Introduction

Due to the advantages of high density, electrodeless design, and multiple operation modes, helicon plasmas are attracting more attention as a thruster or a plasma source in spacecraft propulsion [1,2,3,4]. In helicon plasmas, the electron characteristics are significantly important because electrons are the medium for the input powers and the plasmas. The electron dynamics determine the ionization and acceleration of the ions and lead the establishment of plasma potentials, such as the current-free double layers [5,6,7,8]. Moreover, the ion characteristics are also very important because ions are the contributors of effective thrust. It is thus of interest to understand the relationship between the electron and ion dynamics in such systems.

Much effort has been made to characterize the electron and ion dynamics. Initial studies suggested that the ion beams were created by formation of a double layer (DL) [9, 10]. A DL is a spontaneous freestanding structure that can appear anywhere in a plasma. This region also coincides with a steep drop in the plasma density and/or in the magnetic field [11]. Recent experiments found evidence that the accelerating structure is not a true DL but an acceleration region (potential difference region) with the Debye lengths on the order of 1000 [12,13,14,15].

Many groups have reported observations of high energy electrons streaming from upstream into downstream at the same time the ion beams appear. Hot electrons have been observed traveling along magnetic field lines into a magnetic nozzle [16, 17]. Two electron temperature populations have been identified within the plasma [18, 19]. It was deduced that the downstream electrons came from upstream electrons that have sufficient energy to overcome the potential trap [20]. There are two possible explanations for the energetic electrons: RF skin heating effects in the source and energization by plasma instabilities. The RF skin heating effects hypothesis suggests that the ions are accelerated because energetic electrons were created at the edge of the plasma, and then stream downstream and through the expansion regions with few collisions [17]. A spatially distinct region of ion acceleration must arise through ambipolar fields.

Based on the recent research described above, many studies focused solely on the plasma upstream or downstream of the acceleration region [21, 22]. There is a gap in understanding exactly how the energetic electrons are produced and how they influence/create the ion beam. To explore the relationship of the energetic electrons and ion acceleration in expanding plasmas, we present spatial structures of the high- and low-energy electrons both in upstream and downstream plasmas and investigate the relationship between electrons and ions. The images show that the axial density distribution of the high-energy electrons is asymmetric, with the maximum density located at one end of the antenna after the wave mode is formed. The reverse magnetic field configuration can shift the position of maximum electron density from one end to the other. Assuming that electrons follow a Boltzmann distribution, the spatial potential is also high in areas with high electron density. The axial potential difference in plasma is the main source of ion acceleration. The ion energy testing results show that the ion energy obtained near the ionization/acceleration zone has a significant increase due to the reduced ion energy loss.

Diagnostics

Relative particle density from the line intensities of an optical emission spectroscope (OES)

The Corona model has been used to establish a relationship between the optical emission intensity and the particle density. The corona model has been successfully tested in electrodeless RF discharges in pure Ar and N2 in the pressure range from 0.1 to 1 Pa, with the electron temperature varying between 2 and 10 eV and the electron density between 1015 mand 3 and 1017m-3 [23, 24].

In the Corona model, the excitation to any emitting state is assumed to result from the collision between a plasma electron of sufficient energy and a neutral ground state particle.

Direct excitation by collision between an electron and an Ar atom in the ground state is represented by the following:

$$\mathrm e\;+\;\mathrm{ar}\;\rightarrow\mathrm e\;+\;\mathrm{Ar}\ast.\;\left({{\mathrm k}_{\mathrm{Ar}}}^{\mathrm{dir}}\right)$$
(1)

Here, k Ar dir is the rate coefficient for direct electronic excitation from the ground state.

The spontaneous decay of excited states is regarded as the only response in the Corona model to balance the electron impact excitation processes. Other effects such as from heavy particle interactions are assumed to be negligible in the present case because of the low particle densities. In addition, radiative ion-electron recombination can be neglected at low ionization degrees of 10−3 to 10−2 [23].

