Performance measurement and evaluation of an ionic liquid electrospray thruster

Chengjin HUANG, Jinling LI,*, Mu LI

a School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China

b Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Advanced Material Diagnostic Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China

KEYWORDS Electrospray thruster;Ionic liquids;Performance measurement;Performance estimation;Micro-propulsion

Abstract As a novel micro-propulsion system for small satellites (from micro to nano), the ionic liquid electrospray propulsion system is a promising candidate.However, performance measurement and evaluation of the Ionic Liquid Electrospray Thruster(ILET)is one of the most challenging issues for practical application, due to the difficulties in the development of a prototype and direct measurements of micro-thrust and small flow rate.To address this issue, a Modular Ionic Liquid Electrospray Thruster(MILET)prototype is constructed,and a diagnostic system for thrust and mass flow rate is specially developed based on an analytical balance method.With the ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate as the propellant, a series of experiments is carried out on the MILET prototype under a wide operating condition through changing the applied voltage to control the thrust.Under different applied voltages,the thrust and the mass flow rate of the propellant are directly measured.The propulsive performance parameters of the thruster,such as thrust,specific impulse,thrust-to-power ratio,thruster efficiency,etc.,are comprehensively analyzed.Then, a performance comparison is made between the MILET and other representative ILETs.With a relatively low applied voltage ranging from 1550 V to 2000 V,the MILET achieves a quasi-constant specific impulse of 1263 s with the averaged thrust-to-power ratio of 65.2 μN/W and thruster efficiency of 40.7%.The performance of ILET is also compared with other typical electric propulsions.The results demonstrate that the ILET exhibits an excellent ability of minimalization with high specific impulse and thruster efficiency, which guarantees a great superiority in micro propulsions.Finally, the ways to further improve the performance of ILET are discussed, which further confirms the potential prospect of ILET.The present result helps to advance the development and application of ILET.

1.Introduction

The Ionic Liquid (IL) is a low-melting salt that melts at or below 100 °C, which is normally composed of a large asymmetric organic cation and an inorganic or organic anion.1As environmentally friendly solvents and functional materials,ILs have gained increasing attention in space technology.2In view of the unique and favorable properties of ILs,such as its nonvolatility and large electric conductivity, the idea of using ILs as electrospray propellants was firstly proposed by Ferna′ndez de la Mora.3The basic operating principle of Ionic Liquid Electrospray Thruster (ILET) is similar to that of the field emission electric propulsion.In the ILET, a high voltage is applied between the ionic liquid and the extraction electrode.Under the intense electric field, a conical structure, typically referred to as the Taylor cone, is arisen on the liquid surface to produce the charged species.These charged species are accelerated by an electrostatic field to generate the thrust.In 2001, Gamero-Castan?o and Hruby3experimentally demonstrated the feasibility of the IL 1-ethyl-3-methylimidazolium bis (trifluoromethylsulfonyl) imide and its mixtures as propellants for electrospray thrusters, using a hollow needle to anchor the electrospray and produce particles for electrostatic propulsion.In 2003,in the context of space electric propulsion,a joint investigation4was carried out by the researchers in Yale University and Busek company.Romero-Sanz et al.4experimentally indicated that ILs could achieve pure-ion emission,forming the basis for high-quality electrospray ion sources.Since then, the continuous efforts have been made to develop the ILET for space propulsion.5–7

For a propulsion system applied to space mission, thrust and specific impulse which provides an estimation of the utilization efficiency of propellant are deeply concerned.Furthermore, other performance parameters, such as the thruster efficiency and thrust-to-power ratio, are also important for electric propulsion system.Theoretically, the ILET has excellent potential performances, such as high specific impulse(1000–6000 s), high thruster efficiency (30%–90%), and accurate thrust output (several micronewtons to hundreds of micronewtons for a single thruster).8–10Meanwhile, multiaspect miniaturization capabilities in size, power, and weight makes the ILET exactly suitable for utilization in the micropropulsion system of micro/nano satellites.However, in order to satisfy the particular and harsh requirements raised by complicated missions of micro/nano satellites and develop a highperformance ILET in practice,a large number of scientific and engineering problems need to be solved,in which performance measurement and evaluation of an ILET prototype is one of the most important issues.

