SESSION 2 PLASMA DYNAMICS INSIDE THE SOURCE Antonella Calderelli, Federico Boni, Mansur Tisaev, Eduardo Ahedo 1st International Electrodeless Plasma Thruster Workshop July 3-4, 2025 Universidad Carlos III de Madrid uc3m OUTLINE ● Introduction ● Antonella Calderelli: Parametric analysis of coupling modes in an RF plasma thruster ● Federico Boni: Thrust production mechanisms and plasma properties inside the ECRA thruster ● Mansur Tisaev: Global and collisional radiative modelling for RF xenon plasmas ● Eduardo Ahedo: 2D/3V hybrid modelling of plasma transport in EPTs ● Round table EPT WORKSHOP, JULY 3-4 2025, UC3M INTRODUCTION ● Plasma processes in an EPT 1. Wave-energy deposition in the plasma (session 3) 2. Plasma transport inside the source (this session 2) ● Wave deposited energy in quasistationary plasma equations ● Separation of high-frequency and slow-dynamics scales ● Plasma production ● Dependence on propellant type (session 5) ● Plasma interaction with thruster walls ● Wall properties, velocity distribution functions ● Magnetic confinement ● Anomalous diffusion ● Plasma extraction 3. Plasma acceleration in the magnetic nozzle (MN) (session 4) EPT WORKSHOP, JULY 3-4 2025, UC3M PARAMETRIC ANALYSIS OF COUPLING MODES IN AN RF PLASMA THRUSTER Antonella Caldarelli Department of Industrial Engineering, University of Bologna Rod Boswell & Christine Charles Space Plasma Power & Propulsion Group, The Australian National University Raoul Andriulli & Fabrizio Ponti Department of Industrial Engineering, University of Bologna CONTENT SLIDES ● Research background ● The experimental set-up MOA ● Experimental conditions ● Parametric analysis of plasma coupling modes ● Plasma characteristics ● Axial profiles of ion saturation current ● Radial profiles of ion saturation current ● Plasma potential profiles ● B-Dot measurements of helicon waves ● Analysis of wave damping mechanisms ● Conclusions & open questions EPT WORKSHOP, JULY 3-4 2025, UC3M RESEARCH BACKGROUND How do the experimental conditions (RF power input, pressure and magnetic nozzle configuration) affect plasma generation and ion beam acceleration? ▪ The research focuses on plasma generation and acceleration mechanisms, where the plasma excitation and the magnetic nozzle throat are decoupled ⇒ “story of remote source” ▪ Studies showed that with a non-uniform magnetic field configuration, higher densities can be achieved in the plasma source EPT WORKSHOP, JULY 3-4 2025, UC3M THE EXPERIMENTAL SET-UP MOA Timeline: - Jan 2020 (Covid) - October 2020 – Huia is born - Nov 2021 – Jan 2022: Manufacturing is complete - Feb 2022: Moa is assembled - Mar 2022: First discharge tests - May 2022: Plasma is stable! - June 2022 – Onwards EPT WORKSHOP, JULY 3-4 2025, UC3M EXPERIMENTAL CONDITIONS ▪ RF powers = 50 - 500 W (<1% reflected power) @ 27.12 MHz ▪ Argon flow rate 12 sccm & operating pressures = 0.5 mTorr (70 mPa) – 2 mTorr (270 mPa) ▪ Magnetic field on axis Bz,max = 530 G with peak @ magnetic nozzle (MN) throat (z = −8 cm) ▪ Diagnostics: planar Langmuir probe (Isat and Vf), emissive probe (Vp) and B-Dot probe (helicon waves) Te ~ 4 eV EPT WORKSHOP, JULY 3-4 2025, UC3M PARAMETRIC ANALYSIS OF PLASMA COUPLING MODES ▪ Smooth mode transitions indicating that the different modes may exist simultaneously ▪ Power threshold for mode change decreases as pressure increases ▪ Power transfer efficiency increases with input power but starts to plateau for PRF > 300 W ▪ For PRF > 100 W, plasma resistance and efficiency increases with increasing pressure Modes: E, H, W EPT WORKSHOP, JULY 3-4 2025, UC3M PARAMETRIC ANALYSIS OF PLASMA COUPLING MODES @ Antenna vs @ MN throat ▪ Much steeper density rise at the magnetic nozzle throat than under the antenna as power is increased ▪ While @ MN throat an E-H-W mode transition is observed, under the antenna the plasma might only go through an E-H transition EPT WORKSHOP, JULY 3-4 2025, UC3M MEASUREMENTS OF PLASMA CHARACTERISTICS 