liJPC96.pdf

Lorentz Force Accelerator with an Open-ended Lithium Heat

Pipe

∗

E.Y. Choueiri

†

, V. Chiravalle

‡

, George E. Miller

& Robert G. Jahn

Electric Propulsion and Plasma Dynamics Laboratory (EPPDyL)

MAE Dept.

Princeton University, Princeton NJ 08544.

W. Anderson & J. Bland

Thermacore Inc., Lancaster, PA

AIAA-96-2737

Abstract

A steady-state coaxial Lorentz force accelerator
(LFA), where lithium propellant is supplied by an
open-ended heat pipe, was designed and built. The
open-ended heat pipe provides a novel alternative to
the complex propellant feeding systems previously
used with lithium-fed thrusters. The closed end of
the heat pipe acts as a reservoir containing a liq-
uid lithium pool, and a wick. The main part of the
pipe is embedded in a furnace (1200

◦

C) which va-

porizes the lithium off the wick. The lithium vapor
then travels to the open end which is also the cathode
of the LFA supplying the propellant for the plasma
thruster. The actively heated cathode is a hybrid
hollow-multi-channel cathode consisting of 48 longi-
tudinal channels embedded in a porous tungsten in-
sert. The design promises a substantial decrease in
the erosion rate of the cathode which is the lifetime
limiting component in such thrusters. This paper de-
scribes the design and fabrication of the thruster as
well as the mass flow rate calibration procedure which
relies on careful water calorimetry.

∗

This work is supported through an SBIR contract from NASA-

JPL.

†

Chief Investigator at EPPDyL. Assistant Professor, Applied

Physics Group. Senior Member AIAA.

‡

Student supported by the New Jersey NASA Space Grant

Consortium.

System Engineer, EPPDyL.

Professor of Aerospace Sciences. AIAA Fellow.

Presented at the 32

AIAA Joint Propulsion Conference.

Introduction

1.1

long lifetime and high efficiency
of Li LFA’s

The lithium-fed Lorentz force accelerator (LFA) is
a variant of the magnetoplasmadynamic thruster
(MPDT) that promises long lifetime (

1000 hrs) and

high efficiency (

60%). The extension of the lifetime

of such thrusters to above 1000 hours through the
use of lithium as propellant in multi-channel cath-
odes has been recently shown to be within reach[1],
thus overcoming the main obstacle in the use of such
thrusters for spacecraft propulsion.

This substantial lifetime extension is due to the the

role of lithium in lowering the effective work function

of the cathode (pure tungsten’s

5 eV while

pure lithium’s

9 eV) and the role of the multi-

channels in lowering the current densities, thus allow-
ing lower operating surface temperatures, for a given
total current, and consequently far lower erosion rates
through evaporation. Evaporation has been shown
to be the major erosion mechanism in steady-state
MPDT’s.

It is now also well known[2] that another advantage

of the use of alkali metal propellant is the superior
thrust efficiencies which have been reported to well
exceed 60%. This is believed to be related to the
scaling of the energy sink associated with ionization
(first ionization potential,

, for lithium is 5.4 eV

while

=15.8 eV for argon.) This is especially the

case since ionization is believed to be of anomalously

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

high importance in such devices[3].

The only remaining concern for using the lithium

LFA on actual spacecraft is the contamination issue.
In 1990 an experiment was conducted on the Soviet
spacecraft Progress M-4, specifically to study, using
the quartz microbalance technique, spacecraft con-
tamination from alkali metal plasma sources. The
results of that experiment were recently published
and discussed by Brukhty et. al.[4], who also pre-
sented further experimental and theoretical results
and concluded that the deposition of alkali metals
on spacecraft is not an obstacle for utilizing them as
propellant in electric thrusters. Furthermore, recent
numerical simulations[5] for a lithium MPD thruster
have shown that plume shields can be quite effective
in reducing the backflow of lithium to the spacecraft.

1.2

Advantages and Applications of
Li LFA’s

Among all candidate electric propulsion options, the
Li LFA has the unique capability of offering extremely
high thrust densities (10

to 10

N/m

). This fea-

ture, the LFA’s ability of processing very high power
(10

to 10

W) through a small, compact and simple

device, and its high specific impulse (1000-4000 s)
put it in a class by itself for application to many
thrust-intensive and energetic missions such as de-
manding cargo and piloted planetary missions. For
more power-limited near-term applications the LFA
could also compete with other EP options especially
for applications such as orbit-raising of massive pay-
load.

Since the Li LFA becomes adequately efficient

(

30%) only at higher power level (

30 KW) (see

Ref. [6] for instance) and since no such high power
sources are available in space, the device has been
classified in the US as an “advanced propulsion op-
tion.”

1.3

NASA-sponsored research on the
Lithium LFA

NASA-JPL’s research program on Li LFA’s is con-
centrated primarily on demonstrating engine perfor-
mance in a 100 kW-class thruster and proving the
feasibility of long-lived, high current cathodes. The
program includes the following complementary activ-
ities:

1. The fabrication and testing of a 100 kW Li LFA

at the Moscow Aviation Institute[7] with the goal

of demonstrating an efficiency of 40-45% at an

of 3500-4000 s.

