George C. Soulas

Glenn Research Center, Cleveland, Ohio

Design and Performance of 40 cm Ion Optics

NASA/TM—2001-211275

December 2001

IEPC–01–090
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National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

27th International Electric Propulsion Conference

cosponsored by the AFRL, CNES, ERPS, GRC, JRL, MSFC, and NASA

Pasadena, California, October 14–19, 2001

George C. Soulas

Glenn Research Center, Cleveland, Ohio

Design and Performance of 40 cm Ion Optics

NASA/TM—2001-211275 IEPC–01–090
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

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This report contains preliminary

findings, subject to revision as

analysis proceeds.

Available electronically at http://gltrs.grc.nasa.gov/GLTRS
NASA/TM—2001-211275 1 

Design and Performance of 40 cm Ion Optics 

George C. Soulas 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Phone: 216–977–7419 

Email: George.C.Soulas@grc.nasa.gov

A 40 cm ion thruster is being developed at the NASA Glenn Research Center to obtain 

input power and propellant throughput capabilities of 10 kW and 550 kg, respectively. The 

technical approach here is a continuation of the “derating” technique used for the NSTAR 

ion thruster. The 40 cm ion thruster presently utilizes the NSTAR ion optics aperture 

geometry to take advantage of the large database of lifetime and performance data already 

available. Dome-shaped grids were chosen for the design of the 40 cm ion optics because 

this design is naturally suited for large-area ion optics. Ion extraction capabilities and 

electron backstreaming limits for the 40 cm ion optics were estimated by utilizing NSTAR 

30 cm ion optics data. A preliminary service life assessment showed that the propellant 

throughput goal of 550 kg of xenon may be possible with molybdenum 40 cm ion optics. 

One 40 cm ion optics’ set has been successfully fabricated to date. Additional ion optics’ sets 

are presently being fabricated. Preliminary performance tests were conducted on a 

laboratory model 40 cm ion thruster. 

Nomenclature 

Adome Domed grid area, m2 

d Grid aperture diameter, m 

db Beam extraction diameter, m 

e Electron charge, C 

Eeff Effective elastic modulus of the perforate 

grid region, Pa 

fcorr Sputter yield correction factor 

Fdome Fractional change of the grid area from 

doming 

fflat Beam flatness parameter (ratio of averageto-peak beam current density) 

Fg Accelerator grid view factor 

Foa Grid open area fraction 

Ft Beam divergence thrust correction factor 

g Acceleration of gravity, m/s2 

h Height of the grid dome, m 

Jb Beam current, A 

jb Beam current density, A/m2

Ji Accelerator grid impingement current, A 

kB Boltzmann’s constant, J/K 

kcorr Correction factor for peak beam current 

density, V· m

2

/A 

le Effective acceleration length, m 

lg Grid cold gap, m 

ln Neutralization length, m 

lup Upstream potential well location, m 

mamu Atomic mass of grid material, amu 

md  Discharge chamber mass flow rate, kg/s 

mi Ion mass, kg 

mn Propellant atomic mass, kg 

N Neutral density distribution function 

n Number of gravities (i.e., g-load) 

NA Avogadro’s number, mol–1 

nb Facility background neutral density, m–3

nd Discharge chamber neutral density, m–3

nn Neutral density distribution upstream of the 

neutralization plane, m–3

NPH Normalized perveance per hole, A/V3/2

NPHcorr Correlated normalized perveance per hole, 

A/V3/2

rc Chord radius of domed grid, m 

Rdome Radius of curvature for the grid dome, m 

Rj Ratio of doubly-to-singly charged ion 

current 

R0

max Maximum net-to-total accelerating voltage 

extrapolated to a zero beam current 

T Thrust, N 

Tg Grid temperature, K 
NASA/TM—2001-211275 2 

Tn Neutral propellant temperature, K 

Ts Stiffener temperature, K 

ts Screen grid thickness, m 

Vb Beam voltage, V 

Vd Discharge voltage, V 

Veb Electron backstreaming limit voltage, V 

Vt

lim Impingement-limited total voltage, V 

Vp−g ′  Accelerator grid pit and groove volumetric 

erosion rate per aperture, m3

/s 

Vs

′  Screen grid volumetric erosion rate per 

aperture, m3

/s 

Vw

′  Accelerator grid aperture wall volumetric 

erosion rate per aperture, m3

/s 

Y Sputter yield at an orthogonal angle of 

incidence 

z Axial dimension, m 

α Thrust correction factor for doubly-to-singly 

charged ion current 

αg Grid material thermal expansion coefficient, 

1/C°

αs Stiffener material thermal expansion 

coefficient, 1/C°

ηd

++ Discharge chamber propellant utilization 

efficiency accounting for doubly charged 

ions 

θmax Maximum dome angle from the grid axial 

centerline, rad 

νeff Effective Poisson’s ratio of the perforate 

grid region 

π Pi (3.141593) 

ρ Grid material mass density, kg/m3

ρeff Effective mass density of the perforate grid 

region, kg/m3 

σc-e Charge-exchange cross-section, m2 

σhoopmax Peak circumferential (i.e., hoop) stress, Pa 

σmeridmax Peak meridional stress, Pa 

φ Neutral transparency of the ion optics 

φi Screen grid transparency to discharge ions 

Superscripts 

a

 Accelerator grid 

avg Average 

dwn Charge-exchange ions created downstream 

of the neutralization plane

hot Temperature during thruster operation n

 Orthogonal to the grid surface 

NSTAR NSTAR ion thruster 

pk Peak 

rt Room temperature 

s

 Screen grid 

up Charge-exchange ions created upstream of 

the neutralization plane 

 ́ Per aperture +

 Singly charged ion 

++ Doubly charged ion 

Subscripts 

a Accelerator grid 

s Screen grid 

Introduction 

The success of the NSTAR (i.e., NASA Solar Electric 

Propulsion Technology Applications Readiness 

Program) 30 cm ion thruster system on the Deep 

Space 1 mission has demonstrated the viability of ion 

propulsion for deep space missions.1,2 As a result, ion 

propulsion is a candidate for several deep space 

missions, such as the Neptune Orbiter, Titan Explorer, 

Mars Sample Return, Europa Lander, and others. 

However, ion propulsion system mass and volume 

could be significantly reduced for many of these 

missions by increasing the NSTAR thruster’s 

propellant throughput and peak input power 

capabilities beyond the 140 kg and 2.3 kW, 

respectively, demonstrated by past and ongoing wear 

tests.3–5

 Propulsion system mass and volume 

reductions occur because fewer thrusters and, 

therefore, fewer accompanying power processors and 

propellant feed system components, would be 

required. 

Increasing propellant throughput and thruster power is 

limited, in part, by sputter erosion of the ion optics.6,7

Significant charge-exchange accelerator grid sputter 

erosion can lead to electron backstreaming due to 

accelerator aperture enlargement, grid structural 

failure due to pit and groove erosion of the 

downstream surface, or an unclearable grid short by a 

flake from sputter-eroded accelerator grid material. 

Significant screen grid sputter erosion by discharge 

chamber ions can lead to structural failure of the 

screen grid, as well as exacerbating the 

aforementioned accelerator grid failure mechanisms 

from direct beam ion impingement. 

Long duration tests in the NSTAR program3–5

 and 

others6,7 have demonstrated, however, that sputter 

erosion of the downstream surface and aperture walls 
NASA/TM—2001-211275 3 

of the accelerator grid must be addressed to increase 

ion optics’ longevity. Wear test results from Ref. [3] 

have shown that screen grid sputter erosion is minimal 

for the NSTAR thruster, likely due to the derated 

operating conditions of this engine. Although screen 

grid erosion must be addressed in any ion optics’

service life assessment, lifetimes well beyond those 

demonstrated in Refs. [3] to [5] are expected as long as 

the low discharge voltages and plasma densities are 

maintained and the ratio of doubly-to-singly charged 

ions is not significantly increased. 

Several methods of extending ion optics’ service life 

are presently being pursued at the NASA Glenn 

Research Center (GRC).8

 One method involves 

changing the ion optics’ material to one with a lower 

volumetric sputter erosion rate than molybdenum. Grid 

material technologies presently investigated include 

carbon-based materials, titanium, and ion-implanted 

materials.8-11 Another method for increasing ion optics 

service life involves increasing the accelerator grid 

thickness to provide more material for sputter 

erosion.12 This prevents the loss of the large database 

already available with molybdenum ion optics while 

providing an anticipated 2x improvement in 

accelerator grid service life. While all of these 

methods allow for increases in thruster propellant 

throughput and input power, most improvements are 

anticipated to be modest if the 30 cm thruster diameter 

is maintained.9

 

To obtain input power and propellant throughput 

capabilities of 10 kW and 550 kg, respectively, a 

40 cm ion thruster is being developed at NASA 

Glenn.13 This engine has twice the beam area as the 

NSTAR 30 cm ion thruster, whose beam diameter is 

28 cm. The technical approach here is a continuation 

of the “derating” technique used for the NSTAR ion 

thruster. With regards to the ion optics, this approach 

maintains low beam current densities across the ion 

optics to extend ion optics service life. Therefore, the 

40 cm ion thruster can, at minimum, double input 

power and propellant throughput per thruster for the 

same thrust densities as the NSTAR thruster. The 

40 cm thruster can further offer increased input power 

and propellant throughput when other grid 

technologies are used, such as thick-accelerator-grid 

(TAG) ion optics.12 

This paper reports on the preliminary results of the 

development of 40 cm ion optics for the 40 cm ion 

thruster. Results to date include ion optics design 

considerations, and preliminary service life 

assessments and test results. 

