Jonathan L. Van Noord

Glenn Research Center, Cleveland, Ohio

NEXT Ion Thruster Thermal Model

NASA/TM—2010-216919

November 2010

AIAA–2007–5218
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Jonathan L. Van Noord

Glenn Research Center, Cleveland, Ohio

NEXT Ion Thruster Thermal Model

NASA/TM—2010-216919

November 2010

AIAA–2007–5218

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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NASA/TM—2010-216919 1

NEXT Ion Thruster Thermal Model

Jonathan L. Van Noord

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

As the NEXT ion thruster progresses towards higher technology readiness, it is necessary to develop 

the tools that will support its implementation into flight programs. An ion thruster thermal model has been 

developed for the latest prototype model design to aid in predicting thruster temperatures for various 

missions. This model is comprised of two parts. The first part predicts the heating from the discharge 

plasma for various throttling points based on a discharge chamber plasma model. This model shows, as 

expected, that the internal heating is strongly correlated with the discharge power. Typically, the internal 

plasma heating increases with beam current and decreases slightly with beam voltage. The second is a 

model based on a finite difference thermal code used to predict the thruster temperatures. Both parts of 

the model will be described in this paper. This model has been correlated with a thermal development test 

on the NEXT Prototype Model 1 thruster with most predicted component temperatures within 5 to 10 °C 

of test temperatures. The model indicates that heating, and hence current collection, is not based purely on 

the footprint of the magnet rings, but follows a 0.1:1:2:1 ratio for the cathode-to-conical-to-cylindrical-tofront magnet rings. This thermal model has also been used to predict the temperatures during the worst 

case mission profile that is anticipated for the thruster. The model predicts ample thermal margin for all of 

its components except the external cable harness under the hottest anticipated mission scenario. The

external cable harness will be re-rated or replaced to meet the predicted environment.

Introduction

Spaceflight hardware requires a combination of testing and modeling to simulate the extreme

operational environment. Initially, thermal and mechanical models are used to design the hardware to 

meet environmental requirements. Once the hardware is built, thermal vacuum and mechanical testing

occurs to provide thermal data to validate the design. Thermal testing is also necessary for the 

development of a high fidelity thermal model with minimized uncertainties associated with contact 

resistances and surface emissivities. Once the thermal model has been calibrated to test data, it can be 

used to predict various mission and spacecraft interface scenarios. This thermal model is then used to 

predict the extreme temperatures anticipated for the hardware. These temperatures can be used in cyclic 

thermal vacuum testing to demonstrate that hardware will survive and operate under these conditions.

This paper will focus on the development of a thermal model for the NEXT ion thruster.

Thermal vacuum testing and modeling has occurred on several previous generations of ion thrusters 

including 20-cm mercury ion thrusters (Ref. 1), 30-cm mercury ion thrusters (including the J-series

thruster) (Refs. 2 to 5), and 30-cm xenon ion thrusters (including the NSTAR/DS-1 thruster) (Refs. 6 to 

11). NASA’s Evolutionary Xenon Thruster (NEXT) is the latest generation xenon ion thruster, with a 

beam extraction diameter of 36-cm. This thruster is under development and the latest hardware is a 

prototype model (PM) ion thruster. Thermal testing and related data have been acquired on engineering 

model (EM) and prototype model thrusters. The thermal differences between the two have been 

significant, with the most significant modification being a higher emissivity tiodize coating to the PM

thruster. An early thermal model of the NEXT thruster was built to aid in the design of the PM thruster 

and was part of the rationale that led to the use of higher emissivity coatings.

A higher fidelity thermal model of the NEXT PM ion thruster has been developed and is presented in 

this document. This thermal model was validated through the thermal testing of the PM1 thruster under 
NASA/TM—2010-216919 2

various throttling levels and environmental conditions during the Thermal Development Test (TDT)

(Ref. 12). This model has also been used to predict thruster temperatures of various mission scenarios, 

and supports assessment of the thermal impact of any design changes and spacecraft integration. The 

results from the thermal model have also been used to establish the thermal environmental requirements 

necessary for testing.

This document will detail the model used to predict the heating from the plasma, the comparison of 

the finite difference thermal thruster model to TDT results (Ref. 12), and the maximum predicted flight

thruster temperatures.

Thermal Model of the NEXT PM Ion Thruster

The thermal model consists of two different types of models that are necessary to predict the thruster 

temperatures. The first model predicts the heat flux from the thruster plasma during operation at various 

throttling points. This model is based on a discharge plasma model that assumes the discharge plasma is 

uniform within the discharge chamber. The results from the plasma model heat fluxes are used as an input 

into the second model. This second model is built using a finite-difference, commercially available code

that predicts the thruster temperatures based on the thruster thermal conductivity and surface radiation

properties and also predicts the environmental heat fluxes based on orbital parameters.

Initially, a detailed derivation of the plasma heating model will be described along with the results for 

various throttling levels ranging from the lowest to highest throttling power. This plasma model is also 

useful for identifying the dominant mechanisms for discharge losses. Next, the finite difference model 

will be described and the plasma model will be used in conjunction with the results from the thermal 

development test to validate the model. A facility related plasma heating effect will also be described and 

its impact on the thruster evaluated. Finally, a prediction of the highest temperatures anticipated during 

any of the design reference missions is presented.

Model of Heating From Internal Plasma

The plasma heating model is based on two related discharge chamber plasma models and is a 

derivative of the plasma heating model that was originally created for the NSTAR program (Refs. 13, 14,

and 15) This and the other referenced models assume a 0-D, bulk homogeneous discharge plasma. Within 

the discharge plasma, it is assumed that the electron temperature, the plasma potential, the various 

densities, and the various velocities are constant and uniform. The model is based on the conservation of 

mass and energy.

Derivation of Equations

Neutral and Primary Electron Velocities.—Knowledge of the mean neutral speed, vo, present 

in the discharge chamber is essential to determine the various plasma densities. The neutral speed in 

Equation (1) is determined based on the temperature of the neutral gas, which is assumed to be the same 

as the discharge chamber walls (typically 150 to 300 °C), and follows a Maxwellian distribution.

Xe

n o M

kT

v

π = 8 (1)

In order to determine the average velocity of the primary electrons, it is necessary to calculate the 

energy of these electrons in the bulk plasma. The primary electron energy, Vpe, is determined by taking 

Vpe = VD −VC +VA (2)
NASA/TM—2010-216919 3

Figure 1.—Discharge chamber plasma potential variations from 

cathode to anode.

the discharge voltage, VD, and subtracting off the cathode fall voltage, VC, and adding the anode fall 

voltage, VA (see Eq. 2). It is assumed that the primaries enter the bulk plasma with this energy. The 

plasma potential is depicted in Figure 1. A further discussion of the plasma potential can be found in 

Reference 14. The plasma is generally positive of the anode. Reference 14 includes a term for the plasma 

potential fall between the cathode orifice and the anode sheath. For simplicity, this model will account for 

that fall included in the anode fall term. The model of the discharge plasma is calculated separately from 

the plasma within the cathode and it is assumed that the primary electrons originate at the cathode fall. 

Once the potential drop is derived, the velocity of the mono-energetic primary electrons, vpe, is 

calculated by simply relating the final kinetic energy to the initial potential energy and is described in 

Equation (3).

e

pe

pe M

eV

v

2 = (3)

Plasma and Neutral Densities.—The mass utilization efficiency, ηm, is defined as the ratio of ions 

leaving in the beam to the number of xenon atoms introduced into the chamber and is given in Equation 

(4). The mass flow rate, m , is frequently given in sccm and the value 4.5×1017

e converts the mass flow

of sccm to an ampere equivalent.

m e

IB m 17 4.5×10 η =  (4)

The density of the neutrals, no, can be determined by simply equating the neutral influx and the atoms 

leaving the thruster through the optics in the form of neutrals and ions. This is derived in Reference 14

and given in Equation (5). 