2. In-house work at JPL aimed at the development

of a cathode thermal code incorporating models
of the heat fluxes from the near-cathode plasma
and testing at high current levels to validate
the code[8]. The experiments include number
density measurements using the Pulsed Electron
Beam diagnostic developed at USC.

3. Development and testing of a 30 kW class Li

LFA through a collaboration between Therma-
core Inc. and Princeton University’s EPPDyL

4. Experimental and theoretical studies of the fun-

damental aspects of multi-channel cathodes for
Li LFA’s at Princeton University.

While previous work with lithium plasma thrusters

at EPPDyL[9, 10, 11] concentrated on a “proof of
concept” studies of the benefits of lithium and barium
dispenser cathodes, the new thruster described in this
paper is intended for more extensive and fundamental
studies under realistic LFA conditions.

Among the advanced diagnostics especially devel-

oped for these experiments, is a high resolution six
color video pyrometer (SCVP) (described in ref. [12])
for measuring the high surface temperature of LFA
components without knowing their emmisivities.

1.4

Paper Organization

This paper describes the design, development and im-
plementation of the Li LFA, that is being used for the
studies in Programs 3 and 4 (listed above). In Sec-
tion 2 the design is presented with particular empha-
sis on the novel aspect of the device, namely its use
of an open-ended heat pipe to deliver a metered flow
of lithium without the complexity of previous and
existing systems elsewhere. In Section 3 we present
a description of the LFA Testing Facility. The mass
flow calibration and monitoring, which rely on careful
water calorimetry, are presented in Section 4 where
the experimental results of the calibration are also
discussed. Finally, in the appendix we discuss a the-
oretical fluid/thermal model of the lithium flow that
was helpful in guiding the mass flow calibration.

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

incipient boiling superheats. In unstable boiling, the
heat transfer mechanism oscillates between nucleate
boiling and liquid natural convection, sometimes re-
sulting in violent shaking of the system. The va-
porizer design eliminates potential pool boiling prob-
lems.

Some of the more important design parameters of

the system are listed in Table 1.

The thruster is radiatively cooled and does not

have an applied magnetic field. Although an applied
magnetic field has been shown to substantially im-
proved the performance[7], we will be operating the
thruster in a self-field mode for our fundamental stud-
ies. Future performance study would necessitate an
applied field.

Thermocouples wells were placed in three critical

locations (labeled TC in Figure 1) to provide access
for temperature measurement at 1) the middle height
of the canister (where the evaporation takes place), 2)
the top of the canister and 3) the root of the cathode.

2.2

Cathode Design Considerations

A multi-channel configuration, that has the promise
to yield a larger effective attachment area and also, a
more stable behavior of the discharge, was chosen.
The elementary channel packet is slightly recessed
with respect to the cathode end (about 25% of the in-
ner diameter). This hybrid hollow-multichannel cath-
ode configuration[13], should combine the advantages
of both, a movement of the discharge into the cavity
(as in the hollow cathode) and a larger emitting sur-
face (as in the multi-hollow cathode).

According to a great deal of literature, and also

to some experiments carried out at EPPDyL[14], the
penetration length of the discharge is typically on the
order of a few channel diameters. Considering that
in a multichannel cathode this length is greatly re-
duced with respect to a single channel cathode with
the same hollow cross section area and the same total
gas flow rate, we expect that a length of 5 cm for the
insert containing the channels, is widely in excess of
any possible penetration of the discharge.

Considering the ratio of the total discharge cur-

rent to the cathode cross section area (without the
outer sheath), we predict a current density not larger
than 260 A/cm

. This is about the same value as

the thruster in ref. [1]. If we maintain the same ratio
of hollow cross-section area to the total area (about
13%), using gaps of 2 mm diameter tungsten rods,
as in ref. [1], and cylindrical holes in the tungsten
wick, it follows that sixty-five uniformly spaced 1 mm

diameter channels are needed, having cross section
(0.78 mm

) with gaps of (0.16 mm

2.3

Anode Design Considerations

From a machining and cost point of view, tantalum
is preferable over tungsten for anode material. The
design calculations presented below, however, favor
the use of tungsten.

In order to choose the anode material and estimate

the minimum anode thickness compatible with the
operating conditions of the thruster, the effects of
Joule heating, heat flux to the anode and spot at-
tachments were considered.

2.3.1

Joule heating.

A simple model is considered, in which, once a steady
state is reached, all power generated in the anode by
resistive heating (Joule effect) is rejected by radia-
tion. This model yields an expression for the anode
thickness

πR

)

²σT

(1)

where

is the resistivity of the material,

is the total

emissivity,

is the Stefan-Boltzmann constant,

the temperature in degrees

and

is the total cur-

rent. Using temperature-dependent expressions for
the resistivities of tungsten and tantalum, the melt-
ing temperatures of tungsten (3683 K) and tanta-
lum (3269 K) and assuming an operating current of
1000 A, we obtain a minimum thickness equal to 3.5

µm

for a tungsten anode and to 7.7

µm

for a tanta-

lum anode. These results, show that Joule effect is
not a dominant mechanism in anode heating.

