Kevin D. Diamant, James E. Pollard, and Mark W. Crofton

The Aerospace Corporation, El Segundo, California

Michael J. Patterson and George C. Soulas

Glenn Research Center, Cleveland, Ohio

Thrust Stand Characterization of the NASA 

Evolutionary Xenon Thruster (NEXT)

NASA/TM—2010-216895

November 2010

AIAA–2010–6701
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Kevin D. Diamant, James E. Pollard, and Mark W. Crofton

The Aerospace Corporation, El Segundo, California

Michael J. Patterson and George C. Soulas

Glenn Research Center, Cleveland, Ohio

Thrust Stand Characterization of the NASA 

Evolutionary Xenon Thruster (NEXT) 

NASA/TM—2010-216895

November 2010

AIAA–2010–6701

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Prepared for the

46th Joint Propulsion Conference and Exhibit

cosponsored by the AIAA, ASME, SAE, and ASEE

Nashville, Tennessee, July 25–28, 2010
Acknowledgments

The authors thank Kevin McCormick of the NASA Glenn Research Center for outstanding technical support throughout the 

process of thruster installation, and Mike Worshum, Tom Albright, and Dave Rikimaru of The Aerospace Corporation for many 

excellent suggestions and outstanding technical support in the development and construction of the thrust stand. Robert Csortos of 

Dura Magnetics, Inc., designed the eddy current damper magnet assembly. Special thanks to George Valenzuela of The Aerospace 

Corporation for explaining some of the fi ner points of fi shing line usage, and to Dan Herman of the NASA Glenn Research 

Center for many helpful suggestions. This work was supported under The Aerospace Corporation’s Independent Research and 

Development Program.

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://gltrs.grc.nasa.gov

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

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

either expressed or implied, by the National Aeronautics and 

Space Administration.

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

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2010-216895 1

Thrust Stand Characterization of the 

NASA Evolutionary Xenon Thruster (NEXT) 

Kevin D. Diamant, James E. Pollard, and Mark W. Crofton

The Aerospace Corporation 

El Segundo, California 90245

Michael J. Patterson and George C. Soulas 

National Aeronautics and Space Administration 

Glenn Research Center

Cleveland, Ohio 44135 

Abstract

Direct thrust measurements have been made on the NASA Evolutionary Xenon Thruster (NEXT) ion 

engine using a standard pendulum style thrust stand constructed specifically for this application. Values 

have been obtained for the full 40-level throttle table, as well as for a few off-nominal operating 

conditions. Measurements differ from the nominal NASA throttle table 10 (TT10) values by 3.1 percent

at most, while at 30 throttle levels (TLs) the difference is less than 2.0 percent. When measurements are 

compared to TT10 values that have been corrected using ion beam current density and charge state data 

obtained at The Aerospace Corporation, they differ by 1.2 percent at most, and by 1.0 percent or less at

37 TLs. Thrust correction factors calculated from direct thrust measurements and from The Aerospace 

Corporation’s plume data agree to within measurement error for all but one TL. Thrust due to cold flow 

and “discharge only” operation has been measured, and analytical expressions are presented which 

accurately predict thrust based on thermal thrust generation mechanisms. 

1.0 Introduction

NASA’s Evolutionary Xenon Thruster (NEXT) is engineered to be extremely flexible in terms of 

input power and specific impulse, while maintaining acceptable efficiency, and embodies a number of 

advances over previous ion engine systems. Some of its operating characteristics are being examined in 

detail in a study conducted in a test facility at The Aerospace Corporation (Ref. 1). The work is performed 

under the umbrella of a Space Act Agreement, with NASA participation in readying and operating the 

hardware under test. 

The NEXT throttle table was developed for missions outside of Earth orbit, and incorporates 40 levels 

to account for varying solar power with sun-spacecraft separation. Prior to this work, thrust has been

estimated from terminal parameters and available plume data. Recent plume measurements at The 

Aerospace Corporation have improved the fidelity of those estimates(Ref. 2), however direct thrust 

measurements are needed for benchmarking. 

The majority of thrust measurements reported in the electric propulsion literature have been made 

indirectly, by measuring deflection of the mechanism to which the thruster is mounted, and converting that 

deflection to thrust through some suitable calibration. The mechanism is generally a pendulum, either 

standard (Refs. 3 to 7), inverted (Refs. 8 to 10), or torsional (Refs. 11 to 14), and calibration is accomplished 

through application of a set of weights. By contrast, high thrust chemical engines are generally tested with 

load cells (e.g. Ref. 15). The availability of load cells with sufficient sensitivity permitted their introduction 

by Crofton (Ref. 16) and Brady (Ref. 17) to low thrust measurement applications. Advantages conferred 

through the use of load cells are high accuracy over a wide measurement range due to their high degree of 

linearity, the limiting of thrust stand motion to very small values, and prompt readings. With regard to the 

latter, there is no need for time-consuming force-displacement calibrations, during which thermal drift may 

introduce uncertainty into the measurement. The use of load cells for low thrust measurements has been
NASA/TM—2010-216895 2

demonstrated in References 18 to 20, and is the method adopted here to measure thrust due to ion beam 

extraction. However, the sensitivity required to accurately measure thrust during operation without ion beam 

extraction (cold flow and “discharge only”) exceeded the capability of the load cell, and those 

measurements were made using an inclinometer along with a set of calibration weights. 

