The role of ion magnetization on plasma generation in a magnetic nozzle rf device

Abstract

Two dimensional mappings of the floating potential, Ar II emission and ion saturation currents are used to characterize an 80 cm long magnetized rf plasma column. The data brings new evidence supporting that the level of ion magnetization under the rf loop antenna plays an important role for the efficient generation of plasma over an extended region when the magnetic nozzle is sufficiently separated from the antenna. Densities up to $10^{18}$ m$^{-3}$ and a blue core are observed for an rf power of 200 W and magnetic fields above 400 G when ions are magnetized. The local wall charging under the antenna is probed and observed to change coherently with the local ion magnetization and seems critical to the global creation and transport of energetic electrons, which are indirectly observed far from the antenna when the ion Larmor radius is much smaller than the glass tube radius over the entire region of investigation.

Introduction

Spontaneous acceleration of quasineutral plasmas through a magnetic nozzle (MN) is one of the basic principles of novel spacecraft electric propulsion [1, 2]. One such propulsion technology, the helicon thruster (HT), also called magnetic nozzle rf plasma thruster, has been continuously scrutinized both theoretically and experimentally over the past 20 years. This has recently resulted in the milestone of a prototype achieving a thrust of $\sim 55$ mN and an efficiency of nearly $20\%$ at 4 kW using argon [3]. Efforts are on-going to further improve the understanding of the thrust generation mechanisms and increase the system efficiency in order to make HT competitive with legacy thruster technologies [2]. The motivation comes from the HT promises of longer lifetime and system simplicity, thanks to having no electrode or live elements in contact with the plasma [4].

Several mechanisms contributing to the thrust generation have been identified since the first report of an ion beam-generating current-free double layer in a helicon device in 2003 [4]. From the force balance point of view, the total thrust has two principal positive contributions. The first one is the thermal plasma pressure on the backplate of the thruster source tube. The second one is a Lorentz force owing to an azimuthal diamagnetic electron drift interacting with the radial component of the applied magnetic field [5]. Diamagnetic drifts are induced by radial gradients in electron pressure and tailoring the radial profiles of electron density and temperature is therefore key to achieving a high performing thruster. In particular, peripheral high density and high temperature conical structures have been repeatedly observed downstream of a MN [6,7,8]. Studies have quantified the contribution of these structures to the axial momentum flux, while their geometry would result in a larger plume divergence compared to axially peaked plasma structures [9, 10]. The leading hypothesis for the formation of high density conics is local ionization by electrons energized a few skin depths under the rf antenna and exiting along some of the most radially outward magnetic streamlines capable of escaping the thruster source [6, 7, 11]. A good understanding of the efficient transport of energetic particles is therefore key.

Radial ion fluxes and associated momentum loss to the radial source wall have been identified as affecting the HT’s efficiency [12, 13]. Increasing the magnetic field intensity can reduce the cross-field diffusion and studies have found the level of ion magnetization in the source tube to be a critical parameter in obtaining an ion beam [13,14,15,16,17]. Recent studies have correlated the level of ion magnetization in the source tube with the observations of plasma densities $\ge 10^{18}\ \mathrm {m}^{-3}$ at the MN throat, for relatively low rf powers and magnetic field intensities [18,19,20]. In a similar fashion to the conics, this high density peak at the location of strongest axial magnetic field seems to be predominantly due to remote ionization by energetic electrons transported from the antenna region, while a wave-heated regime has not been identified so far for such configurations [19]. For efficient transport of these high energy electrons, the anisotropic charging of the dielectric source tube could be an important factor [19, 20]. The magnetic behavior of the plasma in the source tube is therefore another key factor to consider for improving the performances of the MN rf thruster. Localized charging under the rf antenna due to an asymmetrical capacitive mode is also anticipated to pay a role in the ion dynamics [21].

This study presents evidence of the role of ion magnetization and associated ion-wall interactions in the generation of high density plasmas in the region from the rf antenna to the MN at a relatively low rf power of 200 W. The hypothesis of ion magnetization-driven local wall charging affecting the transport of hot electrons is investigated through local and volumetric ion saturation and floating potential measurements. The in-situ measurements are completed by nondisruptive optical emission intensity diagnostics. The findings are discussed in terms of their expected impacts on magnetic nozzle rf thruster performances. Section 2 presents the apparatus and employed diagnostics, Section 3 briefly reviews the two modes of operation of the plasma discharge, and Section 4 details the volumetric and glass tube surface floating potentials. Section 5 relates the findings to the efficient generation of high plasma densities.