Design Considerations 

Ion Thruster Performance Goals 

The design goals of the 40 cm ion thruster include a 

1 to 10 kW input power throttling range and a 550 kg 

xenon propellant throughput capability. Emphasis was 

placed on providing a flat beam profile to further 

improve ion optics service life.13 This improvement 

occurs because several ion optics failure mechanisms 

are a result of the local sputter erosion of the ion optics 

that are a function of the local beam current density. 

Ion Optics’ Geometry Performance 

The 40 cm ion thruster is presently envisioned to use 

the NSTAR ion optics aperture geometry, described in 

Refs. [14] and [15], and the thick-accelerator-grid 

geometry, described in Ref. [12]. The following 

analyses will focus on the use of the NSTAR 

geometry. Analyses with this aperture geometry allow 

the 40 cm thruster to take advantage of the large 

database of lifetime and performance data already 

available with this geometry. 

The ion extraction capability of the 40 cm ion optics 

was analyzed first. Because the ion optics’ aperture 

geometry of the NSTAR thruster was utilized, 30 cm 

ion optics data could be used to predict 40 cm ion 

optics’ performance. Average beam currents per 

aperture (or beamlet currents) as a function of the 

impingement-limited total voltage for an NSTAR ion 

thruster are shown in Fig. 1.11,12 The impingementlimited total voltages were defined as the voltage 

where the slope of the accelerator current as a function 

of total voltage (i.e., the sum of the absolute values of 

the beam and accelerator power supply voltages) was 

–0.02 mA/V. 

The ion extraction capability of a given aperture 

geometry can be correlated to other operating 

conditions by utilizing a normalized perveance per 

hole (or NPH): 

2

s

e

2

3

lim

t

b

d

l

V

J NPH 















⋅ ′ = (1) 

where J ́b is the beamlet current, Vt

lim is the 

impingement-limited total voltage, ds is the screen 
NASA/TM—2001-211275 4 

aperture diameter, and le is the effective acceleration 

length. The effective acceleration length is defined as: 

( ) 4

d l l t

2

2 s

e = g + s + , (2) 

where lg is the grid gap and ts is the screen grid 

thickness. The impingement-limited normalized 

perveance per hole for the NSTAR ion optics is plotted 

in Fig. 2 as a function of discharge-to-total voltage 

ratio. As the figure demonstrates, the normalized 

perveance per hole is a function of the discharge-tototal voltage ratio. This effect has been noted in other 

studies16,17 and can be compensated by defining a 

correlated normalized perveance per hole (or NPHcorr): 

q

lim

t

d

corr V

V NPH NPH 













 = ⋅ (3) 

where Vd is the discharge voltage.16 In Ref. [16], q was 

set to 0.2, however, a value of 1.2 was found to yield 

constant correlated value in this study. The correlated 

normalized perveance per hole for the NSTAR ion 

optics is also plotted in Fig. 2. As Fig. 2 shows, the 

correlated normalized perveance per hole is 

approximately 2.4×10–11 A/V3/2 for the NSTAR ion 

optics’ aperture geometry. 

Total voltages for the 40 cm thruster may be 

determined by using the correlated normalized 

perveance per hole to determine the impingementlimited total voltage for a given beam current, and then 

adding voltage margin to the predicted limit. One 

selection criterion for the total voltage at a given beam 

current was that the total voltages provide a minimum 

perveance margin (i.e., the difference between the total 

voltage during normal operation and the impingementlimited total voltage) of at least 200 V. 

High specific impulses are typically best suited for the 

deep space missions anticipated for the 40 cm ion 

thruster. This generally results in thruster operation at 

high R-ratios (i.e., net-to-total accelerating voltages), 

and, therefore, high accelerator voltages. These high 

accelerator voltages are beneficial because they reduce 

accelerator grid erosion rates and, therefore, extend grid 

service life. The upper limit of the accelerator voltage is 

limited, however, by the onset of electron 

backstreaming. This electron backstreaming limit can 

be estimated with a semi-empirical equation derived by 

Kaufman for the maximum R-ratio as a function of the 

ion optics’ aperture geometry.18 However, since the 

40 cm ion optics’ aperture geometry is the same as that 

for the NSTAR ion optics, electron backstreaming limit 

data from NSTAR ion optics’ tests can be used.11,12 

The electron backstreaming limit and, therefore, the 

maximum R-ratio, are also functions of the peak 

beamlet current. This peak beamlet current is directly 

proportional to the peak beam current density just 

downstream of the ion optics, and, therefore, 

proportional to the beam current density divided by the 

beam flatness parameter (i.e., average-to-peak beam 

current density).10,11 Data with the NSTAR 30 cm ion 

optics from Ref. [11] shows that this relation is a 

function of beam power supply voltage and may be 

nonlinear. However, the electron backstreaming can be 

conservatively estimated by assuming a –1 V per 

1 A/m2

 dependence on the peak beam current density. 

The electron backstreaming limit (or Veb) for the 

40 cm ion thruster can, therefore, be estimated by: 

corr

flat

2

b

b

0

max

0

max

eb b k

d f

4 J

R

1 R V V ⋅ π ⋅ ⋅

⋅ +













 − = ⋅ . (4) 

Here, Jb is the beam current, db is the beam extraction 

diameter, fflat is the beam flatness parameter, kcorr is the 

correction for peak beam current density (i.e., –1 V per 

1 A/m2

), and R0

max is a maximum R-ratio extrapolated 

to a zero beam current. The value for R0

max for the 

molybdenum 30 cm ion optics tested in Ref. [11] was 

determined to be 0.918. Equation (4) predicts 30 cm 

ion optics’ electron backstreaming limits to within 

+15 V/–5 V. 

For operation at high R-ratios, the selected accelerator 

voltage was determined by adding voltage margin to 

the predicted electron backstreaming limit. 

A preliminary throttle table for the 40 cm ion thruster 

was developed based, in part, on the predicted 

performance of the ion optics’ aperture geometry.13

Results relevant to the ion optics are shown in Table 1 

for operation at high R-ratios. Assumptions for these 

proposed throttling points include a 24 V discharge 

voltage and a beam flatness parameter of 0.6. As the 

table shows, the lowest perveance margin was 

estimated to be 209 V. This value occurred at the 

lowest thruster input power. The lowest electron 

backstreaming margin (i.e., the difference between the 

absolute values of the accelerator voltage and electron 

backstreaming limit) occurred at the highest beam 

voltage and current and was estimated to be 40 V. 
NASA/TM—2001-211275 5 

Grid Design Considerations 

Dome-shaped grids, similar to those used on the 

NSTAR thruster, were chosen for the design of the 

40 cm ion optics. This was because dome-shaped grids 

are naturally suited for large-area ion optics. Reasons 

for this included: 1) the dome shape mitigates 

thermally induced buckling during thruster operation, 

and, therefore, provides a relatively stable grid gap 

throughout the ion optics’ area; and 2) the dome shape 

provides stiffness under vibration loads during launch. 

Furthermore, there is design heritage with this grid 

design at NASA Glenn. 

As discussed in previous sections, the NSTAR ion 

optics’ aperture geometry was utilized for the 40 cm 

ion optics. As a result, the beam extraction diameter, 

grid thicknesses, and perforated geometries were fixed 

for the 40 cm grids. The only remaining, adjustable 

parameter was the dome height. It will be shown in the 

following paragraphs that selecting a dome height-tochord radius similar to that of the NSTAR grids 

addressed most key issues associated with grid 

fabrication and thruster operation while having little 

impact on other issues concerning thermal expansion 

and launch stresses. 

Fabrication Issues 

The grid dome shape is hydrostatically formed, a 

process developed by NASA Glenn in 1972,19 and the 

apertures are photo-chemically etched. The primary 

concern regarding grid fabrication was that overforming the 40 cm grids could result in aperture 

misalignment, significant residual stresses, and 

possibly even fracture the grid material. Since a grid is 

under a biaxial state of stress during forming (grid 

thicknesses are small enough to assume a thin-walled 

membrane), then the fractional change in area as a 

result of the forming process is the relevant parameter 

here. It can be shown that the area of the domed grid 

(or Adome) is given by: 

( ) 2

c

2

dome A = π⋅ h + r , (5) 

where h is the dome height and rc is the radius at the 

dome base, or the chord radius. The fractional change 

in area from forming (or Fdome) is, therefore, given by: 

( ) 2

c

2

c

2

c

2

c

2

dome

r

h

r

h r r F 













 = π ⋅

π ⋅ + − π ⋅ = . (6) 

As the equation shows, the fractional change in 

area from forming is a function of the dome 

height-to-chord radius. Maintaining the same ratio as 

for the NSTAR 30 cm grids will, therefore, mitigate 

over-forming the 40 cm grids. 

Thruster Operation Issues 

Two thruster operation issues were identified for the 

40 cm ion optics. These included thrust losses due to 

the dome shape and thermally-induced changes in the 

grid gap. 

