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3D Plasma plume characterization of an electrodeless thruster cluster in magnetic arch configuration
Authors:
Sacha A. Huot,
Marco Riccardo Inchingolo,
Jaume Navarro-Cavallé,
Mario Merino
Abstract:
Clustering electrodeless plasma thrusters in pairs with opposing magnetic polarities offers an easy means to scale-up the propulsion system of future missions, and also, to mutually cancel their respective magnetic dipoles. Their magnetic nozzles merges to form a new topology, the `magnetic arch', which can yield a lower plasma plume divergence than two separate magnetic nozzles. This work charact…
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Clustering electrodeless plasma thrusters in pairs with opposing magnetic polarities offers an easy means to scale-up the propulsion system of future missions, and also, to mutually cancel their respective magnetic dipoles. Their magnetic nozzles merges to form a new topology, the `magnetic arch', which can yield a lower plasma plume divergence than two separate magnetic nozzles. This work characterizes the plasma expansion in the fully-closed magnetic arch of a cluster of two electron-cyclotron resonance thrusters with electrostatic probes (Langmuir probes, Faraday cups, and a Retarding Potential Analyzer). Electrostatic potential, plasma density, electron temperature, ion current and energy are measured in the two orthogonal planes of symmetry of the setup for various operating conditions. Results show that a plasma jet can be extracted even from this magnetic configuration, albeit with a reduced ion energy. A slight potential hill and hotter electrons exist in the central part of the arch. Ion current profiles are doubly-peaked in the horizontal plane, likely corresponding to the beamlet of each thruster. Trends with xenon mass flow rate and input power are consistent with the expectations of electrodeless plasma thrusters. The plume experiences an upward or downward deflection depending on the direction of the applied magnetic field, which could be attributed to the effect of the lateral electron drifts in the magnetic arch.
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Submitted 10 July, 2026;
originally announced July 2026.
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Analysis of collisional and facility effects in a magnetic nozzle plasma expansion
Authors:
Manuel Cortés-Hernán,
Mario Merino,
Diego García-Lahuerta,
Eduardo Ahedo
Abstract:
An axisymmetric, quasineutral three-fluid model is proposed to study the plasma expansion in a magnetic nozzle under the presence of neutrals coming either from the plasma source or as an homogeneous background. As a difference with other models, electron cooling in the plume is achieved by treating the electron energy flux as mainly convective and without the need to postulate any anomalous resis…
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An axisymmetric, quasineutral three-fluid model is proposed to study the plasma expansion in a magnetic nozzle under the presence of neutrals coming either from the plasma source or as an homogeneous background. As a difference with other models, electron cooling in the plume is achieved by treating the electron energy flux as mainly convective and without the need to postulate any anomalous resistivity. Solutions are presented for the electron high-magnetization limit, in which the electron main magnitudes can be integrated along magnetic lines. Ionization, elastic and charge-exchange collisions with neutrals do not change the main qualitative features of the plasma expansion, known from previous collisionless models. Ionization enhances the plasma flow in the nozzle, and leads to additional electron cooling, which decreases the electric potential fall along the nozzle. The efficiency of the nozzle is quantified in terms of the gain of magnetic thrust and the plume divergence angle. Two types of boundary conditions are discussed for the electron flow: local current ambipolarity conditions at the nozzle throat and global current-free conditions at the outer boundary (i.e., metallic vacuum chamber walls). These last ones are shown to be physically more reliable: they introduce the influence of the chamber walls on the plasma expansion by shaping the ambipolar electric field; they permit the extrapolation to undisturbed free space conditions; and they approximate better experimental trends with the background pressure.
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Submitted 8 July, 2026;
originally announced July 2026.