Apparatus & diagnostics

The measurements are conducted in Huia, a plasma experiment at the University of Auckland specifically designed to allow flexible study of rf magnetized plasma generation and transport. Huia’s active plasma region is a 150 cm long, 9 cm inner diameter borosilicate glass tube, a section of which is represented in Fig. 1. Huia is complementary to the Australian National University based Echidna experiment, working at different radiofrequencies and using a different rf antenna type [19]. A base pressure of a few $10^{-7}$ Torr is maintained with a 250 l/s turbo pump backed by a primary pump. Argon is injected upstream of the glass tube through a mass-flow controller. The power from a 1 kW rf generator set at 27.12 MHz is fed to a 4/3 turn tightly wound loop antenna, the center of which marks the origin of Huia’s (r, z) reference frame (see Fig. 1). The rf load impedance is matched to $50\ \Omega$ using an L-type matching network. A pair of solenoids of 352 turns each is used in a Helmholtz configuration to create a maximum magnetic flux density of 23.82 G/A on axis. The axial magnetic flux density profile is shown in Fig. 2. The position of the solenoids can be adjusted from $z=-10$ cm to $z=80$ cm, allowing a wide range of magnetic field configurations. The axial position of the center of the solenoids is denoted as $z_{\mathrm {B}}$, which also marks the location of maximum axial magnetic field intensity $B_{0}$.

Fig. 1

Schematic of the Huia plasma device with main components labeled. The loop antenna is located at $z=0$ cm while the movable solenoid pair is centered at $z=z_{\mathrm {B}}=30$ cm. The movable planar Langmuir probe is inserted through a linear/rotary vacuum feedthrough at $z=120$ cm. The axial location of the gas inlet coincides with the axial location of the turbo pump inlet. The light grey elements are all grounded

Fig. 2

Axial magnetic flux density with the solenoids placed at $z_{\mathrm {B}}=30$ cm. The dotted vertical line marks the position of the loop antenna

In the results that follow, the rf power was maintained at 200 W with a reflected power smaller than 1$\%$ at all times. The argon pressure is fixed at 1 mTorr and the antenna-solenoids distance was varied between $z_{\mathrm {B}}=0$ cm and 40 cm. The maximum axial magnetic flux density is varied between 75 G to 950 G.

The plasma floating potential $V_{\mathrm {f}}$ and the ion saturation current $I_{\mathrm {sat}}$ are measured using a 2 mm diameter nickel disk mounted atop a thin ceramic tube to form an uncompensated planar Langmuir probe (LP). The probe is left floating to acquire $V_{\mathrm {f}}$ or is biased at $-100$ V to measure $I_{\mathrm {sat}}$ [22]. Where the electron temperature $T_{\mathrm {e}}$ is known, the ion density $n_{\mathrm {i}}$ is deduced from

$$\begin{aligned} I_{\mathrm {sat}} = 0.61 n_{\mathrm {i}} e A_{\mathrm {p}} u_{\mathrm {B}}, \end{aligned}$$

(1)

where e is the elementary charge, $A_{\mathrm {p}}$ the probe surface area, and $u_{\mathrm {B}}$ the ion Bohm speed. The factor of 0.61 accounts for the presheath-sheath density drop. The probe is mounted at the extremity of an off-center 1.5 m long movable shaft inserted at the downstream end of Huia ($z=120$ cm in Fig. 1). The shaft is covered by a glass sheath to ensure minimum disruption to the predominantly dielectric plasma boundary conditions inside Huia [20]. Taking advantage of the axisymmetric geometry of Huia, the shaft is simply rotated to produce two-dimensional (r-z) scans.

A band-pass optical filter centered around 488 nm with a FWHM of 10 nm is used together with a Raspberry Pi camera module as an optical plasma diagnostic. The camera module is based on a color 12 MP Sony IMX477 CMOS sensor. The images were captured in the RAW format using the open-source libcamera library and the rawpy python module in order to by-pass the on-chip post-processing. When filtered, the light gathered by each color channel is extracted and summed together to produce a grayscale image of the scene. The pictures of the plasma in Huia are shot radially to produce (r-z) two-dimensional maps of the glow in broadband visible (VIS) light and for the Ar II relaxation emission at 488 nm.

