Impact of exterior electron emission on the self-sustaining margin of hollow cathode discharge

Harbin Institute of Technology,Harbin 150001,People’s Republic of China

Abstract

Keywords:hollow cathode,self-sustained discharge,secondary electron emission,ionization oscillations,thermionic emission

1.Introduction

Down-scaled Hall thruster is one of the candidate propulsion systems for orbit entry and station keeping of low and medium orbit space vehicles [1-3].In such systems,the thrustercathode problems[4-9]will become more prominent,among which,the self-sustaining capability of hollow cathode is a crucial one.On one hand,approaching the lower limit of cathode self-sustaining current will significantly increase the extraction voltage and thus the coupling voltage.On the other hand,the cathode gas feed will occupy a quite high proportion of the total propellant consumption,however contributing little to thrust output.As a result,the total efficiency of down-scaled Hall thrusters is usually significantly lower than normally-sized ones.

Currently,the main approach of lowering the self-sustaining margin is to reduce thermal expense [10].Adopting materials with lower work function,such as BaO,can reduce the working temperature from 1600°C in LaB6cases to 1000 °C [11-13].Meanwhile,more delicate optimization of thermal design can reduce the thermal loss [11,14].These measures can lower the discharge margin from 1−2 to 0.5 A[11,12],and flow rate to 0.2 sccm [13].

This paper followed another route.The emission density of ampere level discharge is near the arc regime,in which case throttling structure is needed to provide the high-density plasma inside the inner cavity.However,when the discharge current is 1−2 magnitudes lower,the emission density is shifting to the glow regime,then a plane electrode is more suitable [15].In fact,there have been reports of constantlyheated bare emitters being used as neutralizers [16].Nevertheless,the unstable emission of such designs due to absence of gas feed can disrupt the ionization and acceleration inside the thruster.

Figure 1.Diagram of the experiment assembly.

As a compromise,if conventional orificed hollow cathodes are still used,but exterior surfaces,such as throttling orifice plates and keeper orifice plates,somehow become more emissive,can the margin be lower due to the newly added emission area? For this reason,this paper changed the materials of the orifice plates from refractory metal to LaB6and BaO,and investigated the influence on the self-sustaining margin and discharge oscillations.Section 2 will introduce the hollow cathode and diagnostics.Section 3 will show the results under different materials and section 4 will analyze the details.The conclusions are in the final part.

2.Experimental setup

2.1.Hollow cathode

The adopted hollow cathode was a LaB6emitter cathode.The cathode was heated to thermionic emission temperature,before high voltage was applied to keeper electrode to initiate the discharge.Then the discharge would transition to constant current discharge maintained by an anode power supply,as shown in figure 1.To simulate thruster-cathode coupling[17,18],the anode was 45 mm away from the cathode.All electrodes,including the negative electrode of the cathode,were kept floating throughout the experiment.

For the convenience of changing materials,the keeper orifice plate was removable.Ranking by the work functions,the investigated materials were Ta,LaB6and BaO.There was an additional test when both throttling orifice plate and keeper orifice plate were LaB6(referred to as d-LaB6in the following),so that even higher emission was achieved.

When the tests were about self-sustaining margin,the keeper was kept completely floating.This means the keeper was cut off by a switch from all other electrical connections,so that the fluctuations of keeper potential were not instrumentally affected.Otherwise,the internal filtering modules of power supplies could suppress the oscillations of keeper floating potential and smooth out the higher-frequency fluctuations,even if the power supplies were turned off.When the tests were about the absorption/emission characteristics of keeper itself,the keeper was connected to another power supply to sweep its V-I curve.The current was measured by a 0.5 Ω resistor in series with the keeper.All experiments were done without externally applied magnetic field.

To demonstrate the self-sustaining margin,the V-I curve of cathode was measured.On each point of the V-I curve,the waveforms of keeper floating potential and plume oscillations were recorded.

2.2.Temperature measurement

To estimate the thermionic emission current,the temperatures of keeper plate and throttling orifice plate were measured by a SensorWin®infrared colorimetric thermometer installed outside the flange window on the vacuum tank.Its measurement range was 700 °C−1800 °C.

Because the optical emission of the plasma could interfere with the infrared measurement,when measuring the temperature of the keeper plate,the focal point of the optical paths was set on the edge of keeper plate,which was ∼8 mm away from plume axis.However,when measuring the temperature of the throttling orifice plate,the interference could not be avoided because the optical paths needed to penetrate the plasma inside the keeper orifice.Also,as the thermometer was installed on an angle with respect to the cathode axis,the optical paths could only reach the edge of the throttling orifice plate.So the results of the latter can be of higher errors.

Given the temperature,the thermionic emission current was calculated using the Richardson-Dushman equation:

where,je,thermis the current density of thermionic emission,A is the emission area,D andφ0are the emission constant and work function of the material in [19],respectively.T is temperature,ϵ0is vacuum permittivity.E is the electric field strength near the wall surface,which is difficult to analytically calculate due to the space charge effect enhanced by thermionic emission and gas ionization.Here,it was roughly estimated using the sheath potential drop Δφand sheath thicknessLs:

in whichφsis plasma space potential,φf,kis keeper floating potential,λdeis Debye length calculated using electron temperature Teand density ne:

Except forφf,k,φs,Teand neare actually difficult to measure.This was because when discharge current was low,inserting the probe into the keeper orifice would lead to probe current being comparable to discharge current.Then high amplitude oscillations would arise and terminate discharge in a few seconds.Therefore,theφs,Teand nehere are only estimated values.The density was scaled from the measured ne=7.1×1017m-3under 4 A discharge current in [20],meanwhile Te=0.8 eV and (φs-φf,k)=5 V were kept unchanged during the scaling.

Sensitivity analysis showed that the Schottky effect was negligible in exterior regions,such as the keeper orifice plate and throttling orifice plate,because the density there was lower,the electric field strength in the wall sheath was also lower (∼6×104V m−1),and the Schottky effect could only contribute ∼10%of total emission.However,inside the inner cavity where plasma density is higher,the sheath electric field could reach (6-8)×105V m−1,and the Schottky effect could contribute 45% of total emission.

2.3.Oscillation measurement

The oscillations were evaluated by the current fluctuations on the probe,instead of those on the anode.This was because the adopted anode power supply had an internal filtering module with a ∼50 ms time constant.As the main current carriers of the discharge were electrons,saturated electron current was recorded for evaluation,instead of ion currents or space potentials.

The electron current was measured by a 1 kΩ resistor in series with the probe in figure 1.The Φ0.3×0.8 mm probe tip was inserted only 2 mm before the anode plate through a hole on it and manually biased to anode potential.In this way,the probe could interfere the plume less and the collected current signals could be similar with those on the anode.

After collection,the root-mean-square of the AC component was calculated to denote the amplitude and fast Fourier transform was performed to get the oscillation spectra.

3.Results

3.1.Exterior emission/absorption characteristics

Because the emissive keeper was a new proposal,its own absorption/emission need to be characterized first,before discussing its influence on discharge.Figure 2 shows the V-I curve of keeper electrode.Based on the sign and magnitude of the keeper current.The V-I curve could be divided into 4 regimes:over-heating regime,electron-collection regime,ioncollection regime and electron-emission regime.

When the bias was higher than the normal 3−5 V floating potential,the keeper was operating in electroncollection regime,in which amperes of electron current could be collected due to the large collection area of keeper plate.However,if the bias was higher than a critical value(12−15 V),then the collected current would slowly climb up over time,and fell in the over-heating regime.The reason for the self-boost was that the thermionic emission in the inner cavity had a negative differential resistance.As the keeper provided a constant-voltage bias,the increase in emission current and increase in the temperature(figure 3)could easily form a positive feedback.

Figure 2.Keeper V-I traces under different materials (3 sccm,4 A).

Figure 3.Keeper temperature under different bias voltage (3 sccm,4 A).

When the bias was lower than the floating potential,the keeper could only collect ∼10 mA ion current due to the heavy mass and low velocity of xenon ions.Again,when the bias was lower than another critical value(−5 V),the current could suddenly increase to several amperes,which was denoted as electron-emission regime.This phenomenon was difficult to explain because in figure 3,the temperature was too low to account for such high-density emission.We also confirmed that there was no insulation failure or mistake in electrical circuits.The reason has to remain unknown here.

The emitted/collected current formed two closed current loops.The first loop was from keeper plate to throttling orifice plate through plasma,then to the keeper bias power supply and back to keeper.The second loop was from keeper plate to anode electrode through plume plasma,then through anode power supply to the negative electrode of cathode,finally through keeper bias power supply and back to keeper.

The weight between the two loops is unknown.However,judging from the large gradient of both plasma density and component temperature before and after keeper orifice plate,the first loop should enjoy higher weight.Futuristic numerical modeling is needed to better describe the fluxes.

Note that even in the ion-collection regime,thermionic emission was still present.The emission current could be estimated by substituting the temperature in figure 3 into equation (1).Under 3 sccm,4 A discharge condition,the thermionic emission current of a LaB6keeper was ∼9 μA,which was negligible.However,a BaO keeper was emitting∼95 mA current due to its lower work function of BaO(2.06 eV) and the exponential relation in equation (1).If the throttling orifice plate was LaB6,then the emission current could be significantly increased to ∼220 mA,due to higher temperature of the plate (1350 °C).

Indeed,the thermionic emission was also related to the keeper bias,since the Schottky effect was dependent on the sheath potential drop.However,in this experiment,the keepers were all kept floating,because being electrically floating required the least circuit designs and was most engineeringly favorable.In this case,the emissive keeper was emitting electrons into the plasma on cathode exit.

Figure 4.Cathode V-I curves under different keeper and throttling orifice plate materials.

3.2.Shifting of self-sustaining margin

From the cathode V-I curves in figure 4,the margin shifted with the enhanced exterior emission,which was expected.The minimum discharge current marked in figure 4 was the lower margin that the cathode could reach.Under such value,the discharge could terminate itself in a few seconds.The discontinuity at 4 A was due to the hysteresis between increasing and decreasing discharge currents.

It can be seen that lower work function and higher temperature led to lower self-sustaining margin.The d-LaB6case could reach 0.2 A with discharge voltage stabilized between 80 and 83 V.In fact,0.2 A was still not the lowest possible margin.We could not test 0.1 A because the anode power supply limited the output voltage.Supposing the selfsustaining power remained 0.2 A×80 V=16 W still,the discharge voltage of 0.1 A discharge should be 160 V,which was beyond the 100 V output limit.But inferring from the surprisingly stable cathode plume in 0.2 A,self-sustained 0.1 A or even ＜0.1 A discharge was not impossible.

The keeper floating potential was following the changes in discharge voltage,as shown in figure 5.It was mainly between 2 and 5 V in ＞4 A discharge.In ＜2 A discharge,the keeper floating potential was inversely proportional to discharge current,reaching 53 V in 0.2 A limit.

Although the keeper electrode was spatially closer to the inner cavity,it was obviously more relevant with the anode in physics.In figure 5,despite the magnitude changes in discharge current,the potential difference between the keeper and the anode remained unchanged at 30 V.This follow-up relation could be partly attributed to the backflow of ions produced by ionization in downstream plume [20],and these reactions were ultimately powered by the anode.

Figure 5.Keeper floating potential under different keeper and throttling orifice plate materials.

Figure 6.Plume current oscillation amplitude under different keeper and throttling orifice plate materials (keeper was kept floating).

During the follow-up,the distribution of discharge power among different regions changed.Assuming that the discharge current was equal everywhere on cathode axis,and that the potential difference between the keeper orifice surface and the plasma on orifice axis was 5−6 V regardless of discharge currents,then in 4 A discharge,(35−11) V/35 V=68%discharge power was deposited in the cathode plume region.However,in 0.2 A discharge,only (83−60) V/83 V=28%was deposit in plume region,while the majority (60−6) V/83 V=65% was in the gap between throttling orifice plate and keeper orifice plate(T-K gap in short in the following text),and only 6/83=7% in the inner cavity.

Therefore,higher exterior emission current led to lower self-sustaining margin and more significant power redistribution.This indicates that for orificed thermionic emission cathode,exterior emission,especially the emission in T-K gap,was indeed the limiting factor of the reachable lower self-sustaining margin.

3.3.Oscillations statistics

Figure 7.Oscillation frequency spectra of saturated electron current in plume under different keeper and throttling orifice plate materials(a):Ta keeper plate;(b):d-LaB6 case.

Due to exterior emission,the plume oscillations were suppressed to some extent.In ＜7 A discharges in figure 6,the oscillations amplitude could decrease by 20%−50%.However,in ＞7 A discharge,the amplitude increased by 50%.In this case,the keeper temperature was increased from 740 °C to 800 °C in 10 A discharge and exterior emission current was magnitudes higher.

The frequency spectra of the oscillations in figure 7 indicated that the suppressed components were mainly 5−80 kHz ionization types.These types were dominant in tantalum keeper discharge and disappeared in d-LaB6case.These types were triggered by the irreversible electron beam loss on the cold absorbing walls of keeper electrode[20]and were present as compensation to the beam loss by exterior gas ionization.The enhanced exterior emission could share some of the compensation and ease the burden of exterior gas ionization.As a result,the total reaction rate of exterior ionization could be lower and the amplitude could also decrease.

Together with the saturated electron current,the keeper floating potential was also stabilized.As shown in figure 8,the potential oscillation amplitude dropped by 50% in ＜8 A discharge.It should be noted that,in 0.2 A discharge the amplitude was 0.2 V,which was only 0.3% of the time-averaged value 53 V in figure 5.Meanwhile,in 8−10 A discharge,the relative amplitude was 15%−45%.In other words,the stabilization effect was more significant when closer to lower selfsustaining margin.The stabilization of keeper potential meant the stabilization of T-K gap,which also happened to be the main power deposition region of the discharge.

4.Discussion

The experiment results all pointed to T-K gap.However,both diagnostics and numerical simulations of this gap were quite difficult.The discussions here are based on parametric analysis.

4.1.Outwards relocation of inner emission and ionization

The dependence of lower self-sustaining margin on exterior electron emission suggests that part of the emission and ionization processes were expanded from inner cavity to exterior regions.The detailed mechanisms were believed to be multi-physics and complicated.Here only two known and recognized effects were evaluated.

Figure 8.Oscillation amplitude of keeper floating potential under different keeper and throttling orifice plate materials.

The first effect was the throttling effect of the throttling orifice,including the thermal throttling effect related to temperature and plasma throttling effect related to plasma density [19].The discharge power dropped from 140 W in 4 A discharge to 16 W in 0.2 A discharge.At the same time,the plasma density could also reduce by 20 times if assumed proportional to discharge current.In total,the throttling effect was weakened by 8.7−20 times.

The second effect was the hollow cathode effect,which was characterized as the collision counts during electron bouncing between wall sheaths of inner cavity,which depended on the structural dimensions and sheath thickness.The sheath thickness was related to plasma density,of which the latter can be estimated by the extracted current and emitter surface area:

in which d=3 mm is inner diameter of the emitter,Te=0.7 eV.Substituting into equation (3) and assuming sheath thicknessLs≈10λde,we have Ls=0.075−0.2 mm in 0.2 A discharge,which was non-negligible to the 1.5 mm inner radius of emitter.As a comparison,in 4 A discharge the Ls=0.016−0.04 mm,which was negligible.The mean free path of electron-atom collisions was:

Table 1.Estimated emission and ionization values with and without exterior emission.

in which n0is xenon density,〈σ〉is the cross section of electronatom collision from Lxcat database[21].n0is estimated by ideal gas equation of state:

in which P0is gas pressure readout on a resistance gauge,T0is gas temperature roughly estimated as 3000 K.Substituting into equation (5),we haveλea=0.4 mm.Then the collision counts during one bounce between sheaths in 4 A discharge was:

However in 0.2 A discharge,the counts was (1.5−0.2)×2/0.4=6.5 times due to the thickening of the sheaths,reducing by 1 time.More detailed values were listed in table 1.

In reality,the two effects were coupled.From 4 to 0.2 A,the inner pressure dropped from 770 to 515 Pa (table 1).At the same time,the temperature of throttling orifice plate dropped from 1350 °C to 1190 °C.It can be noticed that the temperature dropped by 12%,while the pressure dropped by 33%,therefore it was more than thermal throttling.Plasma throttling has to be considered,in which less collision counts led to lower plasma density and weaker plasma throttling,then neutral density was even lower and so were the collision counts.

Because the self-sustainment relied highly on the highdensity plasma in inner cavity,the lowered plasma density reduced the self-sustaining temperature of emitter and then reduced the emission current.Given the 1190 °C in 0.2 A discharge,the thermionic emission current density was only∼0.1 A cm−2.Then theoretically,an emission area of 0.94 cm2could only produce 0.094 A electron current.Therefore,to maintain the preset 0.2 A current,other sources of electrons were needed,which caused the outward relocation of emission and ionization region.

4.2.Estimation of exterior emission and ionization

Because the temperature and emission of keeper orifice plate was relatively low,here we only discuss the emission of throttling orifice plate in 0.2 A discharge.Give the area 0.78 cm2and emission current density 0.1 A cm−2,the LaB6throttling orifice plate could emit ∼78 mA electron current(table 1).This means that to maintain 0.2 A discharge,additional 200−94−78=28 mA had to be supplied by gas ionization.Given the 3 sccm total gas feed,28 mA current was equivalent to 13% of ionization ratio.

In the 13% ionization ratio,the contribution of exterior ionization is determined by inner ionization.The ionization ratio of the latter is usually 10% [22],but given the outward relocation,here it was shrank proportionally with the collision counts to 10%×6.5/7.5=8.7%.Then the inner cavity could only provide 71×3×8.7%=18.5 mA,the rest 9.5 mA had to be from exterior ionization.In this case,the weight between inner and exterior ionization was approximately 2:1.

However,if considering the electron loss on keeper,the burden of exterior ionization actually had to be heavier to compensate the loss [20].The actual loss in 0.2 A discharge was difficult to determine,partly due to diagnostics restraints,partly because the electron-deposition area on the keeper was uncertain due to the negligible self-pinch in the self-generated 0.4 Gs azimuthal magnetic field,in which electrons could diffuse freely onto all surfaces of keeper plate.

As a better-than-nothing solution,we increased the keeper bias from its floating potential to 1 V higher and collected 0.043 A keeper current.Given the 0.2 V oscillation amplitude of keeper potential in figure 8,the loss current can be conservatively estimated as:

in which V1=0.2 V is the oscillation amplitude,V2=1 V is the manual bias,Ik=0.043 A is the collected current and thenIe,loss=8.6 mA.As a result,exterior ionization had to provide 9.5 + 8.6=18.1 mA and the weight between inner and exterior ionization was changed to 1:1.

Note that the exterior gas pressure was 2−3 magnitudes lower than that in inner cavity and consequently the metastable atoms were absent.Therefore,it was quite difficult for exterior ionization to achieve the same 8.7% ionization ratio as the inner cavity,especially when exterior λea=0.05−0.1 m,which was even longer than cathode-anode separation.Therefore,in exterior ionization region,high-amplitude ionization oscillations[23]and various associated instabilities[24-26]are necessary to prolong electron dwelling in the plume through local trapping [24],in order to increase the collision-induced reaction rate.However,this was possible at the cost of increasing anode voltage and destabilizing the discharge.

4.3.Impact on oscillations

The outward relocation and electron loss on keeper broke the similarity of cathode physics during condition changes,therefore the exterior ionization reaction rate and oscillation amplitude could not be proportional to discharge current.In table 1,although the discharge current dropped by 20 times,the current produced by exterior ionization remained relatively still around 20 mA.Accordingly,the current oscillation amplitude in figure 6 also remained still.As a result,the relative amplitude (i.e.oscillation amplitude versus timeaveraged current value)increased significantly near the lower margin.As shown in figure 9,from 1 to 0.2 A,the relative amplitude increased rapidly from 23% to 140%.

For standard 4 A discharge,the 140%amplitude was still manageable because the response time of inner temperature and pressure were on the scale of seconds,which were long enough for 5−80 kHz oscillations,so that the discharge was sustainable.However,for the lower margin,the 140%amplitude was capable of terminating the discharge because nearly half of the current was provided by exterior emission and ionization,the response time of the latter could not be long enough for its own oscillations.Furthermore,it can be depicted that the ＞100% amplitude would lead to transient zero current.To regain the 0.2 A current,the exterior ionization needed to achieve 100%,or even higher ionization ratio,which was difficult in the plume.Failure to compensate the current shortage for a consecutive series of oscillation periods would encourage the anode power supply to increase voltage under negative feedback.Then if the voltage reached the maximum output but the current still failed to reach the preset value,the discharge would begin to decrease current until finally terminating itself.

Therefore,suppressing oscillations is particularly important for lower margins.In this paper,the emissive materials proved effective in suppressing oscillations by compensating part of the loss on keeper.Here the compensation was evaluated by estimating secondary electron emission(SEE)current due to ion impingement onto two surfaces:throttling orifice plate and the keeper orifice plate.

Figure 9.Relative amplitude of electron current versus discharge current.

The SEE current on the downstream side of the keeper plate was:

in which γ is the SEE yield,taken as 0.11 for LaB6[27].newas taken as 5×1016m−3because discharge current was low.A′=3.11 cm2was the ion impingement area.viis the flow velocity of ions:

in which ΔVis the 30 V potential difference between keeper and anode,miis xenon atom mass.Substitutingvi=6.6×103m s−1into equation (9),the SEE currentIe,SEE=1.8 mA.

The LaB6throttling orifice plate used the same equations,with a few changes in specific values:A′ was changed to the 0.78 cm2,neto 2×1017m−3in T-K gap,ΔVto 53 V between keeper and throttling orifice plate.The new ion flow velocity was 8.5×103m s−1,correspondingly the SEE current was 2.3 mA.The total SEE current was then 4.1 mA,which was 48% of the 8.6 mA loss current.

If exterior emission and ionization were absent,which was the case of conventional cathode designs without emissive keeper or throttling orifice plates,then the results in section 4.2 would be different.In such cases,the inner cavity still provided 94 mA thermionic emission current,but the 78 mA exterior thermionic emission current and 8.6 mA loss current needed to be all passed on to gas ionization.The 86.6 mA exterior ionization was 4.78 times the requirement in d-La B6case.In such case,total ionization ratio was increased to 50% and only 50%−60% relative oscillation amplitude could terminate the discharge.In fact,in the Ta case in figure 9,only 26%amplitude was enough to terminate the 1 A discharge.

Therefore,it was the low work function that increased both exterior thermionic emission and SEE,that on one hand supplemented the current shortage due to the outward relocation of inner emission and ionization processes under reduced inner temperature and pressure near lower margin,on the other hand,eased the burden of exterior ionization and thus the amplitude of ionization oscillations by nearly 50%.As a result,a 4 A hollow cathode constructed specifically for physics experiment that went through no thermal optimization,lowered its self-sustaining margin from 1 A to 0.1−0.2 A,enabling it to directly couple with a 300−500 W Hall thruster,or a 50−80 W Hall thruster but with higher amplitude oscillations,without applying extra keeper current.This provided more options for R&D of low power Hall thrusters.

From the perspective of physics,although the results in this paper support some of the suppositions in[20],they also revealed some new problems.For instance,the mechanisms behind the follow-up relationship between keeper and anode and the redistribution of power deposition are still unclear.In addition,the fact that oscillation amplitudes are increased instead of being suppressed in high current discharge suggests that there are more physics with exterior emission.

5.Conclusion

This paper enhanced the exterior electron emission of an orificed hollow cathode by changing the materials of its throttling orifice plate and keeper plate from refractory metal to low work function materials.The results regarding the selfsustaining margins indicate that near the lower margin where discharge current was very low,the main power deposition region would migrate from downstream cathode plume to the gap between throttling orifice plate and keeper orifice plate(T-K gap);meanwhile the main thermionic emission and ionization region would also migrate from inner cavity to the T-K gap.As this gap featured low amount emission and poor discharge stability,which was actually undesirable for the self-sustainment,the source and destination of every mA current therein deserve careful treatment on the lower margin.By enhancing the electron-emission capability of the T-K gap,the current shortage due to outward relocation of inner emission and ionization processes was supplemented,while electron loss on exterior cold walls was also partly compensated to reduce oscillation amplitude.Consequently,a poorly designed 4 A hollow cathode without thermal optimization lowered its margin from 1 to 0.1−0.2 A successfully,enabling itself to directly couple with low power Hall thrusters without applying extra keeper current.Apparently,the T-K gap is of great importance to cathode behaviors near selfsustaining margins,or even the scaling of various electric propulsion devices.However,the power deposition mechanisms inside the T-K gap,as well as the negative effects of exterior emission on upper margins,still await investigations.

Acknowledgments

The authors wish to thank National Natural Science Foundation of China (Nos.61571166 and 51736003) for supporting the research.

ORCID iDs