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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

DOE Plasma Science Center - Predictive Control of Plasma Kinetics: Multi-Phase and Bounded Systems (Final Report DE-SC0001939)

Low temperature plasmas (LTPs) are the plasmas of electron-volt (eV) physics and eV technologies. LTPs have characteristic electron temperatures of a few eV and fractional ionizations that are typically small. Since LTPs have electron temperatures commensurate with the threshold energies of excited states in neutral atoms and molecules, power transfer from electrons to these atoms and molecules efficiently produces activated species (e.g., radicals, excited states, photons). Acceleration of ions in the sheaths of LTPs to energies of tens to hundreds of eV enable activation of surface modifying processes – sputtering, etching, deposition. With such properties, LTPs are often and beneficially used in technological devices, ranging from etching and deposition in microelectronics and solar cell fabrication, to hardening of surgical instruments. LTPs harbor fundamental science issues that are intellectually challenging and rewarding. At the same time, there are enormous societal benefits that are enabled by LTPs. The entire present-day and future information technology infrastructure owes its very existence to LTPs. Renewable energy sources, such as solar cell arrays, could not be economically produced in the absence of deposition and etching by LTPs. In acknowledgment of the importance of LTPs, the DOE Office of Fusion Energy Sciences supported the Plasma Science Center for Predictive Control of Plasma Kinetics: Multi-Phase and Bounded Systems from August 2009 to July 2021, consisting of an initial 5-year grant, 3 funded extensions and 2 no-cost extensions. This is the final report of the Center in which the productivity of the Center is discussed in terms of publications, impact and personnel. High-lights of the research performed in the Center are provided.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Dynamics of rapidly spinning blob-filaments: Fluid theory with a parallel kinetic extension

Blob-filaments (or simply “blobs”) are coherent structures formed by turbulence and sustained by nonlinear processes in the edge and scrape-off layer (SOL) of tokamaks and other magnetically confined plasmas. The dynamics of these blob-filaments, in particular, their radial motion, can influence the scrape-off layer width and plasma interactions with both the divertor target and with the main chamber walls. Motivated by recent results from the XGC1 gyrokinetic simulation code reported on elsewhere [J. Cheng et al., Nucl. Fusion 63, 086015 (2023)], a theory of rapidly spinning blob-filaments has been developed for this work. The theory treats blob-filaments in the closed flux surface region or the region that is disconnected from sheaths in the SOL. It extends previous work by treating blob spin, arising from partially or fully adiabatic electrons, as the leading-order effect and retaining inertial (ion charge polarization) physics in next order. Spin helps to maintain blob coherency and affects the blob's propagation speed. Dipole charge polarization, treated perturbatively, gives rise to blob-filaments with relatively slow radial velocity, comparable to that observed in the simulations. The theory also treats the interaction of rapidly spinning blob-filaments with a zonal flow layer. It is shown analytically that the flow layer can act like a transport barrier for these structures. Finally, parallel electron kinetic effects are incorporated into the theory. Various asymptotic parameter regimes are discussed, and asymptotic expressions for the radial and poloidal motion of the blob-filaments are obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On the importance of excited state species in low pressure capacitively coupled plasma argon discharges

In the past three decades, first principles-based fully kinetic particle-in-cell Monte Carlo collision (PIC/MCC) simulations have been proven to be an important tool for the understanding of the physics of low pressure capacitive discharges. However, there is a long-standing issue that the plasma density determined by PIC/MCC simulations shows quantitative deviations from experimental measurements, even in argon discharges, indicating that certain physics may be missing in previous modeling of the low pressure radio frequency (rf) driven capacitive discharges. In this work, we report that the energetic electron-induced secondary electron emission (SEE) and excited state atoms play an important role in low pressure rf capacitive argon plasma discharges. The ion-induced secondary electrons are accelerated by the high sheath field to strike the opposite electrode and produce a considerable number of secondary electrons that lead to additional ionizing impacts and further increase of the plasma density. Importantly, the presence of excited state species even further enhances the plasma density via excited state neutral and resonant state photon-induced SEE on the electrode surface. The PIC/MCC simulation results show good agreement with the recent experimental measurements in the low pressure range (1–10 Pa) that is commonly used for etching in the semiconductor industry. At the highest pressure (20 Pa) and driving voltage amplitudes 250 and 350 V explored here, the plasma densities from PIC/MCC simulations considering excited state neutrals and resonant photon-induced SEE are quantitatively higher than observed in the experiments, requiring further investigation on high pressure discharges.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Large radiation back-flux from Monte Carlo simulations of fusion neutron–material interactions