Single density peak to double peak mode transition

Two separate studies by Bennet et al. and Filleul et al. performed on Echidna and Huia, respectively, have both observed a similar behavior when the separation between the antenna and the solenoids center (i.e. $z_{\mathrm {B}}$) is increased beyond some threshold [19, 20]. Interestingly, it was further shown that the working frequency and the type of antenna, whether a double-saddle type or the loop antenna aforementioned, played no role in the mechanisms at work [20]. The key points of this dynamic are summarized here and reproduced from Ref. [20] to pave the way for the next section.

Fig. 3

Evolution of the axial ion density profiles when the solenoids are located on top of the antenna (orange markers), 30 cm away (red markers) and 40 cm away (blue markers), showing the transition between single to double peak modes. $B_{0}=300$ G for all three cases. The antenna position is marked by the dotted vertical line

The common configuration found in most magnetized rf plasma devices used for the study of helicon thrusters is with the antenna located in the region of uniform magnetic field (minimum axial gradient) [4, 5]. Figure 3 shows the axial density profile measured in Huia in such a configuration when the solenoids are located on top of the antenna ($z_{\mathrm {B}}=0$ cm, orange curve) for $B_{0}=300$ G. It can be seen that the axial plasma density peaks at $\sim 4\cdot 10^{17}\ \mathrm {m}^{-3}$ just 2 cm downstream from the loop antenna and then decreases closely following the axial decay of $B_{0}$ (c.f. Fig. 2). This behavior is not surprising as most of the plasma would be created under the antenna and the locally peaking magnetic field would act in reducing the cross-field diffusion and the plasma losses to the walls. As $B_{0}$ decreases downstream, wall losses would increase and the plasma density decrease in the absence of local plasma creation, as observed in Fig. 3.

When $z_{\mathrm {B}}$ is increased to 30 cm, the axial density profile follows the solenoids and the peak density value is two times higher than when $z_{\mathrm {B}}=0$ cm. This change in the peak location as well as in the maximum density increase takes place monotonously when $z_{\mathrm {B}}$ is progressively increased [19, 20]. For $z_{\mathrm {B}} > 30$ cm, it is observed that the peak density then decreases and at $z_{\mathrm {B}}=40$ cm, a second maximum in density appears under the antenna (blue curve in Fig. 3). For larger $z_{\mathrm {B}}$, this double peak mode is observed to persist for $z_{\mathrm {B}}$ up to 60 cm [19, 20].

It should be noted that the ion densities reported in Fig. 3 have been calculated with Eq. 1, using the ion saturation currents measured with the planar langmuir probe and an axially constant electron temperature of $T_{\mathrm {e}} \simeq 4.5$ eV, measured with an rf compensated Langmuir probe for different $z_{\mathrm {B}}$.

Figure 4 shows the 2D (r-z) maps of the ion saturation. The measurements were carried in the top half of the (r-z) plane and mirrored for clarity. Figure 4(a) is for the same conditions as the red curve of Fig. 3, while Fig. 4(b) is for the blue curve. Figure 4(c) is also for $z_{\mathrm {B}}=40$ cm but at twice the magnetic field intensity $B_{0}=600$ G. It can be observed that the single and double peak features are not restricted to the centreline ($r=0$ cm), as shown in Fig. 3, but exist on axial profiles for which $|r|\lesssim 1$ cm. More interestingly is the fact that doubling $B_{0}$ has returned the plasma to the single density peak mode at $z_{\mathrm {B}}=40$ cm.

The fact that $I_{\mathrm {sat}}$ has increased under the solenoids in the $z_{\mathrm {B}}=40$ cm / $B_{0}=600$ G case compared to $z_{\mathrm {B}}=30$ cm / $B_{0}=300$ G can be attributed to the radial reduction in the magnetized electron column from the antenna to $z_{\mathrm {B}}$, as the electrons are fully magnetized in the entirety of the probed plasma volume. The electron Larmor radius is indeed still of the order of 1 mm at a distance of 30 cm away from the solenoids and when $B_{0}=300$ G. However something is happening in the $z_{\mathrm {B}}=40$ cm / $B_{0}=300$ G which is preventing the high density mode to take place.