2.0 Test Apparatus

Measurements were performed in a 2.4-m diameter by 9.8-m long cryopumped vacuum chamber with 

the thruster oriented along the chamber centerline. Two re-entrant pumps were on the end-dome behind 

the thruster, two more re-entrant pumps were in the beam dump region, and four 1.3-m cryotubs were 

mounted on the cylindrical wall of the tank adjacent to the thruster. The base pressure with no gas load 

was less than 1×10–7 torr, with 90 percent of the residual gas being water vapor, and the remainder being 

air and hydrocarbons. The beam dump was lined with carbon composite sheets and flexible graphite to 

minimize the yield of sputtered material. Lab power supplies and a lab propellant feed system were used 

to operate the PM1R prototype model thruster. Background pressure was measured by an ionization 

gauge located on the tank wall adjacent to the thruster. With an 1800-V, 3.52-A beam the xenon pressure

was 3.6×10–6 torr, applying the correction factor of 0.348 specified by the gauge manufacturer for xenon 

relative to nitrogen. The effective pumping speed for this condition was 2.1×105 liter/s, well in excess of 

the roughly 1.4×105 liter/s needed to ensure that the rate of ingestion of background gas was less than 1

percent of the propellant supply flow. 

Figure 1 shows the main features of the thrust stand, consisting of a standard pendulum with a 

hardened steel knife edge pivot, counterweight, high precision inclinometer (Rieker Electronics model 

SB1U), and eddy current damper. The pivot is shown more clearly in Figure 2, and the gas and electrical 

connections are shown in Figure 3. Electrical power was carried by highly flexible, finely stranded, PVC 

insulated 22 AWG wires. Multiple wires were used so that the maximum current per wire was 1.75 A. 

The eddy current damper consisted of an aluminum plate suspended below the thruster on an aluminum 

rod. The plate swung through the gap between the 2 in. high by 4 in. wide (5.1- by 10.2-cm) poles of a 

permanent magnet assembly consisting of two pairs of NdFeB magnets. The damping force was enhanced

by arranging the pairs (design by Dura Magnetics, Inc.) to produce a field reversal at the center of the 

assembly. By experimentation it was found that a 0.025 in. (0.64 mm) thick aluminum plate provided 

nearly critical damping at a gap such that the maximum magnetic field magnitude at the center of the gap 

was 0.33 T. Perhaps due to the action of the damper, there was no detectable effect of facility vibration on 

the output of the inclinometer or load cell.

The load cell (Transducer Techniques GSO-30) was mounted to a translation stage and connected to 

the back of the thruster, at thruster centerline, by a length of 50-lb test braided fishing line (Fig. 4). Thrust 

was measured by translating the load cell until the tension in the line exceeded the anticipated thrust. This 

was done while running the neutralizer and main discharge, but without ion beam extraction (“discharge 

only” mode). The difference in line tension created by energizing the grids yielded a measurement of 

thrust due to ion beam extraction. Multiple measurements were obtained in relatively short time by 

cycling the grid voltages. This strategy sought to minimize thermal drift of the thrust stand by obtaining 

prompt readings (typically, the switching transient died out within 10 to 15 sec, and a steady reading was 

recorded for 1 to 2 min), and by minimizing the change in currents and power to the thruster. 

The load cell sensitivity was not adequate to accurately measure thrust in “discharge only” mode, or 

with cold flow alone. However, by adjustment of the counterweights it was possible to obtain those 

measurements using the inclinometer. 
NASA/TM—2010-216895 3

Figure 1.—Thrust stand.

Figure 2.—Pivot.
NASA/TM—2010-216895 4

Figure 3.—Propellant and electrical connections.

Figure 4.—Thrust stand operation with load cell.

3.0 Analysis and Calibration

The diagram shown in Figure 5 was used to determine the relations needed to reduce the raw data for 

thrust due to ion beam extraction. The pendulum is shown inclined by an angle θ (positive sense as 

shown) from the vertical. The mass distributed above the pivot (mcw) is assumed to be concentrated at 

some location that we will call the counterweight center of mass, and that below (mT) at a location we will 

call the thruster center of mass. The blue line represents the braided line connecting the load cell (marked 

“s” for “sensor”) to a stud protruding from the back of the thruster, on thruster centerline. The red line 

represents a monofilament connecting the thruster to a calibration weight strung over a pulley. The 

location of the top of the pulley is marked “c” (for “calibration”) and the point of attachment to the 

thruster is at the height of the thruster centerline, but offset in the horizontal plane (Fig. 4). The thrust 

stand is insensitive to such an offset. 
NASA/TM—2010-216895 5

Figure 5.—Measurement schematic.
NASA/TM—2010-216895 6

For thrust measurements the monofilament was absent, and summing moments about the pivot (at 

steady state, =θ=θ 0  ) yields:

sin( cos sin() cos 0)

