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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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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Vidyut3d: A Gpu Accelerated Fluid Solver for Non-Equilibrium Plasmas on Adaptive Grids

We present the numerical methods, programming methodology, verification, and performance assessment of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures, in this work. Our plasma fluid model solves the coupled conservation equations for species transport, electrostatic Poisson and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive-grid/particle management library, AMReX, and is portable over widely available vendor specific GPU architectures. We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth-order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on capacitive discharges and atmospheric pressure streamer propagation. We demonstrate the use of our solver on two 3D simulation cases: an atmospheric streamer propagation in Ar-H2 mixtures and a low pressure twin electrode radio frequency reactor. Our performance studies on three different CPU+GPU architectures indicate approximately 150-400X speed-up using AMD and NVIDIA GPUs per time step compared to a single CPU core for a 4 million cell simulation with 15 species.

Sitaraman, Hariswaran↗
DOE OSTI2024

Virtual Tokamak for Test and Development of Plasma Control Applied to NSTX-U

Safe and efficient operation of tokamak experiments depends on shot preparation prior to the experiment to maximize performance and avoid issues that are predictable consequences of known physics. The General Atomics TokSys toolbox is used to test and develop the plasma control system (PCS) on numerous tokamaks around the world. Tokamaks that use a version of the DIII-D PCS can connect it to a TokSys simulation and control a virtual version of the tokamak with the real PCS. Recent upgrades to the simulation include more detailed profile and transport modeling to support design and implementation of optimized scenarios. The simulation combines a module called “Profiles” that simulates the 1D profiles of density, pressure, and current and a module called “GSevolve'' that evolves the 2D Grad-Shafranov equilibrium. The “Profiles'' module primarily uses simplified models for fueling, heating, and current. The TRANSP code provides precomputed diffusion coefficients and heating/current drive profiles from radio-frequency and neutral beam sources for the scenarios being simulated. The fidelity of a simulation can be enhanced by analyzing it with TRANSP and making corrections to the precomputed values and iterating until convergence. Simulations of the National Spherical Torus Upgrade (NSTX-U) are presented. It is shown that the simulation reproduces the experimental profile evolution. Here, the simulation has also been upgraded to reproduce the experimental outcome at points of bifurcation. This is demonstrated with a simulation of vertical displacement in NSTX-U.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Bottomonium properties in the quark-gluon plasma from a lattice-QCD informed 𝑇-matrix approach

Recent computations of bottomonium correlation functions with extended sources in lattice-discretized quantum chromodynamics (lQCD) provide new insights into heavy-quark dynamics at distance scales which are of the order of the inverse temperature. We analyze these results employing the thermodynamic 𝑇-matrix framework, in a continued effort to interpret lQCD data for quarkonium correlation functions in a nonperturbative and self-consistently solved quantum-many-body approach to a strongly coupled quark-gluon plasma (QGP). Its key inputs are the in-medium driving kernel (potential) of the scattering equation and an interference function which implements 3-body effects in the quarkonium coupling to the thermal medium. A simultaneous description of lQCD results for the bottomonium correlators with extended operators and the previously analyzed Wilson line correlators only requires minor refinements of the potential but calls for stronger interference effects at larger separation of the bottom quark and antiquark. We then analyze the poles of the self-consistent 𝑇 matrices on the real axis to assess the survival of the various bound states. Here, we estimate the pertinent temperatures where the poles disappear for the various bottomonium states and discuss the relation to the corresponding peaks in the bottomonium spectral functions. We also recalculate the spatial diffusion coefficient of the QGP and find it to be similar to that in our previous study.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Construction of generalized quasilinear diffusion coefficient using neural networks with physical restrictions