( )

o g ago c m

B m o v eA

I

n

Φ η η

− η = 4 1 (5)

The primary electron density, np–, was calculated in both References 13 and 14. From Reference 14 the 

derived equation is given in Equation (6) and is based on the assumption that the mean time for a collision 

between a primary electron and a neutral gas atom is much shorter than the mean time for the primary 

electron to be thermalized by the plasma electrons or the ballistic confinement time before a primary 

electron is lost to the anode. Plasma Potential

Cathode Anode

VC

VA

Vpe

VD

Cathode

Orifice
NASA/TM—2010-216919 4

( ) o T pe

e

T pe B m

e o g ago c m p en V v

I

V v I

I v A

n

σ = σ − η

Φ η η − = 4 1 (6)

The plasma ion density, n+, is calculated based on the beam current and the transparency, Φi, and area of 

the grids, Ag, to extract the ions from the discharge plasma. This relationship is detailed in Equation (7)

(Refs. 13 and 16).

b g i

B

v eA

I

n

Φ + = 2 (7)

The Maxwellian electron density, nm–, can be calculated simply based on the assumption that the 

discharge plasma is quasi-neutral and shown in Equation (8).

nm− = n+ (8)

Plasma Electron Temperature.—It is necessary to calculate the plasma electron temperature in order 

to predict the power from the electrons to various surfaces. The most effective way to calculate this 

temperature has been through an iterative method. The iterative approach is depicted in Figure 2.

Initially, the Maxwellian electron temperature, Tm, is estimated. This temperature is then used to 

calculate Bohm velocity, vb, and hence the ion density, n+, in Equation (7). The estimated electron 

temperature and corresponding densities are then used to calculate the Maxwellian electron rate factor for 

ionization neutral atoms, Qo

+ (the product of the ionization collisional cross section averaged over the 

Maxwellian electron energy distribution). 

The Maxwellian electron rate factor for ionizing neutral atoms can be calculated from engine 

parameters by equating the total ions produced in the plasma to those lost from the plasma. The total ions 

produced in the plasma, Ipl

+

, result from interaction of neutrals with Maxwellian electrons, Im–

+ in 

Equation (9), and primary electrons, Ip–

+ in Equation (10), and is calculated using Equation (11). The ion 

production is determined by neutral density, no, the primary electron density, np–, the Maxwellian electron 

density, nm–, the volume of the ion production region, V, and the respective rate factors, Pro

+ and Qo+

. 

Figure 2.—Flow chart describing the derivation of the plasma electron temperature.

Estimate Tm

Calculate vb, n+, nm–

Eqs. (7) to (8)

Calculate Qo

+

Eq. (14)

Calculate Tm

(Figure 3)

Is Tm ≅

Previous Tm?

No

Final 

Tm

Yes
NASA/TM—2010-216919 5

The Maxwellian electron rate factor for ionizing neutral atoms can be calculated from engine 

parameters by equating the total ions produced in the plasma to those lost from the plasma. The total ions 

produced in the plasma, Ipl

+

, result from interaction of neutrals with Maxwellian electrons, Im–

+ in 

Equation (9), and primary electrons, Ip–

+ in Equation (10), and is calculated using Equation (11). The ion 

production is determined by neutral density, no, the primary electron density, np–, the Maxwellian electron 

density, nm–, the volume of the ion production region, V, and the respective rate factors, Pro

+ and Qo+

.

+ − + − − +

m− = nonm eV < σ vm >= nonm eVQo I (9)

+ − + − +

p− = nonp eV < σ v pe >= nonp eVPro I (10)

( ) + − + − +

− +− +

pl = m + p = enoV nm Qo + np Pro I I I (11)

The ion loss rate, Il

+

, is calculated using the Bohm current (Eq. (12)). As shown in Equation (13), the 

total ion loss area, Ai, is the sum of the grid area, Ag, the keeper area, Ak, and the anode area modified (see 

Ref. 14) to account for the magnetic fields and ambipolar flow at the anode. 

i b i lI n ev A 2

1 = + (12) 

i g k ha sa c A = A + A + A + A f (13)

Once equating the ion production in the plasma given in Equation (11) with the ion loss out of the 

plasma in Equation (12), the Maxwellian ionization rate factor can be determined from the discharge 

plasma properties using an assumed electron temperature. Equation (14) shows this derived relation.

+

−

− + = − o

m

p

o

b i o Pr

n

n

n V

v A Q 2 (14)

Once the reaction rate coefficient for xenon is calculated in Equation (14) from thruster-based 

parameters, a corresponding electron temperature can be determined from the experimentally derived 

cross sections that were determined independent of any thruster (Ref. 17). Figure 3 shows this

empirically-derived relationship between the Maxwellian reaction rate factor and the electron 

temperature. As shown in 

Figure 2, if the new temperature derived from Figure 3 is sufficiently different than the previous 

electron temperature, it is used to recalculate the densities in Equations (7) and (8) and the process is 

repeated until the electron temperature is constant throughout the model. 

Ion and Electron Currents

(a) Excitation of Neutrals and Ions from Primary Electrons.—A substantial amount of energy in a 

xenon ion thruster is lost to the excitation of neutrals and some ions. In this model it is assumed that the 

excitation is only from the primary electrons. The rate at which neutrals are excited is related to the 

cathode emission current, Ie, which can be found by subtracting the screen grid current, Isg, from the 

measured discharge current, ID, (See Eq. (15)). 

e D sg I = I − I (15)
NASA/TM—2010-216919 6

Figure 3.—Graph depicting xenon ionization reaction rate factor variation 

with electron temperature.

The rate at which the excitation of neutrals, In*, and ions, I+*, occurs is based on the probability that 

the emitted electrons result in an excitation event. As shown in Equations (16) and (17), this is determined 

by the respective cross sections, σp* or σp+*, the densities and the average length a primary electron travels 

before it is collected, Lp–.

( ( )) In = Ie − − σp*noLp− * 1 exp (16)

( ( )) I+ = Ie − − σp+*niLp− * 1 exp (17)

(b) Screen Grid.—The screen grid ion current, Isg

+

, is determined from the beam current, IB, and 

measured ion transparency of the grids, Φi, and given in Equation (18). Electron current to the screen 

grid, Isg

–

, is then calculated by subtracting the measured screen grid, Isg, from the calculated ion current 

(see Eq. (19)).

( )

i

B i

sg

I I

Φ

− Φ = + 1 (18)

sg sg sg I = I − I − + (19)

(c) Keeper.—Previous work has correlated average beam current density and the average keeper ion 

current density for the NSTAR and NEXT ion thrusters (Ref. 18). The empirical relationship described in 

that reference was used to derive the ion keeper current, Ik

+ (Eq. (20)). The electron current to the keeper, 

Ik

–

, is a sum of the ion current and the current that flows through the resister, Ωk, between the keeper and

anode, and is shown in Equation (21).

k

g

B

k A

A

I I 















= + + 0.283 1.167 (20)

1E-17

1E-16

1E-15

1E-14

1E-13

0 2 4 6 8 10

Electron Temperature, (eV)

Reaction Rate, Qo

+ (m3/s)
NASA/TM—2010-216919 7

k

D k

k k

V V I I

Ω

− = + − + (21)

(d) Anode.—The primary electron current to the anode, Ianp–

, can be calculated based on the

probability that the primary electron will undergo a collision. As shown in Equation (22), Ianp– is 

calculated from the emission current, Ie, the total ionization and excitation cross section, σt, the neutral 

density, no, and the average length traveled by a primary electron before collection by the anode, Lp–.

( − ) − = e − σT o p

p Ian I exp n L (22)

The ion current to the anode, Ian+

, can be calculated by balancing the total ions produced, Ipl

+

(Eq. (11)), to those lost out of the plasma. The discharge plasma ions will be lost either to the anode, 

beam, screen grid, or keeper. It is assumed that any ions created in the discharge cathode remain in the 

cathode and are separate from the discharge plasma. Thus, Equation (23) can be used to determine the ion 

current to the anode.

+ + + + = − − − an pl B sg k I I I I I (23)

The Maxwellian electron current to the anode, Ianm–

, can be determined based on the current measured 

through the discharge power supply (ID), the ion current to the anode (Ian+

), an electron for each beam ion 

that exits the discharge chamber (IB), and the primary electrons that are collected (Ianp–

). Figure 4 depicts 

the electron current flow that corresponds to Equation (24). Note that this includes the electron current 

that corresponds to the beam ions and is not accounted for in the discharge power supply.