Radiative de-excitation is represented by the following:

$$\mathrm{Ar}\ast\rightarrow\mathrm{Ar}\;+\;\mathrm{hv},\;\left({{\mathrm k}_{\mathrm{Ar}}}^{\mathrm{rad}}\right)$$
(2)

where k Ar rad is the rate coefficient for spontaneous radiation of the excited state:

$${k_{Ar}}^{rad}=\;1/\uptau$$
(3)

here, τ is the lifetime of the excited state.

Under such simplifying assumptions described above, the balance between the production of an excited state and its decay can be expressed by

$${n_e}{n_{Ar}}k_{{Ar}}^{{dir}}={n_{Ar*}}k_{{Ar}}^{{rad}}{\text{=}}\frac{{{n_{Ar*}}}}{\tau }$$
(4)

where n e is the electron density (cm-3), n Ar is the density of ground state particles (cm-3), n Ar* is the density of excited state particles (cm-3), k Ar dir is the rate coefficient for direct electronic excitation from the ground state (cm3 s−1), and τ is the lifetime of the excited state (s−1).

For an excited Ar*, the emission intensity I ji due to a transition from an upper level j to a lower state i is

$${I_{ji}}={K_{ji}}{A_{ji}}{n_{Ar*}}\frac{{hc}}{{{\lambda _{ji}}}}$$
(5)

where K ji is a factor depending on the plasma volume, solid angle and spectral response of the spectrometer; A ji is the optical emission probability for the transition (s-1); n Ar* is the density of the excited species (cm-3); c is the speed of light (ms−1); h is the Planck constant (J·s); and λ ji is the wavelength of the transition (nm).

By using Eq. (4), it follows that:

$${I_{ji}}={K_{ji}}{A_{ji}}\frac{{hc}}{{{\lambda _{ji}}}}{n_e}{n_{Ar}}k_{{Ar}}^{{dir}}\tau$$
(6)

In low density plasmas, the electron temperature (which determines k Ar dir) and ground state particle density n Ar are assumed to be constant in the plasma volume [23]. Therefore, except for the electron density n e, the coefficients on the right side of Eq. (6) can be assumed to be a certain value. In that way, Eq. (6) can be simplified as.

$${\mathrm I}_{\mathrm{ji}}={\mathrm{Kn}}_{\mathrm e}{\mathrm{\ or\ n}}_{\mathrm e}\text{=}{\mathrm{kI}}_{\mathrm{ji}}$$
(7)

which is a linear relationship between the emission intensity and the electron density. This means that the emission intensity could represent the “relative” electron density, or the “absolute” density if the coefficient “k” can be calibrated by the electron density derived from an RF compensated Langmuir probe. This relationship has also been mentioned by K. Behringer: “all line intensities are proportional to the electron density [23]. ”

Spatial relative electron density contours from an ICCD and filters

Since the line intensities are proportional to the electron density, an ICCD camera and different filters are used to capture the particle density contours with different excitation electron temperatures.

Absolute electron density and temperature from a RF compensated Langmuir probe

The absolute electron density is calibrated by a RF compensated single Langmuir probe. The detailed data processing method for a Langmuir probe can be found in [25] and [26]. The electron temperature and density are calculated using Eqs. (8) and (9), respectively.

$${T_{ev}}=\frac{{{V_p}}}{{\ln ({I_{total}}{\text{-}}{I_i})}} \approx \frac{{{V_p}}}{{\ln ({I_{\text{e}}})}}$$
(8)
$${n_e}{\text{=}}\frac{{{I_{Bohm}}}}{{eA0.61}}\sqrt {\frac{{{m_i}}}{{k{T_e}}}} =\frac{{{I_{{\text{sat}}}}}}{{eA0.61}}\sqrt {\frac{{{m_i}}}{{k{T_e}}}}$$
(9)

Here, T ev is the electron temperature (eV), V p is the probe voltage (V), I total is the probe current (A), I sat is the ion saturation current (A), I Bohm is the Bohm current (A), n e is the electron density (m-3), e is the electron charge (1.6 × 10−19 C), A is the effective collecting area of the probe (m2), k is the Boltzmann constant (1.38 × 10−23 J/K), T e is the electron temperature (K), and m i is the ion mass (kg).

