Introduction

As a new type of space propulsion technology, electric propulsion has the advantage of high specific impulse compared with traditional chemical propulsion. The principle of electric propulsion technology is to use the input electric energy to heat, ionize the working medium gas into plasma, and then accelerate the charged particles to eject at high speed, convert the electric energy into the kinetic energy of the charged particles, and then generate thrust according to the reaction force. Commonly used electric thrusters include Hall, ion, etc., but they will face serious life problems during the working process. Electrodes of electric thrusters are exposed to plasma, and electrode corrosion can cause thruster lifetime issues and affect performance. In this context, it is of great significance to study electrodeless devices (because there is no direct contact between electrodes and plasma), and RF plasma thrusters are a typical electrodeless thruster.

RF plasmas are gaining attention due to their advantages of high density, electrodeless design, and multiple modes of operation [1,2,3]. The RF plasma thruster is an electrodeless electromagnetic thruster that generates and accelerates plasma through radio frequency energy. It is mainly composed of a discharge chamber, a magnetic field generator, a radio frequency source, a radio frequency antenna, a gas supply device and a nozzle [4]. RF discharge plasma can achieve high ionization rate (100%) and plasma density (1018 m−3), and it belongs to the electrodeless design, which is very suitable for application in the field of space electric propulsion [5]. In the initial research stage, it mainly focused on high-power radio frequency thruster equipment in order to obtain greater thrust or specific impulse. The most famous example is VASIMR (Variable Specific-Impulse Magnetoplasma Rocket) [6]. Under the condition of high power, the RF plasma thruster will have higher performance (such as high specific impulse and high thrust value, which can effectively shorten the planetary detection time), but its high power, high quality, and high magnetic field strength requirements will also limit Its wide application. The development of micro-nano satellites has put forward requirements for the miniaturization, modularization, and integration of satellite thrusters, and the miniaturization of RF plasma thruster has broad prospects [7]. In recent years, many countries and institutions have conducted research on miniature RF plasma thruster.

The fundamental ionization process in RF plasma has been well studied, and the heating mechanism in inductively coupled plasmas has been described in detail in many studies and textbooks, such as Chaps. 11–13 of Lieberman and Lichtenberg (2005) [8]. There are also many studies on the helicon wave plasma source, Boswell and Chen (1997) [9], Boswell (2011) [10], Takahashi (2005) [11] et al. In terms of plasma power coupling, the Helicon/induction plasma thruster [12] exhibits a capacitive coupling mode at low power and an inductive mode at higher power. Charles, C et al. proposed an asymmetric, capacitively coupled radio frequency plasma thruster in 2012 [13], which belongs to the category of electrothermal thrusters. Compared with the research on capacitive coupling mode thrusters, there are more researches on inductive coupling. Shunjiro Shinohara (2014) from Tokyo University of Agriculture and Technology discussed the mechanism of RF plasma acceleration, and proposed three acceleration methods involved in RF plasma thrusters [14]. Their study found that a high magnetic field is required for the purpose of generating a small diameter RF plasma. The general characteristics of helical waves under various modes of acceleration are described through experiments, various acceleration mechanisms are studied, and the thruster performance is tested [15,16,17]. Using its test system SHD (Small Helicon Device) to carry out a series of experiments [18,19,20,21,22], the plasma parameters under the condition of different inner diameters of the discharge chamber were diagnosed. Italy’s research on low power RF plasma thrusters is based on the European Union’s plan. The main goal is to design and develop low-power space plasma thrusters based on helical radio frequency technology. The thruster level is 1.5 mN-50 W, using argon as a propellant, and a target specific impulse of 1200 s [23]. The experimental prototypes EM01 and EM02 working under vacuum conditions were developed, and the engineering prototype QM (Qualification Model) series [24] was further studied. In 2017, the MHT (Mini Helicon Thruster) was developed to influence the propellant type on the performance of the thruster [25]. The Australian National University conducted research on the performance testing and discharge principles of RF plasma thruster. In 2011, T. Lafleur, K. Takahashi and others have conducted basic thrust measurements on a larger inductively coupled thruster (i.e., 5 cm in diameter). The input power range of this thruster is several hundred watts [26, 27]. The pressure is a few millitorr. The results show that a typical power input of 100 W will produce a thrust of approximately 1 mN. In 2020, Dimitrios Tsifakis and others from the Australian National University [28], based on “pocket rocket” research, designed an inductively coupled radio frequency plasma system based on an operating frequency of 40.68Mhz. The thruster discharge chamber has an inner diameter of 4 mm and uses argon gas as working fluid. The typical total thrust is about 1.1mN at 100sccm and RF power of 50W.