2.3.2

Heat Flux to the Anode

For nominal LFA operation the anode heat flux

can

be estimated as:

5
2

(2)

where

is the electron current density,

is the an-

ode voltage fall,

is the electron temperature,

the Boltzmann constant,

is the elementary electric

charge,

is the work function for the anode material

and

is the power radiated from the cathode.

If we now assume that the discharge attaches uni-

formly to the flared part of the anode, which has an

The calculations in this section were carried by Paolo Gessini

at EPPDyL.

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA

DESIGN OEPRATING PARAMETERS

Nominal LFA Power Rating

10-100 kW

Nominal LFA Current Rating

300-2000 A

Nominal LFA Voltage

30-50 V

Nominal Li Flow Rate

2-50 mg/s

Furnace Power

1.2 kW

Potential Drop Near Cathode

5 V

Background Pressure

−

torr

Li Vapor Pressure Next to Active Surface

2 to 20 torr

Maximum Emitting Surface Temperature

3000

◦

DIMENSIONS

Cathode O.D.

2.54 cm

Anode O.D. at Exit

15 cm

Minimum Radii for Corners

.062

Number of Hollow Channels

MATERIAL

Cathode and Anode

Tungsten

Cathode Insert

Porous Tungsten

Cathode & Anode Mounting Flanges

Molybdenum

Inter-Electrode Insulator Flange

Sapphire

Bolt Insulators

Alumina

Canister Envelope

Molybdenum

Vapor Tubes and Thermocouple Wells

Tantalum

Li RESRVOIR & FURNACE

Reservoir Capacity

1000 cm

Furnace Operating Temperature

1500

◦

Furnace Maximum Current

500 A

Furnace Maximum Voltage

10 V

Furnace Active Element

30 cm Tungsten ribbon

CATHODE HEATER

Material

Tantalum wire & alumina beads

Length

2 m wrapped around base of cathode

Operating Temperature

1100

◦

Power Requirements

20 A at 50 V

Table 1: Design Parameters of Lithium LFA.

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

area of 220 cm

, from typical values of the above

physical quantities measured during operation of a
similar device, we estimate that

should not exceed

200 W/cm

. If we further assume that, once a steady

state is reached, only the external surface of the flared
part of the anode is at a uniform temperature and
radiates the power away, using the appropriate val-
ues for emissivity and neglecting the thickness of the
anode, we obtain, at 1000 A, a temperature of about
3050

◦

K for tungsten, and 3280

◦

K for tantalum. This

difference is due to the lower emissivity of tantalum
(about 0.3 as opposed to about 0.4 of tungsten). We
notice that, while with tungsten we are well below the
melting point, with tantalum we are slightly above.
Tungsten thus provides a far better safety margin.

2.3.3

Non-uniform discharge:

spot attach-

ment

We now consider the destructive effects of spot at-
tachment whereas the discharge is not uniform over
the whole anode surface, but concentrated in a finite
number of spots of a certain diameter. In order to
obtain a rough estimate of the temperature evolution
in the anode, we will make a series of assumptions,
based in part on the results of experiments carried
out with a quasi-steady MPD thruster at EPPDyL
[15] which will render our conclusions conservative.

We will assume, from observations of spot traces

in an LFA anode, that the current is concentrated
in spots with 1 mm

area, distributed on the anode

surface with an average density of one spot per cm

This means that only 1% of the surface is affected by
the discharge. For spot lifetime we will assume that
a single spot does not exist in the same location for a
time longer than 100

µs

. Such an assumption, quite

conservative, is based on noise data, which present a
characteristic frequency on the order of 100 KHz and
could be attributed to spot movement on the anode
surface with a characteristic time of 10

µs

Analytical Model.

Under these assumptions, a

first analysis has been carried out using a one-
dimensional model.

Namely, the anode has been

treated like a semi-infinite body, with constant heat
flux at the boundary. In this way, radiation cool-
ing has been neglected, and the temperature increase
may be written as:

∆

"µ

αt

1
2

−

αt

−

erfc

√

αt

(3)

where the heat flux

is now equal to 20000 W/cm

is the thermal conductivity,

is the thermal diffusiv-

ity and erfc = 1

−

erf, where erf is the error function.

Constant values have been assumed for density, ther-
mal conductivity and specific heat. These two last
quantities do actually show a strong dependence on
temperature, but in our range of interest (

≥

3000

K) they both tend asymptotically to a constant value,
with little variation, thus upholding our assumption.
The results are shown in figure 3. We can see that

500

450

400

350

300

250

200

150

100

Temperature Increase [K]

1.0x10

-3

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Radial Distance into Anode Wall [m]

t=0.1 ms

Tantalum
Tungsten

t=1 ms

Figure 3: Temperature profiles at different times.
Comparison between tantalum and tungsten

tungsten gives a slightly better performance than tan-
talum in that temperature is lower at the inner wall,
but then it tends to become equal to that of tanta-
lum toward the outer wall. This means that there
will be a smaller possibility of overheating on the in-
side, and at the same time heat will be conducted
equally efficiently out, where it will be radiated away
by the external surface of the anode. From this sim-
ple model we see that, assuming a steady state oper-
ation temperature like the one previously estimated,
say 3000

◦

K, after 100

µs

temperature is still below

the melting point for both materials. In the case of
tungsten, there is still no melting even after 1 ms.