In this work, a typical electron density and temperature were 5 × 1017 m-3 and 3 eV, respectively, the Debye length was 0.018 mm, and the probe radius was 0.15 mm. The ratio of the probe radius to the Debye length was nearly 10. Therefore, the classical data reduction process of the thin sheath theory for the single Langmuir probe was used. The experimental errors for the electron temperature and density were estimated to be 20% and 50%, respectively [27,28,29].

Ion energy distribution from a retarding field energy analyzer (RFEA)

An RFEA’s collected ion current, I RFEA, can be expressed as [30]:

$${I_{RFEA}}=qA\int_{{{v_{\hbox{min} }}}}^{\infty } {vf(v)dv}$$
(10)

Where q is the electron charge, A is the probe’s effective collecting area, v is an ion’s velocity perpendicular to the plane of the RFEA head, f(v) is the ions’ velocity distribution function, and v min is the lowest ion velocity indicated by:

$${v_{\hbox{min} }}=\sqrt {\frac{{2q{V_{\text{D}}}}}{M}}$$
(11)

Where V D is the discriminator voltage and M is the ion mass. As a result, only ions with a velocity greater than v min will be collected by the FREA. At that point, using Eq. (11) and varying Eq. (10) in relation to V D.

$$\frac{{d{I_{{\text{RFEA}}}}}}{{d{V_{\text{D}}}}}= - A\frac{{{q_e}^{2}}}{{\text{M}}}f({\text{V}})$$
(12)

As a result, the negative derivative of the collected current with respect to the applied discriminator voltage determines the ion velocity distribution function.

Experiment apparatus

In this paper, the experiments were performed in a 1.5-m long and 1.0-m inner diameter stainless-steel vacuum chamber, as shown in Fig. 1. The discharge chamber (tube) consisted of a 4 cm diameter and 40 cm long quartz tube. The quartz tube was surrounded by a water-cooled 15.5 cm long helical antenna. A 13.56 MHz RF source was connected to this helicon antenna. A uniform, axial magnetic field of 0–1200G (with equal current of 0–70 A) in the plasma source was produced by two water cooled electromagnets. The currents of 50 A, 60 A, and 70 A in the magnetic coil correspond to the maximum magnetic field strength of 800G, 1000G, and 1200G at the center, respectively. The argon mass flow rate was 20 standard cubic centimeter per minute (sccm) during the discharge. The vacuum system was pumped down to a base pressure of 5 × 10–3 Pa by a turbo-molecular-rotary pump which was connected to the side of the diffusion chamber downstream. The working pressure was about 5 × 10–2 Pa (~ 0.4 mTorr) and it was measured using an ionization gauge.

Fig. 1
figure 1

Sketch of the experimental setup

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An optical emission spectroscope (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. An intensified charge coupled device (ICCD) (DH334T-18U-E3) camera with 1024 × 1024 pixel array was used to picture the spatial structure of the discharge plasma. This camera was available to match wavelength range requirements from 120 to 1100 nm. Along with the camera, the 480 nm band pass, the 810 nm band pass (with 10 nm full width at half maxima, FWHM), and the 600 nm high pass filters were used in the experiment to transmit the required light and to reject all other unwanted radiation.

A four-grid retarding field energy analyzer (RFEA) was positioned on the centerline at the position of 10 cm from the exit plane of the discharge tube [31,32,33]. The whole assembly was 1.8 cm in length, 1.4 cm in width, and 0.7 cm in height. The four grids consisted of a (in order) floating, negatively biased electron repelling, positively biased ion retarding, and secondary electron suppression, all before a collection plate. The electron repelling grid was maintained at -40 V for nominal test cases while the ion retarding grid was swept from 0 to 150 V. Its aperture hole about 0.3 cm faced the plasma source to measure the current I versus discriminator voltage (V D) characteristic and obtain its derivative, the ion energy distribution function (IEDF).