In this paper, a mini-RF plasma thruster with a discharge chamber inner diameter of 10 mm is designed, and a samarium cobalt permanent magnet is used to provide a magnetic field. Optical emission spectrometry and target thrust measurement were carried out on the thruster to obtain plasma parameters and thruster performance under different operating conditions. The effects of argon flow, magnetic field presence and absence on the thruster discharge process were compared emphatically.

In view of the above research content, the chapters of this paper are arranged as follows: Chap. 1 introduces the research progress of the mini-RF plasma thruster; Chap. 2 is the experimental equipment, which introduces the design parameters of the thruster and the experimental setup; Chap. 3 is the diagnostic theory, introduces diagnostic methods and theories; Chap. 4 describes the experimental process and the results; and the last chapter sums up the content of the article.

Experimental equipment

In this chapter the design of the experimental system with the mini-RF plasma thruster and the experimental system used are described.

Design of a mini-RF plasma thruster

In this study, a mini-RF plasma thruster was designed, using a quartz tube with an inner diameter of 10 mm and a thickness of 3 mm as the discharge chamber; a copper tube with a wire diameter of 4 mm was used to wind an 8-turn loop antenna with m = 0; an RF source with a center frequency of 13.56 MHz and the corresponding RF matcher are customized; and a ring-shaped samarium cobalt permanent magnet with a simple structure and constant magnetic field is chosen as the magnetic field generator device. The structure and object of the thruster model are shown in Fig. 1.

Fig. 1
figure 1

Thruster structure and object

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Considering the overall simplicity of the thruster unit structure and its small external dimensions, the use of copper coils would require additional consideration of water-cooled structures, complicating the system structure. The use of permanent magnets has the advantages of simple structure, constant magnetic field, and does not require redundant circuits. We designed the permanent magnet structure with the goal of generating an axial magnetic field of 1000G. Two annular samarium cobalt permanent magnets with an inner diameter of 48 mm, an outer diameter of 80 mm, and a thickness of 25 mm were used as the source of the magnetic field. An outer frame made of PEEK is wrapped around the magnets to fix them, and the axial magnetic field strength and the magnetic field distribution curve generated by the permanent magnets are shown in Fig. 2.

Fig. 2
figure 2

Permanent magnet axial field strength distribution

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Vacuum equipment and experimental systems

As shown in Fig. 3, the experiments were carried out in a stainless steel vacuum chamber with a length of 1 m and an inner diameter of 0.8 m. The thrusters were fixed at the centre of the side of the chamber as described in Design of a mini-RF Plasma Thruster section. The RF power supply is adjusted by the matcher to be connected to the RF antenna through the flange, and the RF power can be adjusted in the range of (0-200 W). The argon mass flow rate was (0–20) standard cubic centimeter per minute (sccm) during the discharge. The ultimate vacuum of the vacuum system was 1.3 × 10−3 Pa, which was achieved by a DIS-500 dry vacuum pump and a CRYO-U 12HSP condensing cryopump. The working pressure was kept in the range of 10−2 Pa and measured by an ionization gauge.

The center of the exit plane of the thruster discharge chamber is taken as the origin of the coordinate system used throughout the study, that is, (z, r) = (0, 0) cm. The fiber optic probe was placed at (-5, 10) cm to receive the optical emitted by the plasma from the direction perpendicular to the quartz tube. The performance of the thruster is obtained by using the self-developed thrust target. The thrust target can move in the range of 0-20 cm in the axial direction through the displacement mechanism. The signal of the fiber optic probe and the test signal of the thrust target are connected to the spectrometer and data acquisition system through the flange.

Fig. 3
figure 3

Experimental system schematic

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Diagnostic theory

OES emission spectra

Probe measurement is the most direct method, but when the inner diameter of the discharge chamber is reduced to an order of magnitude with the size of the probe, intrusive measurement will interfere with the discharge state of the thruster and affect its normal ionization process. At this point, probes are no longer suitable, and non-contact methods such as optical emission spectrometry (OES) have great advantages.