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Fully-implicit Particle-in-Cell model of a Magnetic Nozzle with electromagnetic power deposition
Authors:
Mario Merino,
Juan Martín-Hernández,
Pedro Jiménez-Jiménez,
Luis Chacón
Abstract:
A fraction of the electromagnetic power used to generate and heat the plasma in helicon sources and electrodeless plasma thrusters can leak into the outer expansion region, interacting with the plasma in the magnetic nozzle and affecting the performance of the device. This work analyzes the properties of the plasma in a convergent-divergent magnetic nozzle when right-hand polarized waves of varyin…
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A fraction of the electromagnetic power used to generate and heat the plasma in helicon sources and electrodeless plasma thrusters can leak into the outer expansion region, interacting with the plasma in the magnetic nozzle and affecting the performance of the device. This work analyzes the properties of the plasma in a convergent-divergent magnetic nozzle when right-hand polarized waves of varying amplitude propagate into it. This is accomplished with a 1D3V fully-implicit, Vlasov-Darwin particle-in-cell model of the collisionless ion and electron plasma in a magnetic tube. The code exactly conserves charge locally and energy globally. It features a nonuniform grid and an enhanced substepping routine for the particle trajectories. The requirement that the expansion be current-free is satisfied thanks to linear closed-loop controllers on the injection and downstream boundary conditions. Wave heating increases the electron perpendicular temperature, especially in the vicinity of an electron cyclotron resonance surface, always present inside the magnetic nozzle of a helicon device. The energized electrons become anisotropic, and drive a more pronounced potential drop and a higher ion acceleration than in the absence of waves, at the expense of the wave power. The computed moments of the ion and electron distributions reveal the dominant balance of the electron thermal terms, electrostatic terms, and ion inertial terms in the momentum and energy equations. Wave heating helps populate otherwise-inaccessible regions of the electrons phase space and modifies the doubly-trapped electron population found in the purely electrostatic case...
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Submitted 8 June, 2026;
originally announced June 2026.
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Benchmark for two-dimensional large scale coherent structures in partially magnetized ExB plasmas -- Community collaboration & lessons learned
Authors:
Andrew T. Powis,
Eduardo Ahedo,
Alejandro Álvarez Laguna,
Nicolas Barléon,
Enrique Bello-Benítez,
Lucas Beving,
Jean-Pierre Boeuf,
Guillaume Bogopolsky,
Anne Bourdon,
Filippo Cichocki,
Bénédicte Cuenot,
Andrew Denig,
Zoltán Donkó,
Paul-Quentin Elias,
Miguel P. Encinar,
Denis Eremin,
Pablo Fajardo,
Farbod Faraji,
Gwenael Fubiani,
Laurent Garrigues,
Kentaro Hara,
Peter Hartmann,
Matthew Hopkins,
Igor D. Kaganovich,
Aaron Knoll
, et al. (16 additional authors not shown)
Abstract:
Low-temperature plasmas are essential to both fundamental scientific research and critical industrial applications. As in many areas of science, numerical simulations have become a vital tool for uncovering new physical phenomena and guiding technological development. Code benchmarking remains crucial for verifying implementations and evaluating performance. This work continues the Landmark benchm…
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Low-temperature plasmas are essential to both fundamental scientific research and critical industrial applications. As in many areas of science, numerical simulations have become a vital tool for uncovering new physical phenomena and guiding technological development. Code benchmarking remains crucial for verifying implementations and evaluating performance. This work continues the Landmark benchmark initiative, a series specifically designed to support the verification of low-temperature plasma codes. In this study, seventeen simulation codes from a collaborative community of nineteen international institutions modeled a partially magnetized ExB Penning discharge. The emergence of large scale coherent structures, or rotating plasma spokes, endows this configuration with an enormous range of time scales, making it particularly challenging to simulate. The codes showed excellent agreement on the rotation frequency of the spoke as well as key plasma properties, including time-averaged ion density, plasma potential, and electron temperature profiles. Achieving this level of agreement came with challenges, and we share lessons learned on how to conduct future benchmarking campaigns. Comparing code implementations, computational hardware, and simulation runtimes also revealed interesting trends, which are summarized with the aim of guiding future plasma simulation software development.
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Submitted 24 October, 2025;
originally announced October 2025.
