3125078

Impact of Dielectric Separation on Transition Point and Accessible Flow Enthalpy ofInductive Plasmas

Ashley R. Chadwick (1), Georg Herdrich (2), Min Kwan Kim (1), Bassam Dally (1), Johanna Hertel (2)

(1) University of Adelaide, North Terrace, Adelaide, 5005, Australia, ashley.chadwick@adelaide.edu.au(2) Institute for Space Systems, University of Stuttgart, Pfaffenwaldring 29, 70569, Stuttgart, Germany,

chadwick@irs.uni-stuttgart.de

KEYWORDS

Electric propulsion; Inductive propulsion; Inductivetransition

ABSTRACT

In order to develop inductive electric propulsionsystems towards flight-ready status, an investigationinto the influence of the dielectric separationbetween plasma and inductive coil has beenconducted. This was completed by varying thewall thickness of the thruster discharge tube. Theinvestigation assessed discharges of argon andan argon-nitrogen mixture. Additionally, resultsof a similar investigation utilising air have beenincluded for comparison. The sum of theseinvestigations showed two contrasting trends. Theargon condition exhibited a preference for thickerwalls, with transitions to the higher inductive regimeoccurring at lower input powers with increasingwall thickness. Results for Ar:N2 and air showedthe opposite, with system thermal power increasingwith decreasing wall thicknesses. This behaviourhas been proposed to include contributions ofboth the mechanical dielectric separation causedby the choice of chamber wall thickness, andthe gasdynamic dielectric separation owing to thedischarge thermal boundary layer.

1. INTRODUCTION

With near-future targets for the development ofhigh-power electric propulsion (EP) being introduced[1], the need for new solutions to long-standingor imminent limitations is evident. Despite theirhigh performance, most conventional EP systemslend themselves to preferable operation with noblegases, relying on the low ionisation energy to

produce a relatively high flux of energetic particlesfor thrust generation. However, these gasesare inherently rare in the natural environment,resulting in prohibitively high production costs whenconsidering such gases for large-scale propulsionpurposes [2]. Many of the current EP systemsare subject to ongoing investigations into theimplementation of more naturally occurring gasesas propellant substitutes, though these gases areoften at cross-purposes with the respective thrusteracceleration mechanisms. Conventional systemsutilising more natural, or ‘alternative’ propellantsusually suffer from both reduced thrust, due tothe greater input energy required to generate ions,and corrosion of the electrode/accelerating gridarrangement resulting from contact with aggressivespecies such as oxygen [3–5].

One branch which does not share thesedisadvantages is Inductive Electric Propulsion (IEP).IEPs separate their excitation mechanism (aninductive coil or antenna) from the working fluidby means of a dielectric containment vessel, thusallowing the use of corrosive species withoutadverse damage to critical components [6]. Thisseparation also affords IEPs a wide variety ofavailable propellants, including naturally-occurringcompounds such as oxygen and CO2. Suchsystems are thus ideally-suited towards missionsrequiring large propellant supplies, such as satelliteorbit-raising or cis-lunar cargo transport operations,making full advantage of their long lifetime (dueto the resultant plasma being contained within achemically-inert vessel) and their ability to be scaledaccording to a given set of mission objectives(without the need for clustering, which in itsexecution requires additional propulsion subsystemmass).

Due to the greatly varying chemical propertiesof available propellants for IEP systems, eachexhibits its own behaviour in the context ofthrust generation which must be understood beforethey are implemented into a mission-capable

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system. This paper focuses on the impactof the dielectric separation between plasma andinductive coil for a number of gases and gasmixtures, expanding on previously published studiesby broadening the number of gases analysedand presenting previously unexpected, contrarybehaviour. In particular the work focuses onthe separation’s influence on the transition pointbetween capacitive and inductive discharge regimesand the accessible enthalpy of the resultant plasmaflow. Through analysing a number of chemicallydiverse propellant configurations, an assessment ismade to help clarify why different compositions showpreferences towards a particular dielectric chamberwall thickness.

2. INDUCTIVE ENERGY COUPLING

In order to effectively utilise gases as propellantwithin an IEP, an inductive discharge must bereached, bypassing the capacitive regime whichis known to occur at lower powers and dischargepressures [6–9]. The inductive regime exhibitsa far more effective energy coupling between thegenerator coil and the plasma [6, 10], thus providinga more energetic flow for thrust generation eitherthrough expulsion of the hot gas or dedicatedacceleration of the charged particles.

