Operating Characteristics of a Wave-Driven Plasma Thruster for Cutting-Edge Low Earth Orbit Constellations

Abstract

This paper outlines the development phases of a wave-driven Helicon Plasma Thruster for cutting-edge Low Earth Orbit (LEO) constellations. The two-stage ambipolar electric propulsion (EP) system combines the efficient ionization of an ultra-compact helicon reactor with plasma acceleration based on an ambipolar electric field provided by a magnetic nozzle. This paper reveals maturation challenges associated with an emerging EP system in the hundreds-watt class, followed by outlook strategies. A 3 cm diameter helicon reactor was operated using argon gas under a time-modulated RF power envelope ranging from 250 W to 500 W with a fixed magnetic field strength of 400 G. Magnetically enhanced inductively coupled plasma reactor characteristics based on half-wavelength right helical and Nagoya Type III antennas under capacitive (E-mode), inductive (W-mode), and wave coupling (W-mode) were systematically investigated based on Optical Emission Spectroscopy. The operation characteristics of a wave-heated reactor based on helicon configuration were investigated as a function of different operating parameters. This work demonstrates the ability of two-stage HPT using a compact helicon reactor and a cusped magnetic field to outperform today’s LEO spacecraft propulsion.

1. Introduction

The emergence of new space business models has fostered a highly competitive environment for EP systems, driving the need for enhancements in reliability, performance, cost, efficiency, and adaptability. Next-generation LEO constellations and Atmosphere Breathing Electric Propulsion (ABEP) platforms require a broad maneuver envelope, including drag force compensation, short periodic orbit maintenance, high-impulse orbit raising operation, low-thrust attitude control, station keeping (SK), and end-of-life disposal. Due to their high specific impulse, which significantly reduces the required onboard propellant mass, fully EP systems are anticipated to be a milestone of emerging LEO constellations in new-space initiatives. As a result, the EPs become a disruptive approach to enhance the expanding commercial incentives associated with Earth Observation (EO) clusters, Internet of Things (IoT) connectivity, LEO communication systems, future global positioning systems, scientific research, digital television, cloud-based, and data-driven. Within this comprehensive framework, the development of a competitive plasma-based space transportation (ST) system will be pivotal for advancing future space exploration.

In the low to intermediate power ranges, Gridded Ion Thrusters (GITs) and Hall Effect Thrusters (HETs) have acquired a substantial spaceflight heritage in large telecom platforms for SK, successful deployment in SMART-1 [1], BepiColombo [2], Dawn [3], Hayabusa 1 [4], and Hayabusa 2 [5] missions. Both HETs and GITs exhibit low efficiency in the milli-Newton thrust level [6]; this working range has a particular relevance since the number of designers and operators of LEO constellations is projected to grow substantially in the next few years. From an operation point of view, HETs and GITs face significant challenges, primary due to critical components like ion-acceleration grids and thermionic cathode neutralizers (CNs), which necessitate stringent plasma plume neutralization to prevent spacecraft charge accumulation. In the context of the “New Space” market, spacecraft operating in LEO encounter several technical challenges. One significant issue is the inability to use a single plasma-powered EP system across the entire operational envelope, including transitioning from parking orbit to transfer orbit, conducting inter-orbit maneuvers, maintaining orbital positions, controlling altitude, and executing de-orbit procedures. Additionally, conventional EP technologies are hampered by limited operational lifetime, low maneuverability, and high energy demands, further complexifying their effective use in low-orbit environments.

To overcome these limitations, modern spacecraft require onboard plasma-heated EP technologies able to ensure high throttle ability and maneuverability, have a long service life in the residual atmosphere, and have high thrust efficiency, reducing power limitations below $1 \mathrm{k}\mathrm{W}$. Furthermore, solar-powered SP systems should be characterized by a high specific impulse value while being compact to accommodate the stringent size and weight limitations of micro-satellites. Enhancing propulsion metrics, including thrust, specific impulse, thrust efficiency, and thrust-to-power ratio, can be achieved by adopting more advanced ionization techniques. One promising strategy is to substitute the less efficient direct current (DC) electron bombardment ionization with radio frequency (RF) wave-plasma energy deposition, which offers superior ionization efficiency. Fully electrodeless Electric Thrusters (ETs) have recently emerged as disruptive SP technologies, distinguished by several advanced features including high plasma density, operation under low magnetic fields, high efficiency, low-pressure functionality, flexibility in propellant choice, prolonged operational lifetime, multiple operation modes, and the potential for precise control over the electron velocity distribution.

Table 1. The impact of HPT strengths on cutting-edge LEO platforms.

ID	Strengths	Impact on the LEO Platform
1	Fully electrodeless design both for ionization and acceleration	Increased overall system simplicity, new mission scenarios, extended operational lifetime
2	High dense plasma	High thrust density
3	Magnetic Nozzle acceleration scheme	Ambipolar acceleration, quasi-neutral plasma, obviating the need for a cathode neutralizer
4	Versatile technology, flexible in propellant choice	Ability to operate with different propellants, reacting gases acceptable (O2), compatible with “air breathing”
5	Scalability in power and size	Capability to translate customers’ specific needs into technical requirements and to scale the system
6	Continuous throttle ability	Variable thrust and specific impulse/large-range thrust throttling ability
7	No channel wall erosion	Extended operational lifetime in LEO/VLEO environment
8	Adjustable power to thrust ratio (TTPR)	Increased mission flexibility
9	Ultra-compact architecture provided by a MEICP reactor	Low mass and high thrust density
10	Stable continuous operations	Continuous thrust along the orbit to compensate for the drag precisely
11	Low magnetic field strength	Low mass and compact design, suitable for commercial LEO satellite buses with masses below 500 kg
12	Low-pressure plasma reactor operation	Compatible with low-pressure VLEO environment
13	At the exhaust, plasma is quasi-neutral	Avoids high-voltage electronics and eliminates the need for complex components like hollow cathode
14	Less sensitive in terms of minimum pressure and mass flow for ignition	Simple operation scheme

highlights the influence of the HPT strengths on commercial LEO satellite buses. These advancements are expected to yield more effective and versatile propulsion solutions, better suited to the diverse and evolving requirements of contemporary space missions. Due to their distinctive peculiarities, helicon sources have multiple applications, including fully electrodeless RF-powered propulsion technologies [7,8,9,10], plasma sources for magnetic fusion studies (heliac fusion devices) [11], Alfven wave propagation [12], RF current drives [13], laser plasma sources [14], electron beam sources, and laser accelerators [15].

The advancement of cutting-edge micro-satellites buses for near-Earth missions has driven the need for the miniaturization, modularization, and integration of helicon-heated ETs. In response to these requirements, many institutions and research groups globally have undertaken extensive research focused on low-power Helicon Plasma Thrusters (LPHPTs), among which can be mentioned: Tohoku University [16], Canberra [17], Auckland University [18], Madrid University [19], Padova University [20], and the University of Bologna [21]. These technologies have the potential to enable formation flying in low Earth orbits ranging from 150 km to 250 km [6], significantly expanding operational capabilities for small satellites within this altitude range. LEO satellite buses under 500 kg require highly precise propulsion parameters, including input power levels typically below 1 kW, thrust capabilities in the milli-Newton range, and specific impulses between 500 and 3000 s. These specifications are critical for optimal performance in low-thrust orbital maneuvers, such as altitude adjustments, plane changes, and phase changes. Relevant RF-powered propulsion technologies relevant for near-Earth missions in formation flying are underlined in

Table 2. Overview of propulsion metrics results of HPT breadboard models (HPT-BMs).

