Lorentz Force Accelerator with an Open-ended Lithium Heat Pipe

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. BlandThermacore Inc., Lancaster, PA

AIAA-96-2737‖

Abstract

A steady-state coaxial Lorentz force accelerator(LFA), where lithium propellant is supplied by anopen-ended heat pipe, was designed and built. Theopen-ended heat pipe provides a novel alternative tothe complex propellant feeding systems previouslyused with lithium-fed thrusters. The closed end ofthe heat pipe acts as a reservoir containing a liq-uid lithium pool, and a wick. The main part of thepipe is embedded in a furnace (1200◦ C) which va-porizes the lithium off the wick. The lithium vaporthen travels to the open end which is also the cathodeof the LFA supplying the propellant for the plasmathruster. The actively heated cathode is a hybridhollow-multi-channel cathode consisting of 48 longi-tudinal channels embedded in a porous tungsten in-sert. The design promises a substantial decrease inthe erosion rate of the cathode which is the lifetimelimiting component in such thrusters. This paper de-scribes the design and fabrication of the thruster aswell as the mass flow rate calibration procedure whichrelies on careful water calorimetry.

∗This work is supported through an SBIR contract from NASA-JPL.

†Chief Investigator at EPPDyL. Assistant Professor, AppliedPhysics Group. Senior Member AIAA.

‡Student supported by the New Jersey NASA Space GrantConsortium.

§System Engineer, EPPDyL.¶Professor of Aerospace Sciences. AIAA Fellow.‖Presented at the 32nd AIAA Joint Propulsion Conference.

1 Introduction

1.1 long lifetime and high efficiencyof Li LFA’s

The lithium-fed Lorentz force accelerator (LFA) isa variant of the magnetoplasmadynamic thruster(MPDT) that promises long lifetime (>1000 hrs) andhigh efficiency (>60%). The extension of the lifetimeof such thrusters to above 1000 hours through theuse 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 suchthrusters for spacecraft propulsion.

This substantial lifetime extension is due to the therole of lithium in lowering the effective work functionφ of the cathode (pure tungsten’s φ ' 4.5 eV whilepure lithium’s φ ' 2.9 eV) and the role of the multi-channels in lowering the current densities, thus allow-ing lower operating surface temperatures, for a giventotal current, and consequently far lower erosion ratesthrough evaporation. Evaporation has been shownto be the major erosion mechanism in steady-stateMPDT’s.

It is now also well known[2] that another advantageof the use of alkali metal propellant is the superiorthrust efficiencies which have been reported to wellexceed 60%. This is believed to be related to thescaling of the energy sink associated with ionization(first ionization potential, εi, for lithium is 5.4 eVwhile εi=15.8 eV for argon.) This is especially thecase since ionization is believed to be of anomalously

1

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

high importance in such devices[3].

The only remaining concern for using the lithiumLFA on actual spacecraft is the contamination issue.In 1990 an experiment was conducted on the Sovietspacecraft Progress M-4, specifically to study, usingthe quartz microbalance technique, spacecraft con-tamination from alkali metal plasma sources. Theresults of that experiment were recently publishedand discussed by Brukhty et. al.[4], who also pre-sented further experimental and theoretical resultsand concluded that the deposition of alkali metalson spacecraft is not an obstacle for utilizing them aspropellant in electric thrusters. Furthermore, recentnumerical simulations[5] for a lithium MPD thrusterhave shown that plume shields can be quite effectivein reducing the backflow of lithium to the spacecraft.

1.2 Advantages and Applications ofLi LFA’s

Among all candidate electric propulsion options, theLi LFA has the unique capability of offering extremelyhigh thrust densities (102 to 105 N/m2). This fea-ture, the LFA’s ability of processing very high power(104 to 107 W) through a small, compact and simpledevice, and its high specific impulse (1000-4000 s)put it in a class by itself for application to manythrust-intensive and energetic missions such as de-manding cargo and piloted planetary missions. Formore power-limited near-term applications the LFAcould also compete with other EP options especiallyfor applications such as orbit-raising of massive pay-load.

Since the Li LFA becomes adequately efficient(>30%) only at higher power level (>30 KW) (seeRef. [6] for instance) and since no such high powersources are available in space, the device has beenclassified in the US as an “advanced propulsion op-tion.”

1.3 NASA-sponsored research on theLithium 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 thefeasibility of long-lived, high current cathodes. Theprogram includes the following complementary activ-ities:

1. The fabrication and testing of a 100 kW Li LFAat the Moscow Aviation Institute[7] with the goal

of demonstrating an efficiency of 40-45% at anIsp of 3500-4000 s.