Figure 1: Inductive discharge cross-section

Once the inductive mode has been reached,

it displays a very characteristic form as seen inFigure 1, where δT is the thermal boundary layer,δ is the skin depth, c is the diffusion zone andd is the cold core flow. In this diagram ERF isthe azimuthal electric field generated by the coilcurrent, HRF is its resultant magnetic field, andEΘ is the opposing electric field generated withinthe plasma. However, the conditions under whichthe transition from capacitive to inductive operationoccurs is subject to a number of thermodynamicand electromagnetic influences. The instigationof the inductive discharge is reliant on the coilmagnetic field exerting sufficient influence over theworking fluid volume to sustain the azimuthal electricfield, EΘ, which is itself generated by the motionof charged species (chiefly electrons) within thedischarge volume. Therefore the magnetic field mustsupply sufficient energy to ionise the gas by meansof Ohmic (collisional) heating to reach the inductivemode.

Figure 2: Impact of discharge chamber dielectricwall thickness on incident magnetic fieldstrength

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The net magnetic field to which the propellantis exposed is heavily dependent on the distancebetween the coil surface and the gas, dictatedprimarily by the thickness of the dielectric dischargechamber. As illustrated in Figure 2, the strength ofthe incident magnetic field decreases rapidly withincreasing distance from the coil surface. Thereforethe greater the discharge chamber wall thickness,termed here td, the lower the magnitude of the netmagnetic field to which the working gas is exposed.While measurements within the discharge chamberduring operation are difficult, this variation in netmagnetic field can be inferred through observationsof the discharge transition point and the resultantsudden increases in both discharge tube and jetthermal power (as discussed in Section 3.).

3. EXPERIMENTAL FACILITY

Figure 3: IPG7 apparatus

The results presented in this paper include previouswork published by Nawaz and Herdich (2009). Whilethe experimental setup for these results is slightlydifferent to that used to produce the original resultsfor this paper, the two systems represent differentgenerations of the Inductive Plasma Generator

(IPG) program at the Institute for Space System(IRS) and thus their behaviours with respect tovariations in discharge chamber wall thickness maybe considered as equivalent.Measurements published previously were performedusing the IPG3 system, while those produced forthe purpose of this paper utilise its successor, IPG7.The two differ only in their mechanical constructionand a slight modification to their geometry (a changein discharge chamber outer diameter from 88 mmto 90 mm and a decrease in chamber lengthfrom 300 mm to 285 mm), with the associatedpower supply, resonant circuit, and other supportingsystems remaining unchanged. A schematic of theIPG7 apparatus is seen in Figure 3, with images ofthe generator and jet during capacitive and inductiveoperation shown in Figures 4 and 5 respectively.

Figure 4: Capacitive discharge (generator and jet),nitrogen

Figure 5: Inductive discharge (generator and jet),nitrogen

The IPG7 is a propellant-flexible radio-frequency(RF) plasma generator, operating at a maximumelectrical input power of 180 kW. A set of 7 capacitors(each with a capacitance of 6 nF ± 20 %) may beused to moderate the generator (capacitive) drivingfrequency between 0.5 and 1.5 MHz. For thisexperiment, 5 capacitors were connected, yieldingan operational frequency of approximately 580 kHz.The generator is connected to a 9.4 m3 vacuum tank,capable of reaching pressures of less than 1 Pawithout propellant flow. During operation, the highpropellant flow rates (in the order of 1-5 g/s) tankpressures typically reach 10-30 Pa.

The gases used within this study were argon

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and a mixture of argon and nitrogen, while resultsextracted from previous publications focused onair [10]. The combination of these gases coversboth the monatomic and diatomic propellant classes,providing useful information on their respectivepreferences. Discharge chamber wall thicknessesinvestigated within this work were between 2.2 and4.0 mm. Thicknesses from previous studies covereda range from 1.25 to 2.3 mm. It should also benoted that experiments from [10] were conductedusing a 4-capacitor arrangement, yielding a slightlyhigher operating frequency (≈ 640 kHz) than thatimplemented in this campaign. However, given thatthe variation is small and the trends with respect towall thickness largely decoupled from the operatingfrequency, the behaviour may be compared withoutconcerns over compatibility.

Measurements of the discharge transition point,jet thermal power, and discharge chamber thermalpower were performed using a combination of thecavity calorimeter [6] and thermometers integratedinto the IPG cooling circuit. An image of thecalorimeter is available in Figure 6.