Abstract Fusion power reactors will generate intense neutron fluxes into plasma-facing and structural materials (SMs). Radiation back-fluxes, generated from neutron–material interactions under these fluxes, can dramatically impact the plasma dynamics, e.g. by seeding runaway electrons during disruptions via Compton scattering of background electrons by wall-emitted gamma radiation. Here, we quantify these back-fluxes, including neutrons, gamma rays, and electrons, using Monte Carlo calculations for a range of SM candidates and first wall (FW) thicknesses. The radiation back-flux magnitudes are remarkably large, with neutron and gamma radiation back-fluxes on the same order of magnitude as the incident fusion neutron flux. Electron back-fluxes are two orders of magnitudes lower, but are emitted at sufficiently high energies to impact the sheath and boundary plasma dynamics. Material configuration plays a key role in determining back-flux magnitudes. The SM chiefly determines the neutron back-flux magnitude, while the FW thickness principally attenuates the gamma ray and electron back-fluxes. In addition to prompt back-fluxes, which are emitted immediately after fusion neutrons impact the surface, significant delayed gamma ray and electron back-fluxes arise from nuclear decay processes in the activated materials. These delayed back-flux magnitudes range from 2% to 7% of the prompt back-fluxes, and remain present during transients when fusion no longer occurs. During disruptions, build-up of delayed gamma radiation back-flux represents potential runaway electron seeding mechanisms, posing additional challenges for disruption mitigation in a power reactor compared with non-nuclear plasma operations. This work highlights the impact of these radiation back-fluxes plasma performance and demonstrates the importance of considering back-flux generation in materials selection for fusion power reactors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Characterizing W sources in the all-W wall, all-RF WEST tokamak environment

In this work, experimental data, together with interpretive modeling tools, are examined to study trends in the tungsten (W) source in the all-W environment of the WEST tokamak, both from the divertor and from the main chamber. In particular, a poloidal limiter protecting an ion cyclotron resonance heating (ICRH) antenna is used as proxy for main chamber sourcing. The key study is carried out by stepping up lower hybrid current drive (LHCD) power, as the only auxiliary power source. Limiter and divertor W sources exhibit a qualitatively similar proportionality to the total power crossing the separatrix, P SEP , although the main chamber source remains substantially lower than the divertor source, for the range of P SEP accessible in the experiments. Intepretive modeling of the limiter source is carried out with a particle-in-cell (PIC) sheath model coupled to a surface sputtering model. Oxygen is used as a proxy for all light impurity species allowing for characterization of the critical W erosion regions. To get a good quantitative match to the data, it is necessary to assume that the oxygen arrives at the surface mostly at high ionization stages (4+ and above). A separate simulation with SOLEDGE-EIRENE, constrained to measured upstream scrape-off-layer plasma profiles, gives oxygen fractional abundances that are compatible with the PIC simulation result. This is understood to arise from transport processes that dominate over recombination. Substituting the LHCD by ICRH, in an equivalent experiment, the local W source exhibits a 3× enhancement. This can be matched by the simulation, by assuming local RF electric field rectification, based on ~100 eV peak-to-peak, near-antennna electric field. This work has highlighted the particular importance of understanding the ion charge state balance of light impurities as these are most likely the dominant sputtering species in fusion devices with high-Z walls.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Impurity transport in PISCES-RF