HPT Breadboard Models	${\mathit{P}}_{\mathit{R}\mathit{F}}$	$\mathit{F}$	$\mathit{F}/{\mathit{P}}_{\mathit{R}\mathit{F}}$	$\mathit{\eta }$
	$\left(\mathbf{k}\mathbf{W}\right)$	$\left(\mathbf{m}\mathbf{N}\right)$	$\left(\mathbf{m}\mathbf{N}/\mathbf{k}\mathbf{W}\right)$	(%)
Takahashi et al. [22]	0.9	3	3.3	0.83
Takahashi et al. [23]	0.8	6	7.5	3
Takahashi et al. [24]	1	11	11	8.4
Charles et al. [25]	0.8	5	6.3	2.1
Williams and Walker [26]	0.6	6	10	0.67
Charles et al. [27]	0.9	6	6.7	2.3
Harle et al. [28]	0.4	1.1	2.75	0.25
Oshio et al. [29]	1	6	6	1.5
Takahashi et al. [30]	1	25	25	7.1
Navarro-Cavalle et al. [31]	0.45	8.5	18.9	14.2
Trezzolani et al. [32]	0.15	1.4	9.3	3.3
Trezzolani et al. [33]	0.07	0.9	12.1	5.2
Siddiqui et al. [34]	0.44	6.2	14.1	9.3

.

To foster a competitive small-satellites LEO market, this paper proposes the development of a disruptive two-stage HPT based on a compact magnetically enhanced inductively coupled plasma (MEICP) reactor with spontaneous acceleration of quasi-neutral plasma through a magnetic nozzle. This innovative design offers a disruptive approach to current ST systems. To achieve an efficient LPHPT, it is mandatory to maximize the power deposited by the RF antenna into the MEICP reactor. Designing a fully electrodeless wave-heated EP system presents several challenges: wave-plasma matching robustness, optimizing RF antenna design, maximizing wave coupling efficiency, facilitating effective wave propagation and absorption, and managing plasma-surface interaction. The primary challenges of Inductively Coupled Magnetized Plasmas (ICMPs) lie in optimizing the plasma reactor to achieve competitive operational performance. Key objectives include: first, achieving high propulsion efficiency with nearly complete propellant utilization and minimal energy loss to reactor walls; second, ensuring subsystems are lightweight, simple, and durable; third, incorporating throttling capabilities to support diverse mission requirements; and fourth, extending the system’s operational lifetime. A consistent theoretical model for the discharge is proposed to validate the fundamental physics and operational principles of helicon-wave-driven ETs. In this regard, two HPT experimental prototypes, designated as HPT-EP01 and HPT-EP02, have been developed and tested under relevant LEO environment conditions, each equipped with distinct $m=+1$ azimuthal mode RF antennas: the half-wavelength right helical (HWRH) and the Nagoya Type III (NTIII) antenna. An experimental investigation is conducted to assess the wave properties and perform parametric analyses of the effects of applied magnetic fields, plasma density, and antenna types on helicon plasma generation. The subsequent sections outline the design and experimental setup of a helicon-heated EP system tailored for commercial satellite platforms, alongside the test configurations employed to validate its proof-of-concept. This includes a comprehensive overview of the experimental validation involving time-modulated RF power and the initial discharge states of the helicon reactor, which were analyzed using Optical Emission Spectroscopy (OES). The performance and characteristics of the system were examined under the operation of both azimuthally asymmetric HWRH and NTIII antennas, with the findings presented and discussed in detail.

2. Methods and Materials

2.1. Design and Characterization of a Magnetically Enhanced Plasma Thruster Based on Helicon Waves

Low-frequency whistler waves, or transverse right-handed circularly polarized wave (RHP), known as helicon waves, appear in a particular area of the Clemmov-Mullaly-Allis (CMA) [35] diagram where the operating frequency $\omega$ lies between the lower-hybrid frequency ${\omega }_{LH}$ and the electron cyclotron frequency, but still much below the plasma frequency. The power deposition mechanism within the helicon reactor, also known as the MEICP reactor, is governed by the synergy between the driving frequency, the ionization chamber’s geometry, and the gyro-frequency. A distinctive feature of MEICP reactor operation is the resonant excitation of helicon waves, which are long-wavelength magnetosonic waves that propagate within the intermediate frequency range between the lower-hybrid and electron cyclotron frequencies $({\omega }_{ci}\ll {\omega }_{LH}<\omega \ll {\omega }_{ce}\ll {\omega }_{pe})$ under magnetic field strengths between 50 G and 2 kG [36].

From a mission-oriented perspective, propulsive maneuvers and orbit transfers must be completed within a designated timeframe to achieve mission objectives. To ensure high operational efficiency, it is crucial to minimize ionization costs. Accordingly, maintaining a minimum thrust-to-power ratio is essential to providing the LEO spacecraft with the necessary velocity increment. To align with the evolving LEO space ecosystem and meet future market demands for high delta-V capabilities, it is proposed to generate dense plasma near lower hybrid frequencies using helicon waves. This approach aims to enhance propulsion efficiency and adaptability, addressing the need for advanced propulsion solutions in response to the growing requirements of modern satellite operations and space missions.

Helicon waves are bounded electromagnetic waves that propagate within the low-hybrid frequency range $\left({\omega }_{ci}\ll \omega \ll {\omega }_{ce}\right)$, situated in the low-frequency whistler region of the fast-wave branch of the cold-plasma dispersion relation. These waves can achieve high plasma densities, exceeding ${10}^{13} {\mathrm{c}\mathrm{m}}^{-3}$, and are capable of generating high ionization rates [11]. In an anisotropic, cold, collisionless plasma under low-pressure conditions, the dispersion relation (DR) for RHP waves is expressed as follows:

$$N^2={\displaystyle \frac{c^2{k}^2}{{\omega }^2}}=1-{\displaystyle \frac{{\omega }_p^2/{\omega }^2}{1-\left({\omega }_{ce}/\omega \right)}},$$

(1)

with $N$ representing the total refractive index.

Within ${\omega }_{LH}\ll \omega \ll {\omega }_{ce}$ in a MEICP reactor, the refractive index is anisotropic and presents resonances at certain angles induced by electron inertia. For an obliquely propagating R-wave, the corresponding wave equation using Stix’s notation can be represented as [37]:

$$\left(\begin{array}{ccc}S-N^2{cos}^2\theta & -iD& N^{2}cos\theta sin\theta \\ iD& S-N^2& 0\\ N^{2}cos\theta sin\theta & 0& P-N^2{sin}^2\theta \end{array}\right)\left(\begin{array}{c}{E}_x\\ E_y\\ E_z\end{array}\right)=0$$

(2)

To achieve a nontrivial solution, the determinant of Equation (2) must vanish [37]. This requirement results in the formulation of the Cold Plasma Dispersion Relation (CPDR), which defines the propagation characteristics of waves in a magnetized plasma. The CPDR links the wave frequency, wave number, and the dielectric properties of the plasma, providing a fundamental framework for understanding how waves interact with the plasma medium. This relation is essential in determining the behavior of wave propagation, including phase velocity, group velocity, and the conditions under which different wave modes can exist within the plasma environment.

$$\begin{array}{c}{\left(iD\right)}^2\left(P-N^2{sin}^2\theta \right)+\left(S-N^2\right)\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}·\left[\left(S-N^2{cos}^2\theta \right)\left(P-N^2{sin}^2\theta \right)-N^4{sin}^2\theta {cos}^2\theta \right]=0\end{array}$$

(3)

By substituting ${cos}^2\theta$ with $1-{sin}^2\theta$, we obtain the following:

$${sin}^2\theta ={\displaystyle \frac{-P\left(N^4-2N^2+RL\right)}{N^4\left(S-P\right)+N^2\left(PS-RL\right)}}$$

(4)

Taking equality $S^2-D^2=RL$ into account, the ${cos}^2\theta$ becomes:

$${cos}^2\theta ={\displaystyle \frac{S{N}^4-\left(PS+RL\right)N^2+PRL}{N^4\left(S-P\right)+N^2\left(PS-RL\right)}}$$

(5)

Considering $2S=R+L$, the cold-plasma dispersion relation becomes:

$${tan}^2\theta =-{\displaystyle \frac{P\left(N^2-R\right)\left(N^2-L\right)}{\left(S{N}^2-RL\right)\left(N^2-P\right)}},$$

(6)

The elements S, N, D, and P are the components of the plasma dielectric tensor, commonly referred to as Stix’s elements [38].

