove erosion rate. As a result, back-sputtered carbon is estimated to have an

insignificant impact on the first failure mode of the NEXT LDT at all operating conditions. These

preliminary estimates will be updated with the results of future post-test measurements.

References

1. Patterson, M.J. and Benson, S.W., 3NEXT Ion Propulsion System Development Status and

Performance, ́ 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA Paper

2007-5199, Cincinnati, Ohio, July 2007.

2. Polk, J.E., et al., 3Demonstration of the NSTAR Ion Propulsion System on the Deep Space One

Mission, ́ 27th International Electric Propulsion Conference, IEPC Paper 2001-075, Pasadena,

California, October 2001.

3. Garner, C.E., et al., 3In-Flight Operation of the Dawn Ion Propulsion System Through Orbit Capture

at Vesta, ́ 47th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2011-

5661, San Diego, California, July-August 2011.

4. Benson, S.W. and Patterson, M.J., 3NEXT Ion Propulsion System Progress Towards Technology

Readiness, ́ 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2008-

5285, Hartford, Connecticut, July 2008.

5. Van Noord, J.L. and Herman, D.A., 3Application of the NEXT Ion Thruster Lifetime Assessment to

Thruster Throttling, ́ 44th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA

Paper 2008±4526, Hartford, Connecticut, July 2008.
NASA/TM22013-216605 25

6. Brophy, J.R., 3Propellant Throughput Capability of the Dawn Ion Thrusters, ́ 30th International

Electric Propulsion Conference, IEPC Paper 2007-279, Florence, Italy, September 2007.

7. Shastry, R., et al., 3NASA¶s Evolutionary Xenon Thruster (NEXT) Long-Duration Test as of 736 kg

of Propellant Throughput, ́ 48th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,

AIAA Paper 2012±4023, Atlanta Georgia, July-August 2012.

8. Van Noord, J.L., Soulas, G.C., and Sovey, J.S., 3NEXT PM1R Ion Thruster and Propellant

Management System Wear Test Results, ́ 31st International Electric Propulsion Conference, IEPC

Paper 2009-163, Ann Arbor, Michigan, September 2009.

9. Soulas, G.C., et al., 3NEXT Ion Engine 2000 Hour Wear Test Results, ́ 40th AIAA/ASME/SAE/ASEE

Joint Propulsion Conference and Exhibit, AIAA Paper 2004-3791, Fort Lauderdale, Florida, July

2004.

10. Sengupta, A., et al., 3An Overview of the Results from the 30,000 hr Life Test of Deep Space 1

Flight Spare Ion Engine, ́ 40th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit,

AIAA Paper 2004-3608, Fort Lauderdale, Florida, July 2004.

11. Polk, J.E., et al., 3The Results of an 8200 Hour Wear Test of the NSTAR Ion Thruster, ́ 35th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA Paper 1999-2446,

Los Angeles, California, June 1999.

12. Polk, J.E., et al., 3The Effect of Carbon Deposition on Accelerator Grid Wear Rates in Ion Engine

Ground Testing, ́ 36th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA

Paper 2000±3662, Huntsville, Alabama, July 2000.

13. Winters, H.F. and Sigmund, P., 3Sputtering of Chemisorbed Gas (Nitrogen on Tungsten) by Low

Energy Ions, ́ Journal of Applied Physics, vol. 45, no. 11, November 1974, pp. 4760±4766.

14. Wasa, K. and Hayakawa, S., Handbook of Sputter Deposition Technology: Principles, Technology,

and Applications, Noyes Publication, Park Ridge, New Jersey, 1992, pp. 10±11.

15. Greene, J.E., 3Nucleation, Film Growth, and Microstructural Evolution, ́ Handbook of Deposition

Technologies for Films and Coatings: Science, Technology and Applications, 2nd Edition, edited by

Bunshah, R.F., Noyes Publication, Park Ridge, New Jersey, 1994, pp. 681±739.

16. Brunauer, S., Emmett, P.H., and Teller, E., 3Adsorption of Gases in Multimolecular Layers, ́

Journal of the American Chemical Society, vol. 60, February 1938, pp. 309±319.

17. Van Noord, J.N., 3NEXT Ion Thruster Thermal Model, ́ 43rd AIAA/ASME/SAE/ASEE Joint

Propulsion Conference and Exhibit, AIAA Paper 2007±5218, Cincinnati, Ohio, July 2007.

18. Ho, C., et al. 3Desorption of Chemisorbed Carbon on Mo (1 0 0) by Noble Gas Ion Sputtering:

Validation of Ground Test Measurements of Ion Engine Lifetimes, ́ Applied Surface Science,

vol. 252, 2006, pp. 2657±2664.

19. Rosenberg, D. and Wehner, G.K., 3Sputtering Yields for Low Energy He+-, Kr+-, and Xe+-Ion

Bombardment, ́ Journal of Applied Physics, vol. 33, May 1962, pp. 1842±1845.

20. Andersen, H.H. and Bay, H.L., 3Sputter Yield Measurements, ́ Sputtering by Particle Bombardment

I, edited by Behrisch, R., Springer Verlag, Berlin, 1981, pp. 153±163.

21. Betz, G. and Wien, K., 3Energy and Angular Distributions of Sputtered Particles, ́ International

Journal of Mass Spectroscopy and Ion Processes, vol. 140, 1994, pp. 1±110.

22. Yamamura, Y. and Tawara, H., 3Energy Dependence of Ion-Induced Sputtering Yields From

Monatomic Solids at Normal Incidence, ́ Atomic Data and Nuclear Data Tables, vol. 62, 1996,

pp. 149±253.

23. Joh, D. et al., 3Energy Distribution of Low-Energy Plasma Ions Reflected from Metal Surfaces by

Using a Monte Carlo Calculation, ́ Journal of the Korean Physical Society, vol. 37, no. 3,

September 2000, pp. 232±235.

24. Farnell, C.C., 3Performance and Lifetime Simulation of Ion thruster Optics, ́ Ph.D. Dissertation,

Department of Mechanical Engineering, Colorado State University, Fort Collins, Colorado, 2007.

25. Brophy, J.R., et al., 3Numerical Simulations of Ion Thruster Accelerator Grid Erosion, ́ 38th

AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2002±4261,

Indianapolis, Indiana, July 2002.
NASA/TM22013-216605 26

26. Wang, J., et al., 3Three-Dimensional Particle Simulations of NSTAR Ion Optics, ́ 27th International

Electric Propulsion Conference, IEPC Paper 2001-085, Pasadena, California, October 2001.

27. Kolasinski, R.D., et al., 3Carbon Sputtering Yield Measurements at Grazing Incidence, ́ 42nd

AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, AIAA Paper 2006±4337,

Sacramento, California, July 2006.

28. Herman, D.A., Soulas, G.C., and Patterson, M.J., 3NEXT Long-Duration Test Plume and Wear

Characteristics After 16,550 h of Operation and 337 kg of Xenon Processed, ́ 44th AIAA/ASME/

SAE/ASEE Joint Propulsion Conference and Exhibit, AIAA Paper 2008±4919, Hartford,

Connecticut, July 2008.

29. Herman, D.A., Soulas, G.C., and Patterson, M.J., 3Status of the NEXT Long-Duration Test After

23,300 Hours of Operation, ́ 45th AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit,

AIAA Paper 2009±4917, Denver, Colorado, August 2009.