Linear plasma devices (LPD) utilizing a helicon plasma source, a high density light ion source, can generate impurities due to progressive erosion of the radio frequency (RF) transmission window caused by rectified sheath voltage. These source-born impurities can entrain and be transported by the plasma toward a target, affecting plasma-material interaction studies. Earlier work on material testing in Prototype-Materials Plasma Exposure eXperiment at ORNL revealed significant source impurity deposition on downstream targets. However, using a similar RF source, no target impurity deposition is observed in Plasma Interaction Surface Component Experimental Station (PISCES)-RF despite evidence of RF window erosion in the source region, thereby motivating the present work. Experimentally, using various magnetic field configurations upstream of the PISCES-RF plasma source and seeding titanium (Ti) impurities at various axial locations, impurity transport and deposition along the machine axis were investigated. It was found that Ti deposition was localized to the side of the plasma source where the Ti impurity was seeded. In contrast, aluminum (Al) deposition, originating from the sputtering of the helicon window, occurred predominantly upstream of the plasma source, suggesting an asymmetry in the axial transport of eroded RF window material. These observations suggest a stagnation of the parallel plasma flow immediately downstream of the plasma source, with impurity ions remaining unmagnetized near the source upstream. Al deposition in magnetic field-free regions in PISCES-RF indicates that sputtered Al impurities likely remained neutral due to their large ionization mean-free path under PISCES-RF conditions. Plasma modeling and simulation supported this, indicating that Al-neutrals transport toward the helicon source upstream for low electron density cases. It was found that the Larmor radius of the Al ions was greater than the plasma radius towards the source upstream and remained weakly magnetized in PISCES-RF, meaning that plasma source-born impurities are not efficiently entrained in the plasma flow. These findings provide critical insights into impurity transport in helicon plasma-based LPDs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Development of multi-scale computational frameworks to solve fusion materials science challenges

Over the past two decades, the US-DOE has funded multiple projects that rely on high-performance computing and exascale computing platforms to accelerate scientific discoveries and address grand scientific challenges, such as harnessing fusion energy. In this article, we review in detail one of these efforts aimed at enhancing our capability to model plasma-facing materials subject to plasma and high-energy ion/neutron irradiation. The plasma surface interactions project has built a multi-scale modeling framework where many of the plasma- and high-energy ion/neutron irradiation-induced effects occurring in tungsten are explored. Here, this knowledge is used to develop atomistically-informed, high-fidelity continuum and meso-scale models that can be validated against experiments. We review the developments within this project, with attention to experimental validation efforts, and specifically highlight activities associated with: helium bubble bursting and equation of state, and hydrogen-helium interactions in tungsten; atomistically-informed model development for beryllium-tungsten material mixing; coupling of scrape-of-layer plasma, sheath and material models; and coupling of stochastic cluster-dynamics and crystal plasticity models to address radiation effects in tungsten under stress. Finally, we present how the project is preparing for future computational architectures, for instance through efforts to adapt atomistic methods to exascale computing.

36 MATERIALS SCIENCE↗
DOE OSTI2020

New heat flux model for non-axisymmetric divertor infrared structures

A convective heat flux model for perturbed plasmas, based on guiding center ion drift in vacuum elds (A. Wingen, et al., Phys. Plasmas 21 (2014) 012509), has been updated. The old model only considered ion heat flux, while here also electron heat flux is included. The updated model predicts divertor heat flux distributions in non-axisymmetric (3D) plasmas with applied Resonant Magnetic Perturbation (RMP) fields, and includes electric scalar potentials. It is found that a radial electric field in the near Scrape-o Layer (SOL) can considerably shift the footprints toroidally, leading to a smearing out eff ect of the incident heat flux, while a simple model for sheath potential has little impact on footprints. Various approaches to model electron heat flux are studied. A convective electron model, based on collisionless free streaming, is found to yield the best agreement with measurements, while a conductive model requires a at temperature gradient inside lobes to yield acceptable peak heat ux values. A heuristic heat flux layer approach, based on a fixed layer width also requires a limited heat flux inside the last closed flux surface (LCFS); by selecting various locations of the LCFS, the results of the conductive or convective model can be recovered respectively. The sum of ion and electron heat fluxes, both obtained by the convective model, is compared to experimental data for multiple time slices in DIII-D. Strike point splitting is observed with peak heat fluxes and layer widths that compare well to infrared camera (IR) measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Electric field and turbulence in global Braginskii simulations across the ASDEX Upgrade edge and scrape-off layer