2. In-house work at JPL aimed at the developmentof a cathode thermal code incorporating modelsof the heat fluxes from the near-cathode plasmaand testing at high current levels to validatethe code[8]. The experiments include numberdensity measurements using the Pulsed ElectronBeam diagnostic developed at USC.

3. Development and testing of a 30 kW class LiLFA 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 forLi LFA’s at Princeton University.

While previous work with lithium plasma thrustersat EPPDyL[9, 10, 11] concentrated on a “proof ofconcept” studies of the benefits of lithium and bariumdispenser cathodes, the new thruster described in thispaper is intended for more extensive and fundamentalstudies under realistic LFA conditions.

Among the advanced diagnostics especially devel-oped for these experiments, is a high resolution sixcolor video pyrometer (SCVP) (described in ref. [12])for measuring the high surface temperature of LFAcomponents 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 thestudies 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 useof an open-ended heat pipe to deliver a metered flowof lithium without the complexity of previous andexisting systems elsewhere. In Section 3 we presenta description of the LFA Testing Facility. The massflow calibration and monitoring, which rely on carefulwater calorimetry, are presented in Section 4 wherethe experimental results of the calibration are alsodiscussed. Finally, in the appendix we discuss a the-oretical fluid/thermal model of the lithium flow thatwas helpful in guiding the mass flow calibration.

CHOUEIRI, CHIRAVALLE, MILLER, JAHN, ANDERSON & BLAND: Li LFA 3

2 Design of an LFA with a

lithium Open-Ended HeatPipe

2.1 General Description

A cross-sectional schematic of the design is shownin Fig. (1). The drawing shows the dimensions of thecomponent and traces the flow of lithium through theheat pipe that acts as the propellant reservoir. A 3-Dschematic of the LFA is shown in Fig. (2).

Figure 1: Cross-sectional schematic of the accelera-tor showing dimensions (in inches) and the flow oflithium vapor.

The open-ended heat pipe provides a novel alter-native to the complex propellant feeding systems pre-viously used with lithium-fed thrusters. Aside from

Figure 2: 3-D schematic of the accelerator.

simplicity, reliability is enhanced by the fact thatthere are no valves or moving parts. The closed endof the heat pipe acts as a reservoir containing a liq-uid lithium pool, and a wick. The main part of thepipe is embedded in a furnace (1200◦ C) which va-porizes the lithium off the wick. The lithium vaporthen travels to the open end which is also the cathodeof the LFA supplying the propellant for the plasmathruster. Capillary forces draw up additional lithiumfrom the reservoir to replace the vaporized lithium.The actively heated cathode is a hybrid hollow-multi-channel cathode consisting of 48 longitudinal chan-nels embedded in a porous tungsten insert.

Rationale for the vaporizer design. The vapor-izer design of the reservoir was deemed superior toa pool boiler for our particular application. Com-pared with more conventional fluids, alkali metalshave high nucleation superheats, high bubble growthrates, long waiting times between bubble nucleations,and high natural convection rates. These conditionscan cause problems with unstable boiling and with


incipient boiling superheats. In unstable boiling, theheat transfer mechanism oscillates between nucleateboiling 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 ofthe system are listed in Table 1.

The thruster is radiatively cooled and does nothave an applied magnetic field. Although an appliedmagnetic field has been shown to substantially im-proved the performance[7], we will be operating thethruster in a self-field mode for our fundamental stud-ies. Future performance study would necessitate anapplied field.

Thermocouples wells were placed in three criticallocations (labeled TC in Figure 1) to provide accessfor temperature measurement at 1) the middle heightof 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 promiseto yield a larger effective attachment area and also, amore stable behavior of the discharge, was chosen.The elementary channel packet is slightly recessedwith respect to the cathode end (about 25% of the in-ner diameter). This hybrid hollow-multichannel cath-ode configuration[13], should combine the advantagesof 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 alsoto some experiments carried out at EPPDyL[14], thepenetration length of the discharge is typically on theorder of a few channel diameters. Considering thatin a multichannel cathode this length is greatly re-duced with respect to a single channel cathode withthe same hollow cross section area and the same totalgas flow rate, we expect that a length of 5 cm for theinsert containing the channels, is widely in excess ofany possible penetration of the discharge.

Considering the ratio of the total discharge cur-rent to the cathode cross section area (without theouter sheath), we predict a current density not largerthan 260 A/cm2. This is about the same value asthe thruster in ref. [1]. If we maintain the same ratioof hollow cross-section area to the total area (about13%), using gaps of 2 mm diameter tungsten rods,as in ref. [1], and cylindrical holes in the tungstenwick, it follows that sixty-five uniformly spaced 1 mm

diameter channels are needed, having cross section(0.78 mm2) with gaps of (0.16 mm2).