)( cos sin)(

− +θ−θ =Σ+θ−θ

φ+−φ−+

T CG CW e

FSFT SSS

Lgm dlgmD M

DXFYLFLF

 (1) 

where FT is thrust, assumed to act normal to the grid surface at thruster centerline, FS is the tension in the 

braided line, ΣMe represents moments due to the gas and electrical connections, and g is the acceleration 

due to gravity at sea level. The counterweight was set so that the magnitudes of θ and φ were at most 0.5 

and 1.5° respectively, and the small angle approximations (cosφ = cosθ = 1, sinφ = φ, sinθ = θ) are valid. 

If we further neglect terms that are second order in θ, and neglect δLFθ relative to δDS (δ is the vertical 

offset between the load cell and thruster centerline), Equation (1) becomes:

[ )( ( ) ] 0 1 1 1  − =Σ−−θ−−θ



 



















 +θ− δ

++ T CG CW e

FS

S

F

S

FS

S

ST MdlgmDLgm LL

D

L

D

LL

D FF (2) 

δ is nominally zero, and will be important only in the uncertainty analysis.

FT was determined by writing Equation (2) once with ion beam extraction, once without, and 

subtracting. This procedure would have been relatively simpler if the inclination, θ, was constant with and 

without ion beam extraction. In practice it was found to vary by a very small amount (0.002° to 0.013°), 

but large enough to require inclusion in the analysis. This variation, corresponding to linear displacements 

from approximately 7.7×10–4 to 5.0×10–3 in. (0.02 to 0.13 mm), arose roughly in equal parts from stretch 

in the braided line and in the strain-gauge based load cell. In any case, subtraction of Equation (2) with 

beam extraction from Equation (2) without beam extraction yields: 

θ∆













  − −



 



















 +θ− δ +∆=

F

CW

F

CG

T

S

S

avg

F

S

FS

S

ST L

l

m

L

L

mg L

D

L

D

LL

D FF 1 1 (3) 

where ∆ indicates a difference in two readings, θavg is the average inclination, and ΣMe is assumed 

constant over the very small variation in θ. In order to arrive at this form it was necessary to assume the 

following: 

( ) ( lmLmg ) L

D FF D

T CG CW

S

S

SS

S << − 















1++

2 21 (4) 

where FS1 and FS2 are readings with and without beam extraction respectively. The validity of this 

assumption will be demonstrated shortly. 

Equation (3) shows that in addition to load cell and inclinometer calibrations, knowledge of the mass 

properties of the pendulum was needed to calculate thrust. The arrangement shown in Figure 4 was used, 

at ambient conditions, to calibrate the mass properties. Simulating a thrust measurement, the load cell was 

translated to produce tensions in the braided line slightly in excess of the desired simulated thrusts, then 

weights were hung from the monofilament line, relieving tension in the braided line. With reference to 

Figure 5, summing moments about the pivot at steady state yields:

( ) ( ) ( ) ( )

( sin cos ) ( sin cos ) 0

cos sin cos sin

− +θ−θ =Σ+θ−θ

φ+−φ−+α+−α−

T CG CW e

FC CCC FS SSS

Lgm dlgmD M

XDFHLF DXFYLF

 (5) 
NASA/TM—2010-216895 7

where FC is the tension in the monofilament line. After applying the small angle approximations 

(magnitude of α was less than 0.5°), neglecting terms that are second order in θ, and neglecting 

δLFθ relative to δDS and δDC, Equation (5) becomes:

[ ( ) ( ) ] 0 1

1 1 1 1

− =Σ−−θ−−θ





 



















 +θ− δ  ++



 



















 +θ− δ

+

T CG CW e

F

S

S

F

S

FS

S

S

C

C

F

C

FC

C

C

MdlgmDLgm L

L

D

L

D

LL

D F

L

D

L

D

LL

D F

 (6) 

As before, we write Equation (6) twice and subtract, yielding: 





















 



















 +θ− δ  +∆+



 



















 +θ− δ +∆

θ∆ =















 −

S

S

avg

F

S

FS

S

S

C

C

avg

F

C

FC

C

C

F

CW

F

CG

T

L

D

L

D

LL

D F

L

D

L

D

LL

D F

L

l

m

L

L

mg

1 1 1 1 1

 (7) 

To arrive at this form it was necessary to assume:

( ) ( ) ( lmLmg ) L

D FF D

L

D FF D

T CG CW

S

S

SS

S

C

C

CC

C << − 















++≈















++ 1

2

1

2 21 21 (8) 

The right hand side (RHS) of Equation (7) involves the difference (∆FC and ∆FS are of opposite sign) 

of two nearly equal numbers, resulting in large uncertainty in the calculated mass properties. Therefore, 

84 measurements were averaged, yielding a value of 8.6×103 mN for the left hand side (LHS) of 

Equation (7), and thereby a value of 4.8×105 mN-cm for the RHS of Equation (8) (LF = 56.4 cm). 