Fig. 4

2D mappings of the ion saturation current measured with the planar Langmuir probe when the solenoids are 30 cm away from the antenna and with $B_{0}=300$ G (a), when $z_{\mathrm {B}} = 40$ cm and $B_{0}=300$ G (b), and $z_{\mathrm {B}} = 40$ cm and $B_{0}=600$ G (c). The solid black lines represent the field lines which intersect the glass tube under the antenna at $r=\pm 4.5$ cm and $z=0$ cm

Fig. 5

2D mappings of the floating potential $V_{\mathrm {f}}$ measured with the planar Langmuir probe when the solenoids are 30 cm away from the antenna and with $B_{0}=300$ G (a), when $z_{\mathrm {B}} = 40$ cm and $B_{0}=300$ G (b), and $z_{\mathrm {B}} = 40$ cm and $B_{0}=600$ G (c)

Combining the radial $I_{\mathrm {sat}}$ profiles in Fig. 4 with radial electron temperature profiles acquired with an rf compensated probe (not reported here), one can calculate the average rf skin depth under the antenna to be around 1.2 cm ($\delta _{\mathrm {rf}} = c / \omega _{\mathrm {pe}}$, with $\omega _{\mathrm {pe}}$ the electron plasma frequency). This implies that most of the rf power is deposited in the first 2 cm under the antenna.

Floating potential and anisotropic wall charging

The observation that a similar mode switching is taking place when the magnetic flux density is increased (c.f. Fig. 4) or when the solenoids are moved away from the antenna (c.f. Fig. 3), whilst the rest of the operating parameters are constant, alludes to the key role played by the plasma magnetization under the antenna. Moreover, it was observed that the mode transition is occuring at the same $z_{\mathrm {B}}$ and $B_{0}$ regardless of changes in rf power (fromm 200 W to 500 W) or in argon pressure (from 0.5 mTorr to 5 mTorr) [19].

Fig. 6

Floating potential profiles measured along the glass tube inner surface, at $r\simeq 4.3$ cm for the conditions of Fig. 5(a) and (c) 2DVf

For ions at room temperature and $B_{0}=300$ G, the ion Larmor radius $r_{\mathrm {Li}}$ stays smaller than the glass tube internal radius of 4.5 cm up to 32.5 cm away from the solenoids. This distance increases to 41.5 cm when $B_{0}=600$ G. Beyond these points, $r_{\mathrm {Li}}$ increases rapidly. Said otherwise, for the cases $z_{\mathrm {B}}=30$ cm / $B_{0}=300$ G and $z_{\mathrm {B}}=40$ cm / $B_{0}=600$ G, the ions are fully and partially magnetized between the solenoids ($r_{\mathrm {Li}}\simeq 0.5$ cm) and the antenna ($r_{\mathrm {Li}}\simeq 3.7$ cm), respectively. For $z_{\mathrm {B}}=40$ cm / $B_{0}=300$ G however, $r_{\mathrm {Li}} \simeq 8$ cm under the antenna and the local ion flux to the wall would be increased in this case. This was previously remarked in Refs. [19, 20] but not supported by measurements of the local charging of the wall.

Figure 5 shows the 2D (r-z) maps of the plasma floating potential $V_{\mathrm {f}}$ measured with the Langmuir probe for the same conditions as in Fig. 4. It can be seen that the floating potentials behave similarly to $I_{\mathrm {sat}}$, i.e. $z_{\mathrm {B}}=30$ cm / $B_{0}=300$ G and $z_{\mathrm {B}}=40$ cm / $B_{0}=600$ G have very similar $V_{\mathrm {f}}$ features and magnitudes whereas the mapping of $V_{\mathrm {f}}$ for $z_{\mathrm {B}}=40$ cm / $B_{0}=300$ G portrays a different plasma dynamic.

Noticeably, $V_{\mathrm {f}}$ is relatively constant and uniform in the dense plasma column under the solenoids when the ions are magnetized under the antenna in Fig. 5(a) and (c). Also similar are the islands of maximum $V_{\mathrm {f}}$ above and below, i.e. radially outward from the dense plasma location, which indicates that the glass tube is significantly positively charged under the solenoids. Finally, another interesting feature in these two mappings is the fact that $V_{\mathrm {f}}$ takes its lowest values right under the antenna. The axial scans of $V_{\mathrm {f}}$ taken closest to the glass tube edge at the coordinate $r=4.3$ cm for the cases $z_{\mathrm {B}}=30$ cm / $B_{0}=300$ G and $z_{\mathrm {B}}=40$ cm / $B_{0}=600$ G are plotted in Fig. 6 for better visualization of the anisotropic charging of the glass tube. $V_{\mathrm {f}}$ has clear global minima that match well with the location of the loop antenna at $z=0$ cm. It should be pointed out that rf sheath dynamics induced by the presence of the antenna could also play a role in the presence and in the magnitude of these local drops in the glass charging [21]. In both cases, the glass tube has a differential charging of around 60 V between the antenna and $z_{\mathrm {B}}$. One last feature worth noting in Fig. 5(a) are the valleys of lower floating potential which follow the last field lines to cross the antenna region. Such a characteristic dip in $V_{\mathrm {f}}$ has been previously associated with the presence of energetic magnetized electrons, presumably excited in the rf skin layer under the antenna and travelling all the way to $z=-60$ cm to potentially contribute to remote ionization [23].