2.3 Anode Design Considerations1

From a machining and cost point of view, tantalumis preferable over tungsten for anode material. Thedesign calculations presented below, however, favorthe use of tungsten.

In order to choose the anode material and estimatethe minimum anode thickness compatible with theoperating conditions of the thruster, the effects ofJoule 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 steadystate is reached, all power generated in the anode byresistive heating (Joule effect) is rejected by radia-tion. This model yields an expression for the anodethickness t,

t =I2ρ

(2πR)2εσT 4. (1)

where ρ is the resistivity of the material, ε is the totalemissivity, σ is the Stefan-Boltzmann constant, T isthe temperature in degrees K and I is the total cur-rent. Using temperature-dependent expressions forthe resistivities of tungsten and tantalum, the melt-ing temperatures of tungsten (3683 K) and tanta-lum (3269 K) and assuming an operating current of1000 A, we obtain a minimum thickness equal to 3.5µm for a tungsten anode and to 7.7 µm for a tanta-lum anode. These results, show that Joule effect isnot a dominant mechanism in anode heating.

2.3.2 Heat Flux to the Anode

For nominal LFA operation the anode heat flux q canbe estimated as:

q =

(Va +

5

2

kBT

e+ φa

)+ PR, (2)

where je is the electron current density, Va is the an-ode voltage fall, Te is the electron temperature, kB isthe Boltzmann constant, e is the elementary electriccharge, φa is the work function for the anode materialand PR 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

1The calculations in this section were carried by Paolo Gessiniat EPPDyL.


DESIGN OEPRATING PARAMETERS

Nominal LFA Power Rating 10-100 kWNominal LFA Current Rating 300-2000 A

Nominal LFA Voltage 30-50 VNominal Li Flow Rate 2-50 mg/sFurnace Power 1.2 kW

Potential Drop Near Cathode 5 VBackground Pressure 10−4 torr

Li Vapor Pressure Next to Active Surface 2 to 20 torrMaximum Emitting Surface Temperature 3000◦ K

DIMENSIONSCathode O.D. 2.54 cm

Anode O.D. at Exit 15 cmMinimum Radii for Corners .062

Number of Hollow Channels 48

MATERIALCathode and Anode TungstenCathode Insert Porous Tungsten

Cathode & Anode Mounting Flanges MolybdenumInter-Electrode Insulator Flange Sapphire

Bolt Insulators AluminaCanister Envelope Molybdenum

Vapor Tubes and Thermocouple Wells Tantalum

Li RESRVOIR & FURNACE

Reservoir Capacity 1000 cm3

Furnace Operating Temperature 1500◦ C

Furnace Maximum Current 500 AFurnace Maximum Voltage 10 V

Furnace Active Element 3×30 cm Tungsten ribbon

CATHODE HEATERMaterial Tantalum wire & alumina beadsLength 2 m wrapped around base of cathode

Operating Temperature 1100◦ CPower Requirements 20 A at 50 V

Table 1: Design Parameters of Lithium LFA.


area of 220 cm2, from typical values of the abovephysical quantities measured during operation of asimilar device, we estimate that q should not exceed200 W/cm2. If we further assume that, once a steadystate is reached, only the external surface of the flaredpart of the anode is at a uniform temperature andradiates the power away, using the appropriate val-ues for emissivity and neglecting the thickness of theanode, we obtain, at 1000 A, a temperature of about3050◦ K for tungsten, and 3280◦ K for tantalum. Thisdifference is due to the lower emissivity of tantalum(about 0.3 as opposed to about 0.4 of tungsten). Wenotice that, while with tungsten we are well below themelting 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 overthe whole anode surface, but concentrated in a finitenumber of spots of a certain diameter. In order toobtain a rough estimate of the temperature evolutionin the anode, we will make a series of assumptions,based in part on the results of experiments carriedout with a quasi-steady MPD thruster at EPPDyL[15] which will render our conclusions conservative.

We will assume, from observations of spot tracesin an LFA anode, that the current is concentratedin spots with 1 mm2 area, distributed on the anodesurface with an average density of one spot per cm2.This means that only 1% of the surface is affected bythe discharge. For spot lifetime we will assume thata single spot does not exist in the same location for atime longer than 100 µs. Such an assumption, quiteconservative, is based on noise data, which present acharacteristic frequency on the order of 100 KHz andcould be attributed to spot movement on the anodesurface with a characteristic time of 10 µs.