Resonances in a plasma can be identified by examining the conditions under which the total refractive index ($N$) approaches infinity. These conditions occur when the wave frequency matches certain natural frequencies of the plasma, such as cyclotron or hybrid frequencies, leading to a dramatic increase in the refractive index. At these points, the wave energy is heavily absorbed or converted within the plasma, indicating resonant interactions between the wave and plasma particles [37].

$${tan}^2{\theta }_{res}=-{\displaystyle \frac{P}{S}}$$

(7)

Resonance occurs when the phase velocity of a wave approaches zero. At resonance, charged particles oscillate at the same frequency as the external electromagnetic waves, resulting in the particles experiencing a quasi-constant field. This synchronization facilitates resonant energy absorption, as the particles efficiently absorb energy from the wave due to their matched oscillation frequencies. In the frequency limit, ${\omega }_{ci}\ll \omega <{\omega }_{ce}<{\omega }_p$ [39]:

$${tan}^2{\theta }_{res}={\displaystyle \frac{{\omega }_{ce}^2}{{\omega }^2}}\to cos{\theta }_{res}={\displaystyle \frac{\omega }{{\omega }_{ce}}}.$$

(8)

When the helicon wave propagates near resonance cone angle, the plasma density peaks in the HPT. The “accessibility condition” is a critical criterion for plasma heating and production, stipulating that the wave must be capable of propagating into the region where absorption occurs. This condition ensures that the electromagnetic wave can traverse the plasma and reach the absorption zone, thereby enabling effective energy transfer and optimizing the heating and production processes within the plasma. In a bounded plasma system, the whistler wave, characterized by frequencies $\left(\omega \ll {\omega }_{ce}\right)$, predominantly exhibits electromagnetic properties. As the frequency nears the electron cyclotron frequency,${\omega }_{ce}$, the wave becomes more electrostatic, and the TG mode (bounded electron cyclotron wave) becomes the dominant mode [39].

For a $m=+1$ mode antenna, the short wavelength near the resonance angle may ensure the specific radiation pattern. Propagation is confined to wavevectors that lie within a cone of half angle $\theta <{\theta }_{max}$ relative to the direction of the applied magnetic field vector, B. Assuming the RHP wave field varies as $e^{i\left(m\theta +kz-\omega t\right)}$, the wave structure inside a helicon wave plasma reactor committed to advanced propulsion concepts can be related to the dispersion relation achieved from Maxwell’s equations and Ohm’s law [40]:

$${\displaystyle \frac{k^2{c}^2}{{\omega }^2}}={\displaystyle \frac{{\omega }_{pe}^2}{\omega \left({\omega }_{ce}cos\theta -\omega \gamma \right)}},$$

(9)

where c is the speed of light$; k$ is the squared total wave number,$cos\theta =k_{\parallel }/k$,$\gamma =1+i\left(\nu /\omega \right)$; $\nu$ is the frequency of electron collisions with neutrals and ions; k is the wave number $\left(k^2=k_{\parallel }^2+k_{\perp }^2\right); \theta$ is the angle between k and B, with $k,k_{\parallel },k_{\perp }$representing the total, parallel, and perpendicular wavenumbers, respectively; and $\omega , {\omega }_{ce},$and ${\omega }_p={\left(n_e{e}^2/{\epsilon }_0{m}_e\right)}^{1/2}$are angular frequencies of RF power, electron cyclotron motion, and plasma oscillations, respectively.

In the case of $\nu =0$ and $cos\theta =1 \left(\theta \ll 1,\omega \ll {\omega }_{ce} \right)$, the above equation was approximatively resolved as a biquadratic equation derived by Shamrai and Taranov as follows [36]:

$$k_{\perp H,TG}^2=k_{\parallel }^2{\displaystyle \frac{1}{2{\gamma }^2{\alpha }^2{\beta }^2}}\left(1-2\gamma \alpha -2{\gamma }^2{\alpha }^2{\beta }^2\pm \sqrt{1-4\gamma \alpha }\right),$$

(10)

where

$$\left\{\begin{array}{c}\alpha ={\displaystyle \frac{{\omega }_{pe}^2{\omega }^2}{{\omega }_{ce}^2{k}_{\parallel }^2{c}^2}}\\ \beta ={\displaystyle \frac{\omega {\omega }_{ce}{k}_{\parallel }^2{c}^2}{{\omega }_{pe}^2{\omega }^2}}\\ \gamma =1+i\left({\displaystyle \frac{\nu }{\omega }}\right)\end{array}\right.$$

(11)

Equation (11) underlines that there are two values of $k_{\perp }$ related to the slow and fast waves. The $k_{\perp +TG}$ corresponds to the TG perpendicular wave number and $k_{\perp -H}$ to the helicon perpendicular wave number. Also, from Equation (10) results the related condition for propagation of both waves: $\alpha <1/4$ and ${\omega }_{pe}^2<{\omega }_{max}^2=\left(1/4\right){\omega }_{ce}^2{N}_{ref\parallel }^2$. Furthermore, for helicon wave propagation, the term within brackets on the right side of Equation (10) must be positive, which occurs under the conditions $\beta <1$ or ${\omega }_{pe}^2>{\omega }_{min}^2=\omega {\omega }_{ce}{N}_{ref\parallel }^2$. In contrast, TG mode is able to propagate in the outer plasma region where $\alpha <1/4$ and $\beta <1$ [36]. Helicon waves and bounded electron cyclotron waves (TG modes) become distinctly separated at higher magnetic field strengths. However, a synergistic interaction occurs between them at certain critical magnetic fields, characterized by $\alpha =1/4$ and $\beta ~1$ $\left(k_{\perp +TG}=k_{\perp -H}\right)$[36]. In a compact HPT exhibiting a radially nonuniform density profile, wave propagation is segmented into three distinct density regions (Figure 1a). The first one is the low-density region $\left(n_e<n_{low}, r>r_{low}\right)$, which supports the propagation of only Trivelpiece-Gould waves. The second region is the intermediate-density region $\left(n_{low}<n_e,<n_{up},r_{up}<r<r_{low}\right)$ and accommodates both helicon and TG waves. The third region is the high-density region $\left(n_e>n_{up}, r<r_{low}\right)$, which is characterized by the evanescence of both wave types [41].

Through excitation within the compact MEICP reactor, the slow wave branch represented by HW induces TG waves in a complementary correlation (Figure 1b). The helicon and TG waves operate by means of distinct channels for RF input, therefore facilitating the distribution of power onto various sections of the plasma column. FWB, represented by TG waves, undergoes significant dampening and predominantly transfers energy within a limited surface layer of the plasma. In Figure 1, the characters have the following specifications: $n_m$—plasma limit for which the plasma becomes opaque for helicon modes; $n_{low}$—low plasma density region; $n_{up}<n_b$—plasma densities in case of long axially long modes; kz(ω2/ω)—product between axial wavenumber and ratio of electron resonance frequency and angular excitation frequency; H-Helicon waves; TG-Trivelpiece-Gould; B₀-external applied magnetic field, Er-radial component of the electric field; Eθ-electric field component in θ cylindrical coordinate.

2.2. Helicon Plasma Thruster Principle of Operation

The wave-driven Helicon Plasma Thruster (HPT) functions through two interconnected stages: plasma generation and plasma acceleration (Figure 2). The initial stage involves plasma generation within the helicon reactor, where argon plasma is created via RF power deposition, facilitated by an $m=+1$ mode antenna. In the subsequent stage, plasma acceleration takes place through an ambipolar potential drop, which is induced by an electron pressure gradient within a surrounding magnetic nozzle (MN). The innovative design of the HPT is characterized by the MEICP reactor, which serves as the core component of the ST system. The MEICP reactor incorporates a novel configuration, utilizing a multi-dipole magnetic confinement system created by neodymium iron boron (NdFeB) permanent magnets. This is coupled with an azimuthally asymmetric RF antenna and a variable-section ionization chamber. Following the plasma reactor, a solenoid-free MN is employed, which generates an ambipolar potential drop that effectively converts electron thermal energy into ion beam energy. The operation of a compact MEICP reactor relies on a variety of linear and non-linear mechanisms, which can be triggered either directly by waves excited through RF fields or indirectly via synergistic interactions.