When the ions are not magnetized under the antenna, i.e. for the case $z_{\mathrm {B}}=40$ cm / $B_{0}=300$ G in Fig. 5(b), while there is still a visible local minimum of $V_{\mathrm {f}}$ under the antenna, the global characteristics of $V_{\mathrm {f}}$ are very different. $V_{\mathrm {f}}$ peaks axially under the antenna and progressively decreases along z to reach $\sim -45$ V downstream of the magnetic nozzle throat. The radial profiles are also more homogeneous with nearly radial $V_{\mathrm {f}}$ isolines in the right-hand side of the MN, contrasting with isolines following the magnetic field lines when the ions are magnetized. Since the floating potential is defined as the potential necessary to equalize the local fluxes of ions and electrons, the region of maximum $V_{\mathrm {f}}$ under the antenna when $z_{\mathrm {B}}=40$ cm / $B_{0}=300$ G can be interpreted as a region of larger ion flux. This is consistent with the local maximum in ion saturation current under the antenna in Fig. 4(b). The picture emerges where local ions with Larmor radii of the order of 8 cm collide with the glass tube surface before even completing 1/4 of their gyration. The ions will be unable to travel downstream along the field lines and will locally contribute to a more positively charged glass tube. Fewer of the warm and energetic electrons excited some skin depths under the antenna will be able to travel downstream, as a result of being electrostatically trapped under the antenna, inducing a local density peak under the antenna. This reduced transport could at least partly explain why the amplitude of the density peak under the solenoids decreased between $z_{\mathrm {B}}=40$ cm and $z_{\mathrm {B}}=30$ cm in Fig. 3.

Fig. 7

$V_{\mathrm {f}}$ (circle symbols, left axis) measured at $z=0$ cm, i.e. under the antenna by placing the LP right against the glass tube wall as a proxy for the local wall charging when the applied magnetic field is increased. The measurements are repeated for increasing value of $z_{\mathrm {B}}$, from 25 cm (a) to 40 cm (d), in 5 cm steps. The ion Larmor radius $r_{\mathrm {Li}}$ under the antenna (solid line, right axis) is also shown. The horizontal dashed line represents the glass tube inner radius

To complete the picture on the role of the local ion magnetization in the generation of high density plasmas in Huia, a Langmuir probe was placed at $r=4.3$ cm and $z=0$ cm, i.e. against the glass tube under the antenna, and $B_{0}$ was progressively increased. The recorded $V_{\mathrm {f}}$ vs $B_{0}$ characteristics are reported in Fig. 7 for four different values of $z_{\mathrm {B}}$, alongside with the calculated values of $r_{\mathrm {Li}}$ under the antenna. The similar shapes and magnitudes of the $V_{\mathrm {f}}$ curves for the four different $z_{\mathrm {B}}$ is striking, suggesting that the local plasma equilibrium conditions are the same in each case but occur for higher $B_{0}$ as the solenoids are progressively moved away from the antenna. For each $z_{\mathrm {B}}$, the floating potential under the antenna shows a sharper decrease for $B_{0}$ values which result in $r_{\mathrm {Li}}=4.5$ cm. This observation brings yet another clue of the importance of local ion-source wall dynamics for the global plasma equilibrium. This also suggests that assuming ions at room temperature is a reasonable approximation, at least under the antenna.

A closer look at the different regions of the characteristics in Fig. 7 reveals some insights of the local flux balance as $B_{0}$ increases. It is worth noting that for all the conditions presented in Fig. 7, the electrons stay magnetized with $r_{\mathrm {Le}} \le 4.5$ mm. $r_{\mathrm {Le}}$ is calculated considering $T_{\mathrm {e}}\sim 10$ eV, which was measured under the antenna against the glass tube with an rf compensated probe. In other words, the magnetization effect on the electrons’ flux to the wall can be taken as constant in what follows. Changes in $V_{\mathrm {f}}$ are expected to be driven mostly by the level of ion magnetization and electrostatic effects.