Numerica Model.

A more detailed picture of the

effect may be obtained with a three-dimensional ax-
isymmetric model including radiation. A 1 cm di-
ameter disk, 2 mm thick, with a 1 mm diameter spot
around its axis of symmetry on one side simulates the
region of a 2 mm thick anode surrounding each single
spot. The boundary conditions are

= 20000W/cm

at the spot,

= 0 on the rest of the inner surface

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA

and on the lateral area (for symmetry),

²σT

the outer surface. The initial condition is a uniform
temperature of 3000

◦

K, and the properties of the

material are again assumed constant, with the same
values as before. Figure 4 shows the results of this
simulation, performed with FEHT, a finite-element
heat transfer program, in the case of tungsten. From

Figure 4: Temperature contours after 1.5 s in a 2 mm
thick tungsten anode. The melting region is 13% of
the anode thickness.

Figure 5: Temperature contours after 1.5 s in a 2 mm
thick tantalum anode. The melting region is 100% of
the anode thickness.

that plot we can note that even after 1.5 s, a period
much longer than the expected lifetime of a spot, the
region above the melting point extends for only about
13% of the anode thickness.

The same analysis, performed with tantalum,

shows a less favorable behavior, with higher tempera-
tures, mainly due to the lower emissivity of tantalum
with respect to tungsten. For comparison, the same
gray level scale has been used in figure 5.

Final Anode Selection

As a result of the above

design consideration a tungsten anode was manufac-
tured by plasma spraying with a thickness of 4.5 mm

LFA Testing Facility

The Li LFA was installed in EPPDyL’s Steady-State
Low Power (SSLP) Facility described in ref. [10]. The
SSLP facility uses a 1.5 m diameter cylindrical carbon
steel tank, 6.4 m in length, evacuated to 10

−

torr

by a set of mechanical and diffusion pumps. Pho-
tographs of the accelerator and furnace assembly with
associated subsystems are shown in Figures 13 to 16.
For the sake of clarity, the cathode heater was re-
moved in these pictures.

In order to avoid contaminating the vacuum pumps

with lithium, a condenser trap was built and posi-
tioned about 2.5 m downstream of the thruster. The
trap consists of two copper plates actively cooled by
chilled water coils and a similarly cooled metallic
cylinder housing a mirror for optical diagnostic ac-
cess (see Fig. (16)). In order to further protect the
mirror from lithium condensation, its surface is kept
at about 700

◦

C using a small heater.

Data Acquisition.

Data is recorded from sensors

inside the vacuum tank using a Keithley System 570
digital acquisition board coupled to a personal com-
puter. Aside from scientific diagnostics, three types
of data are collected during a firing of the lithium-fed
LFA , voltage and current data for the heater and the
thruster both of which have separate power supplies,
mass flow rate data of the reservoir cooling water and
temperature data from thermocouples in the cooling
water and in the walls of the canister.

Power Measurements.

Current measurements

are taken on the outside of the vacuum tank using
magnetic current sensors from Bell Inc. The Keith-
ley System 570 has 16 channels for differential voltage
input. The uncertainty in a current value obtained
from the sensor is quoted as 0.5 %. The heater in-
put voltage is measured directly from the heater elec-
trodes and the signal is passed through a voltage di-
vider before being sent to the Keithley board. The
thruster voltage is measured from the connections at
the window interface.

Water Flow Measurements.

A turbine cage flow

meter from McMillan Company is used to measure
the flow rate of cooling water into the heater cool-
ing jacket. The cooling water flow rate is one of the
parameters required for determining the lithium mass
flow rate by the balance of power into the heater. The
flow meter is powered by a 5 V DC power supply and
the voltage output of the device is proportional to the

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

mass flow rate through the meter. A calibration was
performed to find this relationship and the associated
uncertainty.

Temperature Measurements.

Two sets of ther-

mocouples are used to make measurements of the
temperature of the canister wall and the tempera-
ture of the cooling water. The thermocouples used to
measure the water temperature are Iron-Constantan
junctions. The iron and constantan wires that ex-
tend from the thermocouple junctions are connected
directly to a thermocouple daughter board in the
Keithley system. Reference junction voltage com-
pensation is applied to the thermocouple voltage sig-
nals by a Keithley software routine which computes
the temperature in

◦

C at the thermocouple junc-

tion. Tungsten-Rhenium junctions are used to mea-
sure the temperature of the canister wall at distances
of 0

0508

and 0

1524

from the top of the can-

ister. Cold junction voltage compensators are con-
nected to the high temperature thermocouple lines
and the voltage output from each of these devices is
sent to the Keithley board. A calibration relation
supplied by the manufacturer is used to find the tem-
perature in

◦

Mass Flow calibration

Originally, the intention was to use a tantalum bel-
lows between the reservoir and the thruster. The
mass flow rate of lithium would then be measured us-
ing a load cell underneath the lithium reservoir. The
bellows manufacturer calculated that the .254 mm
tantalum foil used in the bellows should give a very
soft spring, unfortunately, the bellows were so stiff
that they were unusable probably due to work hard-
ening of the tantalum. Annealing the bellows was
unsuccessful. A calorimetry-based mass flow rate cal-
ibration and monitoring system was consequently de-
vised and implemented. This section describes these
activities and presents the results of the calibrations.