For the sake of experimentally investigating propulsive performance,it is necessary to firstly develop an ILET prototype,which is a great challenge.In the past two decades, even though a large number of theoretical and numerical works have been carried out to better understand the physical process of ILET,4,5,7,11the ILET prototype has been successfully developed by only a few institutions.12–19A MEMS-based ion Electrospray Propulsion System (iEPS)12,13with the specific impulse of ～760 s was developed by the group of Lozano in Massachusetts Institute of Technology (MIT).Then, the prototype of Tiled Ionic Liquid Electrospray engine(TILE)14,15was further developed from the iEPS by Accion Systems company, with the specific impulse of TILE up to 1650 s.Natisin and Zamora16in the US Air Force Research Laboratory also developed a laboratory prototype of ILET with the measured specific impulse of 1436 s, which is designated as the Air Force Electrospray Thruster Series 2(AFET-2).16,17In addition, the ILET demonstrator named BET-300-P18,19was developed by Busek company, of which the specific impulse is 850 s.In the last five years,the research on the ionic liquid electric propulsion has been initiated and rapidly developed in China.Liu et al.20studied the fabrication of ILET and performed a voltage-current measurement.Guo et al.21designed an actively supplied ILET with a specific impulse of 250-315 s.Chen et al.22developed a porousceramic-based ILET, which emitted 350 μA current under the applied voltage of -3600 V.The ILETs in the Refs.20–22usually operate under a relatively high applied voltage above 2000-3000 V.In our previous work23,24, the onset process of electrospray was experimentally investigated and the continuous efforts makes the onset voltage of the ILET prototype as low as 740 V.However, the direct measurement of propulsive performance for the ILET prototype remains to be carried out.

The thrust produced by the ILET is usually in a scale of several micronewtons to hundreds of micronewtons, which is so tiny that it is easily blurred by the environment.Hence,direct measurement of thrust produced by the ILET is also a great challenge.Several methods have been adopted to directly measure micro-scale thrust of ILET, including the torsional balance, the magnetically levitated balance, and the mass balance.13,17,19,25,26Legge and Lozano25measured severalmicronewton thrust of an array emitter by a torsional balance of Busek company.A torsional balance was also used by Natisin et al.17to measure the thrust of AFET-2.The thrust of iEPS was measured by several instruments, including a torsional balance, a magnetically levitated balance, and an indirect calculation by the Time-of-Flight (ToF) spectrometry.13Courtney et al.26directly measured the thrust of an ILET by a mass balance, and indirectly calculated the thrust by integrated use of the ToF spectrometry and the retarding potential analyzer.It was found that accurate estimation of the thrust by the ToF spectrometry requires more extra information,including neutral species, energy deficits, and the angular beam distribution, etc.The thrust of BET-300-P was also measured with a mass balance by Fedkiw et al.19.Even though the torsional balance is a frequent method to measure the thrust with a sub-micronewton resolution, specific impulse cannot be insitu measured.The specific impulse of the ILET is also not available by magnetically levitated balance.Hence, the mass balance is a desirable device to measure the thrust and specific impulse of ILET, simultaneously.

The specific impulse is defined as the impulse produced by unit-weight propellant.The calculation of specific impulse requires that both the thrust and the mass flow rate of propellant be measured.As direct measurement of mass flow rate is quite difficult, only the thrust was directly measured in many investigations, while the specific impulse was not involved or only indirectly estimated.8,17,25–27The indirect calculation of mass flow rate typically by the ToF spectrometry is prevalent.13,28–30Petro et al.14indirectly evaluated the specific impulse of TILE by the ToF spectrometry.As a result of ignoring neutral species,the value of specific impulse obtained by the ToF spectrometry is thought to be overestimated to a certain extent.Natisin and Zamora16measured the specific impulse of AFET-2 both by the ToF spectrometry and mass loss methods.However, the results obtained by the two methods show an enormous difference, which is attributed to the neutral species in the plume.Even though the direct measurement of mass flow rate is expected to provide more actual performance,it is still a difficult problem.Most emitters in ILETs are fabricated from porous materials, in which the propellant is usually passively supplied without the external supply line,and the mass flow rate is only with the order of micrograms per second.Thus, neither the methods to measure the mass flow rate based on the pressure difference nor the displacement of meniscus in the capillary is suitable.The mass loss before and after installing the thruster to the vacuum has been used to calculate the specific impulse by Krejci et al.13.However,this procedure may produce a significant error, due to the materials outgoing and gas adsorption.An electric lifting platform was further introduced by Courtney et al.to let the insitu measurement of mass loss available.18,19Especially, in the ILET, a part of species are intercepted by the electrode,and the intercepted current may be up to several percent.While the propellant is consumed, the intercepted species will not reduce the mass of system,which may lead to a significant error.Although the mass loss of system should not contain the mass of intercepted species, the intercepted mass was not considered in previous works.13,18,19

Besides the measurement of the propulsive performance, it is crucial to estimate propulsive performance within operating range of thruster for practical applications.Since the ILET is controlled by the applied voltage8,26, propulsive performance parameters should be functions of the applied voltage in theory.5,26However, the variation of propulsive performance parameters with the applied voltage have been rarely experimentally evaluated for the ILET prototype or only indirectly calculated without full consideration of neutral species,energy deficits,and angular distribution.Rovey et al.31,32assessed theoretical performance of ionic liquids and their mixtures as electrospray propellant, including the specific impulse, the thrust and the thrust-to-power ratio.Nevertheless, only the specific impulse was discussed as a function of the accelerating voltage.Krejci et al.13estimated specific impulse of ILET over a wide range of emitted current by ToF spectrometry; however, the specific impulse and thruster efficiency were only directly measured in an average of the whole operation, and the variation of specific impulse and thruster efficiency on the applied voltage was not explored.Furthermore, Courtney et al.18measured the specific impulse and thruster efficiency of BET-300-P in several current levels, which showed that the values of specific impulse and thruster efficiency decrease with the increase of emitted current.How comprehensive propulsive performance parameters vary with the applied voltage still needs to be studied.