Analytical Model. Under these assumptions, afirst analysis has been carried out using a one-dimensional model. Namely, the anode has beentreated like a semi-infinite body, with constant heatflux at the boundary. In this way, radiation cool-ing has been neglected, and the temperature increasemay be written as:

∆T =2q

k

[(αt

π

) 12

e−x2/4αt − x

2erfc

x

2√αt

], (3)

where the heat flux q is now equal to 20000 W/cm2, kis the thermal conductivity, α 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 lastquantities do actually show a strong dependence ontemperature, but in our range of interest (T ≥3000K) 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

50

0

Tem

per

atu

re I

ncr

ease

[K

]

1.0x10-3

0.80.70.60.50.40.30.20.10.0

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 therewill be a smaller possibility of overheating on the in-side, and at the same time heat will be conductedequally efficiently out, where it will be radiated awayby 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 belowthe melting point for both materials. In the case oftungsten, there is still no melting even after 1 ms.

Numerica Model. A more detailed picture of theeffect 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 spotaround its axis of symmetry on one side simulates theregion of a 2 mm thick anode surrounding each singlespot. The boundary conditions are q = 20000W/cm2

at the spot, q = 0 on the rest of the inner surface


and on the lateral area (for symmetry), q = εσT 4 onthe outer surface. The initial condition is a uniformtemperature of 3000◦ K, and the properties of thematerial are again assumed constant, with the samevalues as before. Figure 4 shows the results of thissimulation, performed with FEHT, a finite-elementheat transfer program, in the case of tungsten. From

Figure 4: Temperature contours after 1.5 s in a 2 mmthick tungsten anode. The melting region is 13% ofthe anode thickness.

Figure 5: Temperature contours after 1.5 s in a 2 mmthick tantalum anode. The melting region is 100% ofthe anode thickness.

that plot we can note that even after 1.5 s, a periodmuch longer than the expected lifetime of a spot, theregion above the melting point extends for only about13% 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 tantalumwith respect to tungsten. For comparison, the samegray level scale has been used in figure 5.

Final Anode Selection As a result of the abovedesign consideration a tungsten anode was manufac-tured by plasma spraying with a thickness of 4.5 mm

3 LFA Testing Facility

The Li LFA was installed in EPPDyL’s Steady-StateLow Power (SSLP) Facility described in ref. [10]. TheSSLP facility uses a 1.5 m diameter cylindrical carbonsteel tank, 6.4 m in length, evacuated to 10−5 torrby a set of mechanical and diffusion pumps. Pho-tographs of the accelerator and furnace assembly withassociated 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 pumpswith lithium, a condenser trap was built and posi-tioned about 2.5 m downstream of the thruster. Thetrap consists of two copper plates actively cooled bychilled water coils and a similarly cooled metalliccylinder housing a mirror for optical diagnostic ac-cess (see Fig. (16)). In order to further protect themirror from lithium condensation, its surface is keptat about 700◦ C using a small heater.

Data Acquisition. Data is recorded from sensorsinside the vacuum tank using a Keithley System 570digital acquisition board coupled to a personal com-puter. Aside from scientific diagnostics, three typesof data are collected during a firing of the lithium-fedLFA , voltage and current data for the heater and thethruster both of which have separate power supplies,mass flow rate data of the reservoir cooling water andtemperature data from thermocouples in the coolingwater and in the walls of the canister.

Power Measurements. Current measurementsare taken on the outside of the vacuum tank usingmagnetic current sensors from Bell Inc. The Keith-ley System 570 has 16 channels for differential voltageinput. The uncertainty in a current value obtainedfrom 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. Thethruster voltage is measured from the connections atthe window interface.

Water Flow Measurements. A turbine cage flowmeter from McMillan Company is used to measurethe flow rate of cooling water into the heater cool-ing jacket. The cooling water flow rate is one of theparameters required for determining the lithium massflow rate by the balance of power into the heater. Theflow meter is powered by a 5 V DC power supply andthe voltage output of the device is proportional to the


mass flow rate through the meter. A calibration wasperformed to find this relationship and the associateduncertainty.

Temperature Measurements. Two sets of ther-mocouples are used to make measurements of thetemperature of the canister wall and the tempera-ture of the cooling water. The thermocouples used tomeasure the water temperature are Iron-Constantanjunctions. The iron and constantan wires that ex-tend from the thermocouple junctions are connecteddirectly to a thermocouple daughter board in theKeithley system. Reference junction voltage com-pensation is applied to the thermocouple voltage sig-nals by a Keithley software routine which computesthe temperature in ◦C at the thermocouple junc-tion. Tungsten-Rhenium junctions are used to mea-sure the temperature of the canister wall at distancesof 0.0508 m and 0.1524 m from the top of the can-ister. Cold junction voltage compensators are con-nected to the high temperature thermocouple linesand the voltage output from each of these devices issent to the Keithley board. A calibration relationsupplied by the manufacturer is used to find the tem-perature in ◦C.