2D maps of Isat [mA] and Floating potential [V] at: - 0.5 mTorr - 1 mTorr - 2 mTorr EPT WORKSHOP, JULY 3-4 2025, UC3M AXIAL PROFILES OF ION SATURATION CURRENT ▪ The peak of plasma density does not occur at the point of plasma excitation (i.e., under the antenna), but at the magnetic nozzle throat ⇒ downstream local ionisation which could be due to either or a combination of: 1. High energetic-electrons travelling along the most radial field lines that reconnect to the antenna + enhanced plasma confinement 2. Helicon waves EPT WORKSHOP, JULY 3-4 2025, UC3M RADIAL PROFILES OF ION SATURATION CURRENT @ Antenna (z = −18 cm) @ MN throat (z = −8 cm) ▪ Under the antenna, the radial density profile shows a “doughnut” plasma shape typical of ICP ▪ It becomes progressively more prominent as input power increases ▪ On the contrary, at the nozzle throat, the density peaks on axis EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA POTENTIAL PROFILES ▪ Strong ion confinement at the magnetic nozzle throat, especially for PRF = 100 W (Er ~ 500 V/m) ▪ Contribution of the radial inward diffusion of the ions to the density axial peak at the MN throat ▪ Higher radial confinement of the ions is expected at the lowest power input ▪ Axial profiles of Vp (with maximum @ MN throat) show an Ez that would accelerate the ions both upstream towards the antenna and downstream the nozzle (vB ~ 10 km/s) EPT WORKSHOP, JULY 3-4 2025, UC3M B-DOT MEASUREMENTS OF HELICON WAVES 400 W, 0.5 mTorr, Bz,max = 530 G (“blue core” 3 cm diameter/15 cm long) It seems we have helicon waves at 400 W! EPT WORKSHOP, JULY 3-4 2025, UC3M B-DOT MEASUREMENTS OF HELICON WAVES 100 W, 0.5 mTorr, Bz,max = 530 G (no blue emissions) But there are no waves recorded at 100 W. EPT WORKSHOP, JULY 3-4 2025, UC3M B-DOT MEASUREMENTS OF HELICON WAVES ▪ For PRF > 100 W, helicon waves are detected with a local peak of the electromagnetic wave amplitude at the magnetic nozzle throat ▪ The density peaks at the nozzle throat even if helicon waves are not detected at 100 W ⇒ Ionization far from the antenna is not due to wave-heating mechanisms, even though helicon waves could enhance the downstream ionization EPT WORKSHOP, JULY 3-4 2025, UC3M ANALYSIS OF WAVE DAMPING MECHANISMS ▪ Collision-less (Landau damping) is unlikely the cause (vth < vph) ⇒ no wave-particle interaction ▪ Collisional damping can’t explain the observed damping since the theoretical δ∥ ~ 5 m ≫ Ld EPT WORKSHOP, JULY 3-4 2025, UC3M ANALYSIS OF WAVE DAMPING MECHANISMS ▪ Collision-less (Landau damping) is unlikely the cause (vth < vph) ⇒ no wave-particle interaction ▪ Collisional damping can’t explain the observed damping since the theoretical δ∥ ~ 5 m ≫ Ld ▪ Then what else? Instabilities? Resonance? TG waves? An effective electron collision frequency at least an order of magnitude higher is needed to interpret the observed data! EPT WORKSHOP, JULY 3-4 2025, UC3M ANALYSIS OF WAVE DAMPING MECHANISMS ▪ Then what else? Instabilities? Resonance? TG waves? In this experiment cos θ ~ cos θres : ▪ Absorption of helicon waves near the resonance cone is correlated with the excitation of electrostatic fluctuations ▪ Low frequency electrostatic instabilities (ion-acoustic-like wave) were measured in the device ▪ The parametrically excited waves could interact with the particles providing an alternative mean for the helicon wave to deposit energy in the plasma, but they are strongly damped at the plasma edge 250 W, 0.5 mTorr, Bz,max = 530 G, probe @ (r, z) = (−5, +6) cm Frequencies: 27.12 MHz ± 25 kHz, 25 kHz EPT WORKSHOP, JULY 3-4 2025, UC3M ANALYSIS OF WAVE DAMPING MECHANISMS ▪ Then what else? Instabilities? Resonance? TG waves? In this experiment cos θ ~ cos θres : ▪ Absorption of helicon waves near the resonance cone is correlated with the excitation of electrostatic fluctuations ▪ Low frequency electrostatic instabilities (ion-acoustic-like wave) were measured in the device ▪ The parametrically excited