The quasilinear diffusion coefficient (D QL ) derived from our machine learning framework shows comparable trends with the ground truth D QL obtained from GENRAY-CQL3D simulations. Additionally, for the strong absorption cases, the radial current drive profiles generated using the D QL from our model exhibit consistent behavior with those obtained from the original simulation. These findings indicate the potential of our surrogate modeling approach with physical restrictions to replicate key wave–plasma interaction characteristics while reducing computational costs. Traditionally, calculating D QL for wave–particle interactions relies on computationally intensive wave simulations coupled with Fokker–Planck solvers. To address this challenge, we developed a machine learning-based surrogate model with physical restrictions derived from cold plasma theory and bounce-averaged damping effects. First, we establish the propagation domain of Lower Hybrid Waves in the (N∥, ρ) space by identifying the accessibility limit and determining the upper and lower bounds of N∥ using the Potential Power Deposition (PPD) method. Subsequently, leveraging a database constructed using Latin hypercube sampling alongside the underlying physical restrictions (e.g. PPD), machine learning methods including U-Net and Recurrent Neural Networks are employed to design a physics-restricted machine learning framework capable of reconstructing D QL .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Development of a Performance Portable Non-Equilibrium Plasma Fluid Solver on Adaptive Grids

This presentation will describe the numerical techniques, programming paradigms, verification, and performance of a non-equilibrium plasma fluid solver that can effectively utilize current and upcoming central processing and graphics processing unit (CPU+GPU) architectures. Our plasma fluid model solves the conservation equations for self-consistent electrostatic Poisson, electron and heavy species transport, and electron temperature on adaptive Cartesian grids. Our solver is written using performance portable adaptive mesh management library, AMReX (Zhang et al., JOSS, 4 (37) 1370, 2019), and can be built and run on widely available vendor specific GPU architectures (NVIDIA/AMD/Intel). We utilize a non-subcycled second order semi-implicit time-stepping method where all adaptive mesh refinement (AMR) levels are advanced with the same time step. The composite multi-level multigrid solver from within AMReX is used for each of the governing equations that are cast into a Helmholtz equation form. We have also developed a python based chemical mechanism parser framework that uses a similar format as CANTERA (Goodwin et al., Zenodo, 2018) yaml files as input. Our custom parser reads the yaml file and provides C++ files with transport and production rate functions that can be executed on both host (CPU) and device (GPU). We present verification of our solver using method of manufactured solutions that indicate formal second order accuracy with central diffusion and fifth order weighted-essentially-non-oscillatory (WENO) advection scheme. We also verify our solver with published literature on low-pressure capacitive and high-pressure streamer discharges. Our initial performance studies indicate 10X speed-up using 20 NVIDIA GPUs versus 200 CPUs for an atmospheric streamer discharge problem solved on a 512 x 1024 x 512 grid.

graphics processing units↗
DOE OSTI2024

Radiation induced non-linear oscillations in ITER baseline scenario plasmas in DIII-D

Abstract This work shows how the radiation brought about by metals or metal-equivalent radiators such as Kr and Xe produces non-linear dynamics on otherwise stationary β N flattops of DIII-D ITER Baseline Scenario demonstration discharges. The Kr and Xe gases are used to reproduce the radiative loss rates of W in present machines that operate at core temperatures much lower than the expected ITER temperature. Experiments on DIII-D with injection of Kr and Xe, as well as with sources of intrinsic metals reach the range of radiated fraction values expected in the ITER core and experience slow oscillations in temperature and radiated power. In many cases of high radiated fraction, the core temperature decreases enough for the safety factor profile to rise above the 1/1 rational surface, naturally eliminating sawteeth and occasionally producing a persistent helical core. The oscillations can be reproduced by a modified Lotka–Volterra system for temperature and radiated fraction if diffusion and noise are included, which indicates that the interplay between temperature and radiation can be the main cause of the cyclic nature of the system. A new physics based model which includes equations for temperature, density and input power can also reproduce the oscillations observed in the experiments. The present results suggest that the non-linearity of the system can be increased by the inclusion of the inherently non-linear alpha heating term, which is proportional to ∼ n e 2 T i 2 , and obtains oscillations in the model when added to an otherwise more stationary system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Fast photodiode arrays for high frequency fluctuation measurements of reconnecting flux ropes