− + − = + + − p D an B an m

an I I I I I (24)

Power Deposition

(a) Ionization and Excitation.—The average power used to ionize each beam ion or to excite the 

neutrals or ions can be found by multiplying the respective currents times their threshold energies (Eqs. 

(25) to (27)). For xenon, the ionization threshold, U+, is 12.13 eV, the excitation of neutrals from ground 

state, Un*, is 8.3 eV, and the excitation of ions, Ui*, is 11.27 eV. The power it takes to ionize a beam ion 

leaves the discharge chamber with the beam ion and does not deposit its energy on the thruster. However, 

Figure 4.—An image depicting the electron flow at anode.

ID

IB

Ian+

anode

IB

Arrow indicates 

electron direction

ID+ IB

Ianp- Ianm-
NASA/TM—2010-216919 8

it is assumed that the power it takes to excite a neutral or ion is contained and radiated inside the 

discharge chamber. If the neutral is left with higher thermal energy from the excitation event, it is 

assumed to eventually deposit that energy on the discharge chamber surface. This power deposition from 

excitation is assumed to be uniformly distributed over the discharge chamber surfaces and equal to the 

power used for excitation. The calculation of the energy to the individual discharge chamber surfaces will 

be simply the fraction of its surface area to the total discharge chamber surface area, Adc, as shown in 

Equation (28) where Aan is the area of the anode, Ag is the area of the optics, and Ak is the area of the 

keeper. The power deposited to the grids will be proportional to their open area and is described in a later 

section.

+ + Pb = IbU (25)

* * * n nUn P = I (26)

* * * i i Ui P = I (27)

Adc = Aan + Ag + Ak (28)

(b) Anode.—The anode is heated by several mechanisms. Power is deposited from primary electrons, 

Pan–

, Maxwellian electrons, Panm–, ions, Pan+, and radiated energy from the excited ions and neutrals, Pan*.

It is assumed that, except for Pan*

, the power is deposited only on the magnets. The initial assumption is 

that the total power deposited is uniformly distributed based on the linear length of the magnet rings along 

the circumference of the discharge chamber. The power from the primary electrons is the total current of 

the primary electrons to the anode times the anode work function, φan, plus the potential between where 

the electrons originated and the anode (Eq. (29)). In this case that potential is the difference between the 

discharge potential, VD, and the cathode fall voltage, Vc.

( ( D C )) an p

an p Pan = I φ + V −V − − (29)

The discharge plasma is assumed to be positive relative to the anode (see Figure 1), so the power 

from the Maxwellian electrons, Panm–

, is determined by their temperature, Tm, and the anode work 

function.

( an m ) m

an m Pan I T2 + 5 = φ − − (30)

The power deposited from an ion neutralizing on the anode is determined by the fall voltage, VA, the 

ion thermal temperature (assumed to be the same as the neutral temperature, Tn), the ionization energy, 

U+, and the anode work function as the ion extracts the electron and neutralizes. If the ion temperature is a 

factor of 10 higher than 5kTn/2e, it will not significantly change the result of this equation since VA and 

U+ are typically at least an order of magnitude larger in value.





 



 = + + + − φ + + an n an an A U

e

kT P I V

2

5 (31)

The radiated energy from the plasma is evenly distributed over the anode surface area, Aan, and is 

based on the fraction of that surface area versus the total discharge chamber visible surface areas, Adc, as 

shown in Equation (32).

( ) * * * n i

dc

an an P P

A

A P = + (32)
NASA/TM—2010-216919 9

(c) Keeper.—The heating of the discharge cathode keeper from the plasma ions, Pk

+

, is determined as 

given in Equation (33) by the ion current, Ik

+

, the plasma potential, VD+VA, the keeper potential, Vk, the 

ion/neutral temperature, Tn, the ionization potential, U+, and the keeper work function, φk. 

( ) 



 



 = + − + + + − φ + + k n k k D A k U

e

kT P I V V V

2

5 (33)

The plasma is positive relative to the keeper, so it is only the most energetic plasma electrons that 

heat the keeper. Equation (34) is the same form as Equation (30) and the heating, Pk

–

, is based on the 

plasma electron current to the keeper, Ik

–

, the keeper work function, φk, and the plasma electron 

temperature, Tm.

Pk Ik ( k Tm ) 2 + 5 = φ − − (34)

Just as with the anode, the heat absorbed from the radiating excited species, Pk

*

, is based on the 

fraction of the keeper area, Ak, to the total discharge chamber area, Adc.

( ) * * * n i

dc

k

k P P

A

A P = + (35)

(d) Screen Grid.—The screen grid is heated by the ions drawn to the optics, but not extracted out of 

the optics. Since the plasma is positive relative to the screen grid the power deposited, Psg

+

, is determined 

by the ion screen grid current, Isg

+

, the potential difference between the plasma and the grids, VD+VA, the 

ion/neutral temperature, Tn, the ionization potential and the screen grid work function, φsg. Equation (36)

shows the power from the ions impacting the screen grid.

( ) 



 



 = + + + + − φ + + sg n sg sg D A U

e

kT P I V V

2

5 (36)

Just as in the previous cases for heating from the plasma electrons, the power is determined by the 

electron screen grid current, Isg

–

, the screen grid work function, φsg, and the plasma electron temperature, 

Tm (Eq. (36)).

Psg Isg ( sg Tm ) 2 + 5 = φ − − (37)

The power radiated from the plasma to the screen grid is calculated as before and is shown in 

Equation (38). The area of the screen grid is calculated using the screen grid open area fraction, Φsgo, and 

the area of the ion grids, Ag.

( ) ( ) * * * 1 n i

dc

sgo g

sg P P

A

A

P + − Φ = (38)

(e) Accelerator Grid.—The accelerator grid is heated primarily from the charge-exchange ions and 

the energy radiated from the plasma in the discharge chamber. The power deposited from the ion impact, 

Pag

+

, is a product of the charge-exchange ion current, Iag

+

, and the sum of the accelerator fall, Vag, which is 

generally the potential the accelerator grid is measured at, the ion/neutral temperature, Tn, the ionization 

potential, U+, and the accelerator grid work function, φg, which is usually the same as the screen grid work 

function since they are generally the same material.
NASA/TM—2010-216919 10





 



 = + + + − φ + + ag n ag ag ag U

e

kT P I V

2

5 (39)

The accelerator grid is partially shielded from the plasma radiation by the screen grid. This shielding

results in the area of the grid to be modified by both the screen grid open area fraction, Φsgo, and the 

accelerator grid open area fraction, Φago, in order to determine the power radiated from the plasma to the 

accelerator grid, Pag*

.

( ) ( ) * * * n i

dc

sgo ago g

ag P P

A

A

P +

Φ − Φ = (40)

(f) Cathode Loss.—Generally, cathode inserts tend to act like fixed temperature devices. That is, for a 

given current required, the insert will be at a given temperature regardless of losses out of the cathode (to 

an extent). The equation describing the relationship between the electron current emitted from the entire

insert, Iins, and the local insert temperature, Tins, is given in Equation (41) and is known as the RichardDushman equation. The Schottky effect is neglected since it will lower the work function on the order of 

0.1 eV and this is well within the uncertainty of the work function value.

dA

T

k I A T

ins

ins

ins ∫ R ins 













 − φ = exp 2 (41)

A detailed thermal/plasma model of the cathode is described in Reference 15 that includes radiation 

heat transfer, convection from the gas, conduction along the insert and cathode tube, ohmic heating of the 

cathode, and heating from the plasma. However, a simple model that considers mainly the thermal 

conduction along the insert is sufficient to predict the peak temperature and gradient along the insert for a 

given current (Ref. 19). Equation (42) defines the temperature gradient in the insert based on modeling it 

using conduction heat transfer. It requires as estimate of the losses out of the insert, Qins, in order to attain 

the gradient.

ins ins cs

ins ins

K A

Q

dx

dT = (42)

The insert thermionic emission current, Iins, is related to the cathode emission, Ie, by the relation 

described in Equation (43). The amount of electrons leaving the cathode, Ie, is equal to those emitted 

through thermionic emission and those freed through ion neutralization on the surface, Ic

+

.