One innovative method for boosting plasma density production utilizes a HWRH antenna, which directs plasma generation along the $m=+1$ helicon mode propagation. Another promising approach for optimizing reactor performance involves employing a non-uniform magnetic field. Additionally, inducing turbulence in the MHz frequency range can enhance RF energy absorption, providing a novel means of controlling the plasma source. The first stage of the thruster features a compact helicon reactor that incorporates an azimuthally antisymmetric antenna encircling the quartz dielectric discharge chamber. Two types of antennas, namely HWRH and Nagoya Type III, are employed to preferentially excite odd azimuthal numbers. These antennas generate a time-varying magnetic field due to the oscillating currents [43], which, according to Faraday’s law, induces an opposing electrostatic field. This spatially oscillating electric field accelerates free electrons within the neutral propellant, ionizing it through collisionless heating mechanisms at low pressures. When an axial magnetic field is applied to the plasma column, the dielectric response of the plasma reactor shifts from a scalar to a tensorial form [44]. This change permits RF waves to propagate within the reactor beyond the skin depth. Helicon waves, in particular, can penetrate deeply into the plasma, thereby significantly enhancing the efficiency of wave energy deposition. As a result, helicon waves can achieve plasma densities typically an order of magnitude higher than those produced by inductively coupled discharges under comparable pressure and RF power conditions. Due to the resonant nature of helicon waves, achieving a precise alignment of operational parameters according to the dispersion relation is crucial.

The driving frequency is maintained within the lower-hybrid frequency range. The azimuthally anti-symmetric antenna is designed to excite various axial and radial eigenmodes in the direction of the applied magnetic field, ensuring effective wave propagation and energy absorption. Helicon-heated plasma relies on either uniform or gradient magnetic fields for efficient operation. Traditionally, electromagnetic coils are used to produce the necessary magnetic induction; however, they are often power-consuming and typically require a cooling system to manage the heat generated during operation. To address these limitations, a multi-dipole cusp magnetic confinement system was introduced as a critical component of the Helicon Plasma Thruster. This system is composed of eight plate-shaped neodymium iron boron (NdFeB) magnets of 38 EH grade, which are gold-plated (Ni-Cu-Ni-Au) to enhance the Currie point limit. The multi-cusp permanent magnet (PM) configuration (Figure 2) generates a stronger magnetic field while minimizing the overall magnet weight. Furthermore, the magnetic field profile can be customized to produce either a uniform or non-uniform field within the ionization region by altering the number or spacing of the magnet bars.

The magnetic field strength is approximately 800 G at the chamber surface, decreasing to 400 G at the plasma core. In regions where the magnetic field is parallel to the chamber walls (region 1), electron flux is reduced due to diminished perpendicular transport coefficients. Conversely, in regions where the magnetic field lines converge towards the walls (region 2) [45], the magnetic mirror effect causes particle deflection, thereby retaining particles within the chamber. This multi-cusp configuration highlighted with red arrows in Figure 2 effectively confines the plasma and reduces electron losses, contributing to increased plasma density. Depending on the magnetic field near the antenna, various modes can simultaneously couple to different helicon modes, thereby transferring power into the plasma, impacting plasma density, and thrust force. These modes can have oblique cyclotron resonance for a critical magnetic field. With a uniform magnetic field, only a single resonance is possible for a mode. When a non-uniform magnetic field is applied, different magnetic field values are available near the antenna for different eigenmode resonance conditions [46].

2.3. Helicon Plasma Thruster Engineering Prototypes

The Helicon Plasma Thruster, which utilizes the MEICP reactor and MN acceleration scheme, features a modular design that enables the testing of various configurations. This flexibility allows for experimentation with different ionization chamber outlet radii, a range of antenna types and lengths, diverse MN shapes, and the adjustable positioning of the MEICP zone along the ionization chamber. Figure 3 provides cutaway views of the experimental prototypes of the HPT. Prototype HPT-EP01, depicted in Figure 3a, is equipped with a half-wavelength right-hand (HWRH) antenna, while HPT-EP02, shown in Figure 3b, features a NTIII antenna. These prototypes highlight the variations in antenna design used to optimize the performance of the thruster system.

The operating frequency of the proposed HPT was determined by two main considerations. Firstly, the frequency was chosen to prevent interference with other radio spectrum users aboard the satellite. Secondly, it was optimized to enhance the thruster’s propulsion performance while adhering to the constraints specific to micro-satellite design. To meet these criteria, the International Telecommunication Union (ITU) has defined a set of globally allocated frequency bands. Suitable frequencies within the HF/VHF spectrum include 13.56 MHz, 27.12 MHz, and 40.68 MHz [35]. To comply with ITU regulations, the 13.56 MHz frequency was chosen to excite helicon waves within the MEICP reactor. This frequency aligns with the globally allocated bands and is specifically selected to optimize the performance of the HPT while minimizing interference with other satellite communication systems.

For a fixed excitation frequency of 13.56 MHz and assuming that the parallel wave number $k_{\parallel }$ is related to the antenna length, this leads to the $n_e/B_0$ scalling law for helicon reactors, which is particularly relevant for advanced ST concepts [47].

$${\displaystyle \frac{n_e}{B_0}}={\displaystyle \frac{c}{4\pi e\omega }}{\left(k_{\perp }^2{k}_{\parallel }^2+k_{\parallel }^4\right)}^{1/2}$$

(12)

This scaling law highlights the relationship between the electron density $\left(n_e\right)$ and the magnetic field strength $\left(B_0\right)$, indicating that the efficiency and performance of Helicon Plasma Thrusters are influenced by how these parameters are balanced within the system. The antenna-plasma coupling can preferentially enhance specific values of $k_{\parallel }$. In wave-heated operational modes, there should be a synergistic correlation, ideally aligning the parallel wavelength $\left({\lambda }_{\parallel }\right)$ with twice the effective length of the RF antenna $\left(2L_{aRF}\right)$. In the reactor core, the axial magnetic field is $400 \mathrm{G}$ and imposing the expected plasma density $~2.4\times {10}^{13} {\mathrm{c}\mathrm{m}}^{-3}$ and the RF of $13.56 \mathrm{M}\mathrm{H}\mathrm{z}$, the axial wavelength comes out to be ${\lambda }_{\parallel }~15.64 \mathrm{c}\mathrm{m}$ [47]:

$${\lambda }_{\parallel }={\displaystyle \frac{3.83B_0}{a{n}_{0}e{\mu }_0\omega }}$$

(13)

The RF antenna has been designed to provide a maximum wave-plasma coupling, having the wavelength ${\lambda }_{\parallel }=2L_{aRF}$. Under this condition, the nominal antenna length was found to be $7.8 \mathrm{c}\mathrm{m}$. In the case of a relatively small plasma radius, approximately $a\approx 3 \mathrm{c}\mathrm{m}$, the parallel and perpendicular wave numbers ($k_{\parallel }$ and $k_{\perp }$, respectively) are related in such a way that $k_{\parallel }{k}_{\perp }$ is nearly proportional to the ratio of the square of the plasma frequency $\left({\omega }_{pe}^2\right)$ to the magnetic field strength $\left(B_0\right)$, according to the dispersion relation.

Two types of azimuthally asymmetric antennas, namely half-wavelength right helical (Figure 4a) and NTIII (Figure 4b), have been proposed as trade-offs to allow overly dense helicon-heated plasma. Both antennas were manufactured from copper (Figure 5), chosen specifically to minimize inductive load and thereby reduce power losses associated with inductive loading.