Results

OES emission spectra

Figure 2 shows the emission lines with their electron excitation energy thresholds of an argon RF discharge. The OES was set outside the discharge tube and was facing the centerline of the tube. Wavelengths of emission lines and their excitation energies were compared with the NIST Atomic Spectra Database Lines in order to meet the international standards (https://physics.nist.gov/PhysRefData/ASD/lines_form.html).

Fig. 2
figure 2

Emission spectrum with electron excitation energy thresholds

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As shown in Fig. 2, all the emission lines with wavelengths ranging from 200 to 1100 nm can mainly divided into two different regions by their different excitation energy thresholds. Totally the information of 50 emission lines with high signal-to-noise ratio in Fig. 2 have been included in the statistics, as shown in Tables 1 and 2. From these tables we can see that the emission lines with wavelengths ranging from 200 to 600 nm are mainly high-energy electron excited ionic (Ar II) lines (≥ 16 eV). Meanwhile, the emission lines with wavelengths ranging from 600 to 1100 nm are mainly low-energy electron excited neutral lines (Ar I) lines (mainly 11–13 eV). Moreover, Fig. 3 shows the variation of 12 emission intensities with RF input power, also with two main trends. Therefore, based on the differences in electron excitation temperature and trends of emission intensity with increasing power, all emission lines are mainly divided into two groups.

Four lines with the highest signal-to-noise-ratio (SNR) in one emission spectrum were used to establish a comparison with different working conditions. These are 434.8 nm, 480.6 nm, 763.5 nm, and 811.5 nm lines. The lines of 434.8 and 480.6 nm are high-energy electron excited ionic lines. The lines of 763.5 and 811.5 nm are low-energy electron excited neutral lines. Their spectra details are listed in Tables 1 and 2, in which wavelengths, particle types, transition probabilities (A ki), statistical weights (g k), excited energy levels (E i, E k), and the electron configurations of the emission lines have been included.

Table 1 High-energy electron excited ionic lines from 300 to 600 nm with the highest signal-to-noise ratio
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Table 2 Low-energy electron excited neutral lines from 600 to 1000 nm with the highest signal-to-noise ratio
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Mode transition

As power or B-field is increased, the helicon discharge modes change from a capacitive (E mode) to an inductive (H mode) to a wave coupling or a helicon discharge (W mode) [34]. The RF at low power is capacitively coupled to the plasma via the voltage on the antenna. At higher power it is the RF magnetic field which excites currents in the plasma after the gas breaks down from the E-field. Finally, the power is high enough to generate a density matching the helicon wave conditions. As shown in Fig. 3, transitions can also be seen at a constant B-field (1000 G) with increasing powers. For Argon gas feed, at E mode, the plasma visually pink and appears to have a rather flat to slightly hollow radial structure with its highest luminosity in the immediate vicinity of the antenna ends. At H mode, the plasma visually also pink and appears to have a slightly higher-center radial structure with its highest luminosity also in the antenna ends. At W mode, the plasma has a well defined blue core indicative of a significant population of Ar II, and extends over the length of the plasma vessel. After reach the W mode, if the input RF power continues to increase, the transitions are from one wave mode (W1) to another (W2, W3…).

Fig. 3
figure 3

Emission spectrum with electron excitation energy thresholds

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Different intensity jumps of ionic and neutral lines

Figure 4 shows the emission spectra with different input RF powers (200-1200 W) under different magnetic field strengths. Figure 4 (a) shows the emission spectra with a central magnetic field strength of 800 G. Figure 4 (b) shows the emission spectra with a central magnetic field strength of 1000 G. From these figures, we can see that the intensity growth rate of the high-energy electron excited ionic population (434.8 nm and 480.6 nm lines) is larger than that of the low-energy electron excited neutral population (763.5 nm and 811.5 nm lines) with the increase of input powers. This phenomenon is more obvious with 1000 G condition. The intensity of the ionic population is higher than the neutral population at 1000 W and 1200W