+

e = ins + c I I I (43)

The heating of the insert is from the ions that recombine on the insert surface. The power out of the 

insert is primarily through the cathode thermal heat loss, Qins, and the cooling from the thermionic 

electrons. This power balance is given in Equation (44).





 



  = + φ +  



 + + + − φ +

e

kT U Q I

e

kT I V Ins

ins ins ins ins

ins c c 2

5

2

5 (44)

Generally, the greater the losses are out of the insert into the cathode, the greater the temperature 

differential will be from the front to the back of the insert. Equations (41) to (44) can be used to determine 

the temperature for the insert for a given emission current with an estimation of cathode thermal loss, Qins.

So the heating from the plasma to the insert and cathode is very dependent on the thermal design of the 

cathode and its losses. Typical thermal losses out of an insert are around 15 W. This value can be 
NASA/TM—2010-216919 11

confirmed from a thermal model of a specific cathode. For the finite difference thermal model presented 

in the later sections, the peak temperature predicted is used as the boundary condition and not a heat flux.

Discharge Power

The model presented is also iterated until the calculated discharge power is equal to the measured

discharge power, Pdc. Often the ion loss area, Ai, is adjusted during the iteration because it is one of the 

terms with the largest uncertainty. Equation (45) provides the sum of all the losses present relevant to the 

discharge power supply. The multiplier (1 – IB/Ianm–

) is used to subtract off the Maxwellian electrons 

associated with the production of beam ions. These Maxwellians heat the anode, but are processed 

through the beam power supply and not the discharge power supply.

k k sg sg ins

p

m an

an

m B

dc b n i an an P P P P P Q I

I P P P P P P + + + + + + 













 = + + + + − − + − + −

−

+ + − 1 * * (45)

Prediction of Internal Plasma Heating for the NEXT PM Thruster 

The NEXT PM1 thruster was used in the thermal development test (Ref. 12). The goal of this test was 

to yield temperature data for the thruster to validate and improve the thermal model. Thruster operational 

data were taken and used as inputs into the plasma model to derive the estimates for plasma induced 

thruster heating. Input parameters with a degree of uncertainty, such as ion loss area, are varied such that 

the predicted discharge losses are consistent with the measured discharge power supply. A typical output 

of the plasma heating model is shown in Figure 5.

The Maxwellian electron temperature is one of the intermediate parameters predicted by the model.

For all of the cases examined, this value is typically predicted to be between 2 and 3 eV. Measurements of 

the electron temperature in the bulk plasma of a NEXT thruster have been 3 to 7 eV (Ref. 20). The 

similarity between the predicted and measured values indicates that the model is producing reasonable 

plasma predictions.

Plasma heating predictions were derived for various thruster operating conditions based on the 

thermal development test thruster performance. These predictions are given in Table 1. Generally, the 

heating of the thruster is highly dependent on the beam current and increases as the beam current 

increases. At a specific beam current, the heating does not change drastically with beam voltage. It is also 

interesting to note that while discharge power includes the power to produce the beam ions, which does

not result in thruster heating, the heating from the Maxwellian electrons associated with the beam ions 

offsets the power due to beam ion production such that the total heating of the discharge chamber is 

approximately equal to the discharge power measured. As with the discharge power, generally for a given 

beam current, the power deposited increases as the beam voltage decreases. This would indicate that the 

hottest thermal case is when the thruster is at its highest beam current and lowest beam voltage.

Finite Difference NEXT PM Thruster Model

Model Description

The finite difference model has been built using commercially available thermal software. There were 

2497 nodes used along with 121 conductors for modeling contact resistance or insulators. An image of the 

model is shown in Figure 6. This model included many of the thruster components including the 

discharge cathode assembly, discharge chamber, magnet rings, accelerator and screen grid optics, 

neutralizer cathode assembly, gimbal pads, plasma screen, and front mask.
NASA/TM—2010-216919 12

Figure 5.—Image capture showing a typical plasma heating model output.

TABLE 1.—THE HEATING VALUES PREDICTED PRIOR TO TESTING TO NEXT PM THRUSTER

Beam voltage (V) 679 1179 1800 1179 1179 1800

Beam current (A) 1.2 1.2 1.2 2.0 3.52 3.52

Discharge power—power supply (W) 271 243 234 335 475 434

Discharge power—model prediction (W) 273 245 238 335 474 449

To anode (W) 235 208 201 278 379 357

To keeper (W) 5.1 5 5 6.9 11.5 11.4

To screen grid (W) 9.9 9.4 9.3 16.9 31 29.7

To accelerator grid (W) 4.5 4.5 4.9 9.0 21 20.2

Out of cathode (W) 15 15 15 15 15 15

Total plasma heating (W) 270 242 235 326 458 433
NASA/TM—2010-216919 13

Figure 6.—An image showing the NEXT PM thruster thermal model geometry.

Figure 7.—A graphic showing the thermal model of the thruster during the

thermal development test.

Validation of Model to PM1 Thermal Development Test

This model along with the prediction of heating from plasma was used to predict the temperatures 

demonstrated during the thermal development test. As typical with thermal models, some of the contact 

resistances and emissivities were adjusted to attain better correlation with the test data. Contact 

resistances are dependent on a number of factors, such as the type of mating materials, how thick these 

materials are, what torque a fastener is under, and the roughness of the surfaces in contact. So these are 

typically estimated and then calibrated through experimentation, as was done here. Some of the 

emissivities were adjusted since experimental data was not available for all the materials and their surface 

finishes. Most of the thruster surfaces have been grit-blasted or have had some texturing for sputter 

retention, which affects their optical properties. 

The test facility was also built into the model. As seen in Figure 7, the thruster was enclosed in a 

shroud that could be cooled via liquid nitrogen. Quartz lamps were used to provide additional 

environmental heat, but when they were used, most of their power went to heating the shroud. This meant 

that when the thruster was heated using the lamps, a majority of the heat flux came from the shroud in the 

infrared wavelength. The shroud contained several thermocouples that were used to set the shroud 

temperature in the model as boundary conditions. The vacuum chamber also had a few thermocouples 

that were used to establish its temperature in the model. 

Thruster

Vacuum Chamber Shroud

Plasma Screen

Neutralizer

Gimbal Pads

Optics
NASA/TM—2010-216919 14

Figure 8.—A schematic showing the thermocouple locations on the NEXT PM1 thruster during the TDT.

The thruster was outfitted with a significant number of thermocouples. The thermocouple locations 

are shown in Figure 8. Several of the thermocouple radial locations listed had additional thermocouples 

on the same component, but at a different azimuthal location (e.g. on the middle of the mask, there was a 

thermocouple near the neutralizer and opposite the neutralizer). These were used to capture any 

asymmetries that might be present. There were a total of 34 thermocouples on the thruster. Each gimbal 

pad had an additional pair that were used to measure the change in temperature across a gimbal 

attachment and, hence, the conducted heat loss out of the gimbal pads. This heat loss out of the gimbal 

pad was typically 0.4 to 0.7 W, so for the model, these interfaces were modeled as having no conductive 

losses out of the thruster. 

A comparison of the test data to the thermal model predictions is shown in Table 2 and Table 3. The 

thruster was modeled under conditions where the shroud was not actively cooled or heated. Predicted 

temperatures were typically within 10 °C of the test data representing a good correlation. Locations with

larger discrepancies included the downstream harness, the cathode tube, the cylindrical magnet rings, near 

the discharge chamber cut-outs, and the plasma screen. At the cathode tube location, there is a large 

temperature gradient, so the discrepancy is likely due to precise location of the thermocouple versus the 

resolution of the model. The rest of the discrepancies were likely the result of external facility-related 

heating. While testing at the highest beam current and voltage, one of the thermocouples on a cylindrical 

magnet ring showed excessive heating and exhibited arcing. This was likely due to electrons from the 

external plasma drifting through the plasma screen and accelerating to the magnets. This was not a form 

of heating that was accounted for a priori and was notably worse with higher background pressures.