Turbulence simulations in diverted geometry across the edge and scrape-off layer (SOL) of ASDEX Upgrade are performed with the GRILLIX code (Stegmeir et al 2019 Phys. Plasmas 26 052517). The underlying global (full-f) drift-reduced Braginskii model allows to concurrently study the self-consistent dynamics of the turbulence and the background as well as the evolution of toroidal and zonal flows. Different contributions to the radial electric field are identified. The dominant contribution on closed flux surfaces comes from the ion pressure gradient, due to the diamagnetic drift in the curved magnetic field. Large deviations can be induced, in particular, by the polarization particle flux, leading to zonal flows. The latter are driven by small-scale eddies, but do not exhibit much impact on the overall transport which is driven by ballooning modes at larger scales. Ion viscosity is found to be important in damping poloidal rotation through adjusting of the parallel velocity profile, but not via direct vorticity damping. The zonal flow drive peaks at the separatrix, where a strong shear layer forms due to the sheath-induced counter-propagating SOL flow, allowing for the formation of a transport barrier. The temperature profile across the separatrix is determined by the competition between cross-field transport and outflow in the SOL, the latter being largely controlled by the parallel heat conductivity.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Dynamic focusing of laser driven positron jets by self-generated fields

Abstract Focusing effect of laser-driven positron jets by self-generated target sheath fields has been observed for the first time experimentally and the results are supported by the computational studies. In the experiment, OMEGA EP short-pulse (0.7 ps, 500 J) irradiates mm-size gold targets with a concave back surface and reference flat-surface targets. Both targets exhibited positrons with quasi-monoenergetic energy peaks while targets with concave curvature also showed increased number of positrons at the detector. The data is consistent with hybrid-PIC simulations confirming that the time-varying electric fields driven by electrons escaping from the target significantly change the trajectories of positrons. These simulations show a small radius of curvature on the rear side increases the relative focusing effect and the positrons to electrons ratio in the escaping plasma. For the smallest radius of curvature, positron jets that are up to 10 times denser can be achieved.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Simulations of divertor heat flux width using transport code with cross-field drifts under the BOUT++ framework

The fluid transport code [trans-electric field (Er) module] under the BOUT++ framework has been used to simulatedivertor heat flux width and boundary Er with all drifts and the sheath potential in the scrape-off layer. The calculated steady state radial Er in the pedestal region has been compared with that of experimental measurements from the Alcator C-Mod tokamak. The magnitude and shape of Er are similar to those of the experimental data. In order to understand the relative role of cross-field drifts vs turbulent transport in setting the heat flux width, four C-Mod enhanced Dα H-mode discharges with a lower single null divertor configuration should be simulated. BOUT++ transport simulations with cross-field drifts included yield similar heat flux width λq to that of experimental measurements (within a factor of 2) from both the probe and the surface thermocouple diagnostics and show a similar trend with plasma current to that of the Eich experimental scaling. The simulations show that both drifts and turbulent transport compete to determine the heat flux width. The magnetic drifts play a dominant role in setting the divertor heat-flux width, while the E × B drift decreases the heat flux width by 10%–25%, leading to improved agreement with the experiment relative to Goldston’s model. A turbulence diffusivity scan (χ) identifies two distinct regimes: a drift dominant regime when χ is small and a turbulence dominant regime when χ is large. The Goldston heuristic drift model yields a lower limit of the width λq.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Basic Research in Edge and Scrape-Off Layer Fusion Plasmas (Final Report)