In this work, a Modular Ionic Liquid Electrospray Thruster (MILET) prototype has been developed and the comprehensive performance of the MILET is evaluated and discussed.The paper is organized as follows.In Section 2,the experimental system as well as the methods to measure the thrust and mass flow rate are introduced.In Section 3,the experimental results are presented and discussed, in which four sub-sections are divided.Section 3.1 shows the operation of the thruster.Section 3.2 demonstrates the propulsive performance parameters, such as thrust, thrustto-power ratio, specific impulse, and thruster efficiency.Section 3.3 compares the experimental performance parameters of the MILET with other typical ILETs and other micro propulsions.Section 3.4 further discusses the ways to improve the performance of ILET.The paper closes with drawn conclusions in Section 4.

2.Experimental system and methods

2.1.Experimental setup and procedures

As illustrated in Fig.1(a),the experimental system is composed of a high voltage power supply system,a data transmission and acquisition system, the MILET, a vacuum chamber system, a balance system (readability of 0.01 mg, sampling rate of 1 Hz), and a computer to store and handle data.The power system is controlled by a function generator (Rigol,DG1022Z)to achieve bipolar high-voltage output with a specific waveform.As sketched in Fig.1(b),the MILET is equipped with an array emitter with 729 tips in an area of 1.69 cm2.The emitter is fabricated from the porous metal, and more details can be found in Ref.24.The MILET is installed on the thrust measurement platform, which is placed on the weighing pan of the balance.The weighing pan and the MILET are screened by an electrostatic shield to eliminate the disturbance of high voltage.The platform can be vertically moved up and down driven by an electric lift.Thus, the thruster can be loaded and unloaded from the thrust measurement platform without breaking the vacuum environment.The charge of plume produced by the thruster is collected by a charge collector and measured by a pico-amperemeter(Keithley,6485).The current exhausted from the thruster is referred to as the collected current Icol, while the current intercepted by the extraction electrode is designated as the intercepted current Iint.The intercepted current is measured by monitoring the potential drop along a 100 kΩ resistor.The balance is controlled and recorded by a lab-constructed wireless communication system.The readings of the balance are recorded in real-time.

The properties of propellant, ionic liquid 1-ethyl-3-methylimidazolium tetrafluoroborate ([EMIM][BF4]), are listed in Table 1.33,34The propellant is exposed to the vacuum environment to remove any volatile impurities.Then,the emitter is soaked in an ionic liquid tank for several hours, and the reservoir of the MILET is also filled up with the propellant.After filling the propellant, the MILET is installed on the thrust measurement platform.Two thin copper wires are used to connect the thruster with the fixed points that are further connected with the high-voltage supply.The copper wires are fine enough that the change of the balance readings is typically 0 mg or less than 0.03 mg at the worst condition after and before reloading the thruster.After all equipment installed,the vacuum chamber is pumped to a low vacuum condition to further remove volatile impurities in the system.After maintaining the low vacuum condition for half to one hour,the vacuum chamber is further pumped below 3×10-2Pa.The balance is preheated for more than 24 h.Then, the balance is internally calibrated.In the whole measurement process,the calibration will be performed again once the change of environment exceeds the allowable value in accordance with the balance requirement.After the preparation finished, bipolar high voltage is applied to the thruster.As shown in Fig.1(c),the high applied voltage is bipolar square wave with a period of 60 s.In every cycle of the applied voltage,the duty ratios α of positive and negative polarities are both 25% of the period.As listed in Table 2, a total of five cases are conducted,two of which measure the mass flow rate.The cases are numbered from 1 to 5 in chronological order of experiments.The operating time for a voltage amplitude is 5 min for Cases 1, 3 and 5, in which the thrust is measured, but the mass flow rate of the propellant is not measured.When the mass flow rate is measured,the operating time is about 20–30 min at least for a voltage amplitude to accumulate a significant mass loss.In every case, several voltage amplitudes are applied.The amplitude ranges of positive and negative applied voltage to be tested are also listed in Table 2.All the measurements are conducted on the same thruster.The systematic errors and random errors are both considered by the error theory to estimate the error of parameters.The error bars in the paper are plotted with the estimated error values.