An OES(AvaSpec-ULS2048CL-8-EVO) with wavelengths ranging from 200 to 1100 nm was used for the optical experiments. The spectroscope has 8 channels, and the average spectral resolution was 0.1 nm. In this paper, the results of plasma density and electron temperature are obtained by the line-ratio method. The basic principle is that selecting an appropriate energy level can make the spectral line ratio only depend on the electron temperature or electron density. The diagnosis theory is introduced as follows.

Electronic temperature \({T}_{e}\)

The electronic temperature processing method in this paper mainly refers to [29]. Generally, in low-pressure RF plasmas, electron shock excitation of the ground state and radiative decay of the excited state are the main excitation and/or de-excitation paths due to the low collision frequency of atoms and ions. The optical emission intensity \({I}_{ij}\) caused by the transition from upper energy level \(j\) to lower energy level \(i\) can be written as [30]:

$${I}_{ij}={K}_{ji}{A}_{ji}{n}_{Ar}^{*}\frac{hc}{\lambda }$$
(1)

In the above formula, \({K}_{ji}\) is the spectral response factor of the spectrometer, \({A}_{ji}\) is the optical emission probability of the transition (Einstein coefficient), \({n}_{Ar}^{*}\) is the density of the excited species, \(c\) is the speed of light in vacuum, \(h\) is the Planck constant, λ is the wavelength of the transition. Since the rates of creation and the loss of the excited state are equal in a stable state, and the formula can be obtained:

$${n}_{Ar}^{*}=\frac{{n}_{e}({n}_{Ar}{k}_{Ar}^{dir}+{n}_{Ar}^{m}{k}_{Ar}^{m})}{{k}_{Ar}^{rad}+{{n}_{Ar}k}_{Ar}^{Ar}}$$
(2)

Where \({n}_{e}\), \({n}_{Ar}\) and \({n}_{Ar}^{m}\) are the electron density, the population densities of the ground state and the metastable state of argon, respectively. \({k}_{Ar}^{dir}\), \({k}_{Ar}^{m}\) and \({k}_{Ar}^{Ar}\) are the rate coefficients considering the direct electronic excitation of the excited state from the corresponding ground state, the electronic excitation via the metastable state and the quenching of the excited state, respectively. \({k}_{Ar}^{rad}=1/\tau\) is the radiation de-excitation rate coefficient, and \(\tau\) is the lifetime of excited state. Substituting formula (2) into (1), the formula (3) can be obtained:

$${I}_{ij}={n}_{e}\left(\frac{{{n}_{Ar}k}_{Ar}^{dir}+{n}_{Ar}^{m}{k}_{Ar}^{m}}{1/\tau +{n}_{Ar}{k}_{Ar}^{Ar}}\right){K}_{ji}{A}_{ji}\frac{hc}{\lambda }$$
(3)

Using the above equations, the electron temperature can be obtained by substituting the ratio of the information of the two selected spectral lines, respectively. In this paper, the argon emission lines at 750.39 and 811.53 nm are chosen, assuming that the Maxwell energy distribution is satisfied. The data were obtained from the reference [31, 32].

Plasma density \({n}_e\)

The plasma density is calculated by extending the coronal model. For the higher excitation energy levels of argon, such as Ar(3p1) and Ar(5p5), their excitation cross sections from the substable state are very small and originate mainly from the excitation of the ground state. Therefore, by extending the coronal model to calculate the plasma density reference [33]:

The line-ratio equation obtained by using the two energy levels of Ar(3p1) and Ar(5p5) is:

$$\frac{{I}_{Ar\left(3{p}_{1}\right)}}{{I}_{Ar\left(5{p}_{5}\right)}}=\frac{{A}_{Ar\left(3{p}_{1}\right)}\cdot {n}_{Ar\left(3{p}_{1}\right)}}{{A}_{Ar\left(5{p}_{5}\right)}\cdot {n}_{Ar\left(5{p}_{5}\right)}}=\frac{{n}_{e}{\cdot n}_{Ar}\cdot {k}_{Ar\left(3{p}_{1}\right)}^{dir}\cdot (1+{n}_{e}/{n}_{Ar,5{p}_{5}}^{*})}{{n}_{e}{\cdot n}_{Ar}\cdot {k}_{Ar\left(5{p}_{5}\right)}^{dir}\cdot (1+{n}_{e}/{n}_{Ar,3{p}_{1}}^{*})}$$
(4)