4 Mass Flow calibration

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

A lithium flow simulation model, discussed in theappendix, was developed to estimate the dependenceof 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 determinethe power radiated from the heater during steady-state operation. This was accomplished by heating

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

In the ideal case liquid lithium would evaporatefrom the screen wick and condense on the surface ofthe vapor tube, transferring heat from the canisterto the vapor tube. The assumption is that the canis-ter walls are heated uniformly so that there would beno condensation on the screen wick which covers thecanister walls and all the lithium vapor condensationwould take place on the walls of the vapor tube. Thisassumption does not truly hold for our actual canisterbecause the tungsten heating element is about 5 cmshorter than the upper extent of the vertcal part ofthe canister and as a consequence the top part ofthe canister is not heated by the heating element.Therefore condensation of lithium vapor is expectedin this region once the temperature in the lower partof the canister is sufficient for vaporization to takeplace. Under such conditions the canister behaves asa heat pipe with lithium as the working fluid. Aftercondensing in the top part of the canister the liquidlithium flows along the screen wick toward the regionof the canister that is actively heated and evapora-tion takes place again. The iron cooling jacket of thecanister (see the photographs in Figures 15 and 16)does not cover the top part of the canister, and in thisregion the canister radiates as a greybody. The lossof radiated power from the walls of the vapor tubeis eliminated through the use of alumina insulatorsand molybdenum foil that cover the vapor tube. Thepower lost to the tank due to greybody radiation ofthe canister is concentrated in the top part of the can-ister. The radiated power loss to the tank from thecanister is an important parameter in determining thelithium mass flow rate using power balance methods.Two experiments were performed in which the powerto the heater was gradually increased in steps and thethermal response of the canister was recorded. Asmentioned earlier measurements of canister temper-ature were made with two thermocouples, one in thetop part of the canister where there is no active heat-ing from the tungsten element and one in the bottompart where there is active heating. The experimentswere roughly four hours in duration each. Fig. 6 andFig. 7 show the results of these experiments.

As Fig. 7 shows a temperature difference betweenthe top and bottom thermocouples readings of about200 deg C was observed during steady state withthe bottom temperature at 700 deg C and the inputpower at 450 W . Once the vaporization thresholdwas reached the temperature gradient was reduced


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100

tem

per

atu

re (

C)

200150100500

time (min)

1000

800

600

400

200

0

pow

er (W)

libottom litop power

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

1000

800

600

400

200

tem

per

atu

re (

C)

200150100500

time (min)

1500

1000

500

0

pow

er (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 notionthat the canister behaves like a heat pipe with a flattemperature profile. The measurements show thatsteady-state conditions were reached when thermo-couple data was constant within 0.1% for a period ofabout three minutes. Cyclic variations in the inputpower to the heater from the power supply were ob-served with amplitude of 10 W . The power radiatedto the tank during steady state was computed usingthe following equation.

PRad = P − mcp∆T (4)

Here P is the input power to the heater computedfrom current and voltage measurements, m is themass flow rate of water through the iron coolingjacket, and ∆T is the difference between the cool-ing water inlet and outlet temperatures. The valuesused in Eq. 4 were obtained by taking an averageof three consecutive steady-state points. A standarddeviation was also computed for each of the param-eters in Eq. 4. An error propagation analysis wasperformed to find the uncertainly in the computedvalues of PRad from the uncertainties in its parame-ters. The values of PRad at several steady-state pointstaken from the two experiments are plotted in Fig. 8versus T 4

Top where TTop is the the temperature at thetop of the canister. A linear fit to the data yielded

700

600

500

400

300rad

iate

d p

ow

er (

W)

1.41.21.00.80.6TTop

4 (10

12 K

4)

Figure 8: Radiated power from the canister as a func-tion of T 4

Top

the following coefficients.

PRad = 57.7 + 4.52× 10−10T4Top (5)


The variance of both of the coefficients above wascomputed to estimate the total error in the mass flowcalibration.