Further discussions quantifying this effect based on the discrepancy between the plasma model 

predictions and the finite difference model are presented in the next section. This effect led not only to a 

noticeable increase in heating, but also resulted in greater asymmetric heating than predicted by the model 

due to differing open area fractions of plasma screen, which affected the local electron current.

 

Neutralizer Keeper Neutralizer Mount

Accelerator Grid Support

Screen Grid Support

Upstream Harness

Downstream Harness Thruster Harness Exit

Cathode Tube

Cathode Sputter Shield

Rear Plasma Screen

Cathode Harness Mount

Mask Middle

Mask Near Optics

Stiffening Ring

Plasma Screen –

Mask/Cylindrical 

Interface

Plasma Screen—

Mask/Cylindrical Interface

Gimbal Pad

Propellant Isolator

Cylindrical 

Cutouts
NASA/TM—2010-216919 15

TABLE 2.—COMPARISON OF THE TEMPERATURES OF TDT (REF. 12)

TO THE MODEL FOR 1.2 A BEAM CURRENT

Beam voltage (V) 679 1179 1800

Beam current (A) 1.2 1.2 1.2

Discharge power (W) 271 243 234

TDT

a

(°C)

Model

(°C)

TDT

a

(°C)

Model

(°C)

TDT

a

(°C)

Model

(°C)

Front magnet ring 171,166 169 161,166 167 162, 167 167

Cylindrical magnet ring 133,143 135-145 134,146 134-143 139, 163 144-155

Conical magnet ring 150,151 147 142,146 141 144, 147 141

Cathode magnet ring 172 171-172 168 168-170 168 169-170

Discharge chamber cutout 130,132, 137,146 133 132,133, 141, 143 132 140, 142, 147, 150 141

Upstream harness 101 105 102 99 107 106

Downstream harness 107 97 107 96 112 100

Propellant isolator 86 88 85 87 87 92

Cathode tube 432 412 426 409 424 408

Cathode sputter shield 157 161 155 159 155 160

Optics mounting ring 112 109 111 106 116 109

Screen grid support 150 147 143 140 145 142

Accelerator grid support 101 106 99 103 107 107

Cathode harness support 124 121 122

Neutralizer keeper 547 546 548 546 553 546

Neutralizer support 89 85 89 85 91 89

Mask optics edge 63,47 55-60 63, 47 55-60 50, 66 57-63

Middle mask 48 52 48 53 52 55

Plasma screen cyl/mask 76, 52 52-72 52, 76 52-73 56, 78 54-76

Gimbal pads 91, 89, 91 88 91, 89, 92 87 92, 93, 97 92

Plasma screen con/cyl 71, 63 61-64 63, 71 61-65 68, 73 65-69

Exit wire harness 70 67 69 66 71 69

Plasma screen rear 62 55 62 56 64 57 a

Multiple TDT values indicate thermocouple readings at different azimuthal locations.
NASA/TM—2010-216919 16

TABLE 3.—COMPARISON OF THE TEMPERATURES OF TDT (REF. 12)

TO THE MODEL FOR 2.0 AND 3.52 A BEAM CURRENTS

Beam Voltage (V) 1179 1179 1800

Beam Current (A) 2.0 3.52 3.52

Discharge Power (W) 335 475 434

TDT

a

(°C)

Model

(°C)

TDT

a

(°C)

Model

(°C)

TDT

a

(°C)

Model

(°C)

Front magnet ring 200 199 241 245 242 249

Cylindrical magnet ring 164 168-182 203, 239 213-231 212, 261 227-248

Conical magnet ring 169, 174 165 213, 215 213 214, 214 215-216

Cathode magnet ring 190 190-191 227 231-233 227 228-231

Discharge chamber cutout 164, 170, 170, 175 165 196, 198, 215, 210 207 209, 209, 216, 222 221

Upstream harness 121 116 165 178 178 184

Downstream harness 127 121 171 156 183 172

Propellant isolator 100 106 139 138 142 146

Cathode tube 448 429 474 460 471 459

Cathode sputter shield 170 171 200 197 203 197

Optics mounting ring 133 128 171 168 175 173

Screen grid support 172 165 221 217 223 221

Accel grid support 120 126 161 169 164 174

Cathode harness support 140 178 179

Neutralizer keeper 544 547 558 563 558 563

Neutralizer support 102 101 136 130 143 137

Mask optics edge 59, 75 68-73 88, 101 94-99 92, 106 100-104

Middle mask 60 65 88 90 92 96

Plasma screen cyl/mask 66, 89 64-85 98, 119 94-110 103, 124 95-115

Gimbal pads 107, 108, 110 106 145, 146, 153 138 150, 152, 163 146

Plasma screen con/cyl 76, 83 74-78 94, 96 106-108 124, 124 112-114

Exit wire harness 83 79 97 114 129 119

Plasma screen rear 68 62 86 90 106 97 a

Multiple TDT values indicate thermocouple readings at different azimuthal locations.
NASA/TM—2010-216919 17

For all cases presented here, the a priori plasma power deposition values were used as initial estimates 

of heating from the discharge plasma on the thruster. The heating on the anode was evenly distributed 

between the magnet rings. These values were then adjusted to obtain agreement with the test data. The 

power deposition that was used corresponding to the temperatures shown in Table 2 and Table 3 are given 

in Table 4 and Table 5, respectively.

Two observations can be made comparing the a priori estimate of heating to those used to replicate 

the testing. The first is that with greater beam current and voltage, a larger amount of heating was 

required over the predictions to duplicate the test temperatures. This is likely due to the previously 

mentioned heating from facility plasma and is described in further detail in the next section. This could 

mean that at 3.52 A and 1800 V, there was an additional 123 W of heating occurring from the background 

plasma. 

TABLE 4.—POWER DEPOSITION PREDICTED FROM PLASMA MODEL ALONG WITH DEPOSITION USED IN 

FINITE DIFFERENCE MODEL TO MATCH TEST TEMPERATURES SHOWN IN TABLE 2

1.2 A/ 679 V 1.2 A/1179 V 1.2 A/1800 V

Pred.

(W)

Used

(W)

% of 

pred.

Pred.

(W)

Used

(W)

% of 

pred.

Pred.

(W)

Used

(W)

% of 

pred.

Cathode magnet ring 18 3 17 16 3 19 15 3 20

Conical magnet ring 51 55.8 110 45 49.7 110 44 47.7 110

Cylindrical magnet ring 84 124.2 148 75 122 164 72 140.0 194

Front magnet ring 82 47 57 73 45.9 63 70 44.3 63

Total anode 235 230 98 209 221 106 201 235 117

DCA keeper 5.1 5.1 100 5.0 5.0 100 5.0 5.0 100

Screen grid 9.9 22 222 9.4 18.9 201 9.3 18.9 203

Accelerator grid 4.5 4 89 4.5 4 89 4.9 4.9 100

DCA insert tip temp 1008 1008 100 1001 1001 100 998 998 100

TABLE 5.—POWER DEPOSITION PREDICTED FROM PLASMA MODEL ALONG WITH DEPOSITION USED IN

FINITE DIFFERENCE MODEL TO MATCH TEST TEMPERATURES SHOWN IN TABLE 3

2.0 A/ 1179 V 3.52 A/1179 V 3.52 A/1800 V

Pred.

(W)

Used

(W)

% of 

pred.

Pred.

(W)

Used

(W)

% of 

pred. 

Pred.

(W)

Used

(W)

% of 

pred.