An array of compact, high-bandwidth (>200 MHz) and low-cost optical photodiodes has been developed and implemented on the PHASe MApping (PHASMA) experiment. Using purpose-built electronics, an array of 16 photodetectors was constructed and used to monitor broadband (1–5 MHz) fluctuations in light intensity emitted by flux ropes undergoing electron-only magnetic reconnection. These measurements reveal a swath of oscillatory behavior, including wave propagation inward toward the diffusion region at approximately the local electron Alfvén speed. Custom 3D-printed collection optics and mounting hardware allow quick reconfiguration of the array for radial or axial measurements. The electronics design is flexible enough to be used with other current-sourcing transducers, such as avalanche photodiodes; silicon photomultipliers; and infrared, x-ray, and UV photodiodes. A noise-rejecting electrical layout allows for low-noise operation close to pulsed plasma discharges. A 16-channel, 64-pixel tomographic array was constructed and initial reconstructions are presented.

Instruments & Instrumentation↗
DOE OSTI2026

Statistical inference of anomalous thermal transport with uncertainty quantification for interpretive 2D SOL models

The critical task of inferring anomalous cross-field transport coefficients is addressed in simulations of boundary plasmas with fluid models. A workflow for parameter inference in the UEDGE fluid code is developed using Bayesian optimization with parallelized sampling and integrated uncertainty quantification. In this workflow, transport coefficients are inferred by maximizing their posterior probability distribution, which is generally multidimensional and non-Gaussian. Uncertainty quantification is integrated throughout the optimization within the Bayesian framework that combines diagnostic uncertainties and model limitations. As a concrete example, we infer the anomalous electron thermal diffusivity $\chi_\perp$ from an interpretive 2D model describing electron heat transport in the conduction-limited region with radiative power loss. The workflow is first benchmarked against synthetic data and then tested on H-, L-, and I-mode discharges to match their midplane temperature and divertor heat flux profiles. We demonstrate that the workflow efficiently infers diffusivity and its associated uncertainty, generating 2D profiles that match 1D measurements. Future efforts will focus on incorporating more complicated fluid models and analyzing transport coefficients inferred from a large database of experimental results.

Bayesian optimization↗
DOE OSTI2025

Fast ion confinement in quasi-axisymmetric stellarator equilibria

This report presents an initial analysis of the fast ion confinement and losses within quasi-axisymmetric stellarator equilibria in consideration by Thea Energy. The equilibria have not yet been explicitly optimized for fast particle confinement and require validation. Modeling with the ASCOT5 code is used to directly examine the fast ion transport. The particle tracking simulations are purely (neo)classical in nature and simply contain the supplied equilibrium and collisions (pitch-angle, energy slowing, and velocity diffusion) from supplied thermal profiles. Uniform marker deposition is used to probe the general confinement properties of the equilibria while a realistic beam-born population is provided from the BEAMS3D code and an alpha particle population is calculated from a fusion source integrator. A first wall is included and defines the loss boundary. Analysis for NBI ions within Thea Energy’s conceptual Eos neutron source are presented along with alpha particles in an enlarged DT-plasma. The fast ions are assessed in regards to their confinement time, pitch, energy, and spatial coordinates. For each population, the impact of collisions and orbit drifts are discussed. It is found that NBI born ions in Eos are strongly confined until slowing-down, owing largely to the tangential injection geometry, while 22% of DT-born alpha energy is lost in the scaled device, indicating that any fusion pilot plant design optimization should include metrics for fast ion confinement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Multi-X-point radiation and its dynamics in up/down asymmetry in plasma detachment regimes in Wendelstein 7-X