Table 1 Properties of propellant (25 °C).33,34

2.2.Measurement of thrust

In every cycle with a period of 60 s, the polarity of applied voltage is switched between positive and negative with a zero-voltage interval of 15 s.As shown in Fig.2, the thrust is measured through the change of the balance reading between the on-duty period and the zero-voltage interval.Thus, the thrust F can be calculated by the following expression

2.3.Measurement of mass flow rate

Fig.2 schematically illustrates the principle of measurement of mass flow rate.The balance readings have a small drift even though the thruster is not in operation, which is attributed to the natural drift of the balance and the outgoing of the system materials in vacuum.As a result,the total drift rates of the balance reading are measured before and after every operation as (˙m0)befand (˙m0)aft, respectively, and their averaged value is be used to compensate the mass flow rate of propellant.As the intercepted mass by the extraction electrode will not affect the mass of the system, the mass loss Δm in the duration Δt contains the mass of propellant exhausted from the thruster and the drift.Supposing that the ion beam is uniform, the charge-to-mass ratio of the intercepted species will be the same as the exhausted species.Consequently, ignoring neutral species produced in the emission process (i.e., the ionization efficiency is assumed to be 1, seeing Appendix A), the total mass flow rate of the consumed propellant is equal to the exhausted mass flow rate divided by the transmission efficiency.Based on these considerations, the mass flow rate can be calculated by the Eqs.(2)–(3).

Fig.2 Schematic diagram of measurement of thrust and mass flow rate.

where ˙mextrepresents the mass flow rate of propellant exhausted from the thruster, α is the duty ratio, and ˙mtis the mass flow rate of consumed propellant.

3.Results and discussion

3.1.Operation of MILET prototype

3.1.1.Voltage-current characteristic

In every test, the applied voltage amplitude is gradually increased, and the variations of current and thrust produced by the MILET are recorded with the applied voltage.Taking as an example, the applied voltage in Case 3 is displayed in Fig.3(a) and the corresponding collected current Icolas well as the intercepted current Iintare plotted in Fig.3(b).As show in Fig.3(a), the amplitude of applied voltage is gradually increased.The polarity of applied voltage is periodically switched, which is referred to as bipolar operation.Accordingly, the collected and intercepted currents in Fig.3(b) are periodically switched between positive and negative current.Fig.3(c) presents the measured transient thrust.Since the thrust is forced in a same direction, the transient thrust in Fig.3(c) is always positive.Fig.3(d) shows the collected current and the applied voltage varying with the time when the emission is initialized.In Fig.3(d),the applied voltage is manually adjusted to acquire the onset voltage of the MILET.As the applied voltage increases,the critical voltage where the significant collected current is detected is taken as the onset voltage, which is 1320 V in this case.Fig.3(e) demonstrates the MILET’s thrust output responding to the collected current,which shows that a stable bipolar operation is successfully achieved by the MILET.As the maximum sampling rate of the balance is 1Hz, the overshoot and high frequency component of collected current are not responded in the signal of thrust.The higher frequency components of the thrust do not affect the results and discussion of this work.

In every case, all the direct data measured under the same commanded applied voltage are time-averaged values in positive-polarity operation and negative-polarity operation,respectively.In this manner, the applied voltage Uapp, the collected current and the intercepted current are computed varying with the time.Based on the variation of the applied voltage and the emitted current with the time, the voltage-current characteristics of the MILET can be obtained.The emitted current Iemiis the sum of the collected current and the intercepted current.The voltage-current curves of all five cases are plotted in Fig.4 (a), and the voltage-current characteristic for Case 5 is drawn separately in Fig.4(b).In the initial stage of the thruster operation (i.e., Case 1), the emitted current ranges from 6 μA to 198 μA, while the applied voltage is increased from 1100 V to 1490 V.In the later stage(i.e.,Cases 2–5), the voltage-current characteristics are similar.The emitted current ranges from 10 μA to 140 μA, when the applied voltage is varied from 1420 V to 2000 V.To obtain the same emitted current,the applied voltage in Case 1 is approximately 500 V lower than those of Cases 2–5.Referring to the spacecharge model put forward by Mair35, the results of Case 1 are fitted to be Eq.(4), and the coefficient of determination R2is 0.934.In Cases 5, when the emitted current is less than 40 μA, the voltage-current curves are fitted to be Eq.(5).As the applied voltage increases, the voltage-curve is fitted to be Eq.(6).

Fig.3 An example of thruster’s operation and measured results.

Fig.4 Measured emitted currents varying with applied voltage and fittings of voltage-current curves.

Even though the emitted current is increased with the applied voltage for all cases, the voltage-current characteristic of Case 1 is obviously different from the others, which is because that the emission of propellant is closely related to the flow impedance of ionic liquid at the tip of the emitter.Theoretically, the current is proportional to the square of the applied voltage as fitted in Eq.(4), if the flow impedance is ignored.35The agreement between the experimental results and the theoretical prediction by ignoring the flow impedance suggests that the propellant is well supplied in Case 1.As observed in our previous work24, after soaking the emitter to the ionic liquid tank, a liquid film covers the surface of the emitter tip, which significantly reduces the flow impedance.However,the supply with a low flow impedance is not durable.As the liquid film on the surface of emitter is sapped or even destroyed with the operation of the thruster, the flow impedance will gradually increase and the effect of flow impedance on the current–voltage characteristics cannot be ignored any longer.As shown in Fig.4 (b), the prediction by the model with the flow impedance ignored is only suitable for the initial rise of the experimental curve, i.e., in the range of the emitted current less than 40 μA.In the later stage of thruster operation when the emitted current is greater than 40 μA, the emitted current is proportional to the square root of the applied voltage, instead of the square of the applied voltage.The similar phenomenon was observed in liquid metal ion sources by Mair35, in which the flow impedance was taken into account to modify the original space-charge model.As a result, it is a critical issue to keep a stable propellant supply in order to achieve a long-time stable operation with consistent performance.