waves could interact with the particles providing an alternative mean for the helicon wave to deposit energy in the plasma, but they are strongly damped at the plasma edge Would this be enough to justify the marked plasma density rise along the axis at the nozzle throat? EPT WORKSHOP, JULY 3-4 2025, UC3M SUMMARY OF KEY POINTS 1. Plasma densities in the order of ~10^18 m^-3 could be achieved at low-mid powers in the device 2. Discharge undergoes E-H-W mode transitions, but no “jumps” are observed 1. Increasing pressure does not change the overall dynamics, apart from an expected increase in density and a depletion of the “blue” core 2. “Doughnut-shaped” plasma under the antenna typical of ICP discharges 3. Smooth mode transitions might indicate that the different modes may exist simultaneously 3. Density peaks at the magnetic nozzle throat, and not under the antenna (non-uniform B field) even when helicon waves are not measured 1. Strong ion confinement due to radial electric fields 2. Local ionisation due to high-energetic electrons generated under the antenna 4. Classic contributions of the helicon waves to the plasma generation could not be identified 1. Absorption of helicon waves near the resonance cone can be correlated with measured excitation of electrostatic fluctuations, but they are strongly damped at the plasma edge Care should be taken in distinguishing between plasma generation due to helicon wave modes or magnetised inductively coupled discharges. EPT WORKSHOP, JULY 3-4 2025, UC3M THRUST PRODUCTION MECHANISMS AND ELECTRON ANISOTROPY IN THE ECRA THRUSTER Federico Boni1 ([email protected]) Sara Correyero1,2, Alvaro Sanchez-Villar2, Romain Pioch1,3, Victor Désangles1, Julien Jarrige1, Paul-Quentin Elias1, Denis Packan1 1ONERA, Université Paris-Saclay (France) 2EP2, Universidad Carlos III de Madrid (Spain) 3LPP, CNRS, Ecole Polytechnique (France) OUTLINE ● Motivation and approach ● Thrust production mechanisms: magnetic and thermal thrusts ● Electron density inside the source ● Electron energy anisotropy inside the source ● Discussion on thrust efficiency, anisotropy ratio, and magnetic thrust ● Conclusion and perspectives EPT WORKSHOP, JULY 3-4 2025, UC3M Motivation ● Understand thrust production → improve ECRA design and efficiency ● Characterize plasma expansion → 2D datasets to help develop more accurate predictive models/simulations ● Investigate electron energy anisotropy → anisotropy is fundamental in ECRA thruster (ECR heating) → accessing anisotropy is challenging Anisotropy / thrust production in Magnetic Nozzle thrusters ● Numerical studies: fluid and kinetic models [1,2,3,4] ● Experimental studies: - FB, FT in HPT: Thrust stand + fluid model [8] (FB/FT ≃ 30 %) - Te,⊥ and Te,∥ in ECRA: Langmuir probe [5] (No results) - pe,⊥ in ECRA: Diag loop (plasma flux at shutoff) [6] (pe,⊥ ~ 0.2 Pa) - pe,⊥/pe,∥ in ECRA: B field + FB and FS (thrust stand) [7] (High anisotropy in ECRA) - ⊥ and ∥ T and p in ECRA: B field + FB and FS + 2D Ne maps (this presentation) EPT WORKSHOP, JULY 3-4 2025, UC3M THRUST PRODUCTION MECHANISMS IN ECRA THRUSTER ● MN thrusters → 2 contributions to total thrust (FT) = magnetic (FB) + thermal (FS) [8,9] ● FS thermal thrust: surface force (electron expansion ∝ pe,∥) ● FB magnetic thrust: volume Lorentz force (azimuthal diamagnetic elec. current and MN) → axial jθe Br balances outward p⊥e ● Preliminary measurements have shown that FB dominates in ECRA [10] ECRA 30W-class specifications: - Diam: 27.5 mm - Length: 20 mm - B0: 875 G - fMW: 2.45 GHz - Prop: xenon - Performance: 30 W, 1 mN, 1500 s, 40% EPT WORKSHOP, JULY 3-4 2025, UC3M DIRECT MEASUREMENT OF MAGNETIC AND THERMAL THRUST TERMS Thermal thrust FS: ● Increases linearly with power ● Increases with flowrate Magnetic thrust FB: ● Largest at 1 sccm ● At low FR, saturation effect for P > 40 W ● At high FR, steady increase with P, no saturation Total thrust FT: ● FT = FB + FS for all tested conditions ● At