Figure 6: Cavity calorimeter during operation withargon

The IPG cooling circuit and calorimeter measurethermal power in the discharge chamber and thrusterjet respectively, and may be combined to determinethe performance of a particular propellant.Given the electrothermal nature of the system, theproportion of input electrical power converted tothermal power is of particular interest, described as:

ηth =Ppl + Q̇RF

PA(1)

where Ppl is the plasma jet thermal power, Q̇RF is

the cooling power of the discharge chamber, andPA is the electrical input power at the power supplyanode. However, when considering this test platformin a thrust application, it is worth determininghow much of the thermal power generated by thedischarge is conveyed into the thruster jet. Thisis termed the effective thermal efficiency (ηth,eff ),given by:

ηth,eff =Ppl

Ppl + Q̇RF

(2)

Analyses of the flow thermal power also allow theimpact of discharge regime transitions on thrusterperformance to be assessed.

Given the different propellant configurationscompared within this paper, it is useful to assesstheir volumetric quantities so as to account for theirrespective chemical properties. A comparison isprovided in Table 1.

Table 1: Propellant volumetric comparison

Propellant Originalunits

Molarmass[kg/mol]

Equivalentflow, Ar[ln/min]

Ar 100 ln/min 40 100Ar:N2 67:41 ln/min 35 124Air [10] 2.75 g/s 29 178

This comparison assists in identifying themagnitude of influences in the experimental resultsand their possible sources.

4. RESULTS

Figures 7 and 8 display the thermal (calorimetric)powers measured within this test campaign.As can be seen, the influence of wall thicknessis substantial on the pure argon flow, with totalthermal powers both in the discharge chamberand in the resultant jet increasing with increasingwall thickness. The transition point at which theinductive conditions are reached is also reducedwith increasing wall thickness, inferring an improvedinteractivity between the inductive coil and the gasflow.Results for the argon-nitrogen mix are, though lessextreme in their variation, substantially different fromthose of pure argon. In these serials thermal

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power shows a slight decrease with increasing wallthickness, with all three variations keeping to similartransition points. This implies that, though slight,the preference for this blend tends towards thinnertubes. A further point of detachment between thetwo is the difference in magnitude of the powersmeasured, with calorimetric power for the 3.0 mmcondition almost a factor of 10 greater in Ar:N2 thanpure Ar. This increase is significantly more than thatwhich could be attributed to the equivalent volumetricflow discussed in Table 1.

Figure 7: Calorimetric thermal power for the jet anddischarge chamber (tube) utilising argon

Figure 8: Calorimetric thermal power for the jetand discharge chamber (tube) utilising theargon-nitrogen blend

In comparing these results to previously explored

conditions with air (Figure 9), it can be seen that theintroduction of nitrogen into the argon flow producessimilar trends with respect to wall thickness variation,while operation with a pure argon flow yields acompletely inverse behaviour.A comparison of visible radiation emitted by the twoconditions, as seen in Figure 10, reveals that theAr:N2 blend has more in common (visually) with apure nitrogen flow than an equivalent argon flow.Hence the dominance of nitrogen order of magnitudethermal energies is not unexpected.

Figure 9: Calorimetric thermal power for the jetand discharge chamber (tube) utilising air(adapted from [10])

Figure 10: Chamber discharge cross-sections for Ar171 kW (left) and Ar:N2 103 kW (right)

It is therefore proposed that the opposing trendsof pure Ar and Ar:N2 are linked to the nature ofchemical reactions present within the discharge,providing an additional aspect to the effectivedielectric separation of plasma and coil. A morethorough discussion of this concept conducted inSection 5.

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Figure 11: Total thermal efficiency for argon andargon-nitrogen blend

Figure 12: Effective thermal efficiency for argon andargon-nitrogen blend

Figures 11 and 12 display the total and effectivethermal efficiencies of the system respectively forthe Ar and Ar:N2 conditions. As is expected,thermal efficiency for the argon flow remains lowexcept in the case of the 4.0 mm condition wheresustained operation in the higher-enthalpy dischargemode (as opposed to short durations at the endof the power scale for 2.2 and 3.0 mm) causesa slight increase in the total thermal efficiency.However, an analysis of the effective efficiencyshows that this increase is dominated by thermalpower within the discharge chamber rather than thejet and hence the usable thermal power for thrustapplications actually decreases. This decrease is ofcourse assuming purely electrothermal thrust, with

acceleration mechanisms such as magnetic nozzlesseen as a way to make use of the greater ionisationdegrees associated with such conditions. Thesehowever are considered purely anecdotally withinthis paper.