The MEICP reactor of the experimental prototypes, HPT-EP01 and HPT-EP02, consists of a cylindrical ionization chamber with a diameter of 30 mm and a length of 150 mm. This chamber features a convergent nozzle at the outlet with a 10 mm diameter. The reactor is equipped with a copper azimuthally asymmetric RF antenna (either HWRH type or Nagoya Type III), which measures 78 mm in length and 1.25 mm in thickness. It also includes a multi-dipole cusp magnetic confinement system made up of eight plate-shaped neodymium iron boron (NdFeB) magnets of 38 EH grade with gold plating. Additionally, the solenoid-free MN is formed by a ring-shaped NdFeB permanent magnet of 38 EH grade, also gold-plated (Ni-Cu-Ni-Au), to enhance its Curie point limit. The HPT breadboard model (HPT-BM) is supported by an aluminum base plate and is shown in Figure 6a,b

2.4. The HPT Experimental Setup and Testing Procedure

The proposed test setup features a compact vacuum chamber with dimensions of 400 mm in length and 508 mm in diameter. This chamber was chosen due to its small volume and straightforward pumping system, which enables rapid and flexible experimental turnover. This setup is particularly well-suited for the successive testing of the HPT-EP01 and HPT-EP02 prototypes, which are designed for commercial satellite buses with masses under 500 kg. The pumping system consists of a multi-stage Roots pump, air-cooled, with a maximum pumping speed of $28 {\mathrm{m}}^3/\mathrm{h}$ (Pfeiffer -ACP−28–40 model) and a turbomolecular pump (Pfeiffer HiPace 400 with TC400 turbo pump controller). A valve with a manual actuator is installed between the mechanical pump and the turbomolecular pump to prevent backflow. Downstream pressure in the vacuum testing facility is measured by a Pfeiffer gauge TPG 361. One end of the quartz tube is attached to the propellant gas flow line, and the other is open to the vacuum chamber. The gas flow is controlled by a digital flow meter (Bronkhorst F-201CV-500-AGD-33-V) located outside the testing facility. All tests were conducted using Argon 6.0 ($\mathrm{p}\mathrm{u}\mathrm{r}\mathrm{i}\mathrm{t}\mathrm{y}\ge 99.999\%$). The magnetic field strength during the experiments was monitored using a teslameter (FM 302 model) in conjunction with an AS-NTM probe. This setup allowed for precise measurement and control of the magnetic field parameters essential for the operation of the HPT experimental prototypes. The proposed vacuum chamber allowed the achievement of a base pressure of $2\times {10}^{-5} \mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$ before the HPT started operating and a background pressure between $3\times {10}^{-3} \mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$ and $5\times {10}^{-3} \mathrm{m}\mathrm{b}\mathrm{a}\mathrm{r}$ during plasma ignition.

The experimental vacuum chamber is also equipped with multiple feedthroughs to accommodate the propellant feedline, electrical connections, RF power line, and various sensors. Additionally, it features two viewing ports that allow for direct observation of the MEICP reactor’s discharge characteristics and the resulting plasma plume, facilitating real-time monitoring and analysis during testing.

Achieving automatic control of the helicon reactor presents a considerable challenge due to mode jumps between electrostatic and inductive operation. These transitions are marked by abrupt increases in plasma density and variations in reflected power from the matching box, which can result in a sudden mismatch. This mismatch leads to increased reflected power and a reduction in the net RF power delivered to the helicon reactor. Without proper management of this mismatch through adjustments in the matching box, the RF power coupling mechanism may fail to transition fully into helicon mode (W), potentially causing a reversion to inductive coupling or even terminating the discharge altogether. Consequently, this complex behavior imposes the use of an effective automatic control system to stabilize the operation. RF power coupling into capacitive, inductive, and wave discharges is a non-linear process that is highly dependent on operational parameters, including reactor geometry, input power, operating pressure, and the topology and strength of the magnetic field. To enable impedance matching between the RF generator and the antenna/plasma system for different operating points and coupling modes (capacitive-inductive-helicon), an automatically L-type tunable Matching Network AMN-600R and an Automatic Matching Network Controller (AMNC) are used to compensate for the anticipated range of load impedance (Figure 7). The forward and reflected RF power are measured within the RF generator. A Coaxial Power Systems RFG 50–600 (0–600 W) RF generator supplies power at a fixed frequency of 13.56 MHz and a standard output impedance of 50 Ω. The variable tuning capacitor $\left(C_T\right)$ in the matching network is specifically designed to neutralize the imaginary component of the impedance, while the variable load capacitor $\left(C_L\right)$ is responsible for keeping the total output impedance near 50 Ω. The L-type tunable matching network exemplified by models like the AMN-600R utilizes two adjustable tuning elements along with an inductor to achieve precise impedance matching, ensuring efficient power transfer to the helicon reactor.

Reactions inside the helicon plasma reactor can be controlled by adjusting RF, system size, RF supply power, or fill-in-pressure. Managing thermal control effectively in the operation of the HPT presents a substantial challenge. The engineering difficulty of controlling heat fluxes transferred from the plasma to the inner confinement surfaces of the MEICP reactor is closely linked to plasma-surface interactions. During operation, the walls of the HPT accumulate significant heat. The excitation of helicon waves within the EP system imposes a substantial thermal load on the discharge chamber and nearby components, such as permanent magnets, mainly due to cross-field particle diffusion and ultraviolet (UV) radiation. To tackle the thermal challenges encountered during operation within the power range of 8 W to 600 W, an optimized test sequence was developed using a pulsed power modulation (PWM) scheme. This approach aims to effectively manage heat loads by dynamically adjusting power delivery, thereby enhancing thermal control and operational efficiency. This approach also facilitates a direct transition from capacitive coupled mode (E-mode) to wave coupled plasma (W-mode) [42,48,49], ensuring more efficient performance under these demanding conditions. Implementing pulsed discharge within a structured testing framework improves the ion-to-neutral influx ratio and allows for swift adjustments of the reactor’s operating modes, thereby optimizing overall efficiency and control. The pulsed power modulation (PWM) is defined primarily by two key parameters: the pulse duty cycle, which indicates the proportion of time the RF power is active within each cycle, and the frequency, which specifies the number of times per second the RF power is switched on and off. These parameters critically influence the reactor’s thermal management and operational stability. Adjusting the duty cycle and pulse frequency allows for the enhancement of plasma reactions within the MEICP reactor, providing a means to control key plasma properties such as electron temperature, plasma density, and the ion-to-neutral flux ratio. At the onset of the pulsed power modulation (PWM), the RF input is supplied at a high level, generating a dense and cold plasma. Following this initial phase, the RF power is switched off, leading to the afterglow period of the cycle, during which plasma parameters gradually decay and specific plasma-surface interactions can be observed and controlled.

The plasma generation efficiency of both the HWRW antenna and the NTIII antenna within the MEICP reactor of the HPT will be evaluated under PWM conditions, maintaining a constant argon mass flow rate of 12 standard cubic centimeters per minute (sccm). This validation process aims to determine the effectiveness of each antenna in generating plasma under controlled pulsing conditions, contributing to optimized reactor performance. In this operational mode, the introduction of gas is synchronized with the RF power pulses, with the gas flow being halted in alignment with the pulse sequence. This synchronization causes a transient rise in pressure within the thruster, which, when coupled with the RF pulses, enhances the efficiency and effectiveness of plasma ignition compared to the continuous mode. This coordinated approach optimizes plasma formation, making the ignition process more responsive and controlled.

Typical experimental conditions involve an RF pulse duration of 0.5 s and a gas flow duration of 1 s with no delay between the initiation of the gas flow and the onset of the RF pulse. The inter-pulse interval ranges from 1 to 2 s. During these experiments, the RF power is typically adjusted between 200 and 600 W while maintaining a constant argon flow rate. These settings are designed to optimize plasma performance and control within the MEICP reactor.