A lithium flow simulation model, discussed in the

appendix, was developed to estimate the dependence
of the lithium mass flow rate on the canister temper-
ature and to determine the useful operating temper-
ature range of reservoir.

4.1

canister Thermal Measurements

A series of measurements were taken to determine
the power radiated from the heater during steady-
state operation. This was accomplished by heating

the canister while it is sealed, i.e. the canister was
disconnected from the thruster and sealed with a tan-
talum swagelock cap.

In the ideal case liquid lithium would evaporate

from the screen wick and condense on the surface of
the vapor tube, transferring heat from the canister
to the vapor tube. The assumption is that the canis-
ter walls are heated uniformly so that there would be
no condensation on the screen wick which covers the
canister walls and all the lithium vapor condensation
would take place on the walls of the vapor tube. This
assumption does not truly hold for our actual canister
because the tungsten heating element is about 5 cm
shorter than the upper extent of the vertcal part of
the canister and as a consequence the top part of
the canister is not heated by the heating element.
Therefore condensation of lithium vapor is expected
in this region once the temperature in the lower part
of the canister is sufficient for vaporization to take
place. Under such conditions the canister behaves as
a heat pipe with lithium as the working fluid. After
condensing in the top part of the canister the liquid
lithium flows along the screen wick toward the region
of the canister that is actively heated and evapora-
tion takes place again. The iron cooling jacket of the
canister (see the photographs in Figures 15 and 16)
does not cover the top part of the canister, and in this
region the canister radiates as a greybody. The loss
of radiated power from the walls of the vapor tube
is eliminated through the use of alumina insulators
and molybdenum foil that cover the vapor tube. The
power lost to the tank due to greybody radiation of
the canister is concentrated in the top part of the can-
ister. The radiated power loss to the tank from the
canister is an important parameter in determining the
lithium mass flow rate using power balance methods.
Two experiments were performed in which the power
to the heater was gradually increased in steps and the
thermal response of the canister was recorded. As
mentioned earlier measurements of canister temper-
ature were made with two thermocouples, one in the
top part of the canister where there is no active heat-
ing from the tungsten element and one in the bottom
part where there is active heating. The experiments
were roughly four hours in duration each. Fig. 6 and
Fig. 7 show the results of these experiments.

As Fig. 7 shows a temperature difference between

the top and bottom thermocouples readings of about
200 deg

was observed during steady state with

the bottom temperature at 700 deg

and the input

power at 450

. Once the vaporization threshold

was reached the temperature gradient was reduced

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA

900

800

700

600

500

400

300

200

100

temperature (C)

200

150

100

time (min)

1000

800

600

400

200

power (W)

libottom
litop
power

Figure 6: First canister thermal response experiment.
Litop refers to the reading from the thermocouple
that is closest to the top of the canister

1000

800

600

400

200

temperature (C)

200

150

100

time (min)

1500

1000

500

power (W)

libottom
litop
power

Figure 7: Second canister thermal response experi-
ment. Litop refers to the reading from the thermo-
couple that is closest to the top of the canister

significantly. This observation supports the notion
that the canister behaves like a heat pipe with a flat
temperature profile. The measurements show that
steady-state conditions were reached when thermo-
couple data was constant within 0

1% for a period of

about three minutes. Cyclic variations in the input
power to the heater from the power supply were ob-
served with amplitude of 10

. The power radiated

to the tank during steady state was computed using
the following equation.

Rad

−

∆

(4)

Here

is the input power to the heater computed

from current and voltage measurements, ˙

is the

mass flow rate of water through the iron cooling
jacket, and ∆

is the difference between the cool-

ing water inlet and outlet temperatures. The values
used in Eq. 4 were obtained by taking an average
of three consecutive steady-state points. A standard
deviation was also computed for each of the param-
eters in Eq. 4. An error propagation analysis was
performed to find the uncertainly in the computed
values of

Rad

from the uncertainties in its parame-

ters. The values of

Rad

at several steady-state points

taken from the two experiments are plotted in Fig. 8
versus

T op

where

T op

is the the temperature at the

top of the canister. A linear fit to the data yielded

700

600

500

400

300

radiated power (W)

1.4

1.2

1.0

0.8

0.6

Top

(10

)

Figure 8: Radiated power from the canister as a func-
tion of

T op

the following coefficients.

Rad

= 57

7 + 4

−

T op

(5)

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

The variance of both of the coefficients above was
computed to estimate the total error in the mass flow
calibration.