4.2 Results of Li Mass Flow Calibra-tion

The mass flow rate of lithium through the thrusterduring 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 resistanceof the tungsten heating element, P , the heat lossfrom 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, PRad. Duringthruster operation, an additional mode of heat lossduring steady state is evaporation of lithium whichcan be expressed as the product of the latent heat ofvaporization of lithium, Λ and the mass flow rate oflithium from the canister, mLi. We essentially mea-sure the rate of heat loss through the evaporation oflithium and with the knowledge of Λ we determinemLi. Since the thruster cathode and the canister aredirectly connected by a tantalum vapor tube, con-duction occurs from the cathode to the heater. Therate of heat transfer through this mode is calculatedfrom the equation below.

q =κA

LδT (6)

Taking the temperature difference between the cath-ode and the canister to be 1000 ◦C, the cross sectionalarea of the vapor tube as 8.639×10−6 m, the thermalconductivity as 100 W

mK and the length of the vaportube as 0.5 m, the power supplied to the canister isonly 1.72 W. This value is negligible compared withthe other transfer modes and has been consequentlyneglected in the analysis.

Having identified the relevant modes of heat trans-fer, equating the power contributions from each ofthese modes leads to the follow expression relatingthe lithium mass flow rate to the other variables.

mLi =P − mcp∆T − PRad

Λ(7)

Λ at the boiling point temperature (1 atm) of1612.1 K is determined from an experimental vaporpressure curve for lithium in Ref. [16] and has thevalue of 21.62 ×106 J

kg . The temperature dependence

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

Λ = 21.62× 106(1− T

3503

1− 1612.13503

)0.38 (8)

Here 3503 ◦K is the critical temperature for lithium.The error in Eq. 7 is given by the following.

σmLi =√σ2P + (cp∆T )2σ2

m + (mcp)2σ2∆T + σ2

Rad

1

Λ(9)

σRad is the error in Eq. 5 which is a function of tem-perature shown below.

σRad =√

32.49 + 69.7× 10−23T 8Top (10)

The uncertainty in the radiated power from the can-

35

30

25

20

15

erro

r in

rad

iate

pow

er (

W)

11001000900800TTop (C)

Figure 9: σRad as a function of TTop

ister is the dominating term in Eq. 9, and this trans-lates into an uncertainty in the lithium mass flow rateof about 0.7 mg/s at 1050 ◦C. The steady-state op-erating range of mass flow rates for lithium-fed LFAoperation 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 ratethrough the thruster.

5 Conclusions

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


Lorentz force accelerator (LFA). The novel conceptin the design is the use of an open-ended heat pipe tosupply 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 andthe power input to a furnace. Based on heat loadcalculations the anode was fabricated out of tung-sten and has a thickness of 4.5 mm. A power balancerelating the input power for the furnace vaporizingthe 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%. Thedevice, along with a six color video pyrometer (de-scribed in ref. [12]) and an emission spectrometer, isintended for use in the studies of various processesrelated to multi-channel cathodes and alkali metalplasma acclerators.

Acknowledgments The authors are thankful toDr. Kevin Diamant for his valuabe help.

References

[1] V.P. Ageyev and V.G. Ostrovsky. High-currentstationary plasma accelerator of high power. In23rd 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 MPDthrusters. 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 23rd 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 23rd International Electric Propulsion Con-ference, Seattle, WA, USA, 1993. IEPC-93-149.

[5] R.I. Samanta Roy and D.E. Hastings. Backflowcontamoniation 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, andV.N. Shutov. Investigation of alkali metal MPD

thrusters. In 24th International Electric Propul-sion Conference, Moscow, Russia, 1995. IEPC-95-104.

[7] V. Tikhonov, S. Semenikihin, J.R. Brophy, andJ.E. Polk. The experimental performance ofthe 100 kW lithium MPD thruster with exter-nal magnetic field. In 24th International ElectricPropulsion Conference, Moscow, Russia, 1995.IEPC-95-105.

[8] K. Goodfellow and J. Polk. Lorentz force accel-rator technolgy development at JPL. In SixthAdvanced 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 25th Joint Propulsion Conference, Mon-terey, CA, USA, 1989. AIAA-89-2706.

[10] J.S. Fillmore. An experimental study of lithiumdispenser cathodes in the MPD thruster. In23rd 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 June1994-December 1994. Technical Report No.EPPDyL-TR-94F, EPPDyL, Princeton Univer-sity, 1994.

[12] E.Y. Choueiri, V.P. Chiravalle, G.E. Miller, andR.G. Jahn. Six-color video pyrometry with ap-plication to MPD thrusters. In 24th 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 performanceand characteristics of MPD thrusters with ap-plied magnetic field. In 3rd Russian-GermanConference on Electric Propulsion Engines andtheir 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, andR.G. Jahn. Characterization of the near-anoderegion of a coaxial MPD thruster. In 30th JointPropulsion Conference, Indianapolis, IN, 1994.AIAA-94-3336.


[16] Roland W. Ohse. Handbook of Thermodynamicand Transport properties of Alkali Metals. Black-well, New York, 1977.