Fig. 4
figure 4

Emission spectra with different RF input powers under different magnetic field strengths. a 800 G. b 1000 G

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Figure 5 shows the emission intensity variations with different input powers of the 434.8 nm, 480.6 nm, 763.5 nm, and 811.5 nm lines under different magnetic field conditions (800G, 1000G, and 1200G). Figure 6 shows the normalized emission intensities of these four lines. These values are normalized by taking the data of 200 W as reference. The results show that the low-energy electron excited neutral populations (763.5 nm and 811.5 nm lines) jump at 400 W and reach the helicon wave mode, and then become to a nearly saturation level. However, the high-energy electron excited ionic populations (434.8 nm and 480.6 nm lines) jump firstly at 400 W and reach a wave mode (W1 mode). After that, they jump for the second time (W2 mode). Instead of reach to a saturation level, their intensity increase almost linearly with the increasing input power. Moreover, the applied magnetic field strengths have an important influence on their relative emission intensity. The relative intensities of the low-energy electron excited neutral lines (763.5 nm and 811.5 nm lines) decrease significantly with the increase of magnetic field strengths, while that of the high-energy electron excited ionic lines (434.8 nm and 480.6 nm lines) increase slightly with the increase of magnetic field strengths.

Fig. 5
figure 5

Emission spectra with different RF input powers under different magnetic field strengths. a 800 G. b 1000 G. c 1200 G

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Fig. 6
figure 6

Normalized emission spectra with different RF input powers under different magnetic field strengths. a 800 G. b 1000 G. c 1200 G

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ICCD images with different filters

Energy coupling with different RF input powers

From the above emission spectra, it can be seen that there are mainly two different particle groups in the Helicon discharge plasma. These are the high-energy electron excited ionic lines (434.8 and 480.6 nm) and the low-energy electron excited neutral lines (763.5 and 811.5 nm). Moreover, these two parts show different intensity jumps with the increase of RF input power. This phenomenon may allow us to have a deeper understanding of the energy coupling between RF input power and plasma. In order to distinguish these two different particles, two different filters (480 nm band pass and 600 nm high pass) were used for ICCD imaging experiments. Originally, 810 nm band pass filter was intended to be used, but there was large fringe noise in the image. Finally, the 600 nm high pass filter was used for a high-quality image.

Figure 7 shows the spatial structure of the high-energy electron excited ionic and low-energy electron excited neutral particles with different RF input powers. For high-energy electron excited ionic particles (480 nm band pass), they are firstly generated at both ends of the antenna and their radial distribution is relatively uniform, see the 200-W case. With the increase of input powers (300 W), they expand to the middle of the antenna to form an axial particle path. After the wave mode has been reached (500 W), their axial intensity distribution is asymmetric. The maximum axial intensity locates at one end of the antenna. At the same time, their radial distribution concentrates towards the center dramatically, and the maximum radial intensity locates on the central axis of the discharge tube.

Fig. 7
figure 7

Spatial structure of the ionic (480 nm band pass) and neutral particles (600 nm high pass) with different RF input powers

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As for the low-energy electron excited neutral particles (600 nm high pass), they are also firstly generated at both ends of the antenna. They expand to the middle of the antenna to form an axial particle path with the increase of input powers. After the wave mode has been reached, the axial particle path is formed. But the higher axial intensities locate at both ends of the antenna. The radial distribution concentrates towards the center slightly.

Plume plasma properties

Figure 8 shows plume plasma structure of the ionic (480 nm band pass) and neutral particles (600 nm high pass) with different RF input powers. The results show that the high-energy electron excited ionic particles are highly directional compared with that of the low-energy electron excited neutral particles. The ionic particles could reach longer axial distances than the neutral ones.