4.2

Results of Li Mass Flow Calibra-
tion

The mass flow rate of lithium through the thruster
during steady-state operation can be determined ex-
perimentally by considering the modes of heat trans-
fer to a system comprising the heater and canister.
Three of these modes were considered in the last sec-
tion, the heat addition from the electrical resistance
of the tungsten heating element,

, the heat loss

from convection of the water through the iron cool-
ing jacket and the heat loss from the greybody radi-
ation of the top part of the canister,

Rad

. During

thruster operation, an additional mode of heat loss
during steady state is evaporation of lithium which
can be expressed as the product of the latent heat of
vaporization of lithium, Λ and the mass flow rate of
lithium from the canister, ˙

. We essentially mea-

sure the rate of heat loss through the evaporation of
lithium and with the knowledge of Λ we determine

. Since the thruster cathode and the canister are

directly connected by a tantalum vapor tube, con-
duction occurs from the cathode to the heater. The
rate of heat transfer through this mode is calculated
from the equation below.

κA

δT

(6)

Taking the temperature difference between the cath-
ode and the canister to be 1000

◦

C, the cross sectional

area of the vapor tube as 8

639

−

m, the thermal

conductivity as 100

and the length of the vapor

tube as 0.5 m, the power supplied to the canister is
only 1.72 W. This value is negligible compared with
the other transfer modes and has been consequently
neglected in the analysis.

Having identified the relevant modes of heat trans-

fer, equating the power contributions from each of
these modes leads to the follow expression relating
the lithium mass flow rate to the other variables.

−

∆

−

Rad

(7)

Λ at the boiling point temperature (1 atm) of
1612.1 K is determined from an experimental vapor
pressure curve for lithium in Ref. [16] and has the
value of 21.62

. The temperature dependence

of Λ is found using the Watson relation described in
Ref. [17] and has the form below.

Λ = 21

(

−

3503

−

1612

3503

)

(8)

Here 3503

◦

K is the critical temperature for lithium.

The error in Eq. 7 is given by the following.

+ (

∆

)

+ ( ˙

)

∆

Rad

(9)

Rad

is the error in Eq. 5 which is a function of tem-

perature shown below.

Rad

49 + 69

−

T op

(10)

The uncertainty in the radiated power from the can-

error in radiate power (W)

1100

1000

900

800

Top

(C)

Figure 9:

Rad

as a function of

T op

ister is the dominating term in Eq. 9, and this trans-
lates into an uncertainty in the lithium mass flow rate
of about 0.7 mg/s at 1050

◦

C. The steady-state op-

erating range of mass flow rates for lithium-fed LFA
operation is between 5 and 50 mg/s.

Based on the above results an algorithm was de-

vloped and implemented on the data monitoring com-
puter for real-time monitoring of the mass flow rate
through the thruster.

Conclusions

This paper documents the design, laboratory im-
plementation and calibration of a new lithium-fed

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA

Lorentz force accelerator (LFA). The novel concept
in the design is the use of an open-ended heat pipe to
supply lithium vapor through a multi-channel cath-
ode.

The device is thus free of valves and mov-

ing parts and the propellant mass flow rate is mon-
itored and metered through water calorimetry and
the power input to a furnace. Based on heat load
calculations the anode was fabricated out of tung-
sten and has a thickness of 4.5 mm. A power balance
relating the input power for the furnace vaporizing
the lithium, the radiated power and the power re-
moved by the flowing lithium vapor allowed a cali-
bration of the mass flow rate to within 10%. The
device, along with a six color video pyrometer (de-
scribed in ref. [12]) and an emission spectrometer, is
intended for use in the studies of various processes
related to multi-channel cathodes and alkali metal
plasma acclerators.

Acknowledgments

The authors are thankful to

Dr. Kevin Diamant for his valuabe help.

References

[1] V.P. Ageyev and V.G. Ostrovsky. High-current

stationary plasma accelerator of high power. In
23

International Electric Propulsion Confer-

ence

, Seattle, WA, USA, 1993. IEPC-93-117.

[2] J.E. Polk and T.J. Pivirotto. Alkali metal pro-

pellants

for

MPD

thrusters. In

AIAA/NASA/OAI Conf. on Ad-

vanced SEI Technologies

, Cleveland, Ohio, 1995.

AIAA-91-3572.

[3] E.Y. Choueiri and H. Okuda. Anomalous ion-

ization in the MPD thruster. In 23

Interna-

tional Electric Propulsion Conference

, Seattle,

WA, USA, 1993. IEPC-93-067.

[4] V.I. Brukhty, V.N. Shutov, A.B. Smirnov, M.P.

Burgasov, and A.A. Chirov. The effect of al-
kali metal electric rocket engines on spacecraft.
In 23

International Electric Propulsion Con-

ference

, Seattle, WA, USA, 1993. IEPC-93-149.

[5] R.I. Samanta Roy and D.E. Hastings. Backflow

contamoniation from lithium MPD thrusters:
A preliminary assessment.

Technical Re-

port No. 959948, NASA-JPL Technical Report,
Pasadena, CA, 1995.

[6] V.A. Petrosov, I.B. Safonov, Y.A Utkin, and

V.N. Shutov. Investigation of alkali metal MPD

thrusters. In 24

International Electric Propul-

sion Conference

, Moscow, Russia, 1995. IEPC-

95-104.

[7] V. Tikhonov, S. Semenikihin, J.R. Brophy, and

J.E. Polk.