Simplified to:

$$\frac{{I}_{Ar\left(3{p}_{1}\right)}}{{I}_{Ar\left(5{p}_{5}\right)}}=C\cdot \frac{(1+{n}_{e}/{n}_{Ar,5{p}_{5}}^{*})}{(1+{n}_{e}/{n}_{Ar,3{p}_{1}}^{*})}$$
(5)
$$C\equiv \frac{{k}_{Ar\left(3{p}_{1}\right)}^{dir}}{{k}_{Ar\left(5{p}_{5}\right)}^{dir}}$$
(6)

The definitions of the symbols in the above formula are the same as the previous ones. According to the cross-section measurement calculation, when \({T}_{e}\gtrsim 1\) eV, because the cross-section is very close to the threshold energy, the ratio \(C\) of the excitation rate coefficient of Ar(3p1) and Ar(5p5) is almost independent of \({T}_{e}\) [34, 35]. Therefore Eq. (4) has nothing to do with \({T}_{e}\) and can be used to determine \({n}_{e}\). The data comes from reference [33].

The spectral curves before and after the mode jump are shown in Fig. 4. The curve is measured in the presence of a magnetic field, argon mass flow rate of 10 sccm, and RF power input power of 40 and 140W, respectively. It can be seen from the curve, mainly for the Ar I spectral lines, ArIIspectral lines relative intensity is very low, the highest relative intensity of the spectral lines for the 811.5 nm spectral lines. The channels of the spectrometer have been calibrated with the HL 2000 halogen light source before use.

Fig. 4
figure 4

CCP and ICP mode emission spectrum

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Principle of target thrust measurement and thrust stand

As shown in Fig. 5, the thrust target stand used for the experiment was improved from the previous study [36], which mainly consists of target board, target hinge, and displacement sensor. Graphite with a diameter of 300 mm was used as the target board, and the graphite material was chosen for its low sputtering rate, which reduces many uncertainties. A hinge is used to provide a restoring force for the target board and a displacement sensor is used to measure the displacement of the target. The accuracy of the sensor is on the order of microns and the displacement of the lowermost part of the target board is 200 microns at a thrust force of 5mN. In open-loop mode, where thrust and gravity are balanced against the elastic force of the target hinge, the displacement of the target board in the axial direction can be measured using the displacement sensor to obtain the thrust force generated by the plume collision. The displacement versus thrust relationship of the target thrust stand was calibrated using a series of precision weights prior to the experiment and the results are shown in Fig. 6.

Fig. 5
figure 5

Target thrust stand

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Fig. 6
figure 6

a Relationship between output voltage and applied weights in open-loop calibration, b Calibration curve for the target thrust stand with weights

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Experimental results and discussion

This chapter describes the experimental study of the mini-RF plasma thruster under different working conditions. Experiments were carried out on the thruster under different power, argon flow rates, and magnetic field strength. Use the emission spectrum results to obtain the influence of specific parameters on the \({n}_{e}\) and \({T}_{e}\), and analyze the relationship between typical working conditions and measurement data. Use the target thrust stand to measure the thrust value of the thruster under different working conditions.

Emission spectrum

Argon gas is used in the experiment, and the flow rates are 2 sccm, 6 sccm, 10 sccm, 14 sccm, and 18 sccm. By adjusting the input power of the RF power supply (0-160 W), the power scan is gradually increased from the lowest power of the discharge. Plasma density is a parameter directly related to the discharge state. This paper focuses on describing and distinguishing the difference in thruster discharge state (CCP and ICP) from the change of plasma density. According to the data processing method introduced in Diagnostic Theory section, the plasma density and electron temperature were calculated.

Discharge characteristics and working mode

In the actual experiment, it was found that with the change of the incoming gas flow rate and RF power, the thruster has the following working states (Table 1), and the background pressure at different flow rates was recorded using the vacuum gauge on the vacuum chamber (Table 2).

Table 1 Summary of thruster discharge phenomena
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Table 2 Background pressure at discharge
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Figure 7 show the variation curves of plasma density with input power when the through gas flow rate is 10sccm and 14sccm under changing magnetic field and flow rate, and the discharge phenomena (a-d) correspond to the Table 1. It can be observed that under the three working conditions, as the power increases, the plasma density has a significant jump, and the discharge state of the thruster changes from capacitively coupled plasma (CCP) discharge mode to inductively coupled plasma (ICP) discharge mode. Next, the effects of different argon flow rates, presence or absence of magnetic field conditions on the discharge characteristics and working modes of the thruster will be discussed.

