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At least 19 records

On transport of electrons in a magnetized plasma sheath

Electron trajectories are analyzed in the plasma sheath region in a magnetic field that intersects the surface at a shallow angle. Depending on the size of the Debye width relative to the electron gyroradius, λ D /ρ e , an electron either drifts in the sheath electric field or follows a sequence of reflections (“bouncing”) on the surface before reversing its parallel velocity. For thin sheath, λ D /ρ e ≪ 1, the conservation of the electron magnetic moment can be violated, depending on the ratio of the electron perpendicular and parallel velocities V ⊥ /V || and the magnetic field pitch angle with respect to the surface. Small-scale waviness of the surface can strongly amplify this effect, leading to violation of the magnetic moment conservation even for λ D /ρ e ≳ 1, which opens a channel of anomalous radial transport for electrons in plasma devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Effects of oxidation and impurities in lithium surfaces on the emitting wall plasma sheath

The use of lithium as a surface coating in fusion devices improves the plasma performance, but the change in the wall properties affects the secondary electron emission properties of the material. Lithium oxidizes easily, which drives the emission yield well above unity. We present here simulations demonstrating the change in the sheath structure from monotonic to the nonmonotonic space-charge limited sheath using an energy-dependent data-driven emission model, which self-consistently captures both secondary emission and backscattering populations. Increased secondary electron emission from the material has ramifications for the degradation and erosion of the wall. The results show that the oxidation leads to an increased electron energy flux into the wall and a reduced ion energy flux. The net transfer of energy to the surface is significantly greater for the oxidized case than for the pure lithium case. High backscattering rates of low-energy particles lead to a high re-emission rate at the wall.

Fusion reactors

Machine learning surrogates for ion energy–angle distributions in thermal and RF plasma sheaths

Ion energy–angle distributions (IEADs) at material surfaces are a critical input for plasma–material interaction (PMI) studies in fusion devices, yet they are computationally expensive to obtain using particle-in-cell (PIC) simulations. In this work, we develop a machine learning surrogate based on a deep deconvolutional neural network (DDeCNN) trained on large databases generated with the hPIC2 code. The surrogate is capable of reconstructing IEADs from sheath parameters for both thermal and radio-frequency (RF) plasmas, including cases with multiple ion species. Across thousands of test cases, the model achieves high accuracy, with over 97 % of predictions classified as good or average based on standard error metrics (MAE, MSE, L2). Even in the more challenging RF and multi-species regimes, the surrogate reliably captures the multi-peak structure of PIC results. Once trained, the surrogate produces IEADs in milliseconds on a common workstation, yielding speedups of six to seven orders of magnitude compared with running a full PIC simulation. This computational gain enables dense parameter scans and direct coupling of IEAD predictions with PMI and erosion models on whole-device scales in fusion-relevant conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

DOE Final Report on Virginia Tech’s contribution to “Tokamak Disruption Simulation”

This work was performed by Virginia Tech in collaboration with multiple institutions led by Los Alamos National Laboratory as a part of the Tokamak Disruption Simulation SciDAC (Scientific Discovery through Advanced Computing) project supported jointly by the Department of Energy Office of Science and Ad- vanced Scientific Computing Research. This report summarizes Virginia Tech’s contributions to the Sci- DAC project. Virginia Tech researchers (presently University of Washington researchers) focused on the fundamental role of plasma-material interaction on transport, which could then have macroscopic effects on simulations of tokamak disruptions. The plasma sheath, which regulates plasma particle and energy fluxes to the wall, is an essential component in the study of plasma-material interaction (PMI). Understanding sheath theory by accounting for finite sheath thickness and transport in the vicinity of the sheath entrance can sig- nificantly modify typical assumptions that are made in the Bohm speed analysis, where the Bohm speed provides the lower bound of the plasma exit flow speed. Our work provides a modified Bohm speed formu- lation that accounts for the critical role of transport and for applications that are away from the asymptotic limits that are typically assumed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Plasma Surface Interactions: Predicting the Performance and Impact of Dynamic PFC Surfaces