In Wendelstein 7-X (W7-X), stable plasma detachment in ECRH hydrogen plasmas is routinely achieved with the standard magnetic configuration, containing five magnetic islands in the scrape-off layer (SOL). Plasma detachment induced by intrinsic carbon impurities is characterized by a high radiation fraction (ƒ rad ) with significantly reduced divertor heat load and particle flux. In this work, we present the radiation dynamics during the detached plasma (DP) phase, such as the shift of radiation zones in radial and poloidal directions towards the X-points as ƒ rad increases (∼0.6–0.9), as well as the penetration of the radiation layer into the confinement region in the deep DP phase with ƒ rad approaching unity. In particular, a structure of multi-X-point radiation (multi-XPR) with an up/down asymmetry in the DP phase is highlighted, which is revealed by bolometer tomography and is further confirmed by video diagnostics. The multi-XPR structure forms helical 3D bands aligned with W7-X field periodicity. Field reversal experiments show that the brightest XPR displaces between the upper and lower SOL regions, suggesting the E× B drift effects. This paper presents the multi-XPR structure observed in the W7-X plasma in detail for the first time. A simplified model considering the influence of the poloidal E× B drift ( V d ) on the impurity flow in the SOL shows that the downstream drift toward the target or target shadow region ( V d < 0) decreases the impurity content, while the upstream drift toward the LCFS ( V d > 0) increases the impurity content. On this basis, the poloidal drift potentially leads to an up/down asymmetry of impurity density in the SOL despite the symmetry magnetic topology. The dynamics of the up/down asymmetry in the multi-XPR structure is also related to the magnitude V d /D (normalized to the impurity diffusivity), with an additional effect owing to the radial inward shift of the emission zone. These results provide new insights into impurity-induced detachment dynamics and provide a basis for improving 3D modeling of impurity transport, which typically does not consider drifts.

E × B drift↗
DOE OSTI2025

Integral X-ray diffuse scattering for studying irradiation-induced dislocation loops in single crystals

Numerical diffuse scattering cross-section calculations are used to establish a rigorous basis for determining the concentration and size distribution of dis­location loops in irradiated single crystals from integral X-ray diffuse scattering (XRDS) measurements. Differential XRDS intensities for prismatic {111} type dislocation loops are numerically calculated as a function of loop radius R and wavevectors q relative to Bragg reflections in tungsten. The results show the well known 1/q 2 Huang scattering form at small q that transitions to a ∼1/q 4 dependence associated with the Stokes–Wilson approximation for q ≳ 1/R. More importantly, they show further that the 1/q 4 falloff is not the asymptotic large-q form of the diffuse scattering for small loops (R < 200 Å) as has often been assumed. Rather, for loop sizes as small as R ≃ 5 Å with strong curvature, the calculations show definitively that the scattering transitions to a robust 1/q 5 falloff at larger q that arises due to the local strains near the dislocation core defining the circumference of the dislocation loops. The presence of this 1/q 5 asymptotic form for both small and large loops is experimentally confirmed using an integral XRDS measurement around the 110 reflection on self-ion-irradiated tungsten combined with numerically calculated integral XRDS cross-sections. Accordingly, the historical two-region theoretical treatment of the cross-sections for integral XRDS is extended to a three-region model that has direct sensitivity to the (first-moment) dislocation line lengths of dislocation loops. In conclusion, these developments enable the use of both numerical and analytically modeled cross-sections to make accurate integral XRDS determinations of dislocation loop sizes and concentrations using modest-intensity laboratory X-ray sources.

42 ENGINEERING↗
DOE OSTI2024

Passivated Contacts for Direct Wafer Product (Final Technical Report)

This TCF project developed a thin-oxide (SiO 2 )/polycrystalline silicon (poly-Si) passivated contact solar cell on CubicPV's (formally 1366 Technologies, Inc.) Direct Wafer® Product (DWP) kerfless wafers. The project used two NREL-developed technologies described in U.S. Patent No. 9,911,873, Hydrogenation of Passivated Contacts and U.S. Patent Application Serial No. 15/890,172, Doped Passivated Contacts . The project was motivated by a potential higher efficiency cell (compared to a PERC cell) using passivated contacts on the ultra-low cost kerfless wafers grown using the Direct Wafer process. The hope was to accelerate market adoption of the cell and wafer by delivering the lowest LCOE in the PV industry. The project tested both n-type and p-type SiO 2 /poly-Si passivated contacts grown by thermal oxidation and plasma enhanced chemical vapor deposition (PECVD) of the poly-Si layer on DWP with varying wafer resistivities. Both deposition techniques are industry standards and thus economically viable methods for commercializing the contacts. The results indicated that both n-type and p-type poly-Si passivated contacts can be formed on polycrystalline DWP wafers, but implied open-circuit voltages (i Voc ) were limited to below 0.65 mV (compared with ~ 730 mV on n-Cz wafers). Diffusion of H to the Si/SiO 2 /poly-Si interface was key to obtaining high i Voc values. In this study, H was diffused from a high-temperature SiN x layer deposited over the poly-Si layer during a high-temperature firing step, similar to one used for screen printed metals. The study concluded that poly-Si passivated contacts on DWP wafers passivated the surface of the wafers as well as PERC passivated surfaces, which use a less expensive dielectric layer stack. The project showed that Direct Wafer Product wafers grown by CubicPV could produce high i Voc values (~0.647 mV), which could produce a cell over 20% efficient with proper processing and metallization. These cells, though not economically viable in 2024 as a stand-alone cell, could be integrated with a wide-bandgap top solar cell to form a two-junction tandem cell that could be viable under certain circumstances. This is because the bottom cell of a 30%, two-terminal tandem only needs to be a 20% cell under one-sun conditions. Thus, the DWP could be an ideal low-cost wafer for tandems. The project also revealed that a TOPCon type cell could be formed on a p-type DWP wafer using a P-diffused emitter and a p-type poly-Si contact. In fact, the p-type version of the poly-Si contact out-performed the n-type version for a variety of wafer resistivities, from highly doped to lowly doped. This curiosity requires more work to understand because on Cz wafers, the n-type poly-Si contact is of much higher quality than the p-type version.