The thrust losses considered here are caused by the 

shape of the dome, which directs beamlets off-axis. 

The following analysis is similar to that done in 

Ref. [19]. The apertures of the NSTAR and 40 cm 

screen and accelerator grids are designed to be aligned 

throughout the grids’ radius, with no beamlet steering 

to collimate the beam. As a result, beamlets are 

directed normal to the surface of the grids. The thrust 

(or T) produced by a domed grid can, therefore, be 

expressed as: 

∫ ∫

πθ

⋅ ⋅α⋅ ⋅ ⋅ θ⋅ θ⋅ θ⋅ φ ⋅ ⋅ =

2

0 0

2

dome

n

t

n

b

b i

max

j F R cos sin d d

e

2 V m T

(7) 

Here, Vb is the beam voltage, mi is the ion mass and e 

is the electron charge. Within the double integral, θmax

is the maximum angle from the centerline of the grids, 

jb

n

 is the beam current density normal to the grid 

surface, Rdome is the radius of curvature of the dome, 

α is the double-to-single ion current correction factor, 

and Ft

n

 is the beamlet divergence correction factor that 

does not account for divergence from the grid dome 

shape. The latter term is used to separate beam 

divergence due to beamlet expansion from beam 

divergence due to the dome shape. To simplify this 

analysis, it will be assumed that the beam current 

density normal to the grid surface and the ratio of 

double-to-single ion current are constant throughout 

the grid. The beam current density can, therefore, be 

reduced to the beam current divided by the area of the 

dome. Equation (7) can be expressed as: 

max

2 2

dome

dome

n b

t

b i R sin

A

J F

e

2 V m T ⋅α⋅ ⋅ ⋅ π⋅ ⋅ θ ⋅ ⋅ = . (8) 

It can be shown that the last two terms in the equation 

above reduce to rc

2

. Using this and equation (5), 

equation (8) reduces to: 

1 2

c

b

n

t

b i

r

h F J 1

e

2 V m T

−































 ⋅α⋅ ⋅ ⋅ + ⋅ ⋅ = . (9) 
NASA/TM—2001-211275 6 

As this equation shows, the thrust is a function of the 

dome height-to-chord radius. Maintaining the same 

ratio as that for the NSTAR 30 cm grids will, 

therefore, keep these thrust losses due to the dome 

shape of the grids the same for the 40 cm grids. 

Grids thermally expand during thruster operation, 

which can change the grid gap when the grids are 

heated to their final operating temperatures. An 

analysis was conducted to compare 30 cm and 40 cm 

grids under thermal loads. The following simplifying 

assumptions were made (similar to those in Ref. [19]): 

1) each grid and its mounting ring were at uniform, but 

different, temperatures; 2) the final shape of the heated 

grids is spherical; 3) both grid diameters investigated 

had the same temperatures and temperature 

distributions; and 4) there are no thermally-induced 

meridional stresses. The chord radius and arc length 

across the grids (or S) during operation are given by: 

( ) s s

rt

c

hot

rc = r ⋅ 1+ α ⋅ ∆T , and (10) 

( ) g g

hot rt S = S ⋅ 1+ α ⋅ ∆T . (11) 

Here, αs and αg are the thermal expansion coefficients 

for the stiffener and grid materials, respectively, while 

û7s DQG û7g are the change in temperatures for the 

stiffeners and grids, respectively. The “rt” and “hot”

superscripts denote parameter values at room 

temperature and temperatures during thruster 

operation, respectively. With equations (10) and (11), 

it can be shown that: 

( ) ( ) g g

rt

rt dome

dome

rt hot c

hot dome

dome

s s

rt

c R 1 T

R

r R arcsin

R

r 1 T arcsin ⋅ ⋅ + α ⋅ ∆ 













 ⋅ = 













 ⋅ + α ⋅ ∆ , 

(12) 

where the radius of curvature for the heated grid is 

solved iteratively. Since it is known that: 

2

c

2

dome dome h = R − R − r , (13) 

the height of the heated grid can be solved with 

equations (12) and (13). 

Temperatures for this analysis were taken from 

Ref. [20] for a NASA J-Series 30 cm ion optics set 

operated at a discharge power of 210 W, which is 

similar to the NSTAR thruster at a 1.44 kW input 

power of and a 1.1 A beam current. Radial grid 

temperatures profiles were curve-fit with second order 

polynomial equations and integrated to determine 

average grid temperature changes. The thermal 

expansion of the grid-mounting hardware was also 

included in the analysis. Note that the results for the 

40 cm grids would not be applicable to the same 

discharge power as for the 30 cm thruster, but would 

correspond to a much higher discharge power (and, 

therefore, beam current) since the 40 cm grids have a 

larger thermal mass. Furthermore, the temperature 

distribution across the grids and mounting hardware 

would not necessarily be the same because of the 

different thermal environments of the two thruster 

sizes. Regardless, the aforementioned assumptions are 

only intended to provide a comparison for the two grid 

diameters. 

Analysis results are shown in Fig. 3, where the fraction 

of the hot-to-room temperature grid gap is plotted as a 

function of dome height-to-chord radius. The predicted 

fraction for the 30 cm ion optics was at the lower 

uncertainty limit of the measured value, indicating that 

the model reasonably predicts thermally-induced grid 

gap changes at this power level. As Fig. 3 further 

demonstrates, the predicted results for the 40 cm ion 

optics show that: 1) there is very little change in the 

fraction of the hot-to-room temperature grid gap over a 

wide range of dome height-to-chord radius ratios; and 

2) the overall hot grid gap is about 2% smaller than 

that for the 30 cm ion optics at steady-state conditions. 

Because the dome height-to-chord radius ratio has 

little effect on the grid gap during steady state thruster 

operation, it is reasonable to utilize the same ratio as 

that for the NSTAR 30 cm grids so that fabrication 

issues and thrust losses are mitigated. 

 

Launch Stress Issues 

The two spacecraft launch issues examined included 

vibration-induced stresses and grid movement. In 

order to simplify the analysis, it was assumed that final 

shape of the grids under these stresses was spherical, 

which requires grid deflections to be small. 

Furthermore, only grid vibrations in the axial direction 

were examined. Since the apertures significantly 

weaken the perforated grid regions, these regions were 

analyzed. The perforated regions were assumed to 

have a tangential top edge support. For thin-walled 

spherical domes under axial loads from there own 

mass, peak meridional and circumferential (i.e., hoop) 

stresses (or σmeridmax and σhoopmax, respectively) are 

given by:21

( ) max

max eff dome

merid 1 cos

n g R

+ θ

⋅ ⋅ ρ ⋅ σ = , and (14) 
NASA/TM—2001-211275 7 

2

max n g eff Rdome

hoop

⋅ ⋅ ρ ⋅ σ = . (15) 

Here, n is the number of gravities (i.e., g-load), g is the 

acceleration of gravity, and ρeff is the effective mass 

density of the grid perforated region. Note that 

1+cos(θmax) ≈ 2 for all cases examined here, so that it 

can be assumed that the meridional and 

circumferential stresses are approximately equal. 

Solving equation (13) for Rdome, it can be shown that: 

c

2

c

c

max eff

hoop

max

merid

r

h

r

h 1

r

4

n g 













 +

⋅ ⋅ ⋅ ⋅ ρ σ ≈ σ = . (16) 

As the above equation shows, maintaining a constant 

dome height-to-chord radius will still result in a stress 

increase proportional to the chord radius. An 

unchanged dome height-to-chord radius would 

increase meridional and circumferential stresses by 

about 40% for the 40 cm grids. However, increasing 

dome height-to-chord radius to account for the 

increased stresses in the 40 cm grids would worsen 

thruster performance. To determine the significance of 

these increased stresses, maximum meridional and 

circumferential stresses were calculated for these grids 

as a function of g-loading. These values were then 

used to determine the maximum webbing stresses22

and compared to the yield strength of the grid material 

to determine if the 40 cm grids were at risk of plastic 

deformation under launch loads in the axial direction. 

The resulting maximum stresses were found to be 

significantly smaller than the material yield stress, 

even at high g-loads. 

Note that this analysis omitted stresses resulting from 

radial motion, which should be included in any 

complete analysis. Unfortunately, this was beyond the 

scope of this initial effort. 

Vibration-induced axial motion was also examined. 

The same assumptions as the prior analysis were 

made. For thin-walled spherical domes under axial 

loads from their own weight, the change in dome 

height (or ûK LV JLYHQ E\21

( )( ) ( ) 



 





















+ θ ⋅ θ + + ν ⋅ ⋅ ⋅ρ ⋅ ∆ =

max

max eff

2

eff

2

eff dome

1 cos

2 sin 1 ln

E

n g R h . 