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Data-driven analysis of anomalous transport and three-wave-coupling effects in E x B plasma discharges
Authors:
Borja Bayón-Buján,
Enrique Bello-Benítez,
Jiewei Zhou,
Mario Merino
Abstract:
Collisionless cross-field electron transport in an E x B configuration relevant for electric propulsion is studied using data from a (z, θ) full-PIC simulation. Higher-order spectral analysis shows that transport is dominated by the in-phase interaction of the oscillations of the azimuthal electric field and the electron density associated to the first electron cyclotron drift instability (ECDI) m…
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Collisionless cross-field electron transport in an E x B configuration relevant for electric propulsion is studied using data from a (z, θ) full-PIC simulation. Higher-order spectral analysis shows that transport is dominated by the in-phase interaction of the oscillations of the azimuthal electric field and the electron density associated to the first electron cyclotron drift instability (ECDI) mode. A secondary contribution emanates from a lower-frequency mode, not predicted by linear ECDI theory, while higher modes have a minor direct impact on transport. However, a bicoherence analysis reveals that strong phase couplings exist among the ECDI modes, and a sparse symbolic regression spectral model, based on the three-wave coupling equations, suggests an inverse energy cascade as the most likely explanation, thus suggesting that higher modes contribute indirectly to transport by quadratic power transfer to the first mode. This work provides new insights into the dynamics of anomalous plasma transport in E x B sources and the underlying processes governing energy distribution across different scales, and supports the validity of weak turbulence theory to examine their behavior.
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Submitted 27 December, 2024;
originally announced December 2024.
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Lower-Hybrid Drift Instabilities in a magnetic nozzle
Authors:
Matteo Ripoli,
Eduardo Ahedo,
Mario Merino
Abstract:
Magnetic nozzles are a key component of electrodeless plasma thrusters, acting as their main acceleration stage. Non-stationary phenomena common to the entire range of $E \times B$ devices, such as oscillations and instabilities, are likely to exist in the magnetic nozzle, according to the mounting experimental evidence. These mechanisms could lead to anomalous cross-field transport, either enhanc…
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Magnetic nozzles are a key component of electrodeless plasma thrusters, acting as their main acceleration stage. Non-stationary phenomena common to the entire range of $E \times B$ devices, such as oscillations and instabilities, are likely to exist in the magnetic nozzle, according to the mounting experimental evidence. These mechanisms could lead to anomalous cross-field transport, either enhancing the plasma plume divergence or favoring electron detachment. In this work we present a local linear analysis of fluid instabilities relevant for said devices, expanding on previous works with the addition of plasma inhomogeneities in the direction parallel to the magnetic field, with a rigorous inclusion of the effects of magnetic curvature, finite Larmor radius and $3$D wave propagation, allowing for a general formulation of drift-driven instabilities in partially magnetized plasmas. Instability conditions are first studied analytically, and then applied to simulation data of a helicon plasma thruster. Finally, the effect of instabilities on wave-driven cross-field electron transport is assessed by means of quasi-linear analysis. This study predicts the onset of essentially-azimuthal instabilities in the $1$ kHz--$1$ MHz range, in qualitative agreement with some of the available experimental data, and highlights the importance of including parallel inhomogeneities in the formulation of the dispersion relation of an $E \times B$ plasma, as these gradients may drive instabilities even in the absence of axial propagation. Lastly, quasi-linear analysis suggests that the induced cross-field transport acts to smooth out the zeroth-order drifts which cause the plasma to destabilize in the first place.
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Submitted 13 December, 2024;
originally announced December 2024.
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Data-driven sparse modeling of oscillations in plasma space propulsion
Authors:
B. Bayón-Buján,
M. Merino
Abstract:
An algorithm to obtain data-driven models of oscillatory phenomena in plasma space propulsion systems is presented, based on sparse regression (SINDy) and Pareto front analysis. The algorithm can incorporate physical constraints, use data bootstrapping for additional robustness, and fine-tuning to different metrics. Standard, weak and integral SINDy formulations are discussed and compared. The sch…
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An algorithm to obtain data-driven models of oscillatory phenomena in plasma space propulsion systems is presented, based on sparse regression (SINDy) and Pareto front analysis. The algorithm can incorporate physical constraints, use data bootstrapping for additional robustness, and fine-tuning to different metrics. Standard, weak and integral SINDy formulations are discussed and compared. The scheme is benchmarked in the case of breathing-mode oscillations in Hall effect thrusters, using PIC/fluid simulation data. Models of varying complexity are obtained for the average plasma properties, and shown to have a clear physical interpretability and agreement with existing 0D models in the literature. Lastly, the algorithm applied is also shown to enable the identification of physical subdomains with qualitatively different plasma dynamics, providing valuable information for more advanced modeling approaches.
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Submitted 11 March, 2024;
originally announced March 2024.