The LHSs of Equation (8) have a maximum value of 3.8×103

, validating Equations (4) and (8). 

The inclinometer was calibrated under vacuum, with the thruster operating, by displacing the thruster 

known amounts using a rod attached to a linear translation stage. The load cell was calibrated (Fig. 6) at 

ambient conditions with a series of 7 weights ranging from 2.5 to 24.5 g (24.6 to 241 mN), spanning the 

nominal throttle table thrust range (25.6 to 236.4 mN). The load cell and inclinometer were heated and 

controlled to their ambient operating temperatures while under vacuum.

Calibration for cold flow and “discharge only” thrust measurements was performed under vacuum 

with the set-up shown in Figure 7. This is the familiar arrangement in which a series of weights was 

lowered by a motor over a pulley and the response of the stand (in this case a change in inclination) was 

recorded. Ten 51 mg washers were used as calibration weights.

4.0 Results

4.1 Discharge Only, Cold Flow 

We will attempt to model the thrust produced by the neutral gas flowing from the discharge chamber 

of an ion thruster under the condition of zero input power using an expression of the form: 

= cfcf  d cmCF , (9) 

where Fcf is the cold flow thrust, Ccf is a factor that accounts for off-axis flow, m ̇ d is the discharge 

chamber mass flow rate, and c is the mean thermal speed of the neutrals, given by:
NASA/TM—2010-216895 8

n

n

m

kT

c

π = 8 , (10) 

where k is Boltzmann’s constant, Tn is the neutral gas temperature, and mn is the gas molecular mass.

Figure 6.—Load cell calibration.

Figure 7.—Calibration for cold flow and discharge only thrust 

measurements.
NASA/TM—2010-216895 9

Ion thruster discharge chambers operate within the free molecular flow regime. For the case of flow 

through thin-walled apertures, the cosine law of molecular effusion applies (Ref. 21). In the case of a flat 

grid we obtain: 

∫

∫

π

π

εεε

εεε

=

2

0

2

0

2

)sin()cos(

cos )sin()(

d

d

Ccf (11) 

where ε is the angle relative to aperture centerline. This expression integrates to the simple result: 

Ccf = 2/3. 

A more realistic analysis must account for finite aperture thickness, grid curvature, and the presence 

of two grids.1 The two cylindrical apertures that a neutral particle must pass through to escape the 

discharge chamber present a difficult problem to model. Fortunately, Kuharski et al. modeled a two 

cylindrical aperture set that had a geometry that was very similar to that of the NEXT thruster (Ref. 22). 

They found that the angular distribution of particles exiting the accelerator grid was well modeled by 

assuming a single accelerator grid cylindrical aperture. This simplification was possible because of the 

large screen aperture diameter and low thickness relative to that of the accelerator grid. This same 

simplifying assumption will be exploited here. 

Clausing was the first to develop an expression for the angular distribution of particles downstream of 

a cylindrical aperture (Ref. 23). His equation assumes that the aperture is a point source and that the flux 

of particles from the walls of the aperture is linear as a function of axial thickness, which is a very 

accurate assumption over a range of aperture thickness-to-radius ratios that span from 0 to about 8 

(Ref. 24). The angular distribution of particles downstream of a cylindrical aperture, Tc(ε), in the far-field 

is given by (Refs. 23 and 25): 











































 



 >ε

ε

κ−

π

+κ





 



 ≤ε

ε





















 



 ε −−

κ−

π

+









































 



 ε − ε  +



 



 ε

κ−

π −

=ε

t

R

R

t

t

R

R

t

R

t

R

t

R

t

R

t

Tc

2 if arctan

2

tan( )

21

3

4

and

2 if arctan

2

tan( )

2

tan( ) 11

)21( 3

4

2

tan( ) 1

2

tan( )

2

tan( ) )1( arcsin 2

)(

2

3

2

2

 (12) 

where:

22

2

22

4

4 2

4

Rt

R R

tRt

+

+

−+

=κ (13) 

 

1 Analysis by George Soulas.
NASA/TM—2010-216895 10

Here, t is the accelerator aperture thickness, ε is the angle that the velocity makes with the aperture 

centerline, and R is the accelerator grid aperture radius. The contribution to Ccf from a single aperture is 

obtained from: 

∫

∫

π

π

εεεε

εεεε

=

2

0

2

0

2

,

)sin()cos()(

)( cos )sin()(

T d

T d

C

c

c

cf hole (14) 

The total Ccf can be found by correcting the contribution per hole for off-axis thrusting due to grid 

curvature:

∫

∫

ψ

ψ

ψψ

ψψψ

= max

max

0

0 ,

)sin(

)sin()cos(

d

d

CC cfcf hole (15) 

where ψ is the angle from grid centerline and ψmax is the angle to the edge of the accelerator grid 

perforated pattern. This analysis assumes that the upstream neutral density is uniform over the grid. For a 

NEXT accelerator grid, the correction factor Ccf is found to be 0.720. 