When the ions are unmagnetized under the antenna (i.e, $r_{\mathrm {Li}} \ge 4.5$ cm), the local $V_{\mathrm {f}}$ asymptotically increases to values around $+50$ V when $B_{0}$ decreases, which would result in a larger fraction of trapped high-energy electrons and a plasma generation more localized to the antenna region. The trend in $V_{\mathrm {f}}$ with $B_{0}$ is similar to the trend of $r_{\mathrm {Li}}$. Below the $r_{\mathrm {Li}}=4.5$ cm threshold, an increasing fraction of ions are magnetized under the antenna, and fewer will collide with the glass tube during their gyration, making $V_{\mathrm {f}}$ more negative.

The minima in $V_{\mathrm {f}}$ in Fig. 7 correspond to an ion gyroradius between approximately 2 and 3 cm. Beyond that point, the floating potential is seen to increase again. The following qualitative picture is proposed as a possible explanation as to why $V_{\mathrm {f}}$ increases again for values of $B_{0}$ that make $r_{\mathrm {Li}} < 2$ cm under the antenna. When $r_{\mathrm {Li}} \simeq 2$ cm, ions in the center of the column under the antenna have Larmor orbits grazing the glass tube and will only collide with the glass tube when moving upstream or downstream from this location. This is promoted by the relatively short ion-neutral collision mean free paths ($\sim 3$ cm at 1 mTorr) which would increase the cross-field diffusion. For larger $B_{0}$, most ions are closely tied to the magnetic field lines as $r_{\mathrm {Li}}\sim 1.5$ cm, the minimum value of $r_{\mathrm {Li}}$ in the conditions of interest. This could promote the increase in ion flux from ions existing along the streamlines that intersect the glass tube under the antenna. The local ion flux to the glass tube increases again and it is seen to plateau as $r_{\mathrm {Li}}$ gets to its minimum value. The plateauing is specially visible in Fig. 7(a). Qualitatively, this is owing to the inhibition of the ion cross-field diffusion. When the field strength is increased to $B_{0}=600$ G for $z_{\mathrm {B}}=30$ cm, the profile of $V_{\mathrm {f}}$ along the glass tube, not presented in this study, shows that there is no further global minima of $V_{\mathrm {f}}$ under the antenna.

High density genereation

Figure 8 shows the ion density on axis under the solenoids, measured with the planar Langmuir probe as $B_{0}$ is increased, for $z_{\mathrm {B}}=30$ cm and $z_{\mathrm {B}}=40$ cm. This figure shows the effectiveness of the plasma generation in the single peak mode. The increase in $n_{\mathrm {i}}$ is the steepest when ions are progressively getting magnetized under the antenna. One continuous and one dash-dotted vertical lines mark the thresholds of ion magnetization under the antenna, as reported in Fig. 7, for $z_{\mathrm {B}}=30$ cm and $z_{\mathrm {B}}=40$ cm, respectively. Beyond these thresholds, the rates of increase of $n_{\mathrm {i}}$ with $B_{0}$ are lower. For $z_{\mathrm {B}}=30$ cm, $n_{\mathrm {i}}$ eventually reaches a saturation point at $1.3\cdot 10^{18}~\mathrm {m}^{-3}$ around 800 G, probably because the plasma cross-field diffusion cannot be further reduced.

Fig. 8

Ion density under the solenoids on axis for increasing magnetic density flux, when $z_{\mathrm {B}}=30$ cm and $z_{\mathrm {B}}=40$ cm. The vertical continuous and dash-dotted line marks the antenna ion magnetization thresholds for $z_{\mathrm {B}}=30$ cm and $z_{\mathrm {B}}=40$ cm, respectively

Figure 9 shows the light emission of plasma as $B_{0}$ is increased and with the solenoids placed 30 cm away from the antenna. The two vertical bands in each image are where the plasma emission is blocked by the solenoids. The scene axially spans slightly over 60 cm. In order to give a faithful color representation, the top row in Fig. 9 was produced with the camera with the stock wide bandwidth UV-NIR filter in place. The bottom row images were produced by removing the UV-NIR filter and by placing the 488 nm filter in front of the objective lens.