Fig. 7
figure 7

Thruster discharge phenomena, a Pre-discharge mode transition (low power), b Post-discharge mode transition (low flow), c Post-discharge mode transition (high flow), d Post-discharge mode transition (with magnetic field)

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Firstly, under the condition of no additional magnetic field, the change rule of discharge characteristics and working mode with RF power and argon flow rate is investigated. Figure 8 shows the trend of plasma density with input power in the without magnetic field when the argon flow rate is 2, 6, 10, 14, and 18 sccm.

Fig. 8
figure 8

Plasma density variation with power without magnetic field

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At lower argon flow rates (2, 6 sccm), no mode jumping was observed in the RF power regulation range. Plasma density fluctuated in the range of 1012 m−3~1013 m−3and was positively correlated with argon flow at the same power.

When a higher argon gas flow rate is introduced, when the argon gas flow rate is 10 sccm and RF power supply is less than 90 W, the plasma density is in the order of 1012 m−3~1013 m−3. The plasma density tends to increase with the increase of the RF power. When the applied power is 100W, a step change in plasma density occurs to the order of 1017 m−3, which is an increase of three orders of magnitude, and it is considered that a mode jump occurs at this point, from the CCP mode to the ICP mode. When 14 sccm of argon is fed, it can be seen that the plasma density increases gradually with the increase of the input power of the RF power supply before the mode jump occurs, from6 × 1013m−3at 10W to 6.5 × 1014m−3 at 80W. And the mode jump occurred at 90 W, and the plasma density jumped to 8 × 1017 m−3, which was an increase of three orders of magnitude. The power at which the mode jump occurs in the experiment is near 85W. At a flow rate of 18 sccm, a mode jump occurred near a power of 76W.

In the absence of a magnetic field, altering the inflow rate of argon gas reveals the following patterns:

  1. (1)

    Under the conditions of three different working gas flow rates (10, 14, and 18 sccm), a transition from CCP to ICP discharge mode occurs, and the plasma density had a step of about 3 orders of magnitude before and after the transition. Experiments have found that when the argon gas flow rate is 2 sccm and 6 sccm, the plasma densities all fluctuated from 1012 m−3 to 1013 m−3 when the RF power increased to about 150W, maintaining a relatively stable range and not experiencing mode jumps.

  2. (2)

    For a given input power, there is a direct correlation between argon gas flow rate and plasma density. As the flow rate increases, the power required for a mode transition decrease. This is due to the effect of increasing argon gas flow rate, which in turn increases the internal gas pressure within the discharge chamber. As a result, the average free path of the electrons decreases and the collision frequency increases. These changes create favorable conditions for increasing plasma density. The transition from CCP to ICP mode is triggered precisely by the increase in plasma density resulting from these conditions.

When the magnetic field is added, at the same argon gas flow rate, the plasma density varies with the RF power supply as shown in Fig. 9.

Fig. 9
figure 9

Plasma density variation with power without magnetic field

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At lower argon gas flow rates (2 and 6 sccm), the plasma density exhibits fluctuations in the range of 1014 m−3 to 1015 m−3 and there is no pronounced occurrence of mode transitions, mirroring the scenario without a magnetic field. For a gas flow rate of 10 sccm, it is observed that at input powers below 130W, the plasma density remains in the order of 1015 m−3 and gradually increases with power. Experimental records indicate that a mode transition occurs around 134W, where the plasma density increases by three orders of magnitude to 4.8 × 1017 m−3. At a flow rate of 14 sccm, the plasma density escalates from 6 × 1014 m−3 to 8.5 × 1017 m−3 at 170W, and a mode transition between 130 and 140W is observed. At a flow rate of 18 sccm, a mode transition between 150 and 160W is observed.

The impact of argon flow rate and magnetic field on discharge characteristics and operational modes can be summarized as follows:

  1. (1)

    The presence of a magnetic field raises the CCP-ICP transition power threshold. The power levels at which discharge mode transitions occur under different conditions are presented in the following Table 3:

Table 3 Mode transition power under different argon flow rates and magnetic field conditions
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The magnetic field direction near the outlet of the discharge chamber no longer aligns axially due to the rapid axial attenuation of the magnetic field generated by the permanent magnet used. As a result, electrons are concentrated where the magnetic field lines are denser and deviate toward the discharge chamber wall. In addition, the plasma interacts with the wall of the quartz tube and forms a strong sheath under the guidance of the magnetic field. This worsens the wall loss of radio frequency energy, making it challenging to achieve higher plasma density and necessitating more power to switch from CCP to ICP mode.