3.1.2.Transmission efficiency

The transmission efficiency ηtris calculated by the ratio of the collected current to the emitted current.The variation of transmission efficiency in Cases 1–5 with the applied voltage is shown in Fig.5,where the results of different cases are not separately labeled.The transmission efficiency in positive-polarity operation shows a similar trend with that in negative-polarity operation.When the applied voltage is lower than 1800 V,the transmission efficiency of the MILET is generally greater than 90%, with the highest transmission efficiency up to 96.8%.However, with further increasing the applied voltage, the transmission efficiency has a significant drop.The transmission efficiency in Fig.5 can be roughly fitted by the expression of Eq.(7).

It is inferred that the drop of transmission efficiency mainly results from the amplification of the divergence angle of the ion beam in the accelerating electric fields.As the decrease of transmission efficiency results in the decay of propulsive performance for ILET, a higher transmission efficiency is desirable to enhance the thrust and reduce the sputtering erosion to the extraction electrode,which can be achieved by fully unitizing the ion beam.

3.1.3.Mass flow rate of propellant and charge-to-mass ratio

Supposing that all the charges of exhausted species are collected by the charge collector,the exhausted current is thought to be the same as the collected current.Fig.6 plots the variation of the mass flow rate of plume with the exhausted current Iext, where the exhausted species are those species that fly out of the thruster.Since the exhausted mass flow rate of species in positive and negative polarities cannot be distinguished,the demonstrated mass flow rate in Fig.6 is the averaged values in positive and negative polarities.From Fig.6, the mass flow rate of exhausted species linearly increases with the exhausted current, which can be well fitted by the function ˙mext=0.00929×Iextwhile the coefficient of determination R2=0.974.

On the basis of the measured collected current and exhausted mass flow rate, the charge-to-mass ratio and degree of solvation can be further analyzed.The charge-to-mass ratio is defined as the ratio of charge to mass of species, and thus it can be calculated by Eq.(8).

where Δmextdenotes the mass of propellant exhausted from the thruster in the duration of Δt.Representing the ionic liquid as A+B-, the emitted species are [AB]nA+in positive-polarity operation and [AB]nB-in negative-polarity operation, where n is the degree of solvation and [AB]ndenotes the clustered species.Assuming that all cations and anions are emitted and the values n for species in positive and negative polarities are the same, the averaged charge-to-mass ratio is derived as in Eq.(9).denote positive polarity and negative polarity, respectively.From Fig.7, the averaged qmand n are (108.6±4.5) C/g and 4±0.2, respectively.

Fig.6 Variation of mass flow rate of plume with exhausted current.

Fig.7 Charge-to-mass ratio and degree of solvation varying with applied voltage.

The charge-to-mass ratio and degree of solvation are closely related to the emission status of the thruster.The species are usually monomers (with n = 0) and dimers (with n = 1)with a small proportion of trimers(with n=2)when the emission is in pure-ion mode.36As the averaged n is 4, it can be inferred that the emission of the MILET is in ion-droplet mixed mode with a small amount of droplets, resulting from the coexistence of jet breakup and ion field-evaporation.37In the MILET where the propellant is passively supplied, the mass flow rate of propellant augments as the applied voltage increases.Since the droplet current I and mass flow rate ˙m show a scaling law of I ∝ ˙m1/2,38the charge-to-mass ratio will decrease with the increase of applied voltage,which is contrary to the experimental results.As the charge-to-mass ratio keeps approximately a constant with the variation of the applied voltage, it can be further deduced that the emission of propellant in the MILET is in a near pure-ion mode, because the charge-to-mass ratio can maintain a constant, once approaching the pure-ion mode.4

To validate the possibility of pure-ion emission in the system, the maximum normal electric field Ekon the surface of Taylor cone is evaluated by a well-known expression of Eq.(10).37,38

where γ is the surface tension, K is the conductivity, ε0is the dielectric permittivity of vacuum,Q is the volumetric flow rate of Taylor cone.Considering 90% emitter tips12, i.e.656 tips,are emitting,the Ekis calculated from the measured mass flow rate of emitted propellant to range from 2.1 V/nm to 1.7 V/nm when the applied voltage varies from 1550 V to 2000 V.The calculated Ekis much greater than a usual critical electric field ～ 1 V/nm for ion evaporation dominance38.Consequently, it is suggested that the MILET operates a near pure-ion mode, and the ionic species are almost unchanged along with the adjustment of applied voltage.