To qualitatively assess the performance of the HPT, OES and high-speed imaging were employed. The OES technique involved collecting the optical spectra emitted by the plasma using a collimator device. This collected light was then transmitted through an optical fiber to the spectrometer for analysis. For calibration purposes, a tungsten lamp with a known continuum emission intensity was used to standardize the measured spectral intensities, ensuring accurate and reliable data collection. The spectrometer was strategically positioned to focus on the central axis of the thruster’s exit plane, thereby capturing the spectra emitted by the exhaust plume. An AvaSpec-ULS4096CL spectrometer was employed for this purpose, offering a measuring range from 200 to 1100 nm. The device provides a spectral resolution ranging from 0.05 to 20 nm, which varies depending on the exposure time, adjustable between 9 μs and 40 s. A BFA200HS02 fiber optic connector with a 200 μm core diameter was used to transmit the collected spectral data from the collimator device to the spectrometer, ensuring precise and efficient data acquisition.

Based on OES theory, the emission lines of argon atoms (Ar I) at 750 nm are primarily generated through electron impact excitation of ground-state argon atoms. In contrast, the emission lines of singly ionized argon (Ar II) at 480 nm are mainly produced by the excitation of ground-state argon ions $\left({Ar}^{+}\right)$. The intensity of the emission at $750 \mathrm{n}\mathrm{m}$ $\left(I_{750 \mathrm{n}\mathrm{m}}\right)$ can be expressed using the following formula [46]:

$$I_{750 \mathrm{n}\mathrm{m}}\propto n_e\times k_{Ar}\left(T_e\right)\times \left[Ar\right],$$

(14)

where $k_{Ar}\left(T_e\right)$ is the coefficient rate for electron impact excitation from the ground state and $\left[Ar\right]$ is the neutral density. If it is assumed that $k_{Ar}\left(T_e\right)$ is constant, the intensity of $I_{750nm}$ is dominated by $n_e$ and $\left[Ar\right]$. In a similar analogy, the emission intensity of $480 \mathrm{n}\mathrm{m}$ $\left(I_{480 \mathrm{n}\mathrm{m}}\right)$ can be written as the following formula:

$$I_{480 \mathrm{n}\mathrm{m}}\propto n_e\times k_{{Ar}^{+}}\left(T_e\right)\times n_{{Ar}^{+}},$$

(15)

where $n_{{Ar}^{+}}$ is the ion density and $k_{{Ar}^{+}}\left(T_e\right)$ is the coefficient rate for electron impact excitation from the ion ground state. If the $k_{{Ar}^{+}}\left(T_e\right)$ constant is considered, then the intensity of the $I_{480 nm}$ is proportional to $n_{{Ar}^{+}}$ and $n_e$ [46]. The evaluation of the emission lines, predominantly in the 400–500 nm range, is measured by OES. The objective was to investigate the influence of RF power and antenna geometry for a constant magnetic field on the coupling mechanism between the waves and plasma in order to optimize the HPT reactor. Increasing the RF power induces a global increase in plasma density $n_e$.

3. Results

The analysis of RF antenna efficiency and the RF power thresholds required for mode transitions was conducted according to a predefined test plan, detailed in

Table 3. Helicon reactor mode transition evaluation for time-modulated RF power envelope-based NTIII and HWRH antennas.

Objective	Determine the ionization efficiency of a MEICP reactor equipped with a NTIII and HWRH antenna of 78 mm length
Test	Compare the high-energy electron-excited ionic lines with low-energy electron-excited neutral lines
Criterion	Agreement of Ar II 434, Ar II 480 nm, and Ar I 750 nm and Ar I 811 nm
HPT Settings
RF power energy in PWM	0–250 W, 0–400 W, 0–500 W toff 0.4 (s), ton 1(s)
Multi-dipole cusp magnetic confinement system	Reactor core strength of 400 G is composed of eight plate-shaped neodymium iron boron (NdFeB) magnets of 38 EH grade, 70 mm in length, 10 mm in width, and 5 mm in thickness
Magnetic Nozzle	800 G strength ring-shaped NdFeB PM of 38 EH grade ring-shape NdFeB magnet with gold plating (Ni-Cu-Ni-Au), D 30 × d 10.2 × h 5 mm
Argon flow rate	12 sccm
Diagnostic Settings
Optical Emission Spectroscope (OES)	Emission intensity of $I_{434} \mathrm{n}\mathrm{m},I_{480}\mathrm{n}\mathrm{m}$and $I_{750} \mathrm{n}\mathrm{m},I_{811} \mathrm{n}\mathrm{m}$

. This test plan outlines specific parameters and experimental conditions, providing a structured approach to evaluating the performance and transition behavior of the RF antenna within the MEICP reactor.

During PWM operation, the RF power was modulated with an average power maintained at 500 W. Specifically, 250 W, 400 W, and 500 W were delivered during the on-time, while power was reduced to 0 W during the off-time with a duty cycle set at 10%. When a short modulation period of 0.4 s was employed, the plasma discharge showed a fast response to the modulated power input. Initially, plasma density surged sharply, reaching peak levels higher than those recorded under Continuous Wave (CW) Mode, before stabilizing at a steady state during the on-time of the pulse.

To investigate the impact of antenna type on plasma generation efficiency, two engineering prototypes, designated HPT-EP01 and HPT-EP02, were designed, manufactured, and analyzed. This approach allowed for a comparative evaluation of different antenna configurations, providing insights into their performance characteristics and their influence on the overall efficiency of plasma generation in the Helicon Plasma Thruster. The first breadboard model HPT-EP01 has a MEICP reactor with a NTIII azimuthally asymmetric antenna. Representative photographs during operation under a time-modulated RF power envelope are underlined in Figure 8. Figure 8 presents representative photographs captured during the operation of the HPT under a time-modulated RF power envelope. These images illustrate the visual characteristics of the plasma discharge during different phases of the RF power modulation, highlighting variations in plasma density, luminosity, and overall behavior under pulsed power conditions. Such visual documentation is crucial for understanding the real-time response of plasma to modulated power inputs, providing valuable insights into the operational dynamics of the system.

Figure 8 clearly shows the accumulation of a tenuous, pink light-emitting plasma on the walls of the MEICP reactor, particularly in the region influenced by the NTIII antenna. The current induced by the NTIII antenna will induce an RF magnetic field inside the HPT-EP01, which will ultimately induce an RF electric field parallel to the applied one. This electric field will cause electrons to move along the magnetic field lines and set up a space charge. Additionally, the perpendicular electrostatic field generated by the space charge is not neutralized, as electrons are confined in the perpendicular direction due to the strong magnetic field. This uncancelled electrostatic field can interact with and potentially couple to the perpendicular space charge field associated with the helicon waves. This coupling mechanism may enhance energy transfer and plasma confinement, influencing the overall plasma dynamics and stability within the MEICP reactor. A sample of the optical emission spectra obtained for an argon plasma plume during PWM under 250 W RF energy is presented in Figure 9.

From the optical emission spectra underlined in Figure 9, the argon neutral emission lines are generally observed to be more pronounced. The spectra acquired from the back window port of the HPT clearly display argon-neutral emission lines at wavelengths of 415.9 nm, 420.06 nm, and 430.01 nm. These emission lines are peculiar to the MN section of the HPT. One plausible reason is that the collection optics at the rear window detect radiation emitted by both the ionized propellant and the region before the antenna, which is situated at a significant depth within the quartz tube. Moreover, the operation of the Helicon plasma source is expected to raise the concentration of neutral argon in the vacuum tank, hence boosting ion-induced excitation collisions and leading to more intense background radiation emissions from neutral argon gas. The high value of argon neutral concentration proves a capacitive coupled plasma (E-mode) within the MEICP reactor. The impedance mismatch between the Matching Box and the MEICP reactor was mitigated by modulating the RF input power in a predefined manner, informed by a global model of time-modulated argon plasma. This approach helped to stabilize the system and ensure effective power coupling during operation.

The variation of forwarded and reflected power during the time-modulated 250 W power envelope is presented in Figure 10.