The experimental performance of

the 100 kW lithium MPD thruster with exter-
nal magnetic field. In 24

International Electric

Propulsion Conference

, Moscow, Russia, 1995.

IEPC-95-105.

[8] K. Goodfellow and J. Polk. Lorentz force accel-

rator technolgy development at JPL. In

Sixth

Advanced Space Propulsion Workshop

, NASA-

JPL, Pasadna, CA, 1995. pp. 129-136.

[9] F.R. Chamberlain, A.J. Kelly, and R.G. Jahn.

Electropositive surface layer MPD thruster cath-
odes. In 25

Joint Propulsion Conference

, Mon-

terey, CA, USA, 1989. AIAA-89-2706.

[10] J.S. Fillmore. An experimental study of lithium

dispenser cathodes in the MPD thruster.

International Electric Propulsion Confer-

ence

, Seattle, WA, USA, 1993. IEPC-93-196.

[11] E.Y. Choueiri.

Contributions to the

Semi-

Annual Progress Report for the period June
1994-December 1994.

Technical Report No.

EPPDyL-TR-94F, EPPDyL, Princeton Univer-
sity, 1994.

[12] E.Y. Choueiri, V.P. Chiravalle, G.E. Miller, and

R.G. Jahn. Six-color video pyrometry with ap-
plication to MPD thrusters. In 24

Interna-

tional Electric Propulsion Conference

, Moscow,

Russia, 1995. IEPC-95-111.

[13] S.A. Semenikhin and V.B. Tikhonov. The in-

fluence of cathode design on the performance
and characteristics of MPD thrusters with ap-
plied magnetic field.

In 3

Russian-German

Conference on Electric Propulsion Engines and
their Technical Applications

, Stuttgart, Ger-

many, 1994. M27-M31.

[14] M. Krishnan.

Physical Processes in Hollow Cath-

odes in High Current Discharges

. PhD thesis,

Princeton University, Princeton, NJ, USA, 1976.

[15] K.D. Diamant, E.Y. Choueiri, A.J. Kelly, and

R.G. Jahn. Characterization of the near-anode
region of a coaxial MPD thruster. In 30

Joint

Propulsion Conference

, Indianapolis, IN, 1994.

AIAA-94-3336.

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA

APPENDIX: Theoretical Mass Flow Rate

Prediction

The mass flow rate of lithium through

the thruster is influenced by two parameters, the tem-
perature of the thruster cathode and the temperature
of the canister wall during steady-state operation.
The temperature of the canister wall is related to
the saturation pressure of lithium vapor in the canis-
ter for temperatures around the vaporization thresh-
old, 800

◦

C. The temperature of the cathode surface

controls the transfer of enthalpy to the lithium vapor
flow through convection as the lithium moves through
the channels of the cathode. A one dimensional fluid
model with heat addition and friction loss was used
to estimate the lithium mass flow rate as influenced
by the above parameters[18].

Model Assumptions

The model describes three

regions of flow behavior under steady state, the condi-
tions in the canister as a function of canister wall tem-
perature and the flow of the lithium vapor through
the vapor tube into the cathode cavity, the adiabatic
expansion of the fluid as it passes from the cathode
cavity into the multi-hollow-channels, and the expan-
sion of the fluid due to friction and heat addition in-
side the vapor channels. The flow in all regions is
considered one dimensional with no boundary layer,
although boundary layer effects are introduced indi-
rectly through friction and heat transfer coefficients.
The basic equations describing the evolution of a one
dimensional flow in terms of Mach number, temper-
ature, velocity, and density are taken from Ref. [19].

The model assumes that at steady-state conditions

lithium exists as a saturated vapor in the canister
where the temperature of the vapor is equivalent to
the temperature of the canister walls. An experi-
mental relation between lithium vapor pressure and
temperature is given in Ref. [16] and has the form
below with pressure,

in Pascal.

= (

)

4942

exp (13

0719

−

18880

659

)

(11)

At 1050

◦

is about 1055 Pa (8 torr) and at this

low pressure the ideal gas assumption is valid. The
density of the vapor can be calculated from this as-
sumption, since the temperature is specified and the
pressure is determined by Eq. 11. The state of the
vapor in the canister is now completely determined.
It is next assumed that the lithium vapor does not
condense on the walls of the vapor tube and the flow
is adiabatic as it travels into the cavity region of the
cathode. Since the vapor tube is well insulated and
has a small cross sectional area there is are no heat

sources to supply the energy for vaporization to oc-
cur. Under steady-state conditions it is therefore ex-
pected that no net condensation takes place on the
wall of the vapor tube. However it is highly probable
that during the start-up phase of heater operation
a surface layer of lithium is deposited on the vapor
tube wall. The flow is considered incompressible as
it travels between the canister and the cavity of the
cathode, since a significant area contraction has not
occurred. The density in the cathode cavity is taken
as the density computed for the vapor in the canis-
ter. A this point in the analysis a guess is made for
the mass flow rate of lithium into the cathode which
is later refined through an iterative procedure. With
knowledge of the cross section area of the cathode
cavity, a velocity is computed and this value coupled
with the stagnation temperature of the flow gives a
value for the temperature of the flow in the cathode
cavity. The stagnation temperature of the flow is the
canister temperature.