Measured values of cold flow “discharge only” thrust (no flow to the neutralizer) are shown in 

Figure 8. These measurements were obtained by cycling the flow on and off and noting the change in 

thrust stand inclination. Six readings were taken and averaged at each flow rate. The selected flow rates 

correspond to thrust levels (TLs) 12, 27, and 40. Measurements were taken after the thruster sat under 

steady vacuum conditions overnight and prior to the application of any electrical power. The thrust stand 

frame temperature was –11 °C, and this was taken to be the temperature of the thruster, and of the neutral 

gas. By including the point (0,0) and fitting the data to a straight line, we obtain Ccf = 0.74. 

4.2 Neutralizer Only

Neutralizer thrust was measured (again by cycling on and off) for the case of warm neutral flow 

(heater at the ignition current level, but no plasma) and for a 3 A keeper discharge. The measurements 

include a correction factor of 2.0 to account for the difference between the neutralizer-to-pivot moment 

arm and that between the point of application of the calibration weights (thruster centerline) and the pivot. 

We will attempt to model both cases using a continuum fluid approach (neutralizer internal pressure 

~ O(10) Torr), and will consider a purely thermal thrust mechanism, for which thrust can be estimated 

from:

+= ApumF eeenn  (16) 

where Fn is the neutralizer thrust, m ̇ n is the neutralizer flow rate, ue is the effective exhaust velocity, pe is 

the pressure at the neutralizer exit aperture, and Ae is the exit aperture area (ambient pressure is assumed 

to be negligible). If we assume an isentropic expansion to Mach number = 1 at the exit plane, we obtain:





 



  + 

 





+ = k k

mF kRTonn

1 1

1

2 21

 (17) 

where k is the ratio of specific heats, R is the specific gas constant, and To is the gas stagnation 

temperature.
NASA/TM—2010-216895 11

Figure 8.—Discharge only cold flow thrust, temperature = –11 °C.

For the warm flow case, at a xenon flow rate of 10 sccm and assumed stagnation temperature of 

1100 °C, Equation (17) yields a predicted thrust of 0.52 mN. The measured value at 10 sccm (average of 

5 measurements) was also 0.52 mN, with an estimated uncertainty of 16 percent. 10 sccm is a larger than 

nominal neutralizer flow, and was selected to improve the measurement signal-to-noise ratio without any 

expectation of altering the physics. 

For the case of a 3 A keeper discharge (heater turned off), the flow rate was 6 sccm, and the 

measured thrust (average of 6 measurements) was 0.41 mN with an estimated uncertainty of 18 percent. 

At Fn = 0.41 mN and m ̇ n = 6 sccm, Equation (17) yields a prediction of 2360 °K for To. Neutral 

temperatures near this value have been experimentally observed (Ref. 26) and predicted by numerical 

simulation (Refs. 27 and 28) in the region near the exit aperture of a hollow cathode. 

4.3 Discharge Only with Plasma

Thrust was measured with power supplied to the main discharge chamber, but with the screen and 

accelerator grid power supplies turned off. The neutralizer ran continuously at 6 sccm with a 3 A keeper 

discharge during this experiment, while the main discharge (power and flow) was cycled on and off to 

determine its contribution to thrust. Main discharge run times were kept short (less than 1 min) to 

minimize heating of the thrust stand in an attempt to avoid thermal drifting. Nevertheless, thermal drifting 

was observed to be significant on the time scale of the measurements, probably as a result of changes in 

electrical cable tension. The contribution to the change in thrust stand inclination due to the cables was 

estimated in the following way. Following shut-down of the main discharge power and flow, the rate of 

change of thrust stand inclination with time was determined at a point at which the gas flow had 

diminished to 5 to 10 percent of its steady value, as determined by vacuum chamber pressure readings 

(thrust assumed to be negligible at that point). This rate was assumed to apply during the period of thrust 

cessation, and was multiplied by the time required to get to 5 to 10 percent of steady flow to obtain the 

contribution from the cables. This was then subtracted from the total inclination change over that same 

period to obtain the main discharge contribution. In our error analysis we arbitrarily assigned an 

uncertainty of 50 percent to the inclination change due to the cables. 
NASA/TM—2010-216895 12

Figure 9.—Discharge only thrust, discharge mass flow and current listed by 

each data point.

Results are shown in Figure 9 for a range of “discharge only” power levels spanning those found in the 

nominal throttle table. Flow rates and discharge currents are listed with each data point. Each point represents 

the average of 2 to 5 measurements. It is evident that thrust scales linearly with discharge power, and that the 

values are significantly greater than those found with cold flow (Fig. 8). If we assume that thrust is generated

by the escape of thermal neutrals and apply the analysis from Section 4.1 (with Ccf = 0.74), we find that neutral 

temperatures from 2100 to 5600 °K are required. This finding conflicts with the common assumption that the 

neutral gas accommodates to the thruster operating temperature (Ref. 29), which for NEXT does not exceed 

approximately 530 °K in the steady state (Ref. 30). Nevertheless, this mechanism appears to be plausible since 

ion temperatures from approximately 5000 to 15000 °K have been measured in an ion thruster discharge 

chamber at a discharge power of 325 W (Ref. 31). Hot neutrals could be created by Xe+

-Xe elastic or charge 

exchange collisions. We estimate the mean free paths for these processes to be 5 to 6 cm (Refs. 32 and 33), 

considerably smaller than NEXT discharge chamber dimensions.