Figure 13: Total thermal efficiency for air (adaptedfrom [10])

Figure 14: Effective thermal efficiency for air(adapted from [10])

Continuing to display discrepancies from itspure counterpart, the Ar:N2 flow maintains amarginally decreasing total thermal efficiency abovethe asymptote of 20%, with minimal variationbetween chamber thicknesses. However, theeffective efficiency shows that usable thermal powerwithin the flow is steadily increasing, with a clearpreference for the thinner chamber walls. Theseresults again show good agreement with results forair (Figures 13 and 14), with the impact of reducing

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wall thicknesses clear.

Figure 15: Discharge transition input powers forvarying gases and wall thicknesses

The gradients of thermal power and efficiencyin Figures 7 - 14 are directly dependent on thedischarge regime exhibited by the IPG. An analysisof the input electrical power required for eachtransition with respect to the varying wall thicknessesis thus displayed in Figure 15.

Transitions are separated into two distinctcategories. The first is a transition from thecapacitive mode to the first or “low” inductive mode,as discussed previously in Section 2. However,inductive plasma generators can support a numberof stable (and unstable) inductive discharges [11],thus defining the second category as transitionsbetween low inductive and high inductive operation.

Transitions to the low inductive mode for argonoccur at very low input powers (≈ 1 kW), at apoint where fluctuations in the power supply currentand potential make precise measurements difficult.However, transitions to the high inductive regimeshow clear results, with a substantial decrease inpower required for greater wall thicknesses. Themagnitude of these decreases is far greater thanthat of geometric-dependant factors such as thedischarge chamber pressure or surface to volumeratio and hence these factors may be neglected forthis analysis.Results for Ar:N2 show the increasing powerrequired to transition into the first inductive regime forincreasing dielectric separation. These results aremuch clearer than their pure argon counterpart asthe addition of nitrogen to the flow requires greater

input power to overcome pre-ionisation processessuch as dissociation and the distribution of energyinto the rotational and vibrational energy modes.In all three conditions, none achieved sufficientpower coupling to instigate a transition to the higherinductive mode. However, this transition was notexpected in the conditions chosen and usuallyrequires a higher operating frequency as well asmechanical nozzle to increase chamber pressure.Comparisons with the air conditions displaysimilarities to Ar:N2, with transitions occurring againat elevated input powers due to the wholly diatomicnature of the propellant and thus a greater quantity ofparticles required to transition through other modesof energy before achieving ionisation. Curiouslythough, while the thinnest wall condition of 1.25 mmyielded the greatest jet thermal power and totalthermal efficiency, it was not able to transitionto the higher inductive regime as the 1.45 mmcondition had. As a result, the 1.45 mm configurationdisplayed the greatest effective thermal efficiencyowing to the inherent decrease in chamber coolingpower once the higher inductive “pinching” modeis reached [6]. A possible theory to explain whyfurther decreases in the discharge wall thickness didnot continue to improve performance is detailed inSection 5.

5. DISCUSSION

Given the discrepancy in results gathered from thisinvestigation as well others previously, a theoryis required to reconcile the inconsistent behaviourrelating to variations of wall thickness within inductivedischarges. Firstly, pure argon operation displays aninverse behaviour to air and Ar:N2 flows, with higherthermal power measured when implementing thickerdischarge chamber walls. Secondly, past a givenvalue within the air investigation campaign, furtherreductions in the chamber wall thickness producedhigher thermal powers but failed to facilitate atransition to the higher inductive mode. In orderto reconcile these differences, the influences ofboth electromagnetic and thermodynamic behaviourwithin the discharge chamber must be considered.

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Figure 16: Thermodynamic and electromagneticbehaviour within the inductive discharge

Increasing the chamber wall thickness acts todecrease the net magnetic field strength to whichcharged particles within the plasma are exposed,as discussed previously in Section 3. However, thisstatement is true for all dielectric or non-conductivemedia, thus requiring consideration of thethermodynamic relationship between the dischargechamber wall and the thermal boundary layer.Consider the inductive discharge cross-section seenin Figure 16, where Q̇H is the heat flux generatedfrom the externally-applied coil magnetic field andQ̇diff,1 and Q̇diff,2 are the diffusion of thermal powerradially inwards and outwards from the skin depthrespectively.

As the wall thickness is decreased, the thermalenergy used to establish the skin depth shouldincrease owing to the greater net magnetic fieldstrength incident on the plasma. However,decreasing the tube wall also reduces the time takenfor a given quantity of thermal energy to traversethe chamber wall and reach to cooling water flowon the other side. As a result, energy flows morefreely through the discharge tube wall and a loweraccumulation from Q̇diff,2 would in turn producea lower internal wall temperature. Dischargeswithin this system are of a relatively high pressure(1000 - 3000 Pa), relying on collisions to distributeenergy within the flow. Hence a lower discharge

chamber wall temperature would in theory providea lower baseline energy for near-wall particles andextract more energy from the skin depth. As aresult, the thermal boundary layer should increase,assuming that the effect of lowering the chamberwall temperature dominates that of supplying moreenergy to the flow through the increased incidentmagnetic field strength.

If the thermal boundary layer is treated as azone of negligible ionisation degree owing to thelow local energy, then the thickness of the boundarylayer may also be considered a dielectric separationbetween coil and plasma. This is an importantassumption given that, as seen in Figure 1, electricfields across the coil surface and those generatedwithin the plasma (particularly those used to formthe skin depth) act in opposing directions. Thereforeany dielectric medium separating the two fields willhave an influence on the magnitude of the resultantazimuthal field within the plasma and the Coulombicinteraction between charged species with opposingtrajectories. The assumption of such behaviourwithin the discharge may be used to explain theresults discussed previously.

The first case considers the pure argondischarge. As can be observed in Figure 10,thermal boundary layers for argon are much smallerthan those involving nitrogen. This is due toargon’s inability to store energy in modes otherthan excitation and ionisation, as opposed todiatomic molecules’ additional processes of rotation,vibration, and dissociation. As a result, the primarydielectric separation in this discharge is produced bythe discharge chamber wall and the net magneticfield strength remains high due to charged particleproximity to the coil surface. This would explainthe observed behaviour, with the increase in wallthickness acting primarily to separate the opposingelectric (and magnetic) fields while the degree ofionisation in the skin depth region remains high dueto a small thermal boundary layer and hence highnet magnetic field strength.

The second case considers the trend ofnon-monatomic flows (Ar:N2 and air) and theirpreference of thinner walls up to a given point,beyond which discharge transitions are hinderedrather than assisted. In these situations, the theorydiscussed previously would account for thinner walls

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providing greater energy coupling by increasingthe separation between charged species within theplasma and on the coil surface. This approach wouldalso provide a possible explanation for the thinnestcondition (1.25 mm) being unable to facilitate atransition to the higher inductive mode, with theincreased thermal boundary layer crossing somepoint beyond which the net magnetic field strengthincident on the flow was inadequately paired with thegas inflow conditions. This hypothesis will form thebasis of future measurement campaigns which willfocus on the magnetic field distribution across thedischarge cross-section.

It is therefore recommended that investigationsconsidering the impact of dielectric separation withininductive plasma discharges consider not onlymechanical separations from component geometry,but also gasdynamic separations generated withinthe discharge volume itself.

This consideration is of particular importancewhen determining the desired propellantconfiguration for a particular mission. As seenthrough the results in this paper, mixtures ofdissimilar gases can exhibit strong characteristicsof a minority constituent, with strong implications onsystem performance for a given thruster geometry.As a result propellants and thruster componentsmay be chosen to take advantage of favourableperformance of a particular gas or the availabilityof a particular resource. In the context of spaceoperations, this may correlate to long-range,multi-destination missions, or those centred arounda propellant supply of varying/cyclic chemicalcomposition. The ability to react to such changesin the operational environment, or tailor a missionsimply by supplying an existing propulsion systemwith a particular propellant mixture, is an example ofIEP’s inherent flexibility and potential for future spaceoperations.

6. CONCLUSION

This paper has investigated not only the influenceof dielectric separation within inductive plasmadischarges, but also what may be considered asa dielectric medium in and around the dischargevolume. Results from argon plasmas show apreference for thicker tubes, with the necessary

power to transition to the higher inductive modedecreasing with increasing wall thickness. Resultsfor Ar:N2, as well as previous investigations forair, show a preference towards thinner tubes,with significant increases in the effective thermalefficiency of the system observed with thinner walls.This behaviour continues up until some criticalpoint, beyond which thermal energy is still producedin greater magnitude but transitions to the higherinductive mode are not observed. It is proposedthat this behaviour stems from the thermal boundarylayer within the inductive discharge behaving as anadditional dielectric separation, adding to that of thedischarge chamber wall thickness. The chamberwall thickness therefore directly and indirectlyaffects the net magnetic field strength incident oncharged particles, partially by containment within thechamber dielectric material as well as by increasingor decreasing the thermal boundary layer by meansof the time taken for thermal energy to travel throughthe chamber walls into the external cooling waterflow.

ACKNOWLEDGEMENTS

This paper would like to acknowledge contributionsmade by both the Sir Ross and Sir Keith Smith Fund(the Fund) and the German Research Foundation(DFG). The Fund supplies funding for personnelwithin this project, while DFG contributes funding forexperimental costs and equipment under Project HE4563/3-1.

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