(17) 

Here, Eeff and νeff are the elastic modulus and 

Poisson’s ratio, respectively, for the perforated region 

of the grids.22 It can be shown that: 

( ) 2

c

2

c

max

r

h 1

r

h 1

cos















 +















 −

θ = , and (18) 

( )

2

2

c

2

c

max

2

r

h 1

r

h 1

sin 1











































 +















 −

θ = − . (19) 

Both equations are merely functions of the initial 

dome height-to-chord radius. Solving equation (13) for 

Rdome, equation (17) can be given: 

2

c

2

2 c

c

eff

eff

r

h 2

r

h 1

r

E

n g k h





























⋅















 +

⋅ ⋅ ⋅ ⋅ρ ⋅ ∆ = , (20) 

where: 

( )( ) ( )















+ θ = θ + + ν ⋅

max

max eff

2

1 cos

2 k sin 1 ln . (21) 

As equations (18) to (21) show, maintaining a constant 

dome height-to-chord radius will still result in a 

change in dome height proportional to the chord radius 

squared. Maintaining a constant dome height-to-chord 

radius would, therefore, approximately double grid 

movement for the 40 cm grids. If this grid movement 

is large enough, the grids could make contact under 

vibration loads. This occurrence, however, is not 

necessarily detrimental to the grids. Both the NSTAR 

30 cm grids and 50 cm were found to make contact 

under vibration loads without detrimental effects.23,24

As a result, this is not expected to be an issue for the 

40 cm grids. 

Preliminary Service Life Assessment 

A preliminary service life assessment was conducted 

to determine the lifetime gain by utilizing 40 cm ion 

optics. Service life analyses included sputter erosion of 

the downstream surface (i.e., pits and grooves) and 
NASA/TM—2001-211275 8 

aperture walls of the accelerator grid, shown in Fig. 4, 

and sputter erosion of the upstream surface of the 

screen grid. 

Accelerator Grid

Accelerator grid erosion is caused by charge-exchange 

ions created both upstream and downstream of the 

neutralization plane that bombard the accelerator grid. 

Accelerator grid erosion from direct impingement of 

beam ions is assumed to be negligible here. Chargeexchange ions created upstream of the neutralization 

plane sputter-erode both the aperture walls and the 

downstream surface of the accelerator grid, while 

those created downstream of the neutralization plane 

only sputter-erode the downstream surface (see Fig. 4). 

This assertion has been demonstrated, in part, by 

several numerical models.25–28 It was also verified via 

testing where a two-grid system that was tested at high 

background pressures exhibited excessive pit and 

groove erosion of the downstream accelerator grid but 

little accelerator aperture enlargement.29,30 

The volumetric erosion rate in the region of a single 

accelerator grid aperture (or Vaccel ′  ) can be expressed 

as: 

( ) dwn

p g

up

p g

up Vaccel Vw V − V − ′ = ′ + ′ + ′     . (22) 

Here, Vw

′  and Vp−g ′  are the volumetric erosion rates of 

the aperture walls and pit and groove erosion, 

respectively, in the region of an aperture. The “up” and 

“dwn” superscripts denote that charge-exchange ions 

were created upstream and downstream of the 

neutralization plane, respectively. The variables in this 

equation can be expressed as: 

h

corr

A

a

amu

a

up

up i

p g

up

w Y f

N

m

e

J

V V ⋅ ⋅ ⋅ ⋅ ρ

′ ′ + ′

− =   , and (23) 

p-g

corr

A

a

amu

a

dwn

dwn i

p g Y f

N

m

e

J V ⋅ ⋅ ⋅ ⋅ ρ

′  ′

− = . (24) 

Here, J ́i is the impingement current per aperture, ma

amu

is the atomic mass of the accelerator grid material, ρa

is the mass density of the accelerator grid, e is the 

electronic charge, NA is Avogadro’s number, Y is the 

grid sputter yield for an orthogonal angle of incidence, 

and fcorr is a sputter yield correction factor. This 

correction factor accounts for non-orthogonal angleof-incidence sputtering, variations in ion sputtering 

energies, re-deposition of sputtered material, and any 

other sputtering phenomena that can affect volumetric 

sputter erosion. Note that the prime superscripts 

denote parameter values per aperture. The 

aforementioned equations could be expressed without 

the prime superscripts to define the volumetric erosion 

rates for the entire accelerator grid. 

All of the above variables are known except for the 

impingement currents per aperture and the sputter 

yield correction factors. These impingement currents 

are from charge-exchange ions created both upstream 

and downstream of the neutralization plane. These 

currents will be determined here as was done by 

Monheiser and Wilbur,31,32 but with some 

modifications. The charge-exchange ion production 

current per aperture is given by:

∫ ′ = ′ ⋅σ ⋅ ⋅ −

n

up

l

l

b c e n

up Ji J n dz , and (25) 

∫

∞

− ′ = ′ ⋅ σ ⋅ ⋅ ⋅

nl

b c e g b

dwn J . (26) i J F n dz

Here, J ́b is the beamlet current, σc-e is the chargeexchange cross-section, nn is the neutral density 

distribution upstream of the neutralization plane from 

discharge chamber neutrals, nb is the vacuum facility 

background neutral density, z is the axial dimension, 

lup is the upstream location of the potential well that 

traps charge-exchange ions in this region, and ln is the 

neutralization length. Fg is the accelerator grid view 

factor for a charge-exchange ion created downstream 

of the neutralization, and, therefore, represents the 

probability that a charge-exchange created in this 

region will impinge the accelerator grid. The 

assumptions for equation (26) include, in part: 

1) potential gradients in the downstream beam plasma 

are too small to divert charge-exchange ions; and 

2) the facility background neutral density has isotropic 

velocity distribution. 

Equations (25) and (26) differ from those derived by 

Monheiser and Wilbur in the following ways. First, the 

integral in equation (25) has lup as the upstream limit 

and not the accelerator grid downstream surface. This 

is because this upstream axial location more accurately 

defines those charge-exchange ions trapped in this 

region by the electrode potential gradients. Second, the 

integral in equation (25) does not include the 

contribution of the facility background neutral density. 
NASA/TM—2001-211275 9 

This simplifying assumption is valid if background 

facility pressures are kept low. This appeared to be the 

case for the NSTAR thruster operated at NASA 

Glenn’s Vacuum Facility 5, where comparisons of 

accelerator currents produced in this facility to those 

produced on the Deep Space 1 spacecraft were within 

0.4 mA (e.g., less than 10% of the total impingement 

at 2 kW).2

 Finally, the contribution of neutrals 

escaping the discharge chamber downstream of the 

neutralization plane were omitted in equation (26). 

This is because these neutrals do not have an isotropic 

velocity distribution, but a velocity distribution 

directed away from the accelerator grids, and, 

therefore, should be omitted. 

It will be assumed here, as was done by Monheiser and 

Wilbur,31,32 that the neutral density distribution along 

the axis of an aperture can be approximated by the 

discharge chamber neutral density, nd, multiplied by a 

distribution function, N(z), so that: 

( ) ∫ ∫ ⋅ ≈ ⋅ ⋅

n

up

n

up

l

l

d

l

l

nn dz n N z dz , (27) 

where N(z) is only a function of the ion optics’

aperture geometry. Furthermore, the same onedimensional view factor utilized by Monheiser and 

Wilbur will be used here. Equations (25) and (26) can, 

therefore, be re-written as: 

( ) ∫ ′ = ′ ⋅σ ⋅ ⋅ ⋅ −

n

up

l

l

b c e d

up Ji J n N z dz , and (28) 

















⋅ + − ′ ⋅σ ⋅ ′ = −

n

2

n

2

dwn b c e b b

i l l

4

d

2

J n J , (29) 

where db is the beam extraction diameter. It can be 

shown that ln << db, so that equation (29) can be 

expressed as: 

4

J n d J dwn b c e b b

i

′ ⋅ σ ⋅ ⋅ ′ = − . (30) 

Because equation (30) utilizes a one-dimensional view 

factor approximation, it will only accurately predict 

impingement current contributions for apertures at the 

accelerator grid center, assuming small beamlet 

divergence half-angles. Equation (30) over-predicts 

impingement current contributions for apertures 

radially away from the accelerator grid center. 

Equation (30) also over-predicts impingement currents 

because potential gradients in the beam plasma were 

assumed to be too small to divert charge-exchange 

ions from the accelerator grid. Plasma potential 

measurements in NSTAR thrusters have demonstrated 

that there are radial and axial potential gradients.3,33

Although these voltage gradients are only on the order 

of a few volts, charge-exchange ions produced in this 

region have significantly lower energies and can, 

therefore, be directed away from the grids. 

The discharge chamber neutral density is determined 

by: 

( )

32

m k T d

1 m

n

2 n B n

b

d d

d

π ⋅ ⋅ ⋅ φ⋅ ⋅

− η ⋅ =

++  . (31) 

Here, ηd

++ is the discharge chamber propellant 

utilization efficiency accounting for doubly charged 

ions, md  is the discharge chamber flow rate, φ is the 

ion optics’ neutral transparency, mn is propellant 

atomic mass, kB is Boltzmann’s constant, and Tn is the 

neutral propellant temperature. 

Because charge-exchange production is a direct 

function of beamlet current, the peak beamlet current 

is necessary for determining the maximum local 

sputter erosion rate of the accelerator grid. This peak 

beamlet current is given by: 

a

flat oa

b

2

b

pk a

b f F

J

d

d

J ⋅ ⋅ 













 ′ = , (32) 

where da is the accelerator aperture diameter, Jb is the 

beam current, and Foa

a

 is the open area fraction of the 

accelerator grid. 

Equations (31) and (32) can be combined with 

equation (28) to yield: 

( ) ( ) ∫⋅ ⋅ π⋅ ⋅ ⋅ φ⋅

−η ⋅ ⋅σ ⋅ ⋅ ′ = ⋅

++

−

n

up

l

n B n l

d d

c e a

flat oa

b

4

b

2

up-pk a

i N z dz

32

m k T

1 m

f F

J

d

d

J  . 