low FR, FB ~ 70 − 80% ⋅ FT FS and FB reliable for further analysis. EPT WORKSHOP, JULY 3-4 2025, UC3M 2D MAPS OF ELECTRON DENSITY INSIDE THE SOURCE: EFFECT OF FLOWRATE Conditions: 1, 2 sccm, 32 W - z = 2 mm (close to backplate) - z = 20 mm (exit section) ● At high FR, density globally increases by 1.4x ● Peak of Ne moves from center to inner conductor when increasing FR ● Near inner conductor and backplate (inj. region) → Ne ↑ lower ΔΦsheath? ● Near outer conductor: steeper grad(Ne) ↓ at high FR ● Stronger confinement ● Lower radial transport (D ~ Te [13]) EPT WORKSHOP, JULY 3-4 2025, UC3M 2D MAPS OF ELECTRON DENSITY INSIDE THE SOURCE: EFFECT OF POWER Conditions: 20, 32, 52 W, 1 sccm - z = 2 mm (close to backplate) - z = 20 mm (exit section) ● At high P, density globally increases by 1.1x (P ↑ 1.6x) ● At low P, density globally decreases by 0.6x (P ↓ 0.63x) ● When P ↑, peak of Ne moves towards outer conductor ● Near outer conductor and backplate: ● High P: density ↑ ● Low P: density ↓ ● Near antenna: ● High P: steeper grad(Ne) → larger ΔΦsheath EPT WORKSHOP, JULY 3-4 2025, UC3M PREVIOUS ESTIMATIONS: p⊥e USING MAGNETIC FLUX [6] ● Diamagnetic loop at shutdown: ∫ V dt ∝ ΦP (plasma flux) mainly from jθe → p⊥e ● Main uncertainties: wall eddy currents + plasma oscillations ● p⊥e estimated using: ● 1D model (∞ unif. column): rad. elec. momentum → ΦP ∝ p⊥e ● 2D model: fluid DIMAGNO code [14] using 2 types of Ne profiles ● electron anisotropy not accounted for Table p⊥e comparison: - 1 sccm: 1D model = 0.18 Pa; 2D model gauss = 0.22 Pa; 2D model poly = 0.21 Pa - 2 sccm: 1D model = 0.14 Pa; 2D model gauss = 0.17 Pa; 2D model poly = 0.16 Pa • 1D model → does not accounts for 2D field-leaking effects • 2D model → accounts finite geom and plasma expansion • p⊥ decreases with FR • p⊥ around 0.2 Pa comparable to p = n kB T (10^11 cm^-3, 20 eV) EPT WORKSHOP, JULY 3-4 2025, UC3M PREVIOUS ESTIMATIONS: QUALITATIVE EST. OF ELECTRON ANISOTROPY [7] ● Particle description for FB [15,16] → FB ~ ∫V μ ne ∇B dV ● 2D axisymmetry ● μ adiabatic invariant ● FB mainly produced in the thruster source [1,17] ● Fluid description for FS [8] → FS ~ ∫Σ p∥ dS ● Uniform radial distribution of p∥ • p⊥/p∥ decreases with increasing FR (higher e-n coll rate → thermalization) • Bell-shaped at low FR, max ~ 5 at 30 W • At high FR, almost constant with power, ~2-3 T⊥ increase → rL ↑ (weaker confinement) → higher wall losses • Using p∥ from FS → estimation of p⊥ ~ 0.5 − 1.2 Pa (larger than [6]) • Next: finer analysis using 2D maps of Ne EPT WORKSHOP, JULY 3-4 2025, UC3M QUANTITATIVE ESTIMATION OF ELECTRON ENERGY ANISOTROPY ● Particle description for FB [15,16] (2D axisymmetry, μ = E⊥/B adiab invariant) → T⊥ ● Fluid description for FS [8] (Uniform radial distrib p∥) → p∥ ● Ideal gas law → p⊥ and T∥ Observations: • T⊥ decreases with FR • T∥ increases with FR • p⊥ and p∥ similar behavior as T • Anisotropy decreases with FR • Tiso and piso consistent with exp and sim [5,19] • p⊥ ~ FB/AS ~ 0.7 Pa ✓ EPT WORKSHOP, JULY 3-4 2025, UC3M ANISOTROPY, MAGNETIC THRUST, AND THRUST EFFICIENCY FB/FT ratio: ● ↓ with FR ● At low FR, bell-shaped with max at 80% at ~30 W ● At larger FR, almost const 60%, consistent with PIC hybrid sim. [19] ● Larger values than HPT ~30-50 % [8] (B0 ~ 200G) Anisotropy ratio T⊥/T∥: ● ↓ with FR ● Low FR, bell-shaped with a max around 6 at 30 W Total thrust efficiency ηT: ● ↓ with FR ● At low FR is bell-shaped (max ~4% at 25-35 W) ● At high FR maximum probably not reach yet Key takeaways: ✓ Trend of FB/FT correlate with ηT and anisotropy ✓ Max around 30 W at low FR, then decrease for higher P ✓ Largest ηT obtained for largest FB/FT ratio and anisotropy ratio EPT WORKSHOP, JULY 3-4 2025, UC3M CONCLUSION • FB saturate at high P at low FR • FB ~ 70-80% of total thrust at low FR • FB/FT ratio > HPT • FS increases linearly with P • pe⊥ ~ 1 Pa and Te⊥ ~ 40 − 60 eV • piso and Tiso consistent with exp and sim • Anisotropy ⊥/∥ ≃ 2 − 6 • Larger anisotropy at low FR • Correlation btw ηT, FB/FT, and T⊥/T∥ • Density spatial distribution varies with P and FR • Variations probably related to sheath, magn. confinement, and plasma transport FUTURE WORKS • Further analysis of these results → are the identified tendencies sound? • Investigate other operating conditions → correlation btw ηT, FB/FT, and T⊥/T∥ confirmed for other operating conditions (power, flowrate)? • Comparison with PIC simulations → validation of codes + guiding design (geometry, B topology, injection schemes) • Investigate ECRA in larger ERIS facility → facility effects? • Study optimized ECRA version → these tendencies will be magnified? EPT WORKSHOP, JULY 3-4 2025, UC3M Open questions Measurement and diagnostic limits: ➢ Why LP measurements failed to access anisotropy? ➢ Can current diag access accurately enough T⊥ and T∥? Are we limited to indirect estimates? Modeling assumptions and comparison with simulations: ➢ Assuming μ = const too strong? ➢ How reliable is the μ∇B approach for estimating full contribution of measured magnetic thrust? Physical mechanisms of anisotropy: ➢ Primary mechanisms controlling anisotropy in ECRA? (e.g., collisionality, elec heating, confinement topology) ➢ Is there an optimum value of anisotropy, or too high T⊥/T∥ would lead to detrimental wall losses? ➢ Role of anomalous transport in relaxing anisotropy? Optimization and scalability: ➢ Can FB/FT and anisotropy trends be generalized across different MN thrusters? ➢ How do facility effects alter the trends found here? ➢ Is the methodology presented here transferable to high-power class ECRA/MN technologies? ➢ Can active control of anisotropy (power modul, B field control) optimize thruster performance across operating conditions? EPT WORKSHOP, JULY 3-4 2025, UC3M Q1: HOW WILL FACILITY EFFECTS AFFECT RESULTS PRESENTED HERE? Results presented here are subject to facility effects (chamber size + pressure) in B09 chamber used in this study [12] [12] Boni et al., IEPC-2024-792 (2024) EPT WORKSHOP, JULY 3-4 2025, UC3M Q2: HOW THE TENDENCIES PRESENTED HERE WILL CHANGE IN THE CASE OF THE OPTIMIZED ECRA THRUSTER VERSION? Results presented here → lower perfs because this version is not the optimized version presented in [11] [11] Désangles et al., JEP 2:10 (2023) EPT WORKSHOP, JULY 3-4 2025, UC3M Q3: COMPARISON WITH PIC NUMERICAL SIMULATIONS ● Comparison of electron properties: density, temperature, pressure in the ECRA source ● validation of codes ● guiding design (geometry, B topology, injection schemes) - Pic-hybrid simulations of ECRA thruster (A Sanchez-Villar, PhD dissertation, UC3M, 2021) - Experimental measurements (F Boni, PhD dissertation, Univ Paris-Saclay, 2022) EPT WORKSHOP, JULY 3-4 2025, UC3M DIRECT MEASUREMENT OF PLASMA DENSITY IN ECRA THRUSTER Curling probe: microwave resonance probe ne ∝ Δf = fr − f0 • Spatial resolution ~ 10 mm • Temporal resolution as low as 5 µs [Boni et al., J Phys D: App Phys 09LT01 (2025)] • Measurement range = 10^7 – 10^11 cm^-3 (other density ranges are accessible with different curling probe designs) • High accuracy (~20 %) • Experimental calibration procedure [Boni et al., RSI 033507 (2021)] → access to absolute Ne value • Sheath correction method available to compensate for plasma sheaths effects (10^9 cm^-3, Te ~ 20 eV → λD ~ 1 mm) [Boni et al., PSST 095018 (2023)] EPT WORKSHOP, JULY 3-4 2025, UC3M INDIRECT MEASUREMENT OF PLASMA DENSITY IN ECRA THRUSTER Probing Xe metastable stable using Laser Induced Fluorescence techniques → inference of plasma density ● Principle: ● Excitation of metastable Xe+ ● Collection of fluorescence signal from radiative decay ● Measure of the ion velocity with Doppler effect ● Inference of the plasma density from integral of the signal (+ some hp) Laser excitation: 834.955 nm; Fluorescence: 541.915 nm EPT WORKSHOP, JULY 3-4 2025, UC3M GLOBAL AND COLLISIONAL RADIATIVE MODELLING FOR RF XENON PLASMAS Mansur Tisaev Postdoc