U.S. Department of Energy (DOE) supported work at Lodestar Research Corporation under grant DE-FG02-97ER54392 is summarized in this final report. The research conducted under this grant addressed key scientific issues associated with boundary plasmas in fusion energy experimental devices. Harnessing the energy that is released in fusion reactions would provide a safe and abundant source of power to meet the growing energy needs of the world population. Lodestar investigated the important cm-scale region near the edge of these devices where hot plasma, close to one million degrees, meets material surfaces in what is known as a scrape-off layer (SOL). This critical region is subject to plasma turbulence and plasma flows which must be understood to optimize fusion performance on future machines. Strong interactions of applied RF waves is also observed to occur in this region, and must be understood to mitigate unwanted effects and enhance overall performance. The work employed theoretical models and theory-based computational models for validation. The models were applied to understand experimental results and to carry out basic theoretical investigations relevant to the production of fusion energy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

General kinetic ion-induced electron emission model for metallic walls applied to biased Z-pinch electrodes

A kinetic ion-induced electron emission (IIEE) model for general applications is developed to obtain the emitted electron energy spectrum for a distribution of ion impacts on a metallic surface. We assume an ionization cascade mechanism and use empirical models for the ion and electron stopping powers. The emission spectrum and the secondary electron yield (SEY) are validated for a variety of materials. The IIEE model is used to study the effect of IIEE on the plasma-material interactions of Z-pinch electrodes. Un-magnetized Boltzmann-Poisson simulations are performed for a Z-pinch plasma doubly bounded by two biased copper electrodes with and without IIEE at bias potentials from 0 to 9 kV. At the anode, the SEY decreases from 0 to 1 kV, but then increases at higher bias potentials. At the cathode, the SEY is much larger due to higher energy ion bombardment and grows with bias potential. As the bias potential increases, the emitted cathode electrons are accelerated to higher energies into the domain, collisionally heating the plasma. Above 1 kV, the heating is strong enough to increase the plasma potential. Despite SEY greater than 1, only a classical sheath forms as opposed to a space-charge limited or inverse sheath due to the emitted electron flux not reaching the space charge current saturation limits. Furthermore, the current in the emissionless cases saturates to a value lower than experiment. With IIEE, the current does not saturate and continues to increase with the 4 kV case, matching most closely with the experiment.

Carbon based materials↗
DOE OSTI2024

Center for Tokamak Transients Simulations

The major goals for the Center for Tokamak Transients Simulations (CTTS) were to develop detailed numerical simulations of disruptive transients in tokamak experiments and to use them in theoretical studies of the thermal-quench (TQ) and current-quench (CQ) phases of disruption. The University of Wisconsin-Madison component of CTTS contributed relevant development for the NIMROD code (https://nimrodteam.org) and applied it to disruptions that involve global vertical displacement. Code-development contributions include boundary conditions that represent sheath effects which occur when tokamak plasma is in contact with the surrounding vessel wall during vertical displacement events (VDEs). We also implemented a reduced model of energetic runaway electrons (REs) to simulate the effect of these energetic electrons on the CQ phase of tokamak disruptions. Our computations of VDEs include 2D and 3D verification through benchmarks with two other widely used macroscale plasma simulation codes, M3D-C1 and JOREK. Over nonlinear evolution to the final termination of plasma current, the 2D simulation results on magnetic axis location, toroidal current, and halo current track each other well. With the 3D benchmark computation, all three codes found the same qualitative behavior of the asymmetric instabilities having increasing growth rate after contact with the wall, followed by nonlinear excitation of other toroidal harmonics. Our NIMROD computations for an idealized configuration show agreement with an analytical assessment by V. D. Pustovitov [Nucl. Fusion 55, 113032 (2015)] that the plasma and non-ideal wall remain in force-balance such that net forces only result from magnetic stresses over the outer surface of the wall. Our study of the influence of boundary conditions on VDEs shows that extended-MHD simulations of VDEs are sensitive to electron energy transport to the wall and that boundary conditions on flow are only significant to the extent that they influence the electron energy transport. Resistive-MHD NIMROD simulations of the tokamak discharges in the Madison Symmetric Torus show that magnetic perturbations of poloidal wavenumber m=3 lead to chaotic magnetic topology over the edge region, which helps deconfine energetic electrons. A second area of RE study shows that the coupled resistive MHD/reduced RE model reproduces the resistive-hose particle-beam instability. With respect to educational opportunities, this effort involved and supported four graduate students at the University of Wisconsin-Madison and one postdoctoral associate. The results of this study have been disseminated through journal publications, conference presentations, technical reports, and PhD dissertations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Three-dimensional cross-field flows at the plasma-material interface in an oblique magnetic field