14 SOLAR ENERGY↗
DOE OSTI2026

Highlight of IC project: w25_dreamxd

(left) The Earth’s radiation belts are donut-shaped regions containing MeV electrons (color contour for density) trapped by the magnetic field (white curves). We use DREAMxD code to model their dynamics. (right) We develop a new method to accelerate a key piece of the code – diffusion coefficient calculation. Comparing the compute time in node hours required by the standard approach to the compute time required for the fast method, it shows that the new method can be 100x faster for a large problem size.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Capturing Secondary Kinetic Instabilities in Three‐Dimensional Dayside Reconnection Using an Improved Gradient‐Based Closure

Magnetic reconnection is a highly dynamic process that excites a wide variety of kinetic waves and instabilities. Transverse current sheet instabilities such as the lower-hybrid drift and secondary drift-kink instabilities in particular have been shown by kinetic simulations to modify the reconnection and introduce significant turbulence and mixing to the reconnection layer. Past studies using the ten-moment fluid model to capture important kinetic physics such as the electron inertia and full representation of the pressure tensor proved advantageous to a two-fluid representation of reconnection, but the model struggled when using a local relaxation closure for the heat flux to replicate the current sheet instabilities and subsequent mixing seen in kinetic simulations. This work uses the Gkeyll software framework to perform simulations of asymmetric reconnection based on the 16 October 2015 MMS crossing of a diffusion region, the Burch event. An improved gradient-based heat flux closure is implemented, showing significant improvement in secondary kinetic instabilities that grow in the current sheet. These instabilities generate turbulence which leads to growth of secondary magnetic islands and flux ropes.

Bradshaw, K. [Princeton University, NJ (United Sta↗
DOE OSTI2025

Thermophysical Properties of Ti3SiC2 MAX Phase Composites with SiC Reinforcement

In the present work, dense (∼100%) Ti 3 SiC 2 composites (TSC) are processed along with 20 vol% of SiC reinforcement (TSC20) via spark plasma sintering at 1400°C, 40 MPa, 15 min, and dynamic vacuum environment. Thermal expansion of both the composites increases from RT to 1273 K and linear fitting of data yields coefficient of thermal expansion (CTE) of 9.4 × 10 −6 K −1 for TSC which decreases to 8.3 × 10 −6 K −1 for TSC20. With increase in temperature from RT to 773 K, specific heat for both TSC and TSC20 composites is observed to increase from 598-850 J.kg −1 .K −1 , whereas thermal diffusivity and thermal conductivity values decrease with testing temperature. SiC reinforcement in Ti 3 SiC 2 resulted in improved thermal diffusivity from 12.7 to 18.7 mm 2 .s −1 and thermal conductivity from ∼57 to ∼79 W.m −1 .K −1 at RT. However, with increase in temperature (773 K), thermal diffusivity and conductivity decrease, and values get closer for both TSC and TSC20 composites. Further extrapolation of thermal conductivity data showed cross-over at ∼973 K due to domination of phonon-phonon scattering and thus lower values of thermal conductivity for TSC20 than TSC. Therefore, reduced CTE and higher thermal conductivity of TSC20 make it a viable choice for applications in high temperatures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nonideal stability analysis of differentially rotating plasmas with global curvature effects