(33) 

This equation can be used with equation (23) to define 

this peak volumetric sputter erosion rate per aperture. 

This is because the ion flux from this equation will 

impinge the aperture region within which it was 

created. However, the impingement current in 

equation (30) can impinge on any pit-and-groove site 

on the accelerator grid. It is, therefore, more 

convenient to utilize an average beamlet current for 
NASA/TM—2001-211275 10 

equation (30). The resulting impingement current can 

be expressed as: 

a

b oa

2

dwn-avg b c e b a

i 4 d F

J n d

J ⋅ ⋅

⋅ σ ⋅ ⋅ ′ = − . (34) 

The effect of beam extraction diameter on accelerator 

grid volumetric erosion rates can now be assessed. 

Comparisons are made at the same operating electrode 

voltages, beam currents, and discharge chamber flow 

rates, so that the relative effects of beam extraction 

diameter can be determined. Because the ion optics’

aperture geometry is unchanged, a peak volumetric 

erosion rate per aperture ratio can be established for 

charge-exchange ions produced upstream of the 

neutralization plane, where: 

( )

( )

( ) NSTAR

d

d

flat

NSTAR

flat

4

b

NSTAR

b

NSTAR up

p g

up

w

up

p g

up

w

1

1

f

f

d

d

V V

V V

++

++

−

−

− η

− η ⋅ ⋅ 













 = ′ + ′

′ + ′

 

  . 

(35) 

Here, the “NSTAR” superscripts denote parameters for 

the NSTAR 30 cm ion thruster. Note that 

equation (35) assumes that changes in lup and ln do not 

affect the neutral density distribution integral in 

equation (28). It can be shown that this is likely the 

case for ln due to the long neutralization plane lengths 

and the exponential decay of neutral density 

downstream of an accelerator aperture. Although 

comparisons are made for the same ion optics’

geometries and electrode voltages, it is presently 

unclear what the exact effect the varying beamlet 

current (and, therefore, varying space-charge) will 

have on lup. 

 

An average volumetric erosion rate per aperture ratio 

can further be established for charge-exchange ions 

produced downstream of the neutralization plane, 

where: 

b

NSTAR

b

NSTAR dwn

p g

dwn

p g

d

d

V

V = ′

′

−

−





. (36) 

It is assumed that background neutral densities are 

independent of beam extraction diameter, which is 

reasonable because discharge chamber flow rates are 

assumed unchanged. 

The results of equations (35) and (36) are shown in 

Fig. 5. In this figure, the discharge chamber propellant 

utilization efficiencies and flatness parameters were 

assumed to be the same for all beam extraction 

diameters. As Fig. 5 demonstrates, increasing the 

NSTAR thruster beam extraction diameter to 40 cm 

reduces peak volumetric erosion rates by chargeexchange ions originating upstream of the 

neutralization plane by a factor of 0.25, or by 75%. 

This is expected since the number of accelerator 

apertures available for erosion was doubled and the 

discharge chamber neutral density available for 

charge-exchange production was halved. 

The 40 cm beam diameter further reduces average 

volumetric erosion rates by charge-exchange ions 

originating downstream of the neutralization plane by 

a factor of 0.7, or about 30%. This occurs because 

although the downstream accelerator grid surface area 

available for sputter erosion doubled for the 40 cm 

thruster, its view factor for downstream chargeexchange ions increased by a factor directly 

proportional to the 40 cm-to-30 cm ion optics diameter 

ratio. 

The service life enhancement due these reduced 

erosion rates requires knowledge of which 

impingement current (i.e., equation (28) or (30)) is 

more dominant. It may be possible to gain insight into 

the relative magnitude of each impingement current 

through short-term testing, which is the topic of 

Appendix A. However, a rough estimate of the 

improvement in accelerator grid propellant throughput 

capability may be made for the 40 cm ion optics if it is 

assumed that operating conditions are the same as 

those of the NSTAR thruster. Two accelerator grid 

failure mechanisms are considered separately. 

The first failure mechanism considered is electron 

backstreaming due to accelerator grid aperture 

enlargement. Since an ongoing life test of an NSTAR 

ion thruster has successfully processed about 140 kg of 

xenon, it will be conservatively assumed that this 

140 kg is the propellant throughput capability of the 

NSTAR ion optics with regards to electron 

backstreaming. Upstream of the neutralization plane, it 

is assumed that the fraction of charge-exchange ions 

that sputter-erode the aperture walls (as opposed to 

those that erode the downstream surface) is either 

constant or decreases with a decreasing beamlet 

current. This assumption is reasonable since NSTAR 

wear test results have shown that aperture wall mass 

loss due to sputter erosion exhibited a smaller flatness 

parameter (i.e., average mass loss per unit grid area 

divided by the peak mass loss per unit grid area) than 
NASA/TM—2001-211275 11 

the beam flatness parameter.3,34 As a result, the ratio of 

accelerator aperture wall volumetric erosion rate per 

hole of the 40 cm thruster to that of the NSTAR 

thruster is equal to equation (35). Assuming that 

discharge chamber propellant utilization efficiencies 

and beam flatness parameters are the same for both 

thrusters, the 40 cm thruster offers a 4x increase in 

propellant throughput. The propellant throughput 

capability of the 40 cm thruster is, therefore, estimated 

to be about 560 kg for this failure mechanism, which 

exceeds the goal of 550 kg. 

The second failure mechanism considered is structural 

failure of the grid due to the pit and groove erosion of 

the downstream surface of the accelerator grid. The 

failure criterion here is assumed to be groove erosion 

through 80% of the grid thickness. Pit erosion is not 

considered because erosion through the grid thickness 

does not compromise the structural integrity of the 

grid. Past analyses based on NSTAR thruster wear test 

results estimated a propellant throughput capability of 

the NSTAR thruster of about 410 kg for this failure 

mechanism.9

 If it is conservatively assumed that 

charge-exchange ions created downstream of the 

accelerator grid dominate groove erosion, then the 

40 cm offers a 1.4x increase in propellant throughput 

capability. The propellant throughput capability of the 

40 cm thruster is, therefore, estimated to be about 

570 kg for this failure mechanism, which exceeds the 

goal of 550 kg. 

The propellant throughput capability of the 40 cm 

thruster is estimated to be about 560 kg for electron 

backstreaming and 570 kg for a structural failure. The 

40 cm thruster is, therefore, anticipated to meet the 

propellant throughput goal of 550 kg of xenon. (Note 

that these preliminary results are rough estimates 

subject to the assumptions made for the calculations.) 

A more accurate service life assessment requires that 

detailed analyses be made at the anticipated operating 

conditions for the 40 cm ion thruster. 

Screen Grid 

Screen grid erosion is caused by discharge chamber 

ions that sputter erode the upstream surface of the 

screen grid. This sputter erosion generally causes a 

chamfering of the screen grid apertures. Failure occurs 

when the screen grid erosion results in the removal of 

the screen grid webbing, allowing beam ions to 

directly impinge on the accelerator grid. NSTAR 

thruster life testing indicated that screen grid erosion 

was peaked at the center on the grid.3

 This is expected 

since the center of the grid is where the radial beam 

current density, and discharge ion current density just 

upstream of the ion optics, is highest. 

Discharge chamber particles that sputter-erode the 

screen grid include both singly and doubly charged 

ions. The screen grid is at discharge cathode potential 

and the discharge chamber plasma is typically 

assumed to be at the discharge anode potential. As a 

result, singly charged ions are assumed to have 

energies equivalent to the discharge voltage while 

doubly charged ions have twice the discharge voltage. 

The volumetric erosion rate in the region of a single 

screen grid aperture (or Vs

′  ) can be defined as: 

++ ++

++

+ +

+

⋅ ⋅ ⋅ ⋅ ⋅ρ

′ ⋅ ⋅ ⋅ + ⋅ρ

′ ′ = s

corr

A

s

amu

s

s s

corr

A

s

amu

s

s

s Y f

N

m

2 e

J

Y f

N

m

e

J

V . 

(37) 

Here, J ́s is the screen grid current per aperture, ms

amu

is the atomic mass of the screen grid material, ρs is the 

mass density of the screen grid, and fs

corr is a sputter 

yield correction factor, similar to that used in the 

previous section. The “+” and “++” superscripts 

denote parameter values for the singly and doubly 

charged discharge chamber ions, respectively. 

Note that NASA xenon ion thrusters are typically 

operated at discharge voltages of about 25 V, which is 

a part of the derated approach. As a result, singly 

charged ions have energies on the order of the sputter 

yield threshold energies.35 Furthermore, sputter yields 

increase exponentially with ion energy at these 

low discharge voltages. Because the ratio of doublyto-singly charged ion current ranges between 0.05 to 

0.25 for the NSTAR ring-cusp discharge chamber,3

 it 

is reasonable to assume that doubly charged ions 

dominate screen grid erosion for these thrusters. 