Other non-thermal mechanisms appear to be less plausible. With the screen and accelerator grid 

power supplies off, the anode and accelerator grid are at the same potential (the screen supply is tied 

between the anode and neutralizer, and the accelerator supply is referenced to the neutralizer), and ions

created near anode potential are unlikely to escape. High energy neutrals can be produced by charge 

exchange with ions accelerating through the sheath upstream of the screen grid, but with Debye lengths 

on the order of 0.01 to 0.1 mm (Ref. 34), sheath thickness on the order of 10 Debye lengths (Ref. 35), and 

estimated charge exchange mean free paths on the order of 10 cm for a 25 eV ion, this mechanism is 

estimated to account for less than 10 percent of the observed thrust. Ions created in the vicinity of the 

cathode with energies (relative to the cathode) in excess of the discharge voltage could escape directly, or 

do so as neutrals following charge exchange collisions, however for cathodes studied in simulated 

discharge chamber environments those ions tend not to be axially directed (Refs. 36 to 38). 

4.4 Ion Beam 

Thrust due to ion beam extraction was measured for the complete 40-level throttle table by the load 

cell method described in Sections 2.0 and 3.0. Sample raw data (6 on-off cycles) from thrust level (TL) 32 

are shown in Figure 10. Six measurements were taken at each TL, with the exception of TLs 5, 9, 13, and 

18, for which 11, 18, 7, and 7 measurements were taken respectively. The neutralizer ran continuously at 

6 sccm with a 3 A keeper discharge during this experiment. The thruster was warmed up daily prior to 

data collection by operating at either TL5 or TL9 for 3.5 to 4 hr, or at TL37 for 2 to 2.5 hr. 
NASA/TM—2010-216895 13

Figure 10.—Sample ion beam thrust measurement raw data, TL32.

Table 1 lists typical values and uncertainties for the parameters involved in data reduction. The quoted 

uncertainties for the various lengths (except δ) reflect the practical difficulty of making measurements on 

and around the thruster. The uncertainty in δ is the displacement observed to occur as a result of vacuumatmosphere cycling on the facility. Noise on the inclinometer output determined the uncertainties in θavg and 

∆θ, and that in ∆FC was determined by the accuracy of the scale used to weigh the calibration weights. The 

results of the load cell calibration (∆FS) show an average uncertainty of 0.14 percent over the tested range 

(24.6 to 241 mN). Thrust uncertainty was dominated by terms containing δ, a situation which, in hindsight, 

could have been most easily avoided by using a longer braided line. 

TABLE 1.—VALUES FOR UNCERTAINTY ANALYSIS

Parameter Typical

value

Absolute

uncertainty

Percentage

uncertainty

LF (cm) 56.4 0.25 -----

LC (cm) 38.9 0.25 -----

LS (cm) 14.6 0.25 -----

DC (cm) 24.4 0.25 -----

DS (cm) 28.2 0.25 -----

θavg (deg) –0.4 to 0.8 0.0008 -----

∆θ (deg) 0.002 to 0.015 0.0008 -----

δ (cm) 0 0.13 -----

∆FC (mN) 24 to 240 0.001 -----

∆FS (mN) 24 to 240 0.14

4.5 Total Thrust 

Total thrust was calculated by summing the contributions from ion beam extraction (Section 4.4), the 

main discharge without beam extraction (Section 4.3), and the neutralizer without beam extraction 

(Section 4.2). Main “discharge only” thrust was determined by applying the linear fit shown in Figure 9 to 

measured “discharge only” power at each TL. No attempt was made to apply a correction for the fact that 

the discharge chamber was not at a steady state temperature during the measurements of discharge only 

thrust. This is rationalized by our conjecture (Section 4.3) that the neutral temperature in the main body of 

the discharge is not governed by the thruster operating temperature. 
NASA/TM—2010-216895 14

Table 2 contains the results (Fmeasured) for the 40 NEXT throttle levels, along with comparisons to the 

nominal NASA Throttle Table 10 (FTT10), and to TT10 with values corrected with plume data recently 

acquired at The Aerospace Corporation (Ref. 2) (Corrected FTT10). Fmeasured represents measurement 

averages, and σ is the measurement standard deviation. Vbps is the beam power supply (screen supply) 

voltage. Standard methods for propagating uncertainties (Ref. 39) were employed to arrive at the values 

shown in the final column of Table 2. 