This project focused on the development and integration of high-performance simulation tools to predict the operating behavior of Plasma-Facing Components in magnetic confinement fusion systems. A key objective at Illinois was to assess the impact of the dynamic interplay between the evolving material surface and the magnetized plasma sheath, and characterize the impact of tungsten-based PFCs on plasma contamination, including phenomena such as surface erosion, dynamic recycling of fuel species, and tritium retention, which are critical for the success of future magnetic fusion devices.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Dust and Ions: Self Organization and Stability (Final Report)

This project explores the stability and structure of systems with non-reciprocal interactions, challenging the traditional understanding based on Newton's third law, which states that every action has an equal and opposite reaction. Reciprocal forces are fundamental to the stability of systems ranging in size from atomic nuclei to galactic clusters. Our research investigates what happens when the forces between two objects are not equal and opposite. We used dusty plasmas as a model system to study non-reciprocal interactions. In a plasma chamber, micron-sized dust particles acquire a negative charge and form 2D planar "dust crystals" when levitated by the electric field present in the plasma sheath at the interface between the plasma and the lower surface of the chamber. This electric field also drives a vertical ion flow, creating a positively charged "plasma wake" downstream of the dust grains. While horizontally aligned dust grains interact reciprocally, a slight vertical displacement causes non-reciprocal interactions due to the attraction of the lower dust grain to the upper dust grain’s ion wake. Our experiments investigated the range of plasma conditions (gas pressure and system power) where stable dusty plasma structures are able to self-organize, aided by the ion wake. We studied systems ranging from pairs of dust particles to large 2D crystals, providing insights into the conditions that lead to stable or unstable structures. We used numerical simulations to investigate how ion wakes changed in response to changes in the operating conditions as well as how the wakes of separate grains interact when dust grains are in close proximity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Similarity for downscaled kinetic simulations of electrostatic plasmas: Reconciling the large system size with small Debye length

A simple similarity has been proposed for kinetic (e.g., particle-in-cell) simulations of plasma transport that can effectively address the long-standing challenge of reconciling the tiny Debye length with the vast system size. This applies to both transport in unmagnetized plasma and parallel transport in magnetized plasmas, where the characteristics length scales are given by the Debye length, collisional mean free paths, and the system or gradient lengths. The controlled scaled variables are the configuration space, x/L, and an artificial Coulomb Logarithm, L ln Λ, for collisions, while the scaled time, t/L, and electric field, LE, are automatic outcomes. The similarity properties are examined, demonstrating that the macroscopic transport physics is preserved through a similarity transformation while keeping the microscopic physics at its original scale of Debye length. To showcase the utility of this approach, two examples of 1D plasma transport problems were simulated using the VPIC code: the plasma thermal quench in tokamaks [Li et al., Nuclear Fusion 63, 066030 (2023)] and the plasma sheath in the high-recycling regime [Li et al., Physics of Plasmas 30, 063505 (2023)].

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Aligning thermal and current quenches with a high density low-Z injection

The conventional approach for thermal quench (TQ) mitigation in a tokamak disruption is through a high- Z impurity injection that radiates away the plasma’s thermal energy before it reaches the wall. The downside is a robust Ohmic-to-runaway current conversion due to the radiatively clamped low post-thermal-quench electron temperature. An alternative approach is to deploy a low- Z (either deuterium or hydrogen) injection that aims to slow down the TQ, and ideally aligns it with the current quench (CQ). This approach has been investigated here via 3D MHD simulations using the PIXIE3D code. By boosting the hydrogen density, a fusion-grade plasma is dilutionally cooled at approximately the original pressure. Energy loss to the wall is controlled by a Bohm outflow condition at the boundary where the magnetic field intercepts a thin plasma sheath at the wall, in addition to Bremsstrahlung bulk losses. Robust MHD instabilities proceed as usual, while the collisionality of the plasma has been greatly increased and parallel transport is now in the Braginskii regime. The main conclusion of this study is that the decreased transport loss along open field lines due to a sufficient low- Z injection slows down the TQ rate to the order of 20 ms, aligned with the CQ timescale for a 15 MA ITER plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