Equation (37) can, therefore, be rewritten as: 

++ ++

++

⋅ ⋅ ⋅ ⋅ ⋅ρ

′ ′ ≈ s

corr

A

s

amu

s

s

s Y f

N

m

2 e

J

V . (38) 

Because screen grid erosion is highest at the center of 

the grid, a peak current is necessary for determining 

the maximum local sputter erosion rate of the screen 

grid in equation (38). It can be shown that this peak, 

doubly charged screen grid current per aperture is 

given by: 
NASA/TM—2001-211275 12 

j

j

s

flat oa

b

2

b

s

i

i pk

s 1 R

R

f F

J

d

1 d J

+ ⋅ ⋅ ⋅ 















⋅ φ

− φ ′ = ++ . (39) 

Here, φi is the screen grid transparency to discharge 

ions, ds is the screen grid aperture diameter, Fs

oa is the 

screen grid open area fraction, and Rj is the ratio of 

doubly-to-singly charged ion current. Note that 

equation (39) assumes that Rj is constant throughout 

the beam. Equation (39) can be plugged into 

equation (38) to determine a peak screen grid 

volumetric erosion rate per aperture. 

The effect of beam extraction diameter on the peak 

screen grid volumetric erosion rate can now be 

assessed. Comparisons are made at the same operating 

discharge voltages, total voltages, and beam currents 

so that the relative effects of beam extraction diameter 

can be determined. Because the ion optics aperture 

geometry is unchanged, a peak screen grid volumetric 

erosion rate per aperture ratio can be established: 

NSTAR

j

NSTAR

j

j

j

flat

NSTAR

flat

2

b

NSTAR

b

NSTAR

i

NSTAR

i

i

i

NSTAR

s

s

1 R

R

1 R

R

f

f

d

d

1

1

V

V

+

+ ⋅ ⋅ 















⋅

φ

− φ

φ

− φ

= ′

′



 . 

(40) 

The results of equation (40) are shown in Fig. 6. In this 

figure, the screen grid discharge ion transparencies, 

ratio of doubly-to-singly charged ion currents, and 

flatness parameters were assumed to be constant for all 

beam extraction diameters. The screen grid discharge 

ion transparency assumption is conservative because 

this ion transparency is known to increase with 

decreasing beam current densities, which can be 

inferred from data in Refs. [11] and [12]. As Fig. 6 

demonstrates, increasing the NSTAR thruster beam 

extraction diameter to 40 cm reduces peak screen grid 

volumetric erosion rates by a factor of 0.5, or by 50%. 

This is expected since the amount of screen grid 

webbing available for erosion was doubled. 

The service life of the 40 cm thruster is assumed to be 

double that of the NSTAR screen grid, given the 

aforementioned assumptions. NSTAR wear test results 

showed that screen grid erosion was minimal after 

processing 88 kg of xenon.3

 From these results, the 

NSTAR screen grid was estimated to have a 460 kg 

propellant throughput capability utilizing a 

conservative failure criterion of sputter erosion 

through half of the screen grid thickness.9

 The 40 cm 

thruster is, therefore, anticipated to be capable of 

processing about 920 kg of xenon, which exceeds the 

goal of 550 kg. 

Preliminary Results 

Fabrication of 40 cm Ion Optics 

One 40 cm ion optics’ set has been successfully 

fabricated to date, and is shown in Fig. 7 with 30 cm 

ion optics for comparison. The dome height-to-chord 

radius was matched to that of the NSTAR 30 cm ion 

optics. Additional ion optics’ sets are presently being 

fabricated. These additional optics’ sets not only 

include the NSTAR aperture geometry, but also a 

thick-accelerator-grid (i.e., TAG) aperture geometry 

for further improvements in accelerator grid service 

life.12 

Preliminary Tests 

Test Hardware 

Preliminary performance tests were conducted on a 

laboratory model 40 cm ion thruster, described in 

Ref. [13]. Because 40 cm ion optics were unavailable 

for these initial tests, 50 cm ion optics from a prior 

NASA program were used.24 These ion optics had an 

ion optics’ aperture geometry similar to the NSTAR 

geometry, with two differences. First, the grid gap was 

15% larger than the nominal NSTAR gap at the grid 

center and 8 to 33% larger at mid-radius. Second, the 

accelerator grid thickness was 25% thinner than the 

nominal NSTAR grid thickness. 

A power console similar to that described in Ref. [36] 

powered the thruster. This power console was 

modified to allow the thruster to be throttled up to 

10 kW. During the tests reported herein, neutralizer 

common was electrically tied to facility ground. A 

high purity gas feed system was used to provide xenon 

to the discharge cathode, discharge chamber, and 

neutralizer through separate mass flow controllers. 

Testing was conducted in Vacuum Facility 11 at 

NASA Glenn. This 2.2 m diameter by 7.9 m long 

facility is evacuated with seven cryogenic pumps and a 

turbomolecular pump. The total measured facility 

pumping speed was greater than 100,000 l/s with 

xenon. 
NASA/TM—2001-211275 13 

During thruster operation, voltages and currents were 

measured with digital multimeters and xenon flows 

with mass flow meters. Beam current density profiles 

were measured with a planar probe mounted onto a 

two-axis probe motion system. Both the probe and 

two-axis probe motion system are described in detail 

in Refs. [11] and [12]. The planar probe of this study 

had an exposed surface area of 0.25 cm2

. 

Test Results

The two measurements reported below include 

impingement-limited total voltages and radial beam 

current density profiles. Although accelerator currents 

and electron backstreaming limits were measured, high 

background pressures, the larger-than-nominal cold 

grid gap, and the smaller-than-nominal accelerator grid 

thickness made comparisons with NSTAR ion optics’

data difficult. Impingement-limited total voltages were 

determined from plots of accelerator current as a 

function of total voltage where the slope was 

–0.02 mA/V. Uncertainties in impingement-limited 

total voltage determinations (and, therefore, perveance 

margins) were within ±10 V. All radial beam current 

density profiles were measured 49 mm downstream of 

the geometric center of the accelerator grid. 

Impingement-limited total voltages were measured at 

beam currents of 1.20, 2.70, 3.52, and 4.75 A. 

Although impingement-limited total voltages for this 

ion optics’ set were decreasing with accumulated 

operation, there was no attempt to burn-in this optics’

set prior to collecting the data presented in this 

paper.11,12 As a result, perveance data are conservative 

and, therefore, preliminary. The resulting average 

beamlet currents as a function of the impingementlimited total voltage are plotted in Fig. 8 with NSTAR 

ion optics’ data for comparison. As Fig. 8 shows, 

impingement-limited total voltages for the 40 cm 

thruster were 150 to 210 V higher than those of the 

NSTAR thruster ion optics. This is expected given the 

larger cold grid gap of the ion optics used on the 

40 cm thruster. Although the accelerator grid used on 

the 40 cm thruster was thinner than that of the NSTAR 

thruster, accelerator grid thickness has been shown to 

have a negligible effect on perveance.12,37,38

To permit comparisons between these 40 cm thruster 

data and the NSTAR ion optics’ data, the 40 cm 

thruster impingement-limited total voltages were 

corrected for an NSTAR grid gap. This was done by 

using equation (1) to determine a normalized 

perveance per hole at a given beam current, and then 

using this value to determine a new impingementlimited total voltage for an effective acceleration 

length equal to that of the NSTAR ion optics. These 

corrected results are also plotted in Fig. 8. As the 

figure shows, corrected impingement-limited total 

voltages for the 40 cm thruster were less than 50 V 

higher than those of the NSTAR thruster ion optics. 

The mean value of the correlated normalized 

perveance per hole for the ion optics of the 40 cm 

thruster was 1.8×10–11 A/V3/2, which is 25% lower 

than the 2.4×10–11 A/V3/2 measured for the 30 cm 

NSTAR ion optics. The cause for this difference is 

presently unknown. Regardless, the 40 cm thruster 

with the 50 cm ion optics was able to successfully 

operate at the lowest total voltages in Table 1 for all 

beam currents tested, albeit with a reduced perveance 

margin. 

Radial beam current density profiles at beam currents 

of 1.20, 2.70, 3.52, and 4.75 A are shown in Fig. 9. 

Beam power supply and accelerator voltages were 

those corresponding to the minimum total voltages for 

each beam current listed in Table 1. Although the 

beam current density profiles exhibited a repeatable, 

slightly irregular profile within a 150 mm radius, there 

was no substantial peak in the profile center as with 

the NSTAR 30 cm ion thruster.10–12 

Conclusions 

A 40 cm ion thruster is being developed at NASA 

Glenn to obtain input power and propellant throughput 

capabilities of 10 kW and 550 kg, respectively. This 

engine has twice the beam area as the NSTAR 

thruster, whose beam diameter is 28 cm. The technical 

approach here is a continuation of the “derating”

technique used for the NSTAR ion thruster. With 

regards to the ion optics, this approach maintains low 

beam current densities across the ion optics to extend 

ion optics service life. The 40 cm thruster can further 

offer increased input power and propellant throughput 

when other grid technologies are used, such as thickaccelerator-grid (TAG) ion optics. 

The 40 cm ion thruster utilizes the NSTAR ion optics 

aperture geometry to take advantage of the large 

database of lifetime and performance data already 

available. The ion extraction capability and electron 

backstreaming limits of the 40 cm ion optics were, 
NASA/TM—2001-211275 14 

therefore, be estimated by utilizing NSTAR 30 cm ion 

optics data. 