  1. (2)

    Higher argon gas flow rates can reduce the power required for mode transition under no magnetic field conditions. In contrast, when a magnetic field is present, increasing the flow rate raises the power necessary for mode transition. A magnetic field predominantly limits the electron motion, compelling them to travel in the field’s direction. Increasing the argon gas flow rate diminishes the duration of particles in the discharge zone, causing them to exit before acquiring sufficient energy necessary for energy accumulation. Therefore, the mode transition threshold increases as a result.

Characterization of plasma parameters

This section analyzes the effect of the magnetic field on the plasma parameters of the thruster by comparing the changes in plasma density and electron temperature with /without the presence of a magnetic field, while maintaining the same working gas flow rate conditions.

As shown in Fig. 10, at lower working gas flow rates of 2 sccm and 6 sccm, no mode transition phenomenon was observed within the range of RF power adjustment, as previously stated. Under the condition of no magnetic field, plasma density fluctuated within the range of 1012 m−3 to 1014 m−3 at the same power. Moreover, plasma density exhibited a positive correlation with argon gas flow rate. In the scenario where magnetic field was present, plasma density fluctuated within a higher range of 1014 m−3 to 1015 m−3 compared to the scenario without a magnetic field. However, the curves for 2 sccm and 6 sccm overlapped, indicating that plasma density was not extremely sensitive to variations in argon gas flow rates.

Fig. 10
figure 10

Variation of plasma density with power for low argon flow (2,6 sccm)

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Figure 11 demonstrates that higher argon gas flow rates of 10 sccm and 14 sccm lead to the following patterns. (1) The presence of a magnetic field contributes to an increase in plasma density, and when a magnetic field is present, the plasma density in ICP mode is higher. (2) The plasma density changes rapidly with power variations in the absence of a magnetic field, as indicated by the red arrows in the graph. In contrast, plasma density changes more gradually when a magnetic field is present (indicated by the blue arrows).

Fig. 11
figure 11

Variation of plasma density with power for high argon flow (10,14 sccm)

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Figure 12 shows that the electron temperature change trend is essentially the same as that of the plasma density. In the absence of mode transition, the electron temperature ranges between 3 eV and 4 eV, consistent with the findings outlined in reference [21]. When the mode transition occurs, there are corresponding changes in the electron temperature, and it is evident that the electron temperature increases in the order of 4 eV to 6 eV. However, due to potential errors in the computational model used, this value may be slightly overestimated.

Fig. 12
figure 12

Electron temperature changes with power (a) different argon flow without magnetic field (b) different argon flow with magnetic field

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Performance of thrust

This section presents the thrust measurement results using a thrust target stand. The thrust determines the propulsion efficiency of the thruster, which is an important macroscopic performance indicator. It is also related to microscopic plasma parameters, such as density and velocity.

In the experiments, it was observed that when the thruster operates at lower power levels, no significant thrust variation can be detected. This could be since the plasma is confined within the discharge chamber without any obvious jet exhaust. As the thrust is gradually increased and the mode transition occurs, distinct thrust values can be measured. In addition, thrust variations become more pronounced as the RF power exceeds 100W. The study documented the measured thrust values at argon flow rates of 14sccm, 18sccm, and 24sccm, and radio frequency powers of 120W, 140W, and 160W.

As shown in Fig. 13, keeping the argon flow rate at 24 sccm and the RF power at 0 means that the gas circuit is opened at this time, but no ionization occurs and the argon gas pushes the target surface, resulting in target board displacement to generate thrust. The thrust values measured under the operating conditions of \({P}_{rf}\) = 0, 120W, 140W, and 160W were measured when the relative positions of the target board and the thruster outlet were 5 cm, 10 cm, and 15 cm, respectively. By adjusting the distance of the target board relative to the thruster outlet, it was found that as the distance between the target surface and the thruster outlet increased, the measured thrust values decreased in all cases. When the distance between the target surface and the thruster outlet is 5 cm and the RF power is 160W, the thrust is approximately 1.4 mN.