A theoretical model for sheath dynamics in the two-plasma mode of a cylindrical filament discharge

We present a refined understanding of cylindrical plasma-facing emitter cathodes by examining the limitations of the conventional space charge limited model, which overlooks ion trapping dynamics within the virtual cathode. While conventional theory distinguishes between temperature-limited and space charge limited regimes based on electron current constraints, our findings reveal that trapped ions can form a quasi-neutral “second plasma,” expanding upstream and interacting with the primary plasma. In cylindrical and other non-planar geometries, an expanding trapped-ions layer produces current enhancement by converting more of the emitted electron flux to passing flux. The current enhancement leads to a complex coupling between the trapped-ions plasma and upstream plasma through ionizing collisions in the upstream region and charge exchange collisions in the virtual cathode. The coupling results in mutual density enhancement and at the same time, antagonistic expansion dynamics between the two plasma layers. The process is understood using a new “aid-compete” model. Numerical solutions, validated against simulations, reveal the model's capacity to predict system evolution and complex discharge behaviors, albeit with qualitative approximations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

A Particle-in-Cell Method for Plasmas with a Generalized Momentum Formulation, Part I: Model Formulation

Here, this paper formulates a new particle-in-cell method for the Vlasov–Maxwell system. Under the Lorenz gauge condition, Maxwell’s equations for the electromagnetic fields can be written as a collection of scalar and vector wave equations. The use of potentials for the fields motivates the adoption of a Hamiltonian formulation for particles that employs the generalized (conjugate) momentum. A notable advantage offered by the Hamiltonian formulation is the elimination of time derivatives in the Lorenz gauge formulation that are required by the standard Newton–Lorentz treatment of the particles. This allows the fields to retain the full time-accuracy guaranteed by the field solver. The resulting updates for particles require only knowledge of the fields and their spatial derivatives. An analytical method for constructing these spatial derivatives is presented that exploits the underlying integral solution used in the field solver for the wave equations. Moreover, these derivatives are demonstrated to converge at the same rate as the fields in both time and space. The Method of Lines Transpose field solver we consider in this work is globally first-order accurate in time and high-order accurate in space (e.g., fourth- and fifth-order) and belongs to a larger class of methods which are unconditionally stable, can address geometry, and leverage $\mathcal {O}(N)$ fast summation methods for efficiency. We demonstrate the method on several well-established benchmark problems on bounded domains, including a plasma sheath as well as a relativistic particle beam. The efficacy of the proposed formulation is established by comparing with a second-order accurate finite-difference time-domain method that employs a leapfrog time advance for particles and a charge conserving map suitable for bounded domains. The new method shows mesh-independent numerical heating properties even in cases where the plasma Debye length is smaller than the grid spacing. This is an important feature of the new method for problems defined on bounded domains, because it permits the use of coarser grids in space in the representation of the fields. Such a capability has significant implications for the simulation of plasmas in bounded domains with complex geometry, where the ratio between the largest and smallest cells can vary significantly. The use of high-order spatial approximations in the new method also means that fewer grid points are required in order to achieve a fixed accuracy. Our results also suggest that the new method can be used with fewer simulation particles per cell compared to the benchmark explicit method, which permits further computational savings.

97 MATHEMATICS AND COMPUTING

The effect of high-power transient events on tungsten and tungsten coatings used for radio frequency launcher applications

High-temperature plasma-facing material coatings used for radio frequency (RF) launchers need to be robust enough to survive RF breakdown arcing or other transient events from the plasma (e.g., an edge localized mode) without causing a catastrophic failure of the coating. High-power transient effects are being explored by using an RF-induced vacuum arc to determine the robustness of tungsten coatings made by a variety of manufacturing methods. A 1/4-wavelength resonant section of vacuum transmission line terminated with an open circuit electrode structure with a well-defined electric field (30-60 kV/mm) produces repeatable arcing conditions. The initial focus is on tungsten as a plasma-facing material, including sintered tungsten, tungsten coatings on steel produced via physical vapor deposition (PVD), and functionally graded tungsten/steel coatings deposited by low-pressure plasma-spraying (LPPS). Thin PVD coatings (1-2 microns) fail catastrophically from an arc and result in severe delamination of the coating. The arc-induced damage of thicker coatings, such as those made via LPPS, tend to be restricted to the top few microns of the surface. Arcing often initiates on sharp surface microstructures and causes localized melting of tungsten at the surface of all the materials studied and results in resolidified melt pools with surface cracks. The resolidified surface results in a reduction in overall deuterium retention when exposed to typical RF plasma sheath conditions.