A preliminary throttle table for the 40 cm ion thruster 

was developed based, in part, on the predicted 

performance of the ion optics’ aperture geometry. The 

lowest perveance margin was estimated to be 209 V 

and occurred at the lowest thruster input power. The 

lowest electron backstreaming margin was estimated 

to be 40 V and occurred at the highest beam voltage 

and current. 

Dome-shaped grids were chosen for the design of the 

40 cm ion optics because they are naturally suited for 

large-area ion optics. A dome height-to-chord radius 

ratio similar to that of the NSTAR grids was further 

utilized because it addressed most key issues 

associated with grid fabrication and thruster operation 

while having little impact on other issues concerning 

thermal expansion and launch stresses. 

A preliminary service life assessment was conducted 

to determine the lifetime gain by utilizing larger area 

ion optics. Utilizing long duration test results with 

NSTAR ion optics, comparisons indicated that the 

propellant throughput goal of 550 kg of xenon is 

possible with 40 cm ion optics utilizing the NSTAR 

ion optics geometry. 

One 40 cm ion optics’ set has been successfully 

fabricated to date. Additional ion optics’ sets are 

presently being fabricated. 

Preliminary performance tests were conducted on a 

laboratory model 40 cm ion thruster. Because 40 cm 

ion optics were not available for these initial tests, 

50 cm ion optics were used. These ion optics had a 

cold gap that was 8 to 33% larger than that of the 

NSTAR ion optics geometry. Impingement-limited 

total voltages were measured at beam currents of 1.20, 

2.70, 3.52, and 4.75 A. The 40 cm thruster with the 

50 cm ion optics was able to successfully operate at 

the lowest predicted total voltages for all beam 

currents tested. Impingement-limited total voltages 

corrected for their larger cold grid gap for the 40 cm 

thruster were less than 50 V higher than those of the 

NSTAR thruster ion optics. 
NASA/TM—2001-211275 15 

Appendix A 

Accurately assessing the accelerator grid service life 

enhancement with 40 cm ion optics requires knowing 

whether charge-exchange ions created upstream or 

downstream (i.e., equation (28) or (30), respectively) 

of the neutralization plane dominate the total 

impingement current. It may be possible to gain 

insight into the relative magnitude of each 

impingement current by comparing impingement 

currents of both 30 and 40 cm ion optics at similar 

operating conditions. Total impingement currents can 

be determined for equations (28) and (30) by replacing 

the beamlet current with the beam current, to yield: 

( ) ( ) ∫ ⋅ ⋅ π ⋅ ⋅ ⋅ ⋅ φ⋅

− η ⋅ = ⋅ σ ⋅

++

−

n

up

l

2 n B n l

b

d d

b c e

up

i N z dz

32

m k T d

1 m

J J  , 

and (A1) 

4

J n d Jdwn b c e b b

i

⋅σ ⋅ ⋅ = − . (A2) 

Because the N(z) and lup are unknown, solving for the 

value of each current is not possible. However, 

impingement current ratios can be used to determine 

the relative magnitude of each term as a function of 

beam extraction diameter. Using the same assumptions 

as with equations (35) and (36), it can be shown that: 

( )





 



 − η

− η ⋅ ⋅ 















= ++

++

NSTAR

d

d

flat

NSTAR

flat

2

b

NSTAR

b

NSTAR up

i

up

i

1

1

f

f

d

d

J

J , 

and (A3) 

NSTAR

b

b

NSTAR dwn

i

dwn

i

d

d

J

J = . (A4) 

Equations (A3) and (A4) show that if 40 cm thruster 

accelerator currents are greater than those for the 

NSTAR thruster at similar operating conditions 

(assuming similar flatness parameters and discharge 

propellant utilization efficiencies), then chargeexchange ions originating downstream of the 

neutralization plane likely dominate the total 

impingement current. However, if 40 cm thruster 

accelerator currents are approximately half those for 

the NSTAR thruster at similar operating conditions, 

then charge-exchange ions originating upstream of the 

neutralization plane dominate the total impingement 

current. 
NASA/TM—2001-211275 16 

References 

[1] Rawlin, V.K., et al. “An Ion Propulsion System 

for NASA’s Deep Space Missions,” AIAA Paper 

99–4612, September 1999. 

[2] Polk, J.E., et al., “In-Flight Performance of the 

NSTAR Ion Propulsion System on the Deep 

Space One Mission,” IEEE Aerospace 

Conference Paper 8.0304, March 2000. 

[3] Polk, J.E., et al., “An Overview of the Results 

from an 8200 Hour Wear Test of the NSTAR Ion 

Thruster,” AIAA Paper 99–2446, June 1999. 

[4] Anderson, J.R., et al., “Performance 

Characteristics of the NSTAR Ion Thruster 

During an On-going Long Duration Ground 

Test,” IEEE Aerospace Conference Paper 8.0303, 

March 2000. 

[5] Personal Communication, Anderson, J.R., Jet 

Propulsion Laboratory, Pasadena, CA, May 2001. 

[6] Rawlin, V.K., “Erosion Characteristics of TwoGrid Ion Accelerating Systems,” IEPC Paper 93–

175, September 1993. 

[7] Brophy, J.R., Polk, J.E., and Rawlin, V.K., “Ion 

Engine Service Life Validation by Analysis and 

Testing,” AIAA Paper 96–2715, July 1996. 

[8] Patterson, M.J., et al., “Ion Propulsion 

Development Activities at NASA Glenn 

Research Center,” AIAA Paper 2000–3810, July 

2000. 

[9] Soulas, G.C., “Grid Technology Analyses for 

CNSR,” Presentation at NASA Glenn Research 

Center, January 2000. 

[10] Soulas, G.C., Foster, J.E., and Patterson, M.J. 

“Performance of Titanium Optics on a NASA 30 

cm Ion Thruster,” AIAA Paper 00–3814, July 

2000. 

[11] Soulas, G.C., “Performance Evaluation of 

Titanium Ion Optics for the NASA 30 cm Ion 

Thruster,” IEPC Paper 01–092, October 2001. 

[12] Soulas, G.C., “Improving the Total Impulse 

Capability of the NSTAR Ion Thruster with 

Thick-Accelerator-Grid Ion Optics,” IEPC Paper 

01–081, October 2001. 

[13] Patterson, M.J., et al., “Development Status of a 

5/10-kW Class Ion Engine,” AIAA Paper 2001–

3489, July 2001. 

[14] Christensen, J.A., et al., “Design and Fabrication 

of a Flight Model 2.3 kW Ion Thruster for the 

Deep Space 1 Mission,” AIAA Paper 98–3327, 

July 1998. 

[15] Sovey, J.S., et al., “Development of an Ion 

Thruster and Power Processor for New 

Millennium’s Deep Space 1 Mission,” AIAA 

Paper 97–2778, December 1997. 

[16] Aston, G., Kaufman, H.R., and Wilbur, P.J. “Ion 

Beam Divergence Characteristics of Two-Grid 

Accelerator Systems,” AIAA Journal, vol. 16, 

no. 5, May 1978, pp. 516–524. 

[17] Rawlin, V.K., “Characterization of Ion 

Accelerating Systems on NASA LeRC’s Ion 

Thrusters,” AIAA Paper 92–3827, July 1992. 

[18] Kaufman, H.R., “Technology of Electron 

Bombardment Ion Thrusters,” Advances in 

Electronics and Electron Physics, vol. 36, Academic 

Press, Inc., New York, 1974, pp. 265–373. 

[19] Rawlin, V.K., Banks, B.A., and Byers, D.C., 

“Design, Fabrication, and Operation of Dished 

Accelerator Grids on a 30-cm Ion Thruster,”

AIAA Paper 72–486, April 1972. 

[20] MacRae, G.S., Zavesky, R.J., and Godder, S.T., 

“Structural and Thermal Response of 30 cm 

Diameter Ion Thruster Optics,” AIAA Paper 89–

2719, July 1989. 

[21] Young, W.C., Roark’s Formulas for Stress and 

Strain, 6th Ed., McGraw Hill, New York, 1989, 

p. 523. 

[22] Horvay, G., “The Plane-Stress Problem of 

Perforated Plates,” Journal of Applied 

Mechanics, September 1952, pp. 355–360. 

[23] Personal Communication, Rawlin, V.K., NASA 

Glenn Research Center, Cleveland, OH, August 

2001. 

[24] Rawlin, V.K. and Millis, M.G., “Ion Optics for 

High Power 50-cm-diam Ion Thrusters,” AIAA 

Paper 89–2717, July 1989. 

[25] Whealton, J.H., Kirkman, D.A., and Raridon, 

R.J., “Electrostatic Ion Thruster Optics 

Calculations,” AIAA Paper 92–3830, July 1992. 

[26] Peng, X., Ruyten, W.M., and Keefer, D., “Further 

Study of the Effect of the Downstream Plasma 

Condition on Accelerator Grid Erosion in an Ion 

Thruster,” AIAA Paper 92–3829, July 1992. 

[27] Peng, X., Ruyten, W.M., and Keefer, D., 

“Charge-Exchange Grid Erosion Study for 

Ground-Based and Space-Based Operations of 

Ion Thrusters,” IEPC Paper 93–173, September 

1993. 