3.2.Propulsive performance

3.2.1.Measurement and prediction of thrust

Fig.8(a) shows the thrust varying with the applied voltage.The variation trend of thrust with the applied voltage is similar to that of current with the applied voltage.In Case 1, the thrust increases from 1.2 μN to 23.1 μN as the applied voltage increases from 1100 V to 1490 V.In Cases 2–5, the thrust ranges from 2 μN to 14.2 μN, when the applied voltage varies from 1400 V to 2000 V.The obvious difference between Case 1 and Cases 2–5 in the voltage-thrust characteristics results from the distinguished voltage-current characteristics.As shown in Fig.8(a),even though the thrust is almost linear to the applied voltage, there are different slopes for different cases and there is also a nonlinear trend.

To predict the thrust produced by ILET for practical application, it is necessary to characterize the thrust with more easily measured parameters, such as the current and the voltage.The thrust F of the ILET can be expressed as follows:

where Uaccis the accelerating voltage.As discussed in Appendix A,ηθ,ηpand ηemidenote the angular efficiency,the polydisperse efficiency and the emission efficiency, respectively.The angular efficiency accounts for the loss of non-axial velocity.The polydisperse efficiency is defined as the ratio of the thrust power to the kinetic power.The emission efficiency measures the voltage loss in the emission process.Consequently, the thrust is expected to be proportional to the collected current and the square root of the applied voltage.By defining the efficiency coefficient Ceand thrust coefficient Cfas in Eq.(12)and Eq.(13), respectively, the thrust can be characterized by Eq.(14).

Fig.8 Characteristics of thrust varying with applied voltage.

3.2.2.Thrust-to-power ratio

The thrust-to-power ratio is defined and calculated as the thrust per unit power consumption, which is a key parameter to evaluate the propulsive performance of the ILET,as the size and weight of the power system are limited for micro propulsion.According to the definition, the thrust-to-power ratio of ILET is calculated and further evaluated as follows,where Pinis the input power.Fig.9 shows the thrust-to-power ratio varying with the applied voltage.In Case 1,the thrust-topower ratio ranges from 178 μN/W to 78 μN/W when the applied voltage is located in the interval of 1100 V to 1490 V.In Cases 2–5, the thrust-to-power ratio varies from 115 μN/W to 51 μN/W, and the averaged thrust-to-power ratio is (71.7±12) μN/W.For all Cases 1–5, the thrust-topower ratio decreases with the augmentation of applied voltage.However, the thrust-to-power ratio of Case 1 is much greater than those of Cases 2–5.The difference between Case 1 and Cases 2–5 in thrust-to-power is caused by the change of emission states during the operation, which is essentially attributed to the raise of flow impedance at the tip of the emitter.

Substituting the Cf=3.14 mN/(AV0.5)and Eq.(7)into Eq.(15), the theoretical results are obtained and plotted in Fig.9.In Cases 2–5, the theoretical values of thrust-to-power ratio agree with the experimental results.However, in Case 1, the theoretical results are much smaller than the experimental ones,which suggests that the thrust coefficient Cfof Case 1 will be much greater than the overall fitting value of 3.14 mN/(AV0.5).

3.2.3.Specific impulse and thruster efficiency

The capability and efficiency of both propellant and thruster are measured by the specific impulse Isp.Based on the definition, the specific impulse can be computed by Eq.(16).Integrating Eq.(14) into Eq.(16), the specific impulse can be further expressed by Eq.(17).

Fig.9 Variation of thrust-to-power ratio with applied voltage.

where Δmtis the consumed mass of propellant,and ηionis ionization efficiency defined in Appendix A.Based on Eq.(16),the specific impulse is calculated as the averaged value of both positive and negative polarities by the mass of consumed propellant and the total impulse.Fig.10(a) summarizes the computed specific impulse varying with the averaged applied voltage.As shown in Fig.10(a), in the tested applied voltage range of 1550 V to 2000 V, the specific impulse keeps almost a constant, and the averaged specific impulse is (1263±147)s.According to Eq.(17), the quasi-constant specific impulse is mainly contributed to the maintenance of charge-to-mass ratio, and the product of ηtrηionCeshould have a reduction as the applied voltage increases, which means greater losses of the thruster.

The thruster efficiency is generally analyzed to evaluate the total efficiency of an electric thruster.The thruster efficiency ηtis defined to be the ratio of the thrust power Pthrustto the input power Pin, i.e., Eq.(18).Substituting the definition of various efficiencies to Eq.(18),the thruster efficiency can be written to Eq.(19) as detailed in Appendix A.

where ˙mtis the mass flow rate of consumed propellant.Based on Eq.(18),the thruster efficiency is computed and summarized in Fig.10(b).The averaged thruster efficiency is(40.7±8.6)%.As shown in Fig.10(b), the thruster efficiency has a decreasing trend with the increase of applied voltage,which is mainly attributed to the decline of transmission efficiency as expressed in Eq.(19).