Caughman, John [ORNL] (ORCID:0000000206091164)

An extended variational method for the resistive wall mode in toroidal plasma confinement devices

The external-kink stability of a toroidal plasma surrounded by a rigid resistive wall is investigated. The well-known analysis of Haney and Freidberg is rigorously extended to allow for a wall that is sufficiently thick that the thin-shell approximation does not necessarily hold. A generalized Haney–Freidberg formula for the growth-rate of the resistive wall mode is obtained. Thick-wall effects do not change the marginal stability point of the mode but introduce an interesting asymmetry between growing and decaying modes. Growing modes have growth-rates that exceed those predicted by the original Haney–Freidberg formula. On the other hand, decaying modes have decay-rates that are less than those predicted by the original formula. The well-known Hu–Betti formula for the rotational stabilization of the resistive wall mode is also generalized to take thick-wall effects into account. Increasing wall thickness facilitates the rotational stabilization of the mode, because it decreases the critical toroidal electromagnetic torque that the wall must exert on the plasma. On the other hand, the real frequency of the mode at the marginal stability point increases with increasing wall thickness.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Modeling rf sheath formation in turbulent tokamak boundary plasma

During ICRF antenna operation, complex interactions between turbulent density profiles, nonlinear RF sheaths, and RF-induced convective transport are observed to alter plasma density in the tokamak edge [D’Ippolito et al., Nucl. Fusion 38, 1543 (1998)]. In this work, we explore the physics of such interactions via numerical modeling, using a nonlinear EM/plasma/sheath code (VSim) and profiles obtained from a fluid plasma turbulence code (Hermes) in a 3D slab domain containing biased side-wall limiters. RF-rectified sheath formation on antenna and limiter surfaces is observed as electromagnetic waves launched by the antenna are refracted through the turbulent density profile. On transport timescales, such sheath potentials have been shown to influence both the mean species density and its RMS fluctuation spectrum [Smithe et al., these proceedings]. On the faster RF timescales, we demonstrate that the converse is also true – regions of high plasma density near material surfaces give rise to the highest sheath potential amplitudes. When density is turbulent and spatially nonuniform, localized regions of high sheath potential (hotspots) may develop where high-density filaments intersect material surfaces. Such hotspots are of particular concern as sources of impurity sputtering, and we explore their behavior in response to changes both to the local plasma density and to antenna operating parameters and structure. Related results exploring the role of Faraday shields and/or enclosing structures in suppressing high sheath potentials for other devices (e.g. SPARC) will also be shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Toward the origins of binding energy shifts and “satellites” formation during plasma-XPS measurements

In-plasma x-ray photoelectron spectroscopy (plasma-XPS) emerges as a powerful platform for real-time, in situ chemical analysis under conditions relevant to semiconductor processing and other plasma-enabled technologies. This study investigates the origins of binding energy (BE) shifts and the formation of “satellite” peaks observed during plasma-XPS measurements across conductive, dielectric, and gas-phase systems. Using a standard laboratory-based ambient pressure XPS apparatus coupled with an alternating current (AC)-driven capacitively coupled plasma source, we demonstrate that metastable surface species, such as transient Au oxides, can be detected during plasma exposure, revealing chemical states that are hardly accessible using conventional ultrahigh vacuum (UHV) XPS. In dielectric samples (e.g., undoped diamond, sapphire), we observe pressure- and plasma-type-dependent BE shifts of more than 50 eV, attributed to x-ray-induced and plasma-mediated surface charging. These shifts are mitigated at higher pressures/plasmas or in electronegative plasmas (e.g., O 2 ), the latter due to enhanced charge compensation mechanisms involving slow negative ions. For gas-phase species, AC-plasma excitation leads to spectral broadening and the emergence of “satellite” peaks with energy separations of a few electron volts, linked to oscillating local plasma potentials in the probing volume. Furthermore, these findings highlight the complex and important interplay between plasma parameters, surface charging, and local electric fields in shaping XPS spectra. Overall, plasma-XPS emerges as a critical metrological tool for probing transient surface chemistry, with implications for semiconductor processing, material synthesis, and plasma diagnostics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Mode transitions and spoke structures in E × B Penning discharge