It is visible in both rows that the plasma stays mostly confined to the antenna region when $B_{0}=75$ G. At higher magnetic fields, the plasma luminosity increases downstream and from 300 G onward the characteristic blue light of the Ar II emissions starts to dominate inside the collimated column under the solenoids (c.f. Fig. 9(c) and (d)). At 600 G, a blue core is formed, which is evident with the strong 488 nm light intensity in Fig. 9(h).

Excitation of an argon ion to a state which then decays by emitting a 488 nm photon can either happen from a direct electron-neutral collision or through a electron-ion collision [24]. However, the latter is 15 to 30 times more efficient than the former [25]. Therefore, most of the 488 nm light seen can be attributed to electron-ion collisions. Moreover, this process has a threshold in electron energy of 17 to 20 eV [24, 26]. Hence, the Ar II light in Fig. 9 is likely a sign of the presence of electrons in the inelastic range far downstream from the antenna, especially since the excited ion state which can emit the 488 nm photon has a lifespan of a few nanoseconds, i.e. far shorter than the travel time of thermal ions from the antenna to the solenoids [27]. Ions created under the antenna are also unlikely to efficiently travel downstream as the ion-neutral collision mean-free paths are around 3 cm at the present working pressure. The sign of a significant fraction of electrons in the inelastic range beyond $z_{\mathrm {B}}$ is suggestive of the non-local plasma ionization in Huia taking place due to the transport of high-energy electrons from the antenna.

The continuous increase in the Ar II light intensity under the solenoids with $B_{0}$ matches the trend of the measured ion density in Fig. 8. The onset of a wave-heated mode is often associated with the observation of a step increase in plasma density with $B_{0}$ [28]. Since no such step increase was observed here, nor wave modes identified in Echnida [19], the data from Figs. 9 and 8 support the hypothesis that the remote ionization far from the antenna could be due to the downstream transport of electrons energized under the antenna. Such energetic electrons have been measured with the rf compensated probe and will be the focus of a future work.

Fig. 9

The top row a-d shows the evolution of the plasma discharge along the glass tube in broadband visible light as $B_{0}$ is increased at a fixed power of 200 W, an argon pressure of 1 Torr and $z_{\mathrm {B}}=30$ cm. The loop antenna is visible as a thin black line at the extreme left of each picture. The bottom row e-h shows the same scene but captured again through the 488 nm filter. The camera’s shutter speed was set at 1/125 s while the analog and digital gain of the sensor were fixed to unity. The white balance was kept constant for the VIS light photographs, and is irrelevant for the filtered ones

Conclusion

Volumetric and localized in-situ measurements, as well as non-disruptive optical measurements, are presented to explore plasma modes in a long converging-diverging magnetized rf column. The experimental conditions can be taken as a proxy of the conditions existing in the source tube of a magnetic nozzle rf thruster before the plasma expands into space.

Two modes of operation are observed. The first one has a single axial high density peak coinciding with the location of maximum magnetic field. The second mode sees the density being double-peaked on axis, with one peak under the antenna and a second under the solenoids. The transition between the two modes takes place either when the solenoids are moved farther away from the antenna at a constant magnetic field, or when the magnetic field flux density is decreased for a given solenoid position. A strong correlation is observed between the level of ion magnetization under the rf antenna and the plasma being in one mode or the other. This is further supported by measurements of the plasma floating potential under the antenna, $\sim 1.5$ mm away from the glass tube, showing changes in the local glass tube charging that match well with the local ion gyroradius becoming smaller than the glass tube radius. When ions are unmagnetized under the antenna, while electrons are always magnetized, the local flux balance causes the glass tube to be locally strongly positively charged, resulting in an electrostatic trapping of high-energy electrons that would have otherwise traveled far downstream. This causes the plasma to be in a double-peaked mode. In the single peak mode, densities up to $10^{18}\ \mathrm {m}^{-3}$ and strong Ar II emission are observed at a modest rf power of 200 W and a magnetic field of at least 400 G. This is seen as a sign of efficient plasma generation in a large volume far from the rf antenna. The observation of intense Ar II emission at 488 nm is also an evidence that electrons in the inelastic range are efficiently travelling far away from the antenna or are remotely excited.

These results highlight the importance of considering the levels of ion magnetization in the source tube of a magnetic nozzle rf thruster. In particular, obtaining high plasma densities at moderate rf powers would be beneficial for achieving a high propellant utilization fraction and thruster efficiency.