TABLE 2.—THRUST COMPARISON

TL Vbps

(V) 

Fmeasured

(mN) 

FTT10

(mN) 

Corrected 

FTT10 

(mN) 

Fmeasured –

FTT10 

(%) 

Fmeasured –

corrected FTT10 

(%) 

σ/Fmeasured 

(%) 

Fmeasured

uncertainty 

(%) 

md = 1.56 mg/s, Jb = 1.00 A 

1 275 25.4 25.6 25.4 –0.8 –0.3 0.2 1.1 

md = 1.75 mg/s, Jb = 1.20 A 

2 300 31.4 31.9 31.5 –1.6 –0.5 0.6 1.2 

3 400 37.1 37.2 37.0 –0.4 0.4 0.5 1.2 

4 650 47.9 48.2 47.7 –0.5 0.5 0.2 1.0 

5 679 49.1 49.2 48.9 –0.2 0.5 0.3 1.1 

6 850 54.5 55.2 54.6 –1.2 –0.2 0.2 0.9 

7 936 56.9 57.9 57.1 –1.7 –0.3 0.2 0.9 

8 1021 59.2 60.5 59.6 –2.1 –0.6 0.2 0.8 

9 1179 63.4 65.1 63.9 –2.5 –0.7 0.2 0.8 

10 1396 68.8 70.8 69.5 –2.8 –0.9 0.2 0.8 

11 1567 72.9 75.1 73.7 –2.9 –1.1 0.1 0.7 

12 1800 77.9 80.3 78.8 –3.1 –1.2 0.1 0.7 

md = 2.33 mg/s, Jb = 1.60 A 

13 1021 79.6 80.6 79.4 –1.3 0.3 0.2 0.8 

14 1179 85.1 86.8 85.3 –2.0 –0.2 0.0 0.8 

15 1396 92.3 94.5 92.8 –2.3 –0.6 0.1 0.7 

16 1567 97.7 100.1 98.4 –2.5 –0.8 0.3 0.6 

17 1800 104.4 107.0 105.2 –2.5 –0.8 0.1 0.6 

md = 2.92 mg/s, Jb = 2.00 A 

18 1021 100.3 100.7 99.5 –0.4 0.8 0.2 0.8 

19 1179 107.0 108.4 106.7 –1.2 0.3 0.1 0.8 

20 1396 115.9 117.9 115.9 –1.7 0.0 0.1 0.7 

21 1567 122.6 125.0 122.9 –1.9 –0.3 0.3 0.7 

22 1800 130.9 133.9 131.8 –2.3 –0.6 0.1 0.7 

md = 3.58 mg/s, Jb = 2.35 A 

23 1021 118.9 118.9 118.1 0.0 0.7 0.1 0.8 

24 1179 127.0 128.0 126.5 –0.8 0.3 0.2 0.7 

25 1396 137.4 139.4 137.6 –1.4 –0.1 0.1 0.7 

26 1567 145.2 147.5 145.6 –1.6 –0.2 0.1 0.7 

27 1800 155.2 157.9 155.8 –1.7 –0.4 0.2 0.7 

md = 4.11 mg/s, Jb = 2.70 A 

28 1021 137.1 136.6 135.8 0.4 1.0 0.2 0.8 

29 1179 146.4 146.9 145.4 –0.4 0.7 0.1 0.7 

30 1396 158.5 160.0 157.9 –0.9 0.4 0.1 0.7 

31 1567 167.1 169.4 167.1 –1.4 0.0 0.1 0.7 

32 1800 178.4 181.4 178.9 –1.6 –0.3 0.1 0.7 

md = 4.72 mg/s, Jb = 3.10 A 

33 1179 168.6 168.7 167.2 –0.1 0.9 0.1 0.7 

34 1396 182.5 183.7 181.4 –0.6 0.6 0.1 0.7 

35 1567 192.6 194.4 191.8 –0.9 0.4 0.1 0.7 

36 1800 205.5 208.4 205.5 –1.4 0.0 0.0 0.7 

md = 5.36 mg/s, Jb = 3.52 A 

37 1179 192.4 191.8 190.2 0.3 1.2 0.1 0.7 

38 1396 208.0 208.8 206.4 –0.4 0.8 0.2 0.7 

39 1567 219.4 220.7 217.9 –0.6 0.7 0.1 0.7 

40 1800 234.6 236.9 233.6 –1.0 0.4 0.1 0.7 
NASA/TM—2010-216895 15

We should note that in our comparison to the TT10 values, the neutralizer thrust contribution is applied 

in an approximate manner. The neutralizer flow rate of 6 sccm differs from the nominal TT10 values, which 

range from 2.5 to 4.0 sccm (6 sccm was chosen to ensure that the keeper discharge would not extinguish 

during extended periods with no ion beam extraction). Also, the change in neutralizer thrust between 

operation with and without ion beam extraction was only partially captured (due to the smaller neutralizerpivot moment arm) by the measurements from Section 4.4. Fortunately, neutralizer thrust is small, and these 

inaccuracies are likely to fall within the quoted total thrust measurement uncertainties.