The second region of flow behavior is the adiabatic

expansion from the cavity into the vapor channels
in the cathode. The area ratio between the cross
section of a channel and of the entire cathode cav-
ity is 9.97, and this value is sufficient together with
the Mach number of the flow in the cavity to com-
pute the entrance Mach number into a channel. The
equations for the adiabatic expansion of a gas are
given in Ref. [19]. It is further assumed that the
mass flow is equally divided among the 48 channel of
the porous tungsten cathode. The conditions at the
channel entrance, specifically the Mach number and
the temperature, are required for the next stage of
the calculations.

The last stage of the algorithm determines the exit

Mach number of the flow from the channel under the
action of convective heat addition from the channel
and of surface friction with the channel walls. It is as-
sumed that the channel walls are all at a uniform tem-
perature which is equal to the external surface tem-
perature of the cathode. In general the temperature
varies across the surface of the cathode, as previous
studies have shown. The flow is treated as laminar
flow in the channels. Ref. [16] gives an experimental
expression for the viscosity of the lithium vapor,

shown below with

given in

kg/ms

= (130

6+0

1014(

−

1000)+4

−

(

−

1000)

)

−

(12)

A Reynolds number for the flow can be estimated
with the canister temperature at 1050

◦

C, by taking

the density in the canister as an estimate for the den-
sity in a channel, by using the speed of sound in

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: LITHIUM LFA

lithium vapor as an estimate for the fluid velocity
in a channel and by using Eq. 12 to find

. For a

channel diameter of .102 mm the Reynolds number is
on the order of 100, which upholds the laminar flow
approximation. Since the length of a channel is only
0.0254 m, far short of the entry length, the flow is
not fully developed and the inviscid approximation is
valid for the flow in the center of a channel[20]. The
flow properties are calculated along the length of a
channel given the initial conditions at the entrance of
a channel and the temperature of the channel walls
which is taken to be the cathode surface temperature
as mentioned earlier. The Mach number of the flow
at the exit is computed and the estimate for the total
lithium mass flow is revised so that the exit Mach
number is one. This choked flow assumption is valid
because the pressure in the vacuum tank, into which
the lithium vapor is discharged, is 10

−

torr which is

roughly five orders of magnitude less than the lithium
vapor pressure in the canister.

Numerical Method for Finding Flow Proper-
ties

For the purposes of numerical integration of

the fluid flow equations the channel length is parti-
tioned into 1000 points. The fundamental equations
that describe the change in the Mach number and
temperature of the lithium vapor flow between the
points in a channel are

dM
M

(1 +

γM

)(1 +

−

)

−

(13)

γM

(1 +

−

)

−

f dx

−

γM

)(1 +

−

)

−

(14)

−

(

−

fdx

where

and

are the change in Mach number

and temperature between the points

and

= 2

−

is the friction coefficient

(Fanning) at

for laminar flow which is given by

16/Re, and

is the stagnation temperature of the

flow.

The stagnation temperature of the flow in-

creases along the initial part of the channel because
heat is being added to the flow.

The stagnation

temperature decreases as the flow reaches the chan-
nel exit because a temperature gradient favorable for
heat addition from the wall is no longer present due to
the effects of frictional heating in the boundary layer.
The change in stagnation temperature

between

the points

and

is given by the following

equation.

(

wall

−

adia

)48

πDdx

(15)

Here

wall

is the channel wall temperature and

the local heat transfer coefficient.

adia

is the adi-

abatic wall temperature and it is a measure of the
temperature in the thermal boundary layer that is
adjacent to the wall of the channel.

adia

is higher

than

due to the presence of viscous heating effects

in the boundary layer. It is

adia

that controls the di-

rection of heat transfer from the channel wall.

adia

is given below.

adia

(1 + 0

−

)

(16)

The coefficient 0.89 in Eq. 16 is the recovery fac-
tor and was determined from subsonic experimental
data. The local heat transfer coefficient is obtained
by considering laminar flow with a Nusselt number
of 3.66 for a channel surface maintained at constant
temperature[20]. The Nusselt number

N u

H D

(17)

where

is the lithium vapor thermal conductivity,

has been measured experimentally and is given in
Ref. [16].

is evaluated at

adia

Computational Results

Following the formalism

above a computer code was written in

to model

the lithium mass flow rate through the thruster. A
series of computations was performed to determine
the mass flow rate during steady state for various
canister wall temperatures, over the range of 920

◦

to 1100

◦

C. In all of these calculations the temperature

of the cathode was taken to be 1900 K. The results are
shown in Fig. 10. It is evident from Fig. 10 that the
operating range of interest for the lithium-fed LFA is
between 950

◦

C and 1070

◦

C where the mass flow rate

varies between 5 and 50 mg/s. The power required to
supply lithium to the thruster at the mass flow rates
calculated above was also determined using Eq. 11,
the results are shown in Fig. 11. Fig. 12 shows the
variation of the the Mach number along the length of
a channel when the canister temperature is 1300 K
and the calculated mass flow rate is 21.7 mg/s