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DOE OSTI2021

Size-Dependent Electrical Transport Properties in Conducting Diamond Nanostripes

With the advances in nanofabrication technology, horizontally aligned and well-defined nitrogen-doped ultrananocrystalline diamond nanostripes can be fabricated with widths in the order of tens of nanometers. The study of the size-dependent electron transport properties of these nanostructures is crucial to novel electronic and electrochemical applications. In this paper, 100 nm thick n-type ultrananocrystalline diamond thin films were synthesized by microwave plasma-enhanced chemical vapor deposition method with 5% N2 gas in the plasma during the growth process. Then the nanostripes were fabricated using standard electron beam lithography and reactive ion etching techniques. The electrical transport properties of the free-standing single nanostripes of different widths from 75 to 150 nm and lengths from 1 to 128 μm were investigated. The study showed that the electrical resistivity of the n-type ultrananocrystalline diamond nanostripes increased dramatically with the decrease in the nanostripe width. The nanostripe resistivity was nearly doubted when the width was reduced from 150 nm to 75 nm. The size-dependent variability in conductivity could originate from the imposed diffusive scattering of the nanostripe surfaces which had a further compounding effect to reinforce the grain boundary scattering.

Zhou, Andrew F. (ORCID:0000000243050409)↗

DOE OSTI2023

Understanding grain boundary segregation under irradiation: A mesoscale modeling study

Grain boundaries (GBs) are an important component in the design of irradiation resistant materials as they play a crucial role as point defect sinks for non-equilibrium vacancies and self-interstitials. However, in the presence of sustained point defect fluxes, the coupled transport of atomic components with inherently different diffusivities often leads to radiation-induced segregation (RIS), with undesired effects on properties such as intergranular corrosion and stress-assisted cracking. In this talk, we investigate the fundamental mechanisms leading to GB segregation in BCC FeCr-based alloys using multiscale modeling and experiments. A phase-field model is employed to account for both thermodynamic and kinetic segregation mechanisms. The full Onsager transport matrix is derived using kinetic Monte Carlo, molecular dynamics, and kinetic cluster expansion (KineCluE) calculations. The thermodynamics of GB segregation is described via an atomic density-based modification to the CALPHAD free energy. The modeling predictions are then compared against segregation data from atom probe characterization for various temperatures, compositions, and neutron irradiation conditions. We will conclude by discussing the utility of the multiscale modeling approach to shed light on the fundamental mechanisms leading to solute-GB interaction.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Neutron diffusion calculation in heterogeneous geometry based on local/global iteration using proper orthogonal decomposition

This study newly proposes a heterogeneous core calculation method based on local/global iteration using proper orthogonal decomposition (POD). By using the singular value decomposition (SVD) and the low-rank approximation, appropriate POD bases for expanding the neutron flux can be obtained from snapshot data of the neutron flux obtained by fine mesh calculations. By projection using the POD bases, the dimension of the target equation (e.g., discretized neutron diffusion equation) can be dramatically reduced. In the proposed method, POD is effectively applied to each single assembly calculation (local calculation). Furthermore, using the local/global iteration, the effective neutron multiplication factor and the neutron flux distribution in the whole core geometry can be obtained by combining the numerical results of the local calculation for each fuel assembly and the global calculation for the whole core. As a feasibility study, the proposed method is applied to a one-dimensional heterogeneous core analysis, and the accuracy is investigated by changing the total number of POD bases. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Geospatial Diffusion for Land Cover Imperviousness Change Forecasting

Land-use and land-cover (LULC) has a significant effect on several Earth system processes. For example, impervious surfaces reduce infiltration and speed water flow, impacting regional hydrology and flood risk. While Earth System models have improved forecasting hydrologic and atmospheric processes at higher resolutions, the ability to forecast LULC change has lagged behind. In this paper, we propose a new paradigm exploiting Generative AI (GenAI) for land cover change forecasting by framing it as a data synthesis problem conditioned on historical and auxiliary data-sources. To demonstrate the feasibility of our methodology, we perform experiments where a diffusion model is trained for decadal forecasting of imperviousness change across the entire United States. We find that our model yields MAE lower than a no-change baseline for resolutions ≥ 0.7 X 0.7km2 on average, demonstrating its ability to capture and project accurate spatiotemporal patterns. Finally, we discuss future research to incorporate Earth's physical properties and enabling scenario simulations via driver variables.