3.2.4.Performance map of thruster

High specific impulse of electric propulsion guarantees the efficient use of propellant at the cost of electric power consumption.Higher thrust-to-power ratio of electric propulsion means a better thrust capability with the same electric power consumption.Higher thruster efficiency guarantees more efficient utilization of propellant and electric power.The relationship among specific impulse, thrust-to-power and thruster efficiency are given by Eq.(20).

3.3.Performance comparison of ILETs and other types of micro thrusters

Fig.11 Performance map of MILET.

Fig.10 Economic parameters of MILET.

Table 3 Typical performance of ILET prototypes.

To assess the performance status of MILET prototype, the performance of the MILET is compared with other representative ILETs.The typical performance of the MILET with[EMIM][BF4] as propellant is listed in Table 3 and compared with other representative ILETs.The onset voltage of the MILET is moderate among these four ILET prototypes,while that of the TILE is the lowest.The operating voltage is below 2000 V for all these ILETs, except that of BET-300-P.The lower voltage is beneficial for the miniaturization and reliability of power system.The thruster size of the MILET is larger than that of TILE, but smaller than that of other ILETs.The thrust density is computed by the thrust over emission area.The emission area is taken as the plane area of the emitter chip,which is smaller than the thruster size.The typical thrust density of these ILETs is ranged from 8 μN/cm2to 12.5 μN/cm2,and the thrust density can be extended to 25 μN/cm2for AFET-2 when the thruster is operated with the maximum thrust.The performance parameters of MILET, including thrust-to-power ratio, specific impulse,and thruster efficiency,are evaluated for the whole operating range of applied voltage 1550 V to 2000 V.The TILE performs the highest thruster efficiency, resulting in a higher specific impulse with a similar thrust-to-power ratio with that of MILET.The thrust-topower ratios of BET-300-P, MILET and TILE are approximately at the same level.The specific impulses of AFET-2,MILET and TILE are much greater than 1000 s.However,due to the relatively low thruster efficiency, BET-300-P and AFET-2 fail to achieve high specific impulse and high thrustto-power ratio at the same time.With a higher thruster efficiency of 40.7% than that of BET-300-P and AFET-2, the MILET achieves a relatively high thrust-to-power ratio and specific impulse, simultaneously.From the discussion above,although there is some performance gaps between the MILET and the TILE, the performance of MILET is comparable to other representative ILETs.

Due to the great need for micro-propulsion,a large number of thrusters based on different principles have been developed.As the specific impulses of cold gas thruster and chemical thruster are much less than that of most electric thrusters,the ILET is compared with other electric propulsions.Fig.12 summarizes the performance of several types of electric propulsions, including ion thruster, Hall thruster, resistojet thruster, Pulse Plasma Thruster (PPT), Field Effect Electric Propulsion (FEEP).The selection of these thrusters and data collection are from Refs.39–47and webpages48,49.The data of ILETs are collected from the references in Table 3.It is noted that Fig.12 aims at generally analysis of various micropropulsion types rather than at a complete collection.Fig.12(a)plots the map of thrust-to-power ratio and specific impulse with different values of thruster efficiency.Fig.12(b)shows the core area and power (P) of every thruster, in which the core area is selected as the sectional area of a thruster without the Power Processor Unit (PPU) and any additional storage.The resistojet thruster heats the propellant by electric power,and the fluid is accelerated by hydrodynamics.Thus,the specific impulse of resistojet is also smaller than 200 s.By ionizing the propellant to be plasma and accelerating the ions by electromagnetic field, conventional electric thrusters, such as the ion thruster and the Hall thruster, achieve a higher specific impulse, which can be much more than 1000 s.Using liquid metal as propellant, the FEEP can achieve a high specific impulse as large as 6000 s.However, if the size of ionization region is further miniaturized, the thruster efficiency of the ion thruster and the Hall thruster drops dramatically41.As illustrated in Fig.12(b), the ion thruster, the PPT, the FEEP,and the ILET have a better capability of minimalization.Nevertheless, as shown in Fig.12(a), the thruster efficiency of the ion thruster and the PPT is less than 20% and even less than 10% for some prototypes.The thruster efficiency of MILET along with other ILETs can be more than 40%.In addition,the applied voltage of the ILET is much lower than that of the FEEP, which greatly reduces the requirement for the power supply.It is obvious that the ILET exhibits an excellent ability of minimalization with high specific impulse and high efficiency, and consequently could better meet the propulsive requirement of micro/nano satellites50,51.

3.4.Ways to improve ILET’s performance

Even though the performance of ILETs is excellent in present,compared with chemical propulsion and other electric propulsions discussed in the Section 3.3, there is still a strong necessity and huge space to improve.The ways to further improve the performance of ILETs are discussed below.

Fig.12 Performance of various miniaturized thrusters.

Fig.13 Ideal vs experimental specific impulses of [EMIM][BF4].