This article describes experimental evidence that the magnetic presheath is a fully three-dimensional structure modified by ion–neutral collisions. Velocity distributions of both ions and neutrals, obtained via laser-induced fluorescence, show that cross field ion drifts do not result from entrainment of ions in a flowing neutral background. Ion flows parallel to E x B arise and accelerate to as much as 0.2c s within several ion gyroradii of the boundary surface, where c s is the sound speed. Within measurement resolution, the onset of the E x B aligned flow occurs at the same distance to the surface that ions begin to deflect from travel along magnetic field lines. Collisional fluid and particle-in-cell simulations of the boundary region are compared to the experimental measurements. We find that, in contrast to the classical collisionless Chodura model, collisional effects between the ions and the non-flowing neutral population are essential to quantitatively predict the observed ion drift velocities. No momentum coupling between ions and neutrals, separable from noise and other effects, is observed in either signal. Here, we discuss several explanations and implications of this observation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A tutorial on the micro-trench technique for incident ion angle, material erosion, and impurity deposition measurements at plasma-facing surfaces

The micro-trench method is a new technique to measure polar and azimuthal incident ion angles, material erosion, and impurity deposition at plasma-facing surfaces, and has been applied in the DIII-D divertor. This article gives a tutorial of the micro-trench technique consisting of six steps: (1) micro-trench fabrication, (2) pre-exposure measurement of the fabricated micro-trench geometry, (3) tracer material deposition, (4) plasma exposure, (5) post-exposure observation of the tracer material, and (6) post-exposure measurement of the micro-trench geometry. Two criteria need to be satisfied to apply the micro-trench method successfully: (i) uniform impurity deposition on the micro-trench floor, and (ii) erosion dominated by the physical sputtering induced by the impinging ions. Furthermore, when those two criteria are satisfied, post-exposure analysis of the impurity deposition patterns on the micro-trench floor may be used to determine the polar and azimuthal incident ion directions (mean values of the ion angle directions), erosion rate, and impurity deposition rate during plasma exposure without computational interpretation.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2021

RF sheath induced sputtering on Proto-MPEX part 2: Impurity transport modeling and experimental comparison

The Prototype Material Plasma Exposure eXperiment (Proto-MPEX) is a pulsed linear plasma device that uses a radio frequency (RF) helicon antenna and a helicon ceramic window as the plasma ionization source. Modeling performed within this work on the helicon operations predicts hot spots on the helicon ceramic window due to an RF-induced sheath. The RF sheath potential leads to physical sputtering of the ceramic window predominantly where the helicon antenna sits around the helicon window. The role of oxygen in sputtering within Proto-MPEX is also investigated and is needed to match the experimental data. Experiments on Proto-MPEX show reasonable agreement with the modeled erosion/redeposition pattern on the helicon window, and the modeled impurity flux to the target shows radial transport within the device as expected from classical collisional impurity transport. Temperature screening of impurities is shown to be needed for Proto-MPEX to reduce impurity flux to the target. The modeling approach used in this work can be applied to other plasma RF applications for the determination of impurity production and transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

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↗