in Plasma Propulsion with Prof. Richard E. Wirz Oregon State University PLASMA, ENERGY, & SPACE PROPULSION WIRZ RESEARCH GROUP Key areas: - Spatiotemporal (FastOES) plasma diagnostics - Facility effects and thruster lifetime models - Plasma material interactions (Volumetrically complex materials) - Cold atmospheric plasmas Collaborations/Funding: NASA, JPL, AFRL, US Air Force, NSF, Oregon State University EPT WORKSHOP, JULY 3-4 2025, UC3M LITERATURE AND CHALLENGES IN THE COMMUNITY - Effect of multi-frequency waveforms on EEDF via constraining electron heating, analyzed using simulations and OES of excited Ar (A.R. Gibson et al., PSST 2019). - Selective electronic excitation of N2 via ns high-V pulse and vibrational excitation of N2 via RF waveform (I. Gulko et al., PSST 2020). - Using recent cross sections in RF global model, comparing I2 to Xe in ion source with extraction (T. Lafleur et al., PSST 2022). EPT WORKSHOP, JULY 3-4 2025, UC3M MOTIVATIONS AND OBJECTIVES High-speed diagnostics and modelling of fundamental plasma behaviour for RF CFE basic science ● Combined experimental diagnostics and modeling to resolve plasma behavior in space and time (FastOES, WideFieldOES) ● First step is Global Plasma Model (GPM) and Collisional Radiative Model (CRM) for Xe Model ⟷ Spatiotemporal diagnostics ⟷ Experiment (Theory, Xe, N2, Ar, Air) EPT WORKSHOP, JULY 3-4 2025, UC3M GLOBAL PLASMA MODEL (GPM) EQUATIONS Particle balance: - Neutrals (gas): dng/dt = Q0/V + ne uB (Aeff'/V) − ne ng Kiz − Γg (Ag/V) - Ions: dne/dt = ne ng Kiz − ne uB (Aeff/V) Power balance: - Neutrals (gas): d/dt (3/2 ng kB Tg) = 3 (me/M) kB (Te − Tg) ne ng Kel + 1/4 M uB^2 ne ng Kin − κ ((Tg − Tw)/Λ0) (A/V) - Electrons: d/dt (3/2 ne kB Te) = Pabs − Ploss EPT WORKSHOP, JULY 3-4 2025, UC3M GLOBAL PLASMA MODEL (GPM) LIMITATIONS Electron power balance: d/dt (3/2 ne kB Te) = Pabs − Ploss Ploss = εiz ne ng Kiz + εex ne ng Kex + 3 (me/M) kB (Te − Tg) ne ng Kel + 7 kB Te ne uB (Aeff/V) RF-plasma transformer model: Pabs = 1/2 [Rind + (ω^2 Lind C)^2 Rcap] Icoil^2 Rind = (2π N^2 / (l ω ε0)) Re [ i k ro J1(k ro) / (εp J0(k ro)) ] Lind = Lcoil (1 − ro^2 / rc^2) + (2π N^2 / (l ω^2 ε0)) Im [ i k ro J1(k ro) / (εp J0(k ro)) ] Edge-to-centre density ratios: Aeff = 2 hr π r l + 2 hl π r^2 hr = ne(rw) / ne(r = 0) hl = ne(lw) / ne(l / 2) EPT WORKSHOP, JULY 3-4 2025, UC3M COLLISIONAL RADIATIVE MODEL (CRM) EQUATIONS dnp/dt = +∑q ne Kqp nq − ∑q ne Kpq np + ni Kip n0 − np KH nH + ∑q nq Aqp − ∑q np Apq p = Initial state, q = Final state, pq = Transition from state p into state q 36 Xe I states included (e.g. 2p6, 2p5, 1s4, 1s5; 823 nm, 828 nm lines) Correction for photon absorption by plasma: Aeff = Γqp A Γqp = (2 − exp(−τqp/1000)) / (1 + τqp) τqp = (λqp^3 / 8π) (gq / gp) Aqp np d sqrt(M / (2π kB Tg)) EPT WORKSHOP, JULY 3-4 2025, UC3M GPM AND CRM COMPARISON TO EXPERIMENT Global Plasma Model results (1.5 sccm Xe, Icoil = 10 A, PRF,abs = 42.1 W): - ng, ne, Tg, Te time evolutions Collisional Radiative Model results: - 0.75 sccm Xe: Te ~ 2.3 eV, ne ~ 2.0 × 10^17 m^-3 - 1.5 sccm Xe: Te ~ 1.8 eV, ne ~ 3.5 × 10^17 m^-3 EPT WORKSHOP, JULY 3-4 2025, UC3M GPM AND CRM UNCERTAINTY SENSITIVITY Sensitivity analysis for hr and hl variations (*0.8, *1.0, *1.2): - 0.75 sccm Xe: - Electron temperature vs Absorbed RF power - Electron density vs Absorbed RF power - 1.5 sccm Xe: - Electron temperature vs Absorbed RF power - Electron density vs Absorbed RF power Comparison showing divergence between GPM predictions and OES+CRM experimental points. EPT WORKSHOP, JULY 3-4 2025, UC3M OPEN QUESTIONS ● Each group rightly focused on individual hypotheses of interest, but what overarching plasma behaviour should be studied by the community to improve the limits in understanding (and performance) of electrodeless plasma thrusters? ● To what degree are the EEDF/IEDF non-Maxwellian at low RF power (<100 W) and flow rate (~1 sccm, 10^-1 - 10^0 Pa, 10^19 - 10^20 m^-3)? How significant is this