The second breadboard model, HPT-EP02, is designed similarly to HPT-EP01, featuring a compact MEICP reactor; however, it utilizes a Half-Wavelength Resonant Helicon (HWRH) antenna for plasma generation. This modification aims to explore the effects of the HWRH antenna on plasma efficiency and stability compared to the NTIII antenna used in HPT-EP01. By integrating the HWRH antenna, HPT-EP02 seeks to optimize plasma coupling, enhance density, and improve the overall performance of the HPT under varying operational conditions, particularly under pulsed power modulation schemes. The right-hand circularly polarized helicon mode pattern can effectively couple to the helicity of the HWRH antenna when the correct sign is applied. This configuration generates a rotating electrostatic field in space, corresponding to the instantaneous pattern of the $m=+1$ mode that propagates parallel to the magnetic field. However, despite the helical design of the HWRH antenna, it does not inherently produce the time-dependent rotational characteristic of the $m=+1$ mode. The antenna field in the HWRH arrangement forms a left-hand helix in line with the helicon wave. It will be $90°$ out of phase with the antenna after a quarter when the plasma wave is in the $m=+1$ mode and propagates in the + z direction; at that point, though, the antenna current is zero [43]. At $180°$ of phase, the wave aligns with the antenna’s opposite leg, causing the antenna current to reverse, therefore enabling the resumption of excitation [43]. Hence, a HWRH antenna efficiently allocates its power between only two modes, enhancing its ability to drive circularly polarized waves compared to a typical straight antenna.

Figure 11 showcases representative images captured during the operation of the system under pulsed power modulation (PWM) with an RF input energy of 250 W. These pictures illustrate the plasma behavior and visual characteristics under modulated conditions, highlighting the spatial distribution and intensity of the plasma glow.

Figure 12 presents the associated optical emission spectrum, which details the specific wavelengths emitted during the plasma operation.

Figure 12 highlights the optical emission spectra for the HPT-EP02 system functioning at 250 W RF power with 6 W reflected, while operating in a pulsed wave mode. The argon plasmas generated by the HPT exhibit visually striking characteristics, as illustrated in Figure 13. In the image, the plasma is heated with 400 W of RF power and subjected to a magnetic field strength of 800 G with an argon flow rate of 12 standard cubic centimeters per minute. The plasma emissions are notably different depending on the antenna configuration used. For the HWRH, the brightest Ar II emissions are observed downstream of the antenna, especially intensified in the MN section. This intensity is attributed to the ambipolar electric field acceleration mechanism. In contrast, the NTIII antenna produces a red-pinkish emission primarily from neutral argon, indicating a capacitive operating regime with poor wave-plasma coupling efficiency. This difference highlights the superior performance of the HWRH antenna in effectively coupling RF power to the plasma, thus enhancing ionization and acceleration processes. The physical appearance of the discharge can be an indicator of the operating mode. In capacitive discharge, the ionization is focused under the antenna leads, with a low value of plasma density and a centrally peaked radial density profile. When the plasma density attains a particular value, the inductive mode (H) is launched. In this mode, there exists a radial density depression due to power deposition in the edges of the discharge from the skin effect. In the inductive mode, a brighter mode becomes visible, with a relatively uniform dispensing of light.

The density jump may be associated with a visual change in plasma structure from a pinkish plasma, dominated by neutral argon emission, to a bring blue-white core, dominated by singly ionized emission, as seen in Figure 13. In the current compact Helicon Plasma Thruster, at moderate RF input powers, an inductive but non-reasoning (H-mode) occurs and the density rises rapidly. The observed peaks in Figure 14, specifically in the region corresponding to Ar II, provide evidence supporting helicon wave coupling and the achievement of W-mode operation. In comparison with the Inductively Coupled Mode (ICP), the appearance of emission lines representing Ar II due to an increase in RF supply power can be related to the presence of electrons with minimum energy $\left(19.5 \mathrm{e}\mathrm{V}\right)$, being considered as an energy threshold for argon excitation plasma. The distinct Ar II emission at power higher than 450 W indicates an abrupt transition into the ICP-HCP mode of operation. This abrupt increase in plasma density, followed by a linear relationship between density and magnetic field strength ($n_e\propto B_0$) is an indicator of RF plasma mode transition.

The observed intensity jump can be attributed to the complex, nonmonotonic relationship between power absorption and plasma density, which is significantly influenced by the reduced power absorption that occurs under the anti-resonance condition of the TG wave. This anti-resonance condition leads to inefficient coupling of RF power to the plasma, resulting in lower energy absorption at specific density ranges. As the plasma transitions through this condition, a sudden increase in density is observed when the absorption efficiency improves, highlighting the intricate interplay between wave propagation, resonance effects, and energy transfer in the plasma.

Optical emission spectra for HPT-EP02 operating with 250 W (Figure 12) and with 400 W (Figure 14) show a reduction in intensity of the low-energy electrons excited neutral line cluster (750–900 nm) with $Ar I<13.5 \mathrm{e}\mathrm{V}$ due to neutral depletion (ND) [49,50]. In this scenario of ND, the neutral density near the core axis nearly vanishes, necessitating a significant rise in electron temperature to maintain the ionization balance. It could be observed that under pulsed power excitation at moderate RF power levels, below 250 W, the HPT undergoes a transition from capacitive mode (E) to helicon wave-sustained discharge (W). This transition is characterized by a rapid increase in argon ion emissions (Ar II). In W-mode, atomic line emissions are governed by neutral density and often reach saturation due to neutral depletion. In contrast, ion emissions, which are closely tied to electron density and temperature, show a substantial increase upon transitioning to the wave-heated mode (W). Conversely, in H-mode, atomic line emissions remain predominant. This experimental research highlights the transition between wave modes (H-W) in a 500 W class Helicon Plasma Thruster, specifically from the surface mode (involving helicon to Trivelpiece-Gould (TG) mode conversion) to the global heating mode dominated by helicon waves. The TG mode plays a crucial role in plasma heating before the H-W transition. In W-mode, under moderate magnetic field conditions, such as the current case with a 400 G field, the plasma heating through mode conversion diminishes, leading to direct heating by the helicon mode, which becomes the primary mechanism for plasma heating. This jump can be attributed to the nonmonotonic relationship between power absorption and plasma density, which is influenced by the decreased power absorption occurring under the antiresonance condition of the TG wave.

4. Discussion

The experimental framework was designed to investigate critical aspects of helicon plasma physics, including wave dynamics, instabilities, plasma generation, and profile formation, with an emphasis on optimizing propulsion performance. This comprehensive approach aimed to deepen the understanding of the underlying physical mechanisms and enhance the operational efficiency of the Helicon Plasma Thruster, ultimately contributing to improved propulsion capabilities. The dynamic behavior of MEIC plasma for space propulsion produced by helicon waves using an exciting $m=+1$ HWRH antenna was investigated in a pulsed wave mode of operation. The aim was to provide a comprehensive understanding of how each discharge state affects the overall performance and characteristics of the thruster. The transition from H-mode to W-mode in MEICP is a critical process that significantly enhances plasma density and power deposition efficiency. Understanding and controlling this transition is essential for optimizing plasma reactors for space propulsion applications. The synergistic correlation between RF input power, magnetic field strength, operating frequency, and electrostatic effects governs this transition, enabling the design of more compact plasma reactors for EP systems.

For the MEICP reactor operating under a fixed magnetic confinement strength of 400 G, utilizing an azimuthally asymmetric NTIII antenna, only a CCP mode of operation was achieved. This mode was characterized by the presence of certain plasma instabilities that negatively impacted the wave-plasma energy deposition process. MEICP reactor at low RF supply power run in the E-mode and H-mode, with transitions between these modes being associated with variations in the power coupling process. At first, the helicon discharges start ignition in capacitive E-mode, whereby the discharge is sustained by the oscillating electric field generated by the voltage drop across the RF antenna. As the RF power surpasses a specific threshold, the discharge mechanism shifts into an inductive H-mode. In this mode, the current flowing through the antenna produces a rotating magnetic field that creates an electric field, therefore maintaining the discharge. Nevertheless, the power in both the E-mode and H-mode is inadequate to sustain the plasma density necessary for the transmission of the helicon wave. At increasing levels of RF power, the plasma density reaches a level that is adequate to meet the dispersion relation of the helicon wave, therefore enabling the wave to propagate efficiently.