Fig. 8
figure 8

Plume plasma structure of the ionic (480 nm band pass) and neutral particles (600 nm high pass) with different RF input powers

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Reversed magnetic field

Figure 9 shows the effects of reversed magnetic field on the plasma structure. For low-energy electron excited neutral particles, the positive and negative magnetic fields have little effect on the radial and axial density distribution. However, for high-energy electron excited ions, the axial density distribution is asymmetric with the maximum density locates at one end of the antenna after reach the W mode. In addition, the reversed magnetic field can change the axial position of the maximum density from one end to the other.

Fig. 9
figure 9

Effects of reversed magnetic field on the plasma structure

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Discussion

For electric propulsion, ion energy distribution is more important because ions are the contributors of effective thrust. The results described above show the different spatial structures and intensity jumps of the high-energy electron excited ionic and the low-energy electron excited neutral particles. Therefore, we want to establish a relationship between the ion energy distribution and the relatively high- and low-energy electrons.a

Figure 10 shows the normalized IEDFs from the RFEA tests with the RF input power from 200 to 1200 W under the − 50 A magnetic field configuration conditions. They were normalized as their integral area to be 1. It shows that the proportion of high-energy components in IEDFs increase as the power increases. Figure 11 shows the variation of maximum (most probable) ion energy with increasing power. It shows the increase of maximum ion energy with increasing power.

Fig. 10
figure 10

Normalized IEDF with different RF input powers

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Fig. 11
figure 11

Maximum ion energy variation with power

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Figure 12 shows the axial electron density distribution derived from a Langmuir probe and the ICCD pictures with the reversed magnetic field. It shows an agreement between the electron density measured by the Langmuir probe and the emission intensity pictures obtained by the ICCD. The results show that the axial density distribution is asymmetric with the maximum density locates at one end of the antenna. And the reversed magnetic field can change the axial position of the maximum density from one end to the other.

Fig. 12
figure 12

Axial electron density distribution from a Langmuir probe

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Figure 13 shows the IEDFs with the reversed magnetic field. The results indicate that the maximum value of the IEDFs increases about 15 eV under the + 50 A magnetic field configuration. This is because the testing point for ion energy is located on the right side (downstream) of the discharge tube. Under the reversed magnetic field condition, the ionization/acceleration (higher density) zone is close to the ion energy testing point, resulting in minimal loss of ion energy. Therefore, the ion energy in helicon thruster can be regulated through changes in input power and magnetic field configuration, making it more suitable for space propulsion applications.

Fig. 13
figure 13

IEDFs with reversed magnetic field

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Conclusion

In this paper, a Langmuir probe, an OES, filters, an ICCD camera, and a RFEA have been used in order to distinguish the particles with different energies, obtain their spatial structure, ion energy distributions and establish a relationship between them. The emission spectrum of the helicon discharge plasma can be mainly divided into two groups. One is the high-energy electron excited ionic lines and the other one is low-energy electron excited neutral lines. Their intensity jumps and growth rates show significant difference with the increase of the RF input powers. Therefore, we use two filters and the ICCD camera to obtain the spatial images of the different particles. The discharge plasma and the plume plasma structures have been studied and the effects of the reversed magnetic field on the discharge plasma have also been investigated.

The helicon discharge modes change from E, H modes to W1, W2 modes as power increases. The intensity of the low-energy electron excited neutral lines become to a saturation level after W mode, but the intensity of the high-energy electron excited ionic lines still increase almost linearly with the increasing input power. The electron density test results both from the Langmuir probe and the ICCD show that the axial density distribution is asymmetric with the maximum density locates at one end of the antenna at W mode. The reversed magnetic field can change the axial position of the maximum density from one end to the other.

The IEDF test results show that the maximum (most probable) ion energy increases with increasing input power. Meanwhile, the reversed magnetic field (+ 50 A) can increase the maximum ion energy by about 15 eV. This is believed to be the ionization/acceleration (higher density) zone is close to the measuring point for ion energy, resulting in minimal energy loss. Therefore, the ion energy in helicon thruster can be regulated through changes in input power and magnetic field configuration, making it more suitable for space propulsion applications.