The linear stability of global nonaxisymmetric modes in differentially rotating, magnetized, nonideal plasma is critical to classifying turbulence and transport phenomena. We investigate the competition between the local magneto-rotational instability (MRI) and the magneto-curvature instability (MCI)—a distinct nonaxisymmetric low-frequency curvature-driven global branch that appears alongside MRI. Here, to accomplish this, we developed a nonideal global spectral method, which is validated against NIMROD code simulations. This spectral approach allows for the direct derivation of an extended effective potential formalism and a resistive Alfvénic resonance condition, providing a framework for direct analysis of energy contributions and confinement mechanisms. Our study reveals that the global, low-frequency MCI persists at low magnetic Reynolds numbers (Rm), whereas the localized, high-frequency MRI is stabilized by diffusive broadening of its structure around its Alfvénic resonances. Consequently, we identify the global MCI branch as the primary onset mechanism for nonaxisymmetric magnetohydrodynamic instability in systems with finite curvature, e.g., astrophysical rotators. We establish distinct parameter regimes for mode dominance: MCI prevails in geometrically moderate-thickness disks with intermediate curvature and radial gaps, while MRI dominates in thin, low-curvature disks with large radial gaps. Mode competition is also highly sensitive to the flow profile, particularly vorticity and its gradient, with nonuniform shear profiles exhibiting more robust instability due to flow curvature (i.e., the second derivative of the flow profile) and shear contributions. A key outcome is the development of spectral diagrams derived from the global spectral method. These diagrams comprehensively map dominant instabilities and their characteristics, offering a predictive tool for critical onset parameters (i.e., flow curvature, magnetic field, and Rm) and facilitating the interpretation of experimental and simulation results. Notably, these diagrams demonstrate that the global MCI is generally the sole unstable mode at the initial onset of nonaxisymmetric instability.

Haywood, Alexander [Princeton Univ., NJ (United St↗
DOE OSTI2025

Time-resolved tracking of cellulose biosynthesis and assembly during cell wall regeneration in live Arabidopsis protoplasts

Cellulose, the most abundant polysaccharide on earth composing plant cell walls, is synthesized by coordinated action of multiple enzymes in cellulose synthase complexes embedded within the plasma membrane. Multiple chains of cellulose fibrils form intertwined extracellular matrix networks. It remains largely unknown how newly synthesized cellulose is assembled into an intricate fibril network on cell surfaces. Here, we have established an in vivo time-resolved imaging platform to continuously visualize cellulose biosynthesis and fibril network assembly onArabidopsis thalianaprotoplast surfaces as the primary cell wall regenerates. Our observations provide the basis for a model of cellulose fibril network development in protoplasts driven by an interplay of multiscale dynamics that includes rapid diffusion and coalescence of nascent cellulose fibrils, processive elongation of single fibrils, and cellulose fibrillar network rearrangement during maturation. This study provides fresh insights into the dynamic and mechanistic aspects of cell wall synthesis at the single-cell level.

Science & Technology - Other Topics↗
DOE OSTI2026

Understanding Large-Scale Dynamos in Unstratified Rotating Shear Flows

For this work, we combine simulations with new analyses that overcome previous pitfalls to explicate how nonhelical mean-field dynamos grow and saturate in unstratified, magnetorotationally driven turbulence. Shear of the mean radial magnetic field amplifies the azimuthal component. Radial fields are regenerated by velocity fluctuations that induce shear of radial magnetic fluctuations, followed by Lorentz and Coriolis forces that source a negative off-diagonal component in the turbulent diffusivity tensor. We present a simple schematic to illustrate this dynamo growth. A different part of the Lorentz force forms a third-order correlator in the mean electromotive force that saturates the dynamo.

accretion disk & black-hole plasma↗