The data from Table 2 are plotted in Figure 11. The structure in the “difference” traces is nearly 

identical in form to that of the thrust correction factor due to beam divergence (β) calculated from plume 

data recorded at The Aerospace Corporation (Fig. 12). This implies a proportionality between the two, and 

suggests the need for additional plume measurements to improve the fidelity of β. Another explanation for 

the difference trace structure which seems less probable (because it doesn’t explain TLs 2-5) is that the true 

ion beam current was reduced due to backstreaming of plume electrons to the anode. Backstreaming, 

possibly through the perforated ground screen, is favored by increasing beam supply voltage. 

Figure 13 compares thrust correction factors (γ) obtained from thrust stand measurements to those 

derived from plume current density and charge-state measurements made at The Aerospace Corporation 

(Ref. 2), and to the NASA TT10 values. γ accounts for thrust losses due to beam divergence and 

multiply-charged ions, and is defined by the well-known expression for the thrust F of an ion engine:

γ= JF 2mVbb q (18) 

where Jb is the ion beam current, Vb is the ion beam voltage (not equal to Vbps), m is the ion mass, and q is 

the elementary charge. The Vb values needed to calculate γ from thrust stand measurements were obtained 

from the NASA TT10. Plotting γ allows us to observe that the error bars for the thrust stand derived 

values and those calculated from plume data overlap for the entire throttle table with the exception of 

TL37. This is remarkably good agreement for measurements made by independent methods. 

Figure 11.—Measured and predicted total thrust (from Table 2, solid symbols). Error bars in 

measured thrust are smaller than the symbols. “Difference” traces shown with lines and 

open symbols. “Measured— NASATT10” trace annotated with beam power supply 

voltages.
NASA/TM—2010-216895 16

Figure 12.—PM1R thrust correction factors (calculated from plume data) for 

doubly-charged ions α, beam divergence β, and their product γ versus throttle 

level (from Ref. 2).

Figure 13.—Thrust correction factors from the nominal NASA TT10, calculated from 

plume ion flux and charge state measurements (Ref. 2), and calculated from direct 

thrust measurements.

PM1R thruster

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1.00

0 5 10 15 20 25 30 35 40

Throttle level (TL)

Thrust correction factor

α

β

γ
NASA/TM—2010-216895 17

Figure 14.—Thrust and total J++/J+ (J++/J+ from Ref. 2) versus utilization at TL9.

Figure 14 shows measured thrust as a function of discharge chamber propellant utilization (ratio of 

ion beam current to discharge chamber mass flow expressed in equivalent amperes) for TL9 (nominal 

discharge propellant utilization for TL9 is 93 percent). Declining thrust with increasing utilization is 

consistent with data from Reference 2 which show that the total doubly ionized current fraction (J++/J+

) 

increases from approximately 2 to 9 percent over the same range of utilization.

5.0 Conclusion

Direct thrust measurements have been made on the NASA NEXT ion engine and compared to the 

NASA throttle table 10 (TT10) for the full set of 40 throttle levels (TLs), as well as for a few off-nominal 

operating conditions. Measurements differ from the nominal TT10 values by 3.1 percent at most, while at 

30 TLs the difference is less than 2.0 percent. When measurements are compared to the TT10 values 

corrected with ion beam current density and charge state data obtained at The Aerospace Corporation, 

they differ by 1.2 percent at most, and by 1.0 percent or less at 37 TLs. Comparison of thrust correction 

factors (γ) calculated from direct thrust measurements to those calculated from The Aerospace 

Corporation’s plume data agree to within measurement error for all but one of the throttle levels.

Measurements of cold flow thrust and thrust with plasma present but without ion beam extraction 

have been made for the main discharge and neutralizer. In all cases thrust is postulated to arise from the 

escape of thermal neutrals, and analytical expressions are given that allow accurate thrust estimation if the 

neutral gas temperature is known. 

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Thrust Stand Characterization of the NASA Evolutionary Xenon Thruster (NEXT) 

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Diamant, Kevin, D.; Pollard, James, E.; Crofton, Mark, W.; Patterson, Michael, J.; Soulas, 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Direct thrust measurements have been made on the NASA Evolutionary Xenon Thruster (NEXT) ion engine using a standard pendulum 

style thrust stand constructed specifically for this application. Values have been obtained for the full 40-level throttle table, as well as for a 

few off-nominal operating conditions. Measurements differ from the nominal NASA throttle table 10 (TT10) values by 3.1 percent at most, 

while at 30 throttle levels (TLs) the difference is less than 2.0 percent. When measurements are compared to TT10 values that have been 

corrected using ion beam current density and charge state data obtained at The Aerospace Corporation, they differ by 1.2 percent at most, 

and by 1.0 percent or less at 37 TLs. Thrust correction factors calculated from direct thrust measurements and from The Aerospace 

Corporation’s plume data agree to within measurement error for all but one TL. Thrust due to cold flow and “discharge only” operation has 

been measured, and analytical expressions are presented which accurately predict thrust based on thermal thrust generation mechanisms.

15. SUBJECT TERMS

Ion thruster; Ion engine 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

25 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18