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Analysis of a cusped helicon plasma thruster discharge
Authors:
Pedro Jimenez,
Jiewei Zhou,
Jaume Navarro,
Pablo Fajardo,
Mario Merino,
Eduardo Ahedo
Abstract:
A compact helicon plasma thruster that features a cusp in its internal magnetic field is analyzed with experiments and simulations. A compensated Langmuir probe and a Faraday cup are used in the former, while a hybrid PIC/fluid transport model combined with a frequency-domain electromagnetic field model are used in the latter. Measurements serve to tune the anomalous transport parameters of the mo…
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A compact helicon plasma thruster that features a cusp in its internal magnetic field is analyzed with experiments and simulations. A compensated Langmuir probe and a Faraday cup are used in the former, while a hybrid PIC/fluid transport model combined with a frequency-domain electromagnetic field model are used in the latter. Measurements serve to tune the anomalous transport parameters of the model and overall show the same trends as the numerical results, including a secondary peak of electron temperature downstream in the magnetic nozzle, where electron cyclotron resonance conditions for the 13.56 MHz excitation frequency are met. The cusp plays a central role in determining the plasma losses to the walls and the profile of electron temperature, which in turn defines the excitation and ionization losses. While losses to the rear wall are reduced, losses to the lateral wall are increased, which, together with the low production efficiency, limit the performance of the device. Shorter chamber lengths and optimization of antenna and cusp location are suggested as potential ways to improve performance.
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Submitted 18 July, 2023;
originally announced July 2023.
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An implicit, conservative electrostatic particle-in-cell algorithm for paraxial magnetic nozzles
Authors:
Pedro Jimenez,
Luis Chacon,
Mario Merino
Abstract:
An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach is adaptive in configuration space by the use of mapped meshes, and exploits the strict conservation of the magnetic moment to reduce the dimensionality of velo…
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An electrostatic, implicit particle-in-cell (PIC) model for collisionless, fully magnetized, paraxial plasma expansions in a magnetic nozzle is introduced with exact charge, energy, and magnetic moment conservation properties. The approach is adaptive in configuration space by the use of mapped meshes, and exploits the strict conservation of the magnetic moment to reduce the dimensionality of velocity space. A new particle integrator is implemented, which allows for particle substepping without the need to stop particle motion at every cell for charge conservation. Particle suborbits are determined from accuracy considerations, and are allowed to span multiple cells. Novel particle injection and expansion-to-infinity boundary conditions are developed, including a control loop to prevent the formation of spurious sheaths at the edges of the domain. The algorithm is verified in a periodic magnetic mirror configuration, a uniform plasma test case (to test particle injection), and a propulsive magnetic nozzle. The algorithm's computational complexity is shown to scale favorably with timestep, and linearly with the number of particles and mesh cells (unlike earlier implicit PIC implementations, which scaled quadratically with the number of mesh cells in one dimension). Numerical experiments demonstrate that the proposed algorithm outperforms both explicit PIC and semi-Lagrangian Vlasov codes by more than an order of magnitude.
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Submitted 11 May, 2023;
originally announced May 2023.
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Automatic segmentation of clear cell renal cell tumors, kidney, and cysts in patients with von Hippel-Lindau syndrome using U-net architecture on magnetic resonance images
Authors:
Pouria Yazdian Anari,
Nathan Lay,
Aditi Chaurasia,
Nikhil Gopal,
Safa Samimi,
Stephanie Harmon,
Rabindra Gautam,
Kevin Ma,
Fatemeh Dehghani Firouzabadi,
Evrim Turkbey,
Maria Merino,
Elizabeth C. Jones,
Mark W. Ball,
W. Marston Linehan,
Baris Turkbey,
Ashkan A. Malayeri
Abstract:
We demonstrate automated segmentation of clear cell renal cell carcinomas (ccRCC), cysts, and surrounding normal kidney parenchyma in patients with von Hippel-Lindau (VHL) syndrome using convolutional neural networks (CNN) on Magnetic Resonance Imaging (MRI). We queried 115 VHL patients and 117 scans (3 patients have two separate scans) with 504 ccRCCs and 1171 cysts from 2015 to 2021. Lesions wer…
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We demonstrate automated segmentation of clear cell renal cell carcinomas (ccRCC), cysts, and surrounding normal kidney parenchyma in patients with von Hippel-Lindau (VHL) syndrome using convolutional neural networks (CNN) on Magnetic Resonance Imaging (MRI). We queried 115 VHL patients and 117 scans (3 patients have two separate scans) with 504 ccRCCs and 1171 cysts from 2015 to 2021. Lesions were manually segmented on T1 excretory phase, co-registered on all contrast-enhanced T1 sequences and used to train 2D and 3D U-Net. The U-Net performance was evaluated on 10 randomized splits of the cohort. The models were evaluated using the dice similarity coefficient (DSC). Our 2D U-Net achieved an average ccRCC lesion detection Area under the curve (AUC) of 0.88 and DSC scores of 0.78, 0.40, and 0.46 for segmentation of the kidney, cysts, and tumors, respectively. Our 3D U-Net achieved an average ccRCC lesion detection AUC of 0.79 and DSC scores of 0.67, 0.32, and 0.34 for kidney, cysts, and tumors, respectively. We demonstrated good detection and moderate segmentation results using U-Net for ccRCC on MRI. Automatic detection and segmentation of normal renal parenchyma, cysts, and masses may assist radiologists in quantifying the burden of disease in patients with VHL.