During RF operation, the plasma undergoes a series of transitions, initially passing through capacitive discharge mode, followed by inductive discharge mode, before finally entering the wave-heated regime. To isolate and study the electron heating effects independently of plasma formation, a double-pulse technique is employed. This technique involves an initial RF pulse with 400 $\mathrm{W}$ to ignite the plasma, followed by a second RF pulse after a specific time delay. In this sequence, the electron temperature initially declines significantly while the electron density remains relatively stable. As a result, helicon waves can propagate effectively from the start of the second RF pulse. The electron density exhibits only a slight reduction until the onset of the second pulse, with the subsequent behavior being influenced by the RF power applied during the second pulse. An increase in RF power during the second pulse intensifies the reduction in density, driven by enhanced electron heating and increased diffusion processes.

From engineering points of view, RF operation induces excessive thermal loads on HPT components due to cross-field particle diffusion and UV radiation. The ionization chamber is bombarded with highly energetic ions with an energy of $5K{T}_e$ (sheath drop) and electrons with an energy of $2K{T}_e$ [51]. The overall radiation losses are concentrated in the UV spectrum, where the dielectric walls absorb resonance radiation. Because the antenna is small compared to the vacuum wavelength of RF waves, the power radiated at the RF is relatively low. Ion transport is influenced by the configuration of the RF wave, the magnetic field, and the pressure profile. Additionally, some of the input RF power is absorbed by the dielectric wall, primarily due to the acceleration of ions towards the wall. The energetic ions strike the ionization chamber with an energy of about $5K{T}_e$ (sheath drop) and the electrons of about $2K{T}_e$ [51]. Also, the flux of the ion-electron pair exhibits an approximate Bohm flux of $1/2n_{e}K{T}_e$ [51]. By neglecting radiation and by inserting the Bohm flux into the Stefan-Boltzmann law, for $K{T}_e=3\mathrm{e}\mathrm{V}$ and a plasma density in the range of $n_e=2.5\times {10}^{13}{\mathrm{c}\mathrm{m}}^{-3}$ the MEICP reactor walls, the average temperature exceeds 1100 K. Under these conditions, the magnetic confinement system based on PMs necessitates precise thermal management to prevent the magnets from nearing their Curie temperature. This thermal issue was effectively mitigated by operating the helicon reactor under a timed pulsed RF power envelope. This approach allowed the system to achieve over 60 min of continuous operation without any demagnetization of the magnetic confinement system or thermal damage to the quartz ionization chamber. The modulated power delivery helped manage the heat load, preserving the structural and functional integrity of the reactor components under extended operational conditions.

This study involved a comparative analysis of plasmas generated using two different RF antennas, each designed to excite the azimuthal mode number $m=+1$. A significant technical challenge in the development of the HPT was the design of the $m=+1$ mode antenna, which needed to accurately replicate the unique field structure of helicon waves. The experimental framework was established to explore key aspects of helicon plasma physics, including wave dynamics, instabilities, plasma generation, and profile formation, with a focus on propulsion performance. The experimental testing campaign proves that the HWRH antenna, designed to emit right-hand circularly polarized waves, demonstrated superior plasma production efficiency and higher RF energy absorption, making it more effective for propulsion applications compared to the NTIII antenna. Helicon waves, which are helical in nature and rotate in both space and time, achieve more effective power coupling when using antennas that also have a helical structure. Given that the HWRH antenna demonstrated superior performance in Continuous Wave Mode (CWM) compared to the NTIII antenna, the decision was made to conduct all subsequent testing in Pulsed Wave Mode (PWM) exclusively with the HWRH antenna. Considering the low aspect ratio of the Helicon Plasma Thruster’s reactor, characterized by a small length-to-radius ratio $\left(L_{re}/a\right)$, it is appropriate to describe the fields as discrete superpositions of various standing waves. Research has shown that these harmonics consist of both the helicon wave, directly excited by the HWRH antenna, and the TG wave, generated through surface mode conversion. Since RF power absorption in the reactor occurs via these TG harmonics, the overall RF power absorption decreases when one of the harmonics enters an antiresonant condition. As different harmonics reach antiresonance at different plasma densities, the variation of absorbed power with respect to density is inherently nonmonotonic. The efficiency of RF power absorption is attributed primarily to the pronounced collisional damping of the TG wave, a quasi-electrostatic wave that is predominantly excited near the antenna and dissipates energy at the plasma surface. In contrast, the helicon wave penetrates deeper into the core of the Helicon Plasma Thruster’s reactor, where it imparts energy to the plasma through collisional interactions. Furthermore, bulk mode conversion (BMC) from the helicon wave to the TG wave occurs at the mode conversion surface, where the dispersion relations of the helicon and TG waves intersect. This mode conversion process is crucial for enhancing core plasma heating, especially under conditions of low collisional frequency.

5. Conclusions

This paper details the design, manufacturing, and validation of an advanced EP system based on a compact helicon reactor combined with a multi-cusp magnetic confinement system. The strategic objective of this development is to achieve competitive propulsion metrics tailored for next-generation LEO microsatellites. By leveraging the compact design and enhanced plasma confinement, the system aims to provide efficient, high-performance propulsion capabilities, meeting the evolving demands of modern space missions involving smaller satellite platforms. This goal was pursued by developing both theoretical and experimental methodologies aimed at optimizing key performance indicators and understanding the generation mechanism of ultra-dense helicon plasma. The two engineering prototypes, HPT-EP01 and HPT-EP02, each utilizing distinct antenna designs, demonstrate successful proof-of-concept for RF-powered propulsion technology based on the MEICP reactor. The HPT breadboard model based on HWRH antenna proved stable operation over an extended operational envelope compared to the breadboard having a NTIII of the same characteristics. The HPT breadboard model equipped with a HWRH antenna demonstrated stable operation over a broader operational envelope compared to the breadboard model utilizing a NTIII antenna with similar characteristics. This stability highlights the superior performance and robustness of the HWRH antenna in sustaining plasma generation under varying conditions, making it a more effective choice for extended and reliable operation in RF-powered propulsion systems. The findings suggest that the HWRH antenna’s design provides better coupling efficiency and thermal management, contributing to its enhanced stability.

During the experimental validation, OES has been used to distinguish particles with different energies, such as Ar I and Ar II. According to the principles of OES, the Ar I lines are generated through collisions between electrons and ground-state argon atoms, whereas the Ar II lines result from the excitation of ionized argon (Ar⁺) in its ground state. To ensure the accuracy of the spectral data, the measured wavelengths and excitation energies of the emission lines were systematically cross-referenced with the NIST Atomic Spectra Database Lines. MEICP reactor at low RF supply power run in the E-mode and H-mode, with transitions between these modes being associated with variations in the power coupling process. At first, the helicon discharges start ignition in capacitive E-mode, whereby the discharge is sustained by the oscillating electric field generated by the voltage drop across the RF antenna. As the RF power surpasses a specific threshold, the discharge mechanism shifts into an inductive H-mode. In this mode, the current flowing through the antenna produces a rotating magnetic field that creates an electric field, therefore maintaining the discharge. Nevertheless, the power in both the E-mode and H-mode is inadequate to sustain the plasma density necessary for the transmission of the helicon wave. At increasing levels of RF power, the plasma density reaches a level that is adequate to meet the dispersion relation of the helicon wave, therefore enabling the wave to propagate efficiently.

This study has highlighted the intrinsic challenges associated with helicon plasma reactors for space propulsion applications, focusing on aspects such as RF wave absorption, wave propagation, wave coupling efficiency, antenna design, and the robustness of impedance matching systems. The stable generation of high-density and low-temperature argon plasma using helicon waves within an HPT breadboard model was experimentally demonstrated. This paper presents the first helicon plasma ignition in an HPT proof-of-concept, showcasing the qualitative evolution of various particles, including high-energy electron-excited ionic species and low-energy electron-excited neutral species. The findings demonstrate that for advancing the technology readiness level of this system, the HWRH antenna will be the optimal solution for equipping the MEICP reactor.