Fig. 13
figure 13

Thrust varies with distance

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Varying the RF power supply to analyze how different argon flow rates (14sccm, 18sccm, 24sccm) affect the thrust. Figure 14 displays the thrust results, which indicate that the thrust value rises in tandem with an increase in the inlet flow rate. Furthermore, it is observed that an increase in input power leads to a more prominent increase in thrust value when inlet flow rate is higher.

Fig. 14
figure 14

Thrust changes with flow rate

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The thrust target stand was fixed at 5 cm from the thruster outlet, the argon flow rate was 14sccm, 24 sccm, and the RF power was varied to investigate the effect of the magnetic field on the thrust. The thrust results are shown in Table 4. The relative value is the ratio of the thrust difference to the thrust when there is a magnetic field.

Table 4 Thrust values at different powers
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Fig. 15
figure 15

Thrust changes with magnetic field

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As shown in Fig. 15, the trend in thrust value is shown to change with variations in the input power, with and without a magnetic field, for flow conditions of 14sccm and 24sccm. Our study discovered that the magnetic field does not constantly enhance the thrust. Instead, we found that the magnetic field has a positive effect on the thrust when the flow is small and the power is high; when the flow is large, an inappropriate magnetic field has a negative effect on the thrust value.

In reference to the alteration of plasma parameters with magnetic field and flow rate in Emission Spectrum section, it is hypothesized that magnetic field increases plasma density in the discharge chamber at low flow rate in this study. Simultaneously, higher input power can excite more plasma, leading to the improvement of thrust value. It can be observed that the measured thrust values in the presence of a magnetic field when the flow rate is 24 sccm are consistently smaller than those obtained without a magnetic field. This could be due to the influence of the magnetic field configuration. While the magnetic field can increase the plasma density within the discharge chamber, it’s not a typical magnetic nozzle configuration. At the thruster outlet, the magnetic field lines intersect the discharge chamber axis at a relatively large angle, almost perpendicular. This arrangement effectively intercepts the outward diffusion of electrons. The plasma experiences the effect of the divergent magnetic field, resulting in a more intense interaction with the chamber walls at the outlet. As a result, thrust is reduced.

Fig. 16
figure 16

Relationship between plasma density and thrust (14,24sccm)

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The relationship of the thrust and the plasma density is shown in Fig. 16 with different input power conditions (Prf = 0,120W, 140W, 160W), argon flow rates (14 sccm and 24 sccm) and magnetic field (with or without the magnetic field). We have observed a positive correlation between the density of plasma and the values of thrust. As compared to the results with no magnetic field, the magnetic field can enhance plasma density and thrust at a higher plasma density with the gas flow rate of 14 sccm. However, at the gas flow rate of 24 sccm, the magnetic field reduces plasma density and thrust value.

Due to the relatively small inner diameter of the thruster, the sheath effect becomes more pronounced. Therefore, it is recommended to select a magnetic field setup that attempts to prevent electron interactions with the chamber walls. Such interactions could otherwise impact the discharge and thrust performance of the thruster.

Conclusions

This paper describes the design and experimental testing of a mini-RF thruster with two permanent magnets. The spectrogram, electron density and electron temperature were obtained using an optical emission spectrometry (OES) and a target thrust stand under different argon flowrate, RF power and magnetic field conditions. The following conclusions are drawn:

  1. (1)

    As the RF power increases, there is a transition from the CCP mode to the ICP mode. During this mode transition, the discharge state undergoes significant changes, resulting in a sudden increase in plasma density by 2 to 3 orders of magnitude and an increase in electron temperature.

  2. (2)

    The magnetic field helps to increase plasma density at low power levels, but it can also delay the input power from CCP mode to ICP mode. With no magnetic field, the mode transition (from CCP to ICP) occurs between 70 and 90 W. The RF power required for the mode transition decreases as the argon gas flow rate increases. However, with the applied magnetic field, the RF power required for the mode transition (from CCP to ICP) increases to approximately 140W, and the mode transition power becomes not significant as the argon gas flow rate increases.

  3. (3)

    A correlation was established between macroscopic thrust performance and microscopic plasma parameters. The magnetic field can affect the plasma density in the discharge chamber, thereby influencing the thrust. Therefore, the strength and configuration of the applied magnetic field must be carefully designed and selected.