Cathode magnet ring 21 5 23 29 10 34 27 8 29

Conical magnet ring 60 65.5 109 82 100 122 77 100 129

Cylindrical magnet ring 100 180 180 136 250 184 128 285 223

Front magnet ring 97 62 64 132 87.1 66 124 87.1 70

Total anode 278 313 112 379 447 118 356 480 135

DCA keeper 6.9 6.9 100 11.5 11.5 100 11.4 11.4 100

Screen grid 16.9 24 142 31.0 39 126 29.7 39 131

Accelerator grid 9.0 9.0 100 20.7 20 97 20.2 20.7 102

DCA insert tip temp 1035 1035 100 1063 1063 100 1057 1057 100
NASA/TM—2010-216919 18

A second observation can be made from the comparison of data to modeling. The relative amount of 

heating to the magnet rings does not appear to be based purely on the length of the magnet ring footprint 

around the circumference. The percent of power added at each magnet ring from the predicted amount is 

fairly consistent for all of the cases except at the cylindrical magnet rings. The cylindrical magnet rings 

were in the region that exhibited electrons penetrating the plasma screen from the background plasma. If 

this effect is subtracted out, the ratio of heating to the various magnet rings remains fairly constant at 

0.1:1:2:1 for the cathode-to-conical-to-cylindrical-to-front magnet rings over the throttling range 

examined. This is quite different than the ratio of plasma heating that is based on the magnet rings 

footprint of 0.2:0.6:1:1. This would indicate that the cylindrical magnet rings receive the largest amount 

of current from the discharge plasma, followed by the conical and front magnet rings. There would then 

be virtually no current collected back by the cathode magnet rings. The mission analysis presented here 

will use the 0.1:1:2:1 ratio for the hottest case mission predictions. The heating in those cases correspond 

to the 3.52 A and 1179 V throttling point with the exception that the cylindrical heat flux will be 200 W 

instead of 250 W, which includes the facility plasma effect. 

Facility Effects on Thermal Measurements

As previously mentioned, there was a facility-related effect that provided additional heating to the 

thruster. This effect became more pronounced at the higher beam voltages and currents. This heating was 

a result of external plasma electrons drifting through the plasma screen, being accelerated to the anode 

and then following the magnetic field lines to the magnets. The external plasma density decreases from 

the exit plane of the thruster to its upstream side (Ref. 21). As a result, this heating effect was most 

pronounced on thermocouples in the cylindrical region of the thruster near the exit plane. It was these 

thermocouples that registered the largest temperature increases (see Tables 2 and 3). These temperature 

increases were counter to the decreasing discharge power and heating that occurs as the beam voltage 

increases at a fixed beam current.

It is important to quantify this effect in order to determine the amount of heating that a thruster will 

experience in a vacuum facility versus a spaceflight mission. Figure 9 shows the amount of power used at 

the magnet rings in the modeling of the thermal development test as a percentage of the total predicted 

anode internal plasma power deposition. At the lowest beam current and voltage, the total anode power 

applied was essentially equal to the predicted amount. As the beam current and voltage increase, the 

percent of power used for the cathode, conical and front magnet rings remains fairly constant. The 

increase in applied power primarily comes at the cylindrical magnet rings. It does not appear that the 

internal plasma is redistributing itself during these throttling changes since the power at all of the noncylindrical magnet rings is constant. Therefore, it appears that the increase is primarily due to the external 

plasma. At 3.52 A and 1800 V, this heating is 134 percent of the predicted value. This translates into 

about 120 W of additional heating. This could be accounted for by as little as 68 mA of electrons being 

accelerated through 1800 V. This would be processed by the beam power supply and only represents

2 percent of the measured beam current, which would be difficult to discern during testing. It is important 

to realize that this effect is a result of the background plasma and, hence, the background pressure. During 

testing of the NEXT PM1 thruster in a larger vacuum facility (NASA Glenn VF6), which operated with a 

lower background pressure, the anomalous change in the magnet temperatures was less pronounced as the 

beam voltage increased (Ref. 22). In that test, the two different cylindrical magnet ring temperatures 

changed by –3 °C and +9 °C when increasing in beam voltage from 1179 V to 1800 V at 3.52 A beam 

current. During the TDT, as can be seen from Table 3, these same thermocouples locations changed by 

+9 °C and +22 °C. A rigorous thermal model was not done to quantify the effect on the testing in VF6, 

but based on an evaluation of the temperature changes at different throttling points, it would be expected 

that these backstreaming electrons represent <1 percent of the measured beam current. Because of 

concern that this facility effect could overheat critical thruster components, the NEXT PM thruster design 

now has a solid panel around the cylindrical region and the open area fraction was reduced from 50 to 20

percent in the conical region. The thermal effect of that design change is predicted in the following 

section.
NASA/TM—2010-216919 19

Figure 9.—Trend showing the percent of power deposition to the magnet ring or anode out of the total predicted 

anode power deposition for various throttling points.

Prediction of PM Thruster Temperatures for Hottest Case Anticipated from Potential Missions

It is necessary to model the ion thruster under the hottest expected thermal environment to ensure that 

all of its components have sufficient thermal margin for operation. The NEXT PM thruster currently does 

not yet have a spaceflight application. However, a deep space design reference mission (DSDRM) was 

derived from the study of spaceflight applications using the NEXT ion thruster. For those DSDRM, the 

maximum environmental heating occurred at 0.85 AU, when the sun angle was 38° off the thruster axis

(Ref. 23).

The spacecraft interface is critical to the thermal modeling effort. Currently, there is no spacecraft 

interface defined since there is no application. Based on the previous ion thruster missions of Deep Space 

One and Dawn, it is conservative to assume that the thruster will be mounted in an adiabatic can (Refs. 24

and 25). This adiabatic can will have to encompass the gimbal footprint and likely extend downstream as 

far as the gimbal interface. Any further would probably interfere with gimbal articulation. Generally, the 

smaller the gap between the thruster and the can, the hotter the thruster will be. It is also possible that a 

mission using the NEXT thruster will include multiple thrusters. The most conservative case to model is 

one thruster in an adiabatic can acting as a mirror to all incident heat that encapsulates its gimbal footprint 

with minimal gap. Figure 10 shows the comparison of a can around one thruster versus three thrusters.

The solid lines indicate a line of symmetry for the multiple thrusters and could be modeled as a single 

thruster with an adiabatic surface along that line to model its view to space. This demonstrates that 

modeling a single thruster in a small adiabatic can would allow for much less of the thruster to view, and 

hence radiate to, space. That is, the single thruster in the smallest adiabatic can will produce the highest 

temperatures. The case modeled here is shown in Figure 11.

0%

20%

40%

60%

80%

100%

120%

140%

1 2 3 4 5 6

Percent of Total Predicted 

Anode Power Deposition

Total Anode

Cylindrical Magnet Ring

Conical Magnet Ring

Front Magnet Ring

Cathode Magnet Ring

1179 V 1800 V

1.2 A 1.2 A 2.0 A 3.52 A 1.2 A 3.52 A

679 V
NASA/TM—2010-216919 20

Figure 10.—Image showing the comparison of the envelope of one thruster versus three thrusters.

Figure 11.—Image depicting the model of the spacecraft interface for highest mission temperatures.

The largest amount of heating from the internal plasma corresponds to the highest beam current and 

lowest beam voltage. For this thruster that would be 3.52 A beam current and 1179 V beam voltage. The 

heating values that were used in this model are the same as those shown in Table 3 for the TDT at 3.52 A 

and 1179 V except that the cylindrical magnet rings received 200 W instead of the 250 W that included 

the facility plasma heating. Two cases were modeled under the same internal and environmental heating.

One case modeled the plasma screens with an open area of 50 percent as found on PM1 during the TDT.

The second case modeled represents the revised PM design with a solid plasma shield in the cylindrical 

region and a 20 percent open area plasma screen in the conic portion. The result of the 50 percent open 

area plasma screen is shown in Figure 12. The second case would look quite comparable because the 

temperatures shifted somewhat uniformly with a maximum shift of only around +10 °C. Table 6 contains 

the maximum temperature for several of the thruster components along with component margin for both 

cases. There is margin for all thruster components with the exception of the external harness leaving the 

thruster. Presently, the harness is rated only to 150 °C. However, during the TDT, the harness reached 

192 °C without any observable damage. The cable is currently under investigation for re-rating or 

replacement, otherwise, the thermal design of the NEXT thruster is sufficient for the DSDRM.