[28] Arakawa, Y. and Nakano, M., “An Efficient 

Three-Dimensional Optics Code for Ion Thruster 

Research,” AIAA Paper 96–3198, July 1996. 
NASA/TM—2001-211275 17 

[29] Brophy, J.R., Polk, J.E., and Pless, L.C., “Test-toFailure of a Two-Grid, 30-cm Dia. Ion 

Accelerator System,” IEPC Paper 93–172, 

September 1993. 

[30] Polk, J.E., Brophy, J.R., and Wang, J., “Spatial 

and Temporal Distribution of Engine Accelerator 

Grid Erosion,” AIAA Paper 95–2924, July 1995. 

[31] Monheiser, J.M., and Wilbur, P.J., “Effects of 

Design and Operating Conditions on Accelerator 

Grid Impingement Current,” IEPC Paper 93–174, 

September 1993. 

[32] Monheiser, J.M., and Wilbur, P.J., “Development 

and Verification of a Model to Predict 

Impingement Currents for Ion Thrusters,” NASA 

Contractor Report CR–195322, April 1994. 

[33] Foster, J.E., Soulas, G.C., and Patterson, M.J., 

“Plume and Discharge Plasma Measurements of 

an NSTAR-type Ion Thruster,” AIAA 2000–

3812, July 2000. 

[34] Polk, J.E., et al., “The Effect of Carbon 

Deposition on Accelerator Grid Wear Rates in 

Ion Engine Ground Testing,” AIAA Paper 2000–

3662, July 2000. 

[35] Stuart, R.V. and Wehner, G.K., “Sputter Yields at 

Very Low Bombarding Ion Energies,” Journal of 

Applied Physics, vol. 33, no. 7, July 1962, 

pp. 2345–2352. 

[36] Pinero, L.R., Patterson, M.J., and Satterwhite, 

V.E., “Power Console Development for NASA’s 

Electric Propulsion Outreach Program,” IEPC 

Paper 93–250, September 1993. 

[37] Rawlin, V.K., “Performance of 30-cm Ion 

Thrusters with Dished Accelerator Grids,” AIAA 

Paper 73–1053, October-November 1973. 

[38] Rovang, D.C. and Wilbur, P.J., “Ion Extraction 

Capabilities of Two-Grid Accelerator Systems,”

IEPC Paper 84–86, July 1984. 
NASA/TM—2001-211275 18 

Table 1. Preliminary 40 cm thruster ion optics’ currents and voltages 

for operation at high R-ratios.a

Input 

Power,b

kW 

Beam 

Current,b

A 

Beam 

Voltage,b

V 

Accelerator 

Voltage,b

 V 

Total 

Voltage,b

V 

Total 

Voltage 

Limit,c

 V 

Electron 

Backstreaming 

Limit,d V 

10.0 5.80 1567 -257 1824 1196 -217 

8.2 4.75 1567 -257 1824 1111 -203 

6.1 3.52 1567 -257 1824 994 -186 

4.7 2.70 1567 -257 1824 901 -175 

2.2 1.20 1567 -257 1824 667 -156 

7.4 4.75 1396 -243 1639 1111 -187 

5.5 3.52 1396 -243 1639 994 -171 

4.2 2.70 1396 -243 1639 901 -160 

2.0 1.20 1396 -243 1639 667 -140 

4.7 3.52 1179 -227 1406 994 -152 

3.6 2.70 1179 -227 1406 901 -141 

1.7 1.20 1179 -227 1406 667 -121 

3.2 2.70 1021 -216 1237 901 -127 

1.5 1.20 1021 -216 1237 667 -107 

1.1 1.20 679 -197 876 667 -76 a

A discharge voltage of 24 V and a flatness parameter of 0.6 were assumed. 

b

Preliminary operating point. 

c

Predicted impingement-limited total voltage based on the average beamlet current. 

d

Predicted limit. 

3.0E-05

5.0E-05

7.0E-05

9.0E-05

1.1E-04

1.3E-04

600 650 700 750 800 850 900 950 1000

Impingement-Limited Total Voltage, V

Average Beamlet Current, A

Fig. 1. Average beamlet current as a function of impingement-limited total voltage 

for the NSTAR ion optics. Data taken from Refs. [11] and [12].
NASA/TM—2001-211275 19 

1.0E-09

1.2E-09

1.4E-09

1.6E-09

1.8E-09

2.0E-09

2.2E-09

0.022 0.024 0.026 0.028 0.030 0.032 0.034 0.036 0.038 0.040

Discharge-to-Total Voltage Ratio

Uncorrelated NPH, A/V3/2

2.0E-11

2.2E-11

2.4E-11

2.6E-11

2.8E-11

3.0E-11

3.2E-11

Correlated NPH, A/V3/2

Uncorrelated NPH

Correlated NPH

Fig. 2. Normalized perveance per hole as a function of 

discharge-to-total voltage ratio for the NSTAR ion optics. 

0.90

0.92

0.94

0.96

0.98

1.00

0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10

Dome Height-to-Chord Radius

Fraction of Hot-to-Room Temperature Grid Gap

Measured - 30 cm Ion Optics

Predicted - 30 cm Ion Optics

Predicted - 40 cm Ion Optics

Fig. 3. Fraction of hot-to-room temperature grid gap for 30 cm and 40 cm ion optics. 

Measured datum is from Ref. [20]. 
NASA/TM—2001-211275 20 

Fig. 4. Typical accelerator grid erosion sites. 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

25 30 35 40 45 50 55 60

Beam Extraction Diameter, cm

Ratio of Accelerator Grid Volumetric 

Erosion Rate/Hole to That of the NSTAR 

Thruster

C-E Ions Created Upstream of

Neutralization Plane

C-E Ions Created Downstream of

Neutralization Plane

Fig. 5. Ratio of accelerator grid volumetric erosion rate per hole to that of the NSTAR thruster. 

Discharge chamber propellant utilization efficiencies and flatness parameters 

are assumed to be the same for all beam extraction diameters. 

New Grid

Eroded Grid

Aperture 

Enlargement 

Pits Bridge 
NASA/TM—2001-211275 21 

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

25 30 35 40 45 50 55 60

Beam Extraction Diameter, cm

Ratio of Peak Screen Grid Volumetric Erosion 

Rate/Hole to That of the NSTAR Thruster

Fig. 6. Ratio of peak screen grid volumetric erosion rate per hole to that of the NSTAR thruster. 

Screen grid discharge ion transparencies, ratios of doubly-to-singly charged ion currents, discharge 

voltages, and flatness parameters are assumed to be the same for all beam extraction diameters. 

Fig. 7. Photograph of 40 cm screen grid (left foreground) and 40 cm accelerator grid (right foreground) 

with a 30 cm accelerator grid (center background) for comparison. 
NASA/TM—2001-211275 22 

3.0E-05

5.0E-05

7.0E-05

9.0E-05

1.1E-04

1.3E-04

1.5E-04

1.7E-04

600 700 800 900 1000 1100 1200 1300 1400

Impingement-Limited Total Voltage, V

Average Beamlet Current, A

NSTAR Ion Thruster

40 cm Ion Thruster

40 cm Ion Thruster-Corrected

Fig. 8. Average beamlet current as a function of impingement-limited total voltage 

for the 40 cm and NSTAR ion thrusters. Data for the 40 cm thruster include 

measured data and data corrected for an NSTAR effective acceleration length. 

0

1

2

3

4

5

6

7

8

-300 -200 -100 0 100 200 300

Radius, mm

Beam Current Density, mA/cm2

4.75 A Beam Current

3.52 A Beam Current

2.70 A Beam Current

1.20 A Beam Current

Fig. 9. Radial beam current density profiles for the 40 cm ion thruster at 49 mm downstream 

of the ion optics’ center for beam currents of 1.20 A, 2.70 A, 3.52 A, and 4.75 A. 
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NASA TM—2001-211275

IEPC–01–090

E–13074

WU–713–81–66–00

28

Design and Performance of 40 cm Ion Optics

George C. Soulas

Ion thruster; Ion optics; Grids

Unclassified -Unlimited

Subject Category: 20 Distribution: Nonstandard

Prepared for the 27th International Electric Propulsion Conference cosponsored by the AFRL, CNES, ERPS, GRC,

JRL, MSFC, and NASA, Pasadena, California, October 14–19, 2001. Responsible person, George C. Soulas,

organization code 5430, 216–977–7419.

A 40 cm ion thruster is being developed at the NASA Glenn Research Center to obtain input power and propellant

throughput capabilities of 10 kW and 550 kg, respectively. The technical approach here is a continuation of the

“derating” technique used for the NSTAR ion thruster. The 40 cm ion thruster presently utilizes the NSTAR ion optics

aperture geometry to take advantage of the large database of lifetime and performance data already available. Domeshaped grids were chosen for the design of the 40 cm ion optics because this design is naturally suited for large-area

ion optics. Ion extraction capabilities and electron backstreaming limits for the 40 cm ion optics were estimated by

utilizing NSTAR 30 cm ion optics data. A preliminary service life assessment showed that the propellant throughput

goal of 550 kg of xenon may be possible with molybdenum 40 cm ion optics. One 40 cm ion optics’ set has been

successfully fabricated to date. Additional ion optics’ sets are presently being fabricated. Preliminary performance

tests were conducted on a laboratory model 40 cm ion thruster.