Two-dimensional particle-in-cell simulations in the (radial-azimuthal) plane perpendicular to the axial direction of a cylindrical $E$ x $B$ Penning discharge are presented. The low-pressure discharge is self-consistently supported by plasma ionization from the electron beam injected axially, along the direction of the external magnetic field. It is shown that with the increasing strength of the external magnetic field, the discharge undergoes a sequence of transitions between several azimuthal modes. Azimuthal m > 1 spiral arm structures are excited at low magnetic field values as plasma confinement improves and the radial density profile becomes peaked. With a larger field, spiral arms with m > 1 are replaced by the m = 1 spoke mode, most clearly seen in plasma density. A transition from spiral arms to the spoke regime occurs when the plasma potential in the center changes from weakly positive (or zero) to negative. Further increase in the magnetic field results in a well-developed m = 1 spoke mode with additional small-scale higher-frequency m > 1 structures inside and around the spoke. It is shown that while ionization and collisions affect some characteristics of the observed fluctuations, the basic features of the spoke and m > 1 spiral structure remained similar without ionization. The role of energy conservation in small-scale high-frequency modes and spoke dynamics is discussed. It is demonstrated that in regimes with the m = 1 spoke mode, additional m = 4 harmonics of the ion and electron fluxes to the wall appear due to the square boundary. The frequency of the m = 1 mode is weakly affected by the geometry of the boundary.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY

The Implications of Collisions on the Spatial Profile of Electric Potential and the Space-Charge-Limited Current

The space-charge-limited current (SCLC) in a vacuum diode is given by the Child-Langmuir law (CLL), whose electric potential ϕ(x) ∝ (x/D) 4/3 , where x is the spatial coordinate across the gap and D is the gap separation distance. For a collisional diode, SCLC is given by the Mott-Gurney law (MGL) and ϕ(x) ∝ (x/D) 3/2 . Here, we apply a capacitance argument for SCLC and use the transit time from a recent exact solution for collisional SCLC to show that ϕ(x) ∝ (x/D)ξ for a general collisional gap, where 4/3 ≤ ξ ≤ 3/2 . Furthermore, ξ is strictly a function of νT, where ν is the collision frequency and T is the electron transit time. Using this definition of ξ, we estimate the spatial dependence of the electron velocity and use the gap capacitance to derive an analytic equation for collisional SCLC that agrees within ~4.5% of the exact solution that requires solving parametrically through T. This analytic equation for general ξ asymptotically recovers the CLL as ν → 0 and the MGL as ν → ∞. As a result, matching these limits shows that ξ ≈ 1.40 and V ∝ D 2 ν 2 at the transition from a vacuum to a collisional diode for any device condition.

Anodes

Design and Preliminary Experimental Results on a Uniform-Field Test Fixture for Power Flow Experiments

Electrodes that produce a uniform electric field across their surfaces are desired for a variety of high-voltage systems including spark-gap switches and transversely excited atmospheric lasers. Here, the implementation of uniform-field electrodes to a parallel-plate load is described for the study of vacuum power flow under pulsed-power applications. We begin with an overview of general uniform-field geometries, and provide an open-source program that generates these geometries as described by Ernst. Following that, a modification to an existing power-flow experimental platform, that adopts a uniform-field geometry, is introduced and its utility is described. Lastly, preliminary experimental results are presented and future steps are outlined.

Capacitors