Adiabatic Spacecraft 

Interface

Solar Heating at 0.85 AU 

and 38° off Thruster axis

(Size set to allow for 

gimbal footprint and 

articulation)

Gimbal

Thruster

Adiabatic Enclosure for 

Multiple Thrusters

Adiabatic Enclosure for 

a Single Thruster 

Line of Symmetry—Indicates 

Effective Adiabatic Enclosure for One 

of Three Thrusters
NASA/TM—2010-216919 21

Figure 12.—An image showing the thruster temperatures predicted for the 

hottest case mission and operation.

TABLE 6.—A TABLE CONTAINING THE MAXIMUM PREDICTED TEMPERATURES AND 

MARGINS FOR KEY COMPONENTS WITH TWO DIFFERENT PLASMA SCREEN SCHEMES

Beam voltage Maximum 

allowable 

temperature

1179 V Margin 1179 V Margin

Beam current 3.52 A 3.52 A

Discharge power 475 W 475 W a

Cylindrical plasma screen OAF 50% 0% a

Conical plasma screen OAF 50% 20%

Front magnet ring 360 °C 279 °C 81 °C 286 °C 74 °C

Cylindrical magnet ring 360 °C 239-255 °C 105 °C 250-266 °C 94 °C

Conical magnet ring 360 °C 257-258 °C 102 °C 264-265 °C 95 °C

Cathode magnet ring 360 °C 280-283 °C 77 °C 286-288 °C 72 °C

Propellant isolator 265 °C 187 °C 78 °C 195 °C 70 °C

Optics harness 260 °C 193 °C 67 °C 210 °C 50 °C

Titanium mounting ring b 211-275 °C b 223-276 °C b

Screen grid support b 251-270 °C b 259-270 °C b

Accel grid support b 267-304 °C b 276-305 °C b

Gimbal pads b 132-187 °C b 141-195 °C b

Exit wire harness 150 °C 194 °C c–44 °C 199 °C c–49 °C a

OAF = open area fraction

b

Margin well exceeds 100 °C c

Harness currently rated to 150 °C, program is proceeding by either re-rating or replacing the harness
NASA/TM—2010-216919 22

Conclusion

A thermal model has been presented that predicts the heating from the plasma on the NEXT thruster 

and the temperatures of the thruster under various environmental and operating conditions. Plasma 

heating was predicted primarily using a discharge chamber plasma model. This model is based on 

measured performance voltages and currents from a thruster. It predicts power deposition to the anode, 

discharge keeper, screen grid, accelerator grid, and cathode. Input parameters with a degree of 

uncertainty, such as ion loss area, are varied such that the predicted discharge losses are equal to the

measured discharge power. These power deposition predictions are then used as inputs in a NEXT 

thruster thermal model. This thermal model uses commercially available finite difference thermal 

software.

Critical plasma self-heating values and contact resistances were adjusted to match the thermal data 

taken during the thermal development test. Besides the model’s primary purpose to predict the thruster 

temperatures, another determination from the model included a facility heating effect from a small current

of background plasma electrons penetrating the plasma screen and heating the anode. This effect is a 

function of the facility background pressure.

It was determined that the heating and current collection to the anode magnet rings is not purely

related to the footprint of the magnet rings. If the current collection and related heating to the anode 

was equally distributed based on the magnet ring footprints, the relative amount of power deposition

would be 0.2:0.6:1:1 for the cathode-to-conical-to-cylindrical-to-front magnet rings. However, after 

subtracting out the facility heating effects, the ratio of heating the model requires was 0.1:1:2:1. This 

indicates that the current density collection is not equal at the respective magnet rings, with the 

cylindrical magnet ring collecting the highest density. This also demonstrates the added uncertainty of 

the ion and electron loss area. 

The thermal model predicts most thermocouple temperatures within 10 °C for several throttling 

points during the thermal development test. When the thermal model is used to predict the temperatures 

from a worst case mission scenario, the temperature margin for all but the external wire harness is greater 

than 50 °C. The temperature of the wire harness exiting the thruster currently exceeds its rating, so the 

cable is under investigation for re-rating or replacement to provide sufficient margin. Aside from the 

cable, the thermal design of the NEXT thruster has ample thermal margin.
NASA/TM—2010-216919 23

Appendix A.—Symbols List

Aan anode surface area, m2

Adc surface area of discharge chamber, m2

Ag area of ion grids, m2

Aha hybrid anode area (electron loss area at cusp), m2

Ai ion loss area, m2

Ains cs insert cross sectional area, m2

Ak area of keeper face, m2

AR Richardson’s coefficient, 60 A/cm2 K2 (for tungsten)

Asa surface area of anode, m2

dA differential surface area of insert, m2

dx differential axial length of insert, m

e elementary charge, 1.60×10–19 C

fc fraction of Bohm current to anode (Ian+

/IBohm), fraction

IB beam current, A

ID discharge current, A

Iag+ accelerator grid ion current, A

Ianm– Maxwellian electron current collected by anode, A

Ianp– primary electron current collected by anode, A

Ian+ ion current to anode, A

Ic

+ ions to cathode insert surface, A

Ie cathode emission current, A

Iins insert thermionic emission, A

Ik

+ keeper ion current, A

Ik

– electron current to keeper, A

Il

+ discharge plasma ion loss rate, A

Im–

+ ions from Maxwellian electron collisions, A

In

* excitation of neutrals, equiv. A

Ipl

+ total ions produced from electron collisions, A

Ip–

+ ions via primary electron collisions, A

Isg screen grid current, A

Isg

+ screen grid ion current, A

Isg

– screen grid electron current, A

I+

* excitation of ions, equiv. A

k Boltzmann constant, 1.38×10–23 J/K

Kins thermal conductivity of insert, W/m K

Lp– average primary electron path length to anode, m

m mass flow rate, sccm

Me electron mass, 9.11×10–31 kg

MXe mass of xenon atom, 2.18×10–25 kg
NASA/TM—2010-216919 24

ni ion density, /m3

nm– Maxwellian or plasma electron density, /m3

no neutral density, /m3

np– primary electron density, /m3

n+ ion density, /m3

Pag* power to accelerator grid from excited neutrals and ions, W

Pag+ power to accel grid from ions, W

Panm– power to anode from Maxwellians, W

Panp– power to anode from primaries, W

Pan+ power to anode from ions, W

Pan* power to anode from excited neutrals and ions, W

Pb

+ power to create ions in beam, W

Pdc total power deposited on discharge chamber, W

Pi

* power to excite ions, W

Pk

+ power to keeper from ions, W

Pk

– power to keeper from Maxwellians, W 

Pk

* power to keeper from excited neutrals and ions, W

Pn

* power to excite neutral, W

Psg

+ power to screen grid from ions, W

Psg

– power to screen grid via electrons, W 

Psg

* power to screen grid from excited neutrals and ions, W

Pro

+ primary electron rate factor, <σ+vpe>, m3

/s

Qins heat flux out of cathode insert, W

Qo

+ Maxwellian electron rate factor, <σ+ve>, m3

/s

Tins temperature along insert, K

Tm Maxwellian electron temperature, eV

Tn neutral gas temperature, K

Ui* ion excitation energy from lowest state, V

Un* neutral excitation energy from ground state, V

U+ ionization potential, V

V ion production region volume, m3

VA plasma potential relative to anode, V

Vag accelerator grid fall voltage, V

vb Bohm velocity, (kT/M)

1/2

vo neutral velocity, m/s

VC cathode fall voltage, V

VD discharge voltage, V

Vk keeper voltage, V

vm– Maxwellian electron velocity, m/s

Vpe primary electron energy, eV

vpe primary electron velocity, m/s
NASA/TM—2010-216919 25

ηc clausing factor, fraction

ηm mass utilization, fraction

σp* primary neutral excitation cross sectional area, m2

σp+* primary-ion excitation cross sectional area, m2

σT total (σ++σp

*

) cross sectional area, m2

σ+ ionization cross sectional area, m2

φan anode work function, eV

Φi screen grid ion transparency, fraction

φins insert work function, eV

φk keeper work function, eV

φsg screen grid work function, eV

φag accelerator grid work function, eV

Φago accelerator grid open area fraction, fraction

Φsgo screen grid open area fraction, fraction

Ωk anode to keeper resistance, Ohms
NASA/TM—2010-216919 26

References

1. Wen, L., Crotty, J.D., and Pawlik, E.V., “Ion Thruster Thermal Characteristics and Performance,” 

Journal Spacecraft and Rockets, Vol. 10, No. 1, Jan. 1973, pp. 35–41.