effect on global model results? ● How accurate are the global model assumptions for edge-to-centre electron density ratios (and so wall losses) in H/inductive mode? Can we gain insights using spatially-resolved OES+CRM? ● What degree of photon absorption should be assumed in the CRM to account for spatial distribution of excited species’ generation? ● Molecular plasmas are hard! How representative is using a similar-AMU noble gas as a tracer? EPT WORKSHOP, JULY 3-4 2025, UC3M 2D/3V HYBRID MODELLING OF PLASMA TRANSPORT IN EPTS Eduardo Ahedo on behalf of Equipo de Propulsión Espacial y Plasmas (EP2) Universidad Carlos III de Madrid (UC3M) 2D (Z,R) HYPHEN Architecture modules: - W-module: Maxwell eqs, Cold dielectric tensor, FE and FD versions, Frequency domain - E-module: Magnetized fluid drift-diffusive (inertialess), Quasineutrality, B-aligned mesh, FV + FD - I-module: PIC-MCC model, Multiple heavy species - S-module: Debye sheath collisionless, unmagnetized, SEE, Non-Maxwellian VDF Performance: In our workstations, a simulation takes O(10 hours) with partial parallelization. EPT WORKSHOP, JULY 3-4 2025, UC3M HYPHEN ● W-module solves the interaction of the HF wave fields B_HF, E_HF with plasma represented by ε(z, r, ω) ● Rest of modules solve for the slow dynamics (and the steady state) for thruster + plume ● The EM fields are the applied static B from coils and the ambipolar E = −∇ϕ as output ● Electron model equations: quasineutrality, continuity, momentum, energy, and heat flux ● High-frequency (HF) waves leave a 2D map of absorbed power in the electron energy equation: ∇ ⋅ (5/2 Te ne ue − K_e ⋅ ∇Te) ≃ j ⋅ E − Qinel + Qabs, Qabs = ⟨j ⋅ E⟩_HF ● From momentum equation: j ⋅ E = ue ⋅ ∇pe + νe me ne ue^2 ● Empirical submodels are needed (for physics not solved within HYPHEN): ● Wall properties (SEE, ion energy accommodation, depletion of eVDF) in Sheath-module ● Turbulent/anomalous diffusion due to azimuthal instabilities (AI) or mid/high frequency: 0 = j⊥e B − (νe + αt ωce) me ne uθe, αt jθe B = −⟨e ne Eθ⟩_AI − ⟨me D/Dt (ne uθe) + (∇ ⋅ p_e)θ⟩_AI ● We know from Hall thrusters that with αt = 0, the cross-field current j⊥e (i.e. cross-field diffusion) is too low when compared to empirical data. ● This seems to happen in EPTs too. There is partial evidence in recent experiments. EPT WORKSHOP, JULY 3-4 2025, UC3M TWO APPLICATIONS ● Two application/validation cases: ● Simulation of ECRT from ONERA (H2020-MINOTOR) ● Sánchez-Villar et al., PSST 30, 045005 (2021) ● Sánchez-Villar et al., PSST 32, 014002 (2023) - Parameters: 2.45 GHz, 30W, 2sccm Xe, 2cm x 1.38 cm ● Simulation of HPT from EP2 (H2020-HIPATIA) ● Jiménez et al., PSST 32, 105013 (2023) - Parameters: 13.6 Mhz, 450W, 12-20 sccm Xe, 6cm x 1.25 cm EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN ECRT (Sanchez-Villar, 2021) ● RF power is deposited around the ECR surface ● Magnetic thrust = ∫ (−jθe Br) dV ● Central rod bad for magnetic thrust: ● jθe Bz ∇r pe needs to compensate ● Maximum Te at ECR surface ● Te ≃ const along magnetic lines (contrary to empirical evidence; Heat flux model does not work fine) ● Complex map of ϕ due to Te, BCs, and central rod ● Ion acceleration in plume affected by downstream plume conditions (dielectric vs metallic) EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN ECRT (Sanchez-Villar, 2023) ● A larger plume was simulated ● Measurements exist in plume only ● Adjustment of turbulent parameter needed [αt(r) = const] ● αt ↑: cross-diffusion, beam divergence ↑ ● αt = 0.05 gives the best fit ● Relative good agreement on ion-related magnitudes (solved with PIC I-module) ● Discrepancy exists among probes too! EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN ECRT ● Worse agreement on ϕ and, especially Te ● Electron energy model does not reproduce well anomalous diffusion of energy, due likely to: ● Wave-based turbulence and diffusion (different than from mass diffusion?) ● Non-Maxwellian eVDF in plume (i.e., collisionless cooling; evidence from kinetic MN model) ● Empirically-adjusted polytropic model, i.e., Te ∝ ne^(γ−1) yields much better agreement (γ ≈ 1.34) ● In energy equation this would mean to change (5/2 Te ne ue − K_e ⋅ ∇Te) by (γ / (γ−1)) Te ne ue or change K_e EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN ECRT Comparison table: - Thrust F (μN): Exp = 601 ± 15; αt=0.035 -> 934; αt=0.05 -> 877; αt=0.08 -> 781 - Specific impulse Isp (s): Exp = 312 ± 8; αt=0.035 -> 484; αt=0.05 -> 455; αt=0.08 -> 405 - Thrust efficiency ηF (%): Exp = 3.1 ± 0.2; αt=0.035 -> 7.4; αt=0.05 -> 6.5; αt=0.08 -> 5.2 - Ion beam current Ib (mA): Exp = 62 ± 3; αt=0.035 -> 67; αt=0.05 -> 62; αt=0.08 -> 56 - Utilization efficiency ηu (%): Exp = 43 ± 2.1; αt=0.035 -> 47.1; αt=0.05 -> 44.4; αt=0.08 -> 40.7 - Energy efficiency ηen (%): Exp = 13.4 ± 0.6; αt=0.035 -> 15.7; αt=0.05 -> 15.5; αt=0.08 -> 13.7 - 90%-current angle ψ90% (°): Exp = 60 ± 1; αt=0.035 -> 58; αt=0.05 -> 60; αt=0.08 -> 61 - Maximum Ei,max (eV): Exp = 65; αt=0.035 -> 71; αt=0.05 -> 75; αt=0.08 -> 74 ● Relatively good agreement in several magnitudes ● 12% overestimation of Ei,max ● Thrust F highly overestimated. Possible explanation: No background pressure (BGP) on simulations (Wach et al. 2020: 37% decrease in F when BGP 0.13 → 3.5 × 10^-5 mbar) EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN HPT ● Cusped B-field topology with perm. magnets ● Why? Several works (Virko; Trezzolani; Ito; Takahashi) suggest better performances ● No optimization carried out here ● Cusped field was a challenge for HYPHEN ● Half-helical antenna is used ● HYPHEN needs to solve azimuthal modes with m ≠ 0 ● Power deposition in HPT is more complex ● Takes place in source and plume ● Extends until external ECR Surface (B=5G) ● External deposition per electron can be large → effect on Te EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN HPT ● Fitting of the turbulent parameter νq αt ~ 1.5% ● Fitting of parameter νq for parallel electron cooling ● Novelty from previous ECRT simulations ● Unclear if this is better than a polytropic fitting ● Kinetic studies of MN suggests that a combination of both approaches would yield the best fitting EPT WORKSHOP, JULY 3-4 2025, UC3M PLASMA DISCHARGE IN HPT ● Relative good agreement experiment/simulations ● Temperature profile presents an external maximum, recovered in the simulations, and located at ECR surface ● Ion current profile presents wings, not recovered in simulations ● Likely an effect of BGP EPT WORKSHOP, JULY 3-4 2025, UC3M CONCLUSIONS AND OPEN QUESTIONS ● HYPHEN has proven to be a good tool to study EPTs plasma discharge and performance ● The comparison with experimental data is reasonable ● But mainly it highlights the aspects we still do not understand/model well. ● Most of them are related to the electron population, more specifically to electron energy; e.g. ● If a fluid model is used, we lack a reliable closure for the heat flux vector ● The model could be different in source (more collisional, walls) and plume (kind of free expansion) ● Perhaps a (5-moment) fluid model will never work well ● Affordable kinetic simulations are needed to increase our understanding of EPTs ● Very limited clues on wave-based turbulence in EPTs. More evidence is needed ● Turbulent transport could explain weak magnetic confinement, large wall losses, and low efficiency ● Advances need to be made in having models with more consistent separation of the temporal scales ● Or do we rely on an electromagnetic code with a single temporal scale? ● More research is needed on optimizing magnetic topology and channel geometry for the different EPTs ● HYPHEN has also been used to study ABEP with EPTs: Zhou et al, Propul. Power Research 13, 459 (2024) EPT WORKSHOP, JULY 3-4 2025, UC3M Thank you! 1st International Electrodeless Plasma Thruster Workshop https://eptworkshop.uc3m.es July 3-4, 2025 Universidad Carlos III de Madrid uc3m