Varshney, Debvrat [ORNL] (ORCID:0000000188981736)↗

DOE OSTI2023

Convection-Induced Compositional Patterning at Grain Boundaries in Irradiated Alloys

We consider the stability of precipitates formed at grain boundaries (GBs) by radiation-induced segregation in dilute alloys subjected to irradiation. Here, the effects of grain size and misorientation of symmetric-tilt GBs are quantified using phase field modeling. A novel regime is identified where, at long times, GBs are decorated by precipitate patterns that resist coarsening. Maps of the chemical Péclet number indicate that arrested coarsening takes place when solute advection dominates over thermal diffusion right up to the precipitate/matrix interface, preventing interfacial local equilibrium and overriding capillary effects. This contrasts with liquid-solid mixtures where convection always accelerates coarsening.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Anionic Effects on Concentrated Aqueous Lithium Ion Dynamics

In this article, the structural dynamics, chemical reactivity, anisotropy, diffusivity, viscosity, and density were measured for concentrated lithium salt solutions, including lithium chloride (LiCl), lithium bromide (LiBr), lithium nitrite (LiNO 2 ), and lithium nitrate (LiNO 3 ), with methyl thiocyanate as an infrared vibrational probe molecule, using two-dimensional infrared spectroscopy (2D IR), nuclear magnetic resonance (NMR) spectroscopy, and viscometry. 2D IR, NMR, and viscosity results show that LiNO 2 exhibits longer correlation times, lower diffusivity, and nearly four times greater viscosity when compared to the other lithium salt solutions of the same concentration, suggesting that nitrite anions may strongly facilitate structure formation via strengthening water-ion interactions, directly impacting bulk solution properties at sufficiently high concentrations. Additionally, the LiNO 2 and LiNO 3 solutions show significantly reduced chemical reactivity with respect to lithium cations coordinating with the methyl thiocyanate when compared to the lithium halide salts.

2D IR↗

DOE OSTI2020

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

Here, we report benchmark calculations of the energy per particle of pure neutron matter as a function of the baryon density using three independent many-body methods: Brueckner–Bethe–Goldstone, Fermi hypernetted chain/single-operator chain, and auxiliary-field diffusion Monte Carlo. Significant technical improvements are implemented in the latter two methods. The calculations are made for two distinct families of realistic coordinate-space nucleon-nucleon potentials fit to scattering data, including the standard Argonne v 18 interaction and two of its simplified versions, and four of the new Norfolk Δ -full chiral effective field theory potentials. Primarily because of the advancements in the auxiliary-field diffusion Monte Carlo, we observe good agreement among the three many-body techniques up to nuclear saturation density—the maximum difference in the energy per particle is within 1.5 MeV for all the potentials we consider. At higher densities, the divergences become more important, and are mainly driven by the Fermi hypernetted chain/single-operator calculations. We also study the connection between nucleon-nucleon scattering data and the energy per particle of pure neutron matter. Our results suggest that fitting to higher-energy nucleon-nucleon scattering helps reduce the spread of energies among the models.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Reimagining full wave rf quasilinear theory in a tokamak

The velocity dependent resonant interaction of particles with applied radiofrequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto ( J. Plasma Phys. , vol. 86, 2020, 815860302). The behaviour is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston ( Phys. Fluids , vol. 14, 1971, pp. 2719–2726) and Auerbach ( Phys. Fluids , vol. 20, 1977, pp. 1836–1844). For a wave of parallel wave number ${k_{||}}$ interacting with weakly collisional plasma species of collision frequency $\nu$ and thermal speed ${v_{\textrm{th}}}$ , the effective collision frequency becomes of order $\nu {({k_{||}}{v_{th}}/\nu )^{2/3}} \gg \nu $ . The narrow boundary layers that arise because of the diffusive nature of the collisions allow a physically meaningful wave–particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behaviour of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave–particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