2 Oglebay, J.C., “Thermal Analytical Model of a 30 cm Engineering Model Mercury Ion Thruster,” 

NASA Technical Memorandum, NASA TM X–71680, Mar. 1975.

3. Mirtich, M.J., “The Effects of Exposure to LN2 Temperatures and 2.5 Suns Solar Radiation on 30-cm 

Ion Thruster Performance,” NASA Technical Memorandum, NASA TM X–71652.

4. Mirtich, M. J., “Thermal-Environment Testing of a 30-cm Engineering Model Thruster,” NASA 

Technical Memorandum, NASA TM X–73522, Nov. 1976.

5. Bechtel, R. T., and Dulgeroff, C. R., “J Series Thruster Thermal Test Results,” AIAA 82–1906, 16th

International Electric Propulsion Conference, New Orleans, LA, Nov. 1982. 

6. Van Noord, J., Gallimore, A., and Rawlin, V., “Numerical thermal Model of a 30-cm NSTAR Ion 

Thruster,” IEPC 97–185, 25th International Electric Propulsion Conference, Cleveland, OH, Aug. 1997.

7. Sovey, J. S., et al., “Development of an Ion Thruster and Power Processor for New Millennium’s Deep 

Space 1 Mission,” AIAA 1997–2778, 33rd AIAA joint Propulsion Conference, Seattle, WA, Jul. 1997.

8. Rawlin, V., Patterson, M., and Becker, R., “Thermal Environmental Testing of NSTAR Engineering 

Model Ion Thruster,” IEPC 97–051, 25th International Electric Propulsion Conference, Cleveland, OH, 

Aug. 1997.

9. Christensen, J.A., et al., “Design and Fabrication of a Flight Model 2.3 kW Ion Thruster for the Deep 

Space 1 Mission,” AIAA 1998–3327, 34th AIAA Joint Propulsion Conference, Cleveland, OH, Jul. 1998.

10. Van Noord, J., Gallimore, A., and Rawlin, V., “Numerical Thermal Model of NASA Solar Electric 

Propulsion Technology Application Readiness Ion Thruster,” Journal of Propulsion and Power, Vol. 16, 

No. 2, 2000, pp. 357–364.

11. Sarver-Verhey, T.R., Domonkos, M.T., and Patterson, M.J., “Thermal Characterization of a NASA 30-

cm Ion Thruster Operated up to 5 kW,” AIAA–2000–36943, 36th AIAA Joint Propulsion Conference, 

Huntsville, AL, Jul. 2000.

12. Anderson, J. A., Snyder, J. S., Van Noord, J. L., and Soulas, G. C., “Thermal Development Test of the 

NEXT PM1 Ion Engine,” AIAA–2007–5217, 43rd AIAA Joint Propulsion Conference, Cincinnati, OH, 

Jul. 2007.

13. Brophy, J.R., “Ion Thruster Performance Model,” Ph.D. Dissertation, Colorado State Univ., Fort 

Collins, CO, also NASA CR–174810, Dec. 1984.

14. Goebel, D.M., Wirz, R.E., and Katz, I., “Analytical Ion Thruster Discharge Performance Model,” 

AIAA–2006–4486, 

15. Van Noord, J.L., “Thermal Modeling of an Ion Thruster,” Ph.D. Dissertation, University of Michigan, 

Ann Arbor, MI, also NASA/CR—2000-209792, Feb. 2000.

16. Chapman, B., Glow Discharge Processes, John Wiley& Sons, Inc., New York, NY, 1980.

17. Rapp, D., Englander-Golden, P., “Total Cross Sections for Ionization and Attachment in Gases 

by Electron Impact. I. Positive Ionization,” Journal of Chemical Physics, Vol. 34, No. 5, 1965, 

pp. 581–589.

18. Domonkos, M.T., Foster, J.E., and Soulas, G.C., “Wear Testing and Analysis of Ion Engine Discharge 

Cathode Keeper,” Journal of Propulsion and Power, Vol. 21, No. 1, 2005, pp. 102–110.

19. Van Noord, J.L., Kamhawi, H., and McEwen, H.K., “Characterization of a High Current Long Life 

Hollow Cathode,” IEPC–2005–321, 29th International Electric Propulsion Conference, Princeton, NJ, 

Nov. 2005, also NASA/TM—2006-214095.

20. Herman, D.A., “The Use of Electrostatic Probes to Characterize the Discharge Plasma Structure and 

Identify Discharge Cathode Erosion Mechanisms in Ring-Cusp Ion Thrusters,” Ph.D. Dissertation, 

University of Michigan, Ann Arbor, MI, 2005. 

21. McEwen, H., Foster, J., Patterson, M., Pencil, E., and Diaz, E., “Characterization of Plasma Flux 

Incident on Multi-Thruster Array,” AIAA–2006–5183, 42nd AIAA Joint Propulsion Conference, 

Sacramento, CA, Jul. 2006.
NASA/TM—2010-216919 27

22. Herman, D., Soulas, G., and Patterson, M., “Performance Evaluation of the 40-cm NEXT Prototype 

Model Ion Thruster,” 43rd Joint Propulsion Conference and Exhibit, AIAA–2007–5212, Cincinnati, 

OH, Jul. 8–11, 2007.

23. Hoskins, W.A., Wilson, F.C., Polaha, J., Talerico, L., Patterson, M.J., Soulas, G.C., and Sovey, J., 

“Development of a Prototype Model Ion Thruster for the NEXT System,” AIAA–2004–4111, 40th 

AIAA Joint Propulsion Conference, Ft. Lauderdale, FL, Jul. 2004.

24. Davis, V.A., Katz, I., Mandell, M.J., Brinza, D.E., Henry, M.D., Wang, J.J., Young, D.T, “Ion 

Generated Charge Exchange Environment: Comparison Between NSTAR Flight Data and Numerical 

Simulations,” AIAA–2000–3529, 36th AIAA joint Propulsion Conference, Huntsville, AL, Jul. 2000.

25. Brophy, J. R., et al., “Development and Testing of Dawn Ion Propulsion System,” AIAA–2006–4319, 

42nd AIAA Joint Propulsion Conference, Sacramento, CA, Jul. 2006.
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4. TITLE AND SUBTITLE

NEXT Ion Thruster Thermal Model 

5a. CONTRACT NUMBER

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6. AUTHOR(S)

Van Noord, Jonathan, L. 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

As the NEXT ion thruster progresses towards higher technology readiness, it is necessary to develop the tools that will support its 

implementation into flight programs. An ion thruster thermal model has been developed for the latest prototype model design to aid in 

predicting thruster temperatures for various missions. This model is comprised of two parts. The first part predicts the heating from the 

discharge plasma for various throttling points based on a discharge chamber plasma model. This model shows, as expected, that the internal 

heating is strongly correlated with the discharge power. Typically, the internal plasma heating increases with beam current and decreases 

slightly with beam voltage. The second is a model based on a finite difference thermal code used to predict the thruster temperatures. Both 

parts of the model will be described in this paper. This model has been correlated with a thermal development test on the NEXT Prototype 

Model 1 thruster with most predicted component temperatures within 5 to 10 °C of test temperatures. The model indicates that heating, and 

hence current collection, is not based purely on the footprint of the magnet rings, but follows a 0.1:1:2:1 ratio for the cathode-to-conical-tocylindrical-to- front magnet rings. This thermal model has also been used to predict the temperatures during the worst case mission profile 

that is anticipated for the thruster. The model predicts ample thermal margin for all of its components except the external cable harness 

under the hottest anticipated mission scenario. The external cable harness will be re-rated or replaced to meet the predicted environment.

15. SUBJECT TERMS

Ion engines; Plasmas (physics) 

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