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Submitted 6 January, 2023;
originally announced January 2023.
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Kinetic Electron Cooling in Magnetic Nozzles: Experiments and Modeling
Authors:
June Young Kim,
Kyoung-Jae Chung,
Kazunori Takahashi,
Mario Merino,
Eduardo Ahedo
Abstract:
As long-distance space travel requires propulsion systems with greater operational flexibility and lifetimes, there is a growing interest in electrodeless plasma thrusters that offer the opportunity of improved scalability, larger throttleability, running on different propellants, and limit device erosion. The majority of electrodeless designs rely on a magnetic nozzle (MN) for the acceleration of…
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As long-distance space travel requires propulsion systems with greater operational flexibility and lifetimes, there is a growing interest in electrodeless plasma thrusters that offer the opportunity of improved scalability, larger throttleability, running on different propellants, and limit device erosion. The majority of electrodeless designs rely on a magnetic nozzle (MN) for the acceleration of the plasma, which has the advantage of utilizing the expanding electrons to neutralize the ion beam without the additional installation of a cathode. The plasma expansion in the MN is nearly collisionless, and a fluid description of electrons requires a non-trivial closure relation. Kinetic electron effects, and in particular electron cooling, play a crucial role in various physical phenomena such as energy balance, ion acceleration, and particle detachment. Based on the experimental and theoretical studies conducted in recognition of this importance, the fundamental physics of the electron cooling mechanism revealed in MNs and magnetically expanding plasma are reviewed. Especially, recent approaches from the kinetic point of view are discussed, and our perspective on the future challenges of electron cooling and the relevant physical subject of MN is presented.
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Submitted 14 December, 2022;
originally announced December 2022.
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Perspectives on Physics of ExB Discharges Relevant to Plasma Propulsion and Similar Technologies
Authors:
Igor D. Kaganovich,
Andrei Smolyakov,
Yevgeny Raitses,
Eduardo Ahedo,
Ioannis G. Mikellides,
Benjamin Jorns,
Francesco Taccogna,
Renaud Gueroult,
Sedina Tsikata,
Anne Bourdon,
Jean-Pierre Boeuf,
Michael Keidar,
Andrew Tasman Powis,
Mario Merino,
Mark Cappelli,
Kentaro Hara,
Johan A. Carlsson,
Nathaniel J. Fisch,
Pascal Chabert,
Irina Schweigert,
Trevor Lafleur,
Konstantin Matyash,
Alexander V. Khrabrov,
Rod W. Boswell,
Amnon Fruchtman
Abstract:
This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in pla…
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This paper provides perspectives on recent progress in the understanding of the physics of devices where the external magnetic field is applied perpendicularly to the discharge current. This configuration generates a strong electric field, which acts to accelerates ions. The many applications of this set up include generation of thrust for spacecraft propulsion and the separation of species in plasma mass separation devices. These ExB plasmas are subject to plasma-wall interaction effects as well as various micro and macro instabilities, and in many devices, we observe the emergence of anomalous transport. This perspective presents the current understanding of the physics of these phenomena, state-of-the-art computational results, identifies critical questions, and suggests directions for future research
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Submitted 17 July, 2020;
originally announced July 2020.