[17] J.M. Prausnitz R.C. Reid and T.K. Sherwood.The Properties of Liquids and Gases. McGrawHill, New York, 1977.

[18] W.B. Anderson. Porous cathode for alkali pro-pellant mpd thrusters, quarterly report no.4,nasa sbir contract nas7-1308. Technical Re-port 8, Thermacore Inc., 1996.

[19] Ascher H. Shapiro. The Dynamics and Thermo-dynamics of Compressible Fluid Flow. RolandPress, New York, 1953.

[20] Frand P. Incorpera and David P. DeWitt. Funda-mentals of Heat and Mass Transfer. John Wiley,New York, 1990.


APPENDIX: Theoretical Mass Flow RatePrediction The mass flow rate of lithium throughthe thruster is influenced by two parameters, the tem-perature of the thruster cathode and the temperatureof the canister wall during steady-state operation.The temperature of the canister wall is related tothe saturation pressure of lithium vapor in the canis-ter for temperatures around the vaporization thresh-old, 800◦C. The temperature of the cathode surfacecontrols the transfer of enthalpy to the lithium vaporflow through convection as the lithium moves throughthe channels of the cathode. A one dimensional fluidmodel with heat addition and friction loss was usedto estimate the lithium mass flow rate as influencedby the above parameters[18].

Model Assumptions The model describes threeregions 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 throughthe vapor tube into the cathode cavity, the adiabaticexpansion of the fluid as it passes from the cathodecavity 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 isconsidered 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 onedimensional flow in terms of Mach number, temper-ature, velocity, and density are taken from Ref. [19].

The model assumes that at steady-state conditionslithium exists as a saturated vapor in the canisterwhere the temperature of the vapor is equivalent tothe temperature of the canister walls. An experi-mental relation between lithium vapor pressure andtemperature is given in Ref. [16] and has the formbelow with pressure, p in Pascal.

p = (1

T)0.4942 exp (13.0719− 18880.659

T) × 106 (11)

At 1050◦C, p is about 1055 Pa (8 torr) and at thislow pressure the ideal gas assumption is valid. Thedensity of the vapor can be calculated from this as-sumption, since the temperature is specified and thepressure is determined by Eq. 11. The state of thevapor in the canister is now completely determined.It is next assumed that the lithium vapor does notcondense on the walls of the vapor tube and the flowis adiabatic as it travels into the cavity region of thecathode. Since the vapor tube is well insulated andhas 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 thewall of the vapor tube. However it is highly probablethat during the start-up phase of heater operationa surface layer of lithium is deposited on the vaportube wall. The flow is considered incompressible asit travels between the canister and the cavity of thecathode, since a significant area contraction has notoccurred. The density in the cathode cavity is takenas the density computed for the vapor in the canis-ter. A this point in the analysis a guess is made forthe mass flow rate of lithium into the cathode whichis later refined through an iterative procedure. Withknowledge of the cross section area of the cathodecavity, a velocity is computed and this value coupledwith the stagnation temperature of the flow gives avalue for the temperature of the flow in the cathodecavity. The stagnation temperature of the flow is thecanister temperature.

The second region of flow behavior is the adiabaticexpansion from the cavity into the vapor channelsin the cathode. The area ratio between the crosssection of a channel and of the entire cathode cav-ity is 9.97, and this value is sufficient together withthe Mach number of the flow in the cavity to com-pute the entrance Mach number into a channel. Theequations for the adiabatic expansion of a gas aregiven in Ref. [19]. It is further assumed that themass flow is equally divided among the 48 channel ofthe porous tungsten cathode. The conditions at thechannel entrance, specifically the Mach number andthe temperature, are required for the next stage ofthe calculations.

The last stage of the algorithm determines the exitMach number of the flow from the channel under theaction of convective heat addition from the channeland 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 temperaturevaries across the surface of the cathode, as previousstudies have shown. The flow is treated as laminarflow in the channels. Ref. [16] gives an experimentalexpression for the viscosity of the lithium vapor, µ,shown below with µ given in kg/ms.

µ = (130.6+0.1014(T−1000)+4.55×10−6(T−1000)2)×10−7

(12)A Reynolds number for the flow can be estimatedwith the canister temperature at 1050◦C, by takingthe density in the canister as an estimate for the den-sity in a channel, by using the speed of sound in


lithium vapor as an estimate for the fluid velocityin a channel and by using Eq. 12 to find µ. For achannel diameter of .102 mm the Reynolds number ison the order of 100, which upholds the laminar flowapproximation. Since the length of a channel is only0.0254 m, far short of the entry length, the flow isnot fully developed and the inviscid approximation isvalid for the flow in the center of a channel[20]. Theflow properties are calculated along the length of achannel given the initial conditions at the entrance ofa channel and the temperature of the channel wallswhich is taken to be the cathode surface temperatureas mentioned earlier. The Mach number of the flowat the exit is computed and the estimate for the totallithium mass flow is revised so that the exit Machnumber is one. This choked flow assumption is validbecause the pressure in the vacuum tank, into whichthe lithium vapor is discharged, is 10−5 torr which isroughly five orders of magnitude less than the lithiumvapor pressure in the canister.

Numerical Method for Finding Flow Proper-ties For the purposes of numerical integration ofthe fluid flow equations the channel length is parti-tioned into 1000 points. The fundamental equationsthat describe the change in the Mach number andtemperature of the lithium vapor flow between thepoints in a channel are

2dM

M=

(1 + γM 2)(1 + γ−12 M 2)

1−M 2

dToTo

(13)

+γM 2(1 + γ−1

2 M 2)

1−M 2

4fdx

D

dT

T=

(1− γM 2)(1 + γ−12 M 2)

1−M 2

dToTo

(14)

− γ(γ − 1)M 4

1−M 2

2fdx

D,

where dM and dT are the change in Mach numberand temperature between the points xi and xi + dxand dx = 2.54 × 10−5. f is the friction coefficient(Fanning) at xi for laminar flow which is given by16/Re, and To is the stagnation temperature of theflow. The stagnation temperature of the flow in-creases along the initial part of the channel becauseheat is being added to the flow. The stagnationtemperature decreases as the flow reaches the chan-nel exit because a temperature gradient favorable forheat addition from the wall is no longer present due tothe effects of frictional heating in the boundary layer.The change in stagnation temperature dTo between

the points xi and xi + dx is given by the followingequation.

dTo =H(Twall − Tadia)48πDdx

mLicp(15)

Here Twall is the channel wall temperature and H isthe local heat transfer coefficient. Tadia is the adi-abatic wall temperature and it is a measure of thetemperature in the thermal boundary layer that isadjacent to the wall of the channel. Tadia is higherthan T due to the presence of viscous heating effectsin the boundary layer. It is Tadia that controls the di-rection of heat transfer from the channel wall. Tadiais given below.

Tadia = T (1 + 0.89γ − 1

2M 2) (16)

The coefficient 0.89 in Eq. 16 is the recovery fac-tor and was determined from subsonic experimentaldata. The local heat transfer coefficient is obtainedby considering laminar flow with a Nusselt numberof 3.66 for a channel surface maintained at constanttemperature[20]. The Nusselt number

Nu =HD

κ, (17)

where κ is the lithium vapor thermal conductivity,has been measured experimentally and is given inRef. [16]. κ is evaluated at Tadia.

Computational Results Following the formalismabove a computer code was written in C++ to modelthe lithium mass flow rate through the thruster. Aseries of computations was performed to determinethe mass flow rate during steady state for variouscanister wall temperatures, over the range of 920◦Cto 1100◦C. In all of these calculations the temperatureof the cathode was taken to be 1900 K. The results areshown in Fig. 10. It is evident from Fig. 10 that theoperating range of interest for the lithium-fed LFA isbetween 950◦C and 1070◦C where the mass flow ratevaries between 5 and 50 mg/s. The power required tosupply lithium to the thruster at the mass flow ratescalculated above was also determined using Eq. 11,the results are shown in Fig. 11. Fig. 12 shows thevariation of the the Mach number along the length ofa channel when the canister temperature is 1300 Kand the calculated mass flow rate is 21.7 mg/s


50

40

30

20

10

mas

s fl

ow r

ate

(mg

/se

c)

10401000960

cannister temperature (C)

Figure 10: Model predictions for the lithium massflow rate at several values of canister temperature

1200

1000

800

600

400

200

pow

er (

W)

5040302010

mass flow rate (mg/sec)

Figure 11: Calculated power required to vaporizelithium as a function of lithium mass flow rate

0.7

0.6

0.5

0.4

0.3

0.2

0.1

Mac

h n

um

ber

2.52.01.51.00.50.0

distance along the channel (cm)

Figure 12: Calculated Mach number variation alonga channel


Figure 13: Close up front view. (Anode O.D.is 15 cm)

Figure 14: Front view showing furnace and electricalleads.

Figure 15: Close up back view showing heat pipe andthermocouples.

Figure 16: Back view showing water calorimetric sub-system and lithium condenser trap (downstream)

Documents

Lorentz Force Accelerator with an Open-ended Lithium Heat Pipe