Physics↗

DOE OSTI2021

Reimagining full wave rf quasilinear theory in a tokamak

The velocity dependent resonant interaction of particles with applied radio frequency (rf) waves during heating and current drive in the presence of pitch angle scattering collisions gives rise to narrow collisional velocity space boundary layers that dramatically enhance the role of collisions as recently shown by Catto (J. Plasma Phys., vol. 86, 815860302, 2020). The behavior is a generalization of the narrow collisional boundary layer that forms during Landau damping as found by Johnston (Phys. Fluids, vol. 14, 1971, pp. 2719-2726) and Auerbach (Phys. Fluids, vol. 20, 1977, pp. 1836-1844). For a wave of parallel wave number k|| interacting with weakly collisional plasma species of collision frequency ν and thermal speed vth , the effective collision frequency becomes of order ν(k_||v_th /ν)^2/3>> ν . The narrow boundary layers that arise because of the diffusive nature of the collisions allows a physically meaningful wave-particle interaction time to be defined that is the inverse of this effective collision frequency. The collisionality implied by the narrow boundary layer results in changes in the standard quasilinear treatment of applied rf fields in tokamaks while remaining consistent with causality. These changes occur because successive poloidal interactions with the rf are correlated in tokamak geometry and because the resonant velocity space dependent interactions are controlled by the spatial and temporal behavior of the perturbed full wave fields rather than just the spatially local Landau and Doppler shifted cyclotron wave-particle resonance condition associated with unperturbed motion of the particles. The correlation of successive poloidal circuits of the tokamak leads to the appearance in the quasilinear operator of transit averaged resonance conditions localized in velocity space boundary layers that maintain negative definite entropy production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Moving beyond the Aerosol Climatology of WRF-Solar: A Case Study over the North China Plain

Numerical weather prediction (NWP), when accessible, is a crucial input to short-term solar power forecasting. WRF-Solar, the first NWP model specifically designed for solar energy applications, has shown promising predictive capability. Nevertheless, few attempts have been made to investigate its performance under high aerosol loading, which attenuates incoming radiation significantly. The North China Plain is a polluted region due to industrialization, which constitutes a proper testbed for such investigation. Here, in this paper, aerosol direct radiative effect (DRE) on three surface shortwave radiation components (i.e., global, beam, and diffuse) during five heavy pollution episodes is studied within the WRF-Solar framework. Results show that WRF-Solar overestimates instantaneous beam radiation up to 795.3 W m -2 when the aerosol DRE is not considered. Although such overestimation can be partially offset by an underestimation of the diffuse radiation of about 194.5 W m -2 , the overestimation of the global radiation still reaches 160.2 W m -2 . This undesirable bias can be reduced when WRF-Solar is powered by Copernicus Atmosphere Monitoring Service (CAMS) aerosol forecasts, which then translates to accuracy improvements in photovoltaic (PV) power forecasts. This work also compares the forecast performance of the CAMS-powered WRF-Solar with that of the European Centre for Medium-Range Weather Forecasts model. Under high aerosol loading conditions, the irradiance forecast accuracy generated by WRF-Solar increased by 53.2% and the PV power forecast accuracy increased by 6.8%.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations

We developed a new class of physics-informed generative adversarial networks (PI-GANs) to solve forward, inverse, and mixed stochastic problems in a unified manner based on a limited number of scattered measurements. Unlike standard GANs relying solely on data for training, here we encoded into the architecture of GANs the governing physical laws in the form of stochastic differential equations (SDEs) using automatic differentiation. In particular, we applied Wasserstein GANs with gradient penalty (WGAN-GP) for its enhanced stability compared to vanilla GANs. We first tested WGAN-GP in approximating Gaussian processes of different correlation lengths based on data realizations collected from simultaneous reads at sparsely placed sensors. We obtained good approximation of the generated stochastic processes to the target ones even if there is a mismatch between the input noise dimensionality and the effective dimensionality of the target stochastic processes. We also studