Design and Performance Estimates of an Ablative Gallium

Electromagnetic Thruster

Robert E. ThomasNASA Glenn Research Center, Cleveland, OH 44135

Email: Robert.E.Thomas@nasa.gov

Abstract

The present study details the high-power condensable propellant research being conducted at NASAGlenn Research Center. The gallium electromagnetic thruster is an ablative coaxial accelerator designed tooperate at arc discharge currents in the range of 10-25 kA. The thruster is driven by a four-parallel line pulseforming network capable of producing a 250 µs pulse with a 60 kA amplitude. A torsional-type thrust standis used to measure the impulse of a coaxial GEM thruster. Tests are conducted in a vacuum chamber 1.5m in diameter and 4.5 m long with a background pressure of 2 µtorr. Electromagnetic scaling calculationspredict a thruster efficiency of 50% at a specific impulse of 2800 seconds.

Nomenclature

e = Electron charge, CE = Discharge energy, JIb = Impulse bit, N-sJ = Discharge current, Ak = Boltzmann’s constant, J/Kks = Spring constant, kg/s2

L = Inductance, Hmb = Mass bit, kgra/rc = Anode to cathode radius ratio, mT = Thrust, NTe = Electron temperature, eVV = Voltage, VZ = Ionic charge stateue = Exhaust velocity, m/sµo = Vacuum permittivity, H/mGEM = Gallium electromagneticPFN = Pulse forming networkMPDT = Magnetoplasmadynamic thruster

Introduction

Magnetoplasmadynamic thrusters (MPDTs) areelectromagnetic accelerators capable of providing ahigh thrust density over a wide range of exhaustvelocities, making them potentially attractive can-didates for lunar and Mars cargo missions. Unfortu-nately, erosion of the central cathode severely lim-its the lifetime of the thrusters [1]. Additionally,poor thruster efficiences (< 40%) have traditionallybeen obtained in the specific impulse (Isp) rangesof interest. The gallium electromagnetic (GEM)

thruster [2-6] was conceived to address these twoissues. The GEM thruster is a quasi-steady, coaxialaccelerator that utilizes ablated cathode mass forpropellant. The thruster is currently designed tooperate in a self-field mode (no applied magneticfield) with arc discharge currents on the order of10-25 kA. The thruster exploits cathode ablation,inherent in MPDTs, to create microsecond time-scale injection of propellant mass and significantlyincrease thruster lifetime. A photograph of a 20 Jlaboratory model is shown in Fig. 1. The thrusteris designed to ablate a thin layer of liquid galliumthat is continuously fed through the porous centralelectrode. Electrode erosion is treated as an inte-gral aspect of operation rather than a unavoidable,detrimental side effect.

Figure 1: Low-energy breadboard model utilizing asintered tungsten porous cathode [3].

The advantages of using gallium as a propellantinclude:

1. Storability : Gallium has a density of 5.99g/cm3 and a melting point of 30 C. It can be stored

https://ntrs.nasa.gov/search.jsp?R=20120018050 2018-06-06T13:21:36+00:00Z

as a solid and melted into a liquid with minimalthermal management.

2. Propellant Feeding : Liquid gallium can be fedto the thruster through the use of mechanically ro-bust electromagnetic pumps. This reduces the num-ber of moving parts and eliminates the need forpulsed gas valves.

3. Ground Based Testing : Gallium is non-toxic,relatively inexpensive, and can be pumped (con-densed) on a cooled baffle, which significantly re-duces facility requirements and costs.

4. Ionization: The first ionization potential ofgallium is only 5.99 eV, minimizing frozen flowlosses, which are the major loss mechanism for MW-level MPDTs.

The present study discusses the ongoing high-power, condensible propellant MPDT research atNASA Glenn Research Center. A description of thethruster, pulse forming network, and thrust standis presented. Electromagnetic scaling relations arethen discussed, and calculations of the thruster ef-ficiency and specific impulse are given.

Apparatus

GEM Thruster

A photograph of the GEM thruster is shown in Fig.2. The annular anode has an inner diameter of25.5 mm. The 8.5 mm diameter gallium electrode(99.999% purity) is electrically insulated from theouter electrode by boron nitride. Tests will be com-pleted using both flat-tip and conical-tip galliumelectrodes. The baseline configuration to be testedis an anode-to-cathode radius ratio of ra/rc = 3.Several annular electrodes have been fabricated thatwill permit testing of electrode radius ratios of 3, 5,7, and 10.

Figure 2: Photograph of 8.9 cm O.D. GEM thruster.

It should be noted that while a flight-like model

will utilize a porous central electrode that is con-tinuously replenished with liquid propellant (akinto Fig. 1), a solid gallium cathode is used in thepresent experiments. This is done to obtain accu-rate measurements of the mass ablated per pulse(mass bit). The energy required to melt solid gal-lium (0.06 eV/atom) is much less than the heatof vaporization (2.6 eV/atom), so the phase differ-ence is not expected to alter the performance of thethruster.

Vacuum Facility and Thrust Stand

Tests are conducted at NASA GRC vacuum facility3 (VF-3), which has a diameter of 1.5 m and is 4.5m in length. The chamber is evacuated by four oildiffusion pumps with a background pressure of 2µtorr prior to each thruster shot.

A torsional-type thrust stand is used to performimpulse measurements [7]. The impulse is deter-mined in terms of the thrust stand deflection x,spring stiffness k, and natural frequency ωn

Ib =ksx

ωn(1)

In practice x is measured as the maximum deflectionof the thrust stand after an impulse is applied, k isdetermined by exerting a known force and observ-ing the deflection, and ωn is determined by countingthe undamped frequency of the thrust stand oscil-lation. In-sitsu calibration weights are used to ap-ply a known force to determine the deflection ofthe thrust stand. The stand has a 2% uncertaintyin the impulse-bit measurement. Fig. 3 shows a aschematic of the thrust stand and Fig. 4 shows pho-tograph of the thruster mounted on the stand.

Figure 3: Top view schematic of thrust stand [7].

Figure 4: GEM thruster mounted on thrust stand.A polycarbonate mounting plate electrically isolatesthe thruster from the thrust stand.

Pulse Forming Network

The GEM thruster is powered by a four parallel linepulse forming network (PFN). Each line consists ofsix C = 600 µF capacitors charged to a maximum of800 V, yielding a total of 24 capacitors and a bankenergy of 4.6 kJ. The L = 400 nH coiled induc-tors are constructed of 10 gauge magnet wire. ThePFN impedance is (L/C)1/2/4 = 6.5 mΩ, whichis designed to match the thruster impedance. Thiseliminates the need for a matching resistor and max-imizes the energy transferred to the thruster. A cop-per sheet with punched holes is laid over the capaci-tors to provide a common ground (ground plane) asshown in Fig. 5. The PFN is mounted adjacent toVF-3 to minimize parasitic effects within the trans-mission lines. The PFN is capable of providing 60kA discharge currents for a duration of 250 µs. Anumerically simulated discharge current waveformfor a charging voltage of 300 V is shown in Fig. 6.A low-energy spark igniter mounted inside VF-3 isused to discharge the capacitors (similar to a pulsedplasma thruster). A schematic showing electricallythe PFN, igniter, and thruster is shown in Fig. 7.

Thruster Performance

The discharge current, arc voltage (electric poten-tial across thruster electrodes during current pulse),mass bit, and impulse bit are directly measuredand can be used to characterize the thruster per-formance. The specific impulse is found though Isp= Ib/mb. The impulsive efficiency is calculated us-ing

η =I2b

2mbE(2)

Figure 5: Side view of the six-ladder, four parallelline pulse forming network.

Figure 6: Simulated discharge current pulse for acharging voltage of 300 V.

where the discharge energy is found through

E =

∫Varc(t)J(t) dt (3)

An effective thrust and mass flow rate can be cal-culated from the impulse and mass bit by defininga quasi-steady time duration [8]

∆t =

∫J2(t) dt

< J >2(4)

where < J > is the quasi-steady current, averagedbetween 20-140 µs for the pulse shown in Fig. 6.Dividing each term in Eqn. (2) by (4), one arrivesat the familiar form for the thruster efficiency

η =T 2

2mP=

T 2

2mJVarc(5)

The following paragraphs provide analytical expres-sions for the thrust, arc voltage, and thruster effi-ciency. These calculations were used to design thethruster and to provide insight on the major energyloss mechanisms. Prior experimental data is used toestimate some of the necessary input parameters.

Figure 7: Electrical schematic of the pulse forming network and pulse igniter.

Prior GEM thruster experiments have shown thatthe mass ablated per pulse scales quadratically withthe discharge current m ∝ J2 [6]. This yields anexhaust velocity (and efficiency) that is invariantwith input power. This can be seen through theexamination of thrust and exhaust velocity relationsfor a coaxial electromagnetic accelerator [9]

T =1

2L′J2,where L′ =

µo2π

(lnrarc

+3

4

)(6)

ue = 12L′J

2

m(7)

Therefore, in order to increase the performanceof the thruster it is necessary to increase the induc-tance gradient L′. This is accomplished by increas-ing the anode to cathode radius ratio ra/rc. Effi-ciency predictions using ra/rc as a variable can bemade through the use of Eqns. (5), (6), and (8). Thearc voltage is the sum of the electromagnetic, elec-trothermal (heating and ionization), and the sheathvoltage contributions

Varc =T 2

2mJ+m(Ze

∑εi + 3/2kTe)

Jmion+ Vsheath (8)

where εi is the ionization potential in eV and mion

is the ion mass. The first, second, and third ion-ization potentials for gallium are 6, 20.5, and 30eV. The electron temperature Te is taken to be4 eV, which has been found experimentally usingLangmuir probes. Ionization calculations within theinter-electrode region yield Z = 2−3. A sheath volt-age of 30 V is used, which is estimated by extrapo-lating a previously obtained Varc − J curve to zerodischarge current [4]. The calculated performanceis shown in Figs. 8 and 9, for a fixed discharge cur-rent of 23 kA. The power during the quasi-steadyportion of the pulse is calculated to be 4.5 MW,yielding a thrust-to-power ratio of 36 N/MW. Thecorresponding thrust density is 2.6× 104 N/m2.

A summary of MPDT performance [8-12] isshown in Table 1 for various propellants. It can

1 6 0 0 1 8 0 0 2 0 0 0 2 2 0 0 2 4 0 0 2 6 0 0 2 8 0 0

2 5

3 0

3 5

4 0

4 5

5 0

Thrus

ter Ef

ficien

cy

S p e c i f i c I m p u l s e , s

Figure 8: Estimated thruster efficiency vs. specificimpulse for 3 < ra/rc < 10. At an electrode radiusratio of 10, the efficiency is 50% at an Isp of 2800 s.

0 1 2 3 4 5 6 7 8 9 1 0 1 19 0

1 0 0

1 1 0

1 2 0

1 3 0

1 4 0

1 5 0

1 6 0

1 7 0

T h r u s t E x h a u s t V e l o c i t y

E l e c t r o d e R a d i u s R a t i o , - -

Thrus

t, N

1 6

1 8

2 0

2 2

2 4

2 6

2 8

Exha

ust V

elocity

, km/

s

Figure 9: Estimated thrust and exhaust velocity asa function of electrode radius ratio.

be seen that the GEM thruster efficiency comparesfavorably with prior MPDT research, with an Ispin the moderate range of 3000 s. Further increasesin efficiency (>50%) may be possible through theoptimized use of applied magnetic fields [13].

Table 1: Comparison of MPDT performance withvarious propellants.Propellant Prop. Inj. Isp, sec Efficiency

H2 Gas-fed 10,000 55Li Vapor-fed 6,000 50C2 Ablation 5,000 19

Teflon Ablation 1,400 25Ga Ablation 2,800 50

Testing Plan

Hardware fabrication is complete and testing is cur-rently underway to ascertain the influence of elec-trode geometry on ablative thruster performance.As shown in Table 2, testing will be conducted in the10-25 kA discharge current range, with ra/rc = 3-10.At lower power levels, anode sheath losses are an-ticipated (Eqn. 8) to be the major loss mechanism,while frozen flow losses may dominate at higher cur-rent levels. Emission spectroscopy will be used tocharacterize the ionization losses. The use of a low-strength applied field perpendicular to the anodemay reduce sheath losses at the lower power levels[14].

Table 2: Testing plan for GEM thruster.Current ra/rc ra/rc ra/rc ra/rc

10 3 5 7.5 1015 3 5 7.5 1020 3 5 7.5 1025 3 5 7.5 10

Summary

High-power MPDT research utilizing gallium as apropellant has been described. The GEM thrusteris a MW-level ablative accelerator designed to mit-igate the life-limiting cathode erosion inherent inMPDTs. The experimental apparatus has beendescribed, which includes the thruster, PFN, andthrust stand. Utilizing a thruster with an elec-trode radius ratio of 10 yields an estimated thrust-to-power ratio of 36 N/MW. Efficiency calculationspredict a thruster efficiency of 50% at a specific im-pulse of 2800 s. Testing is currently underway tovalidate these predictions.

References

[1] Sovey, J. S. and Mantenieks, M., “Performanceand Lifetime Assessment of Magnetoplasmady-namic Arc Thruster Technology,” Journal of

Propulsion and Power , Vol. 7, No. 1, 1991,pp. 71–83.

[2] Polzin, K., Markusic, T., Burton, R., Thomas,R., and Carroll, D., “Gallium Electromag-netic (GEM) Thruster Concept and Design,”42nd AIAA/ASME/SAE/ASEE Joint Propul-sion Conference, Sacramento, CA, July 9-122006, AIAA-2006-4652.

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AIAA/ASME/SAE/ASEE Joint Propul-sion Conference, Cincinnati, OH, July 8-112007, AIAA-2007-5855.

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[10] Paccani, G., Chiarotti, U., and Deininger,W., “Quasisteady Ablative Magnetoplasma-dynamic Thruster Performance with Differ-ent Propellants,” Journal of Propulsion andPower , Vol. 14, No. 2, 1998, pp. 254–60.

[11] Ducati, A. and Jahn, R., “Investigation ofPulsed Quasi-Steady MPD Arc Jets,” Tech.rep., NASA Langley Research Center, 1971.

[12] Polk, J., Tikhonov, V., Semenikhin, S., andKim, V., “Cathode Temperature Reduction byAddition of Barium in High- Power LithiumPlasma Thrusters,” AIP Conference Proceed-ings, Vol. 504, 2000, p. 1556.

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