Assuming that the thruster efficiency is 100%, the ideal specific impulse of ionic liquid is derived in Appendix B and plotted in Fig.13 for [EMIM][BF4].With the same applied voltage, the experimental specific impulse ranges only from 1000–1400 s, while the ideal specific impulse in theory is as high as 5000–6000 s.Since the actual performance is still far below the levels of ideal performance,there is a huge space for the improvement of specific impulse.The specific impulse can be increased in several ways.Firstly, as shown in Fig.13, the specific impulse is theoretically expected to increase with the applied voltage.However, the discharge risk and the decay of thruster efficiency in the ILET may limit the applied voltage to further increase.Multi-stage acceleration is a method to further increase the accelerating voltage.Secondly, reducing the value of n (i.e., degree of solvation) can improve the specific impulse significantly.Thirdly, it is necessary to reduce various losses in the thruster, such as angular loss, transmission loss,and especially the polydisperse loss.As the polydisperse efficiency can be as low as 53%13, the polydisperse loss may be dominant in the ILET.

4.Conclusions

The direct measurement and evaluation of propulsive performance are important for the ILET’s development and application.A MILET prototype is developed in Northwestern Polytechnical University.A diagnostic system based on an analytical balance method has been constructed to directly measure the thrust and the mass flow rate of the propellant.The following conclusions can be drawn:

(3) The performance of the MILET is compared with other representative ILETs developed by Massachusetts Institute of Technology & Accion Systems Company, Busek Company, and US Air Force Research Laboratory.A performance comparison is also made between ILETs and other typical micro thrusters.With a relatively low applied voltage ranging from 1550 V to 2000 V, the MILET achieves an averaged thrust-to-power ratio of 65.2 μN/W with a quasi-constant specific impulse of 1263 s and an averaged thruster efficiency of 40.7%.The results suggest that the performance of the MILET is comparable to other representative ILETs.Compared with other typical electric propulsions,the ILET exhibits an excellent ability of minimalization with high specific impulse and thruster efficiency,which guarantees a great superiority in micro propulsions.

(4) Even though the experimental performance of the ILET is excellent for micro-propulsion mission, there is still a strong necessity and huge space to enhance the performance of the ILET.Consequently, the ways to further improve the performance of ILET are discussed, which further confirms the potential prospect of ionic liquid electric propulsion.In future research, the investigation of the propellant selection could be a direction of performance breakthrough.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This study was co-supported by NSAF, China (No.U1730134); the National Natural Science Foundation of China(No.11772310);the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University, China(No.CX202034); and the Innovation and Entrepreneurship Fund of the Student Affairs Department of Northwestern Polytechnical University, China (No.2021-CXCY-005).The experiments were conducted in the laboratory of Sichuan Mutianyixing Sci-tech Ltd, China.

Appendix A.Definition of various efficiencies and derivation of thruster efficiency

The thruster efficiency is defined as the ratio of thrust power Pthrustto input power Pin, which measures the total efficiency of an electric thruster.To estimate the thruster efficiency,a series of efficiencies related to the physical process are defined.During the emission process, there is a voltage deficit due to the Joule heating and other non-charged-particle emission.The voltage loss in emission process is evaluated on the basis of the emission efficiency as follows:

where ˙memiis the mass flow rate of charged species, ˙mneuis the mass flow rate of neutral species, and ˙mtis the mass flow rate of consumed propellant.In ionic liquid electrospray thruster,the emitted species will be partially intercepted by the extraction electrode.The ratio of exhausted mass flow rate to the emitted mass flow rate is defined as the transmission efficiency.Supposing that the charge-to-mass ratio of intercepted species is the same as the exhausted species,the transmission efficiency can be written as follows:

where ˙mextis the mass flow rate of species exhausted from the thruster,and ˙mintis the mass flow rate of species intercepted by the extraction electrode.Iintis the intercepted current.Icolis the collected current in experimental measurement, which is thought to be equal to the current exhausted from the thruster Iext.It is well known that the thrust power is equal to the kinetic power of the plume only if the ion beam is monodisperse.Once the ion beam is polydisperse,the thrust power will be less than the kinetic power.In general, polydisperse efficiency ηpis defined as the ratio of the thrust power Pthrustto the kinetic power Pkineticas follows:

Based on Eqs.(A6)–(A9), the thruster efficiency ηtcan be written as follows:

Appendix B.Ideal specific impulse of ionic liquid

With an ionic liquid AB as propellant,the ionic liquid electrospray thruster can work in bipolarities to emit both cation and anion.As a result, the performance should be evaluated for bipolar emission.Assuming that the degree of solvation is the same for both positive and negative operation, the molar masses of species in positive and negative emission are

where Mpos, Mneg, MA, MB, MABare molar mass of species in positive emission, molar mass of species in negative emission,molar mass of cation, molar mass of anion, and molar mass of ionic liquid AB, respectively.Assuming that all cations and anions are emitted and the thruster efficiency is 100%,the ideal specific impulse for an ionic liquid can be explicitly computed as follows:

where FC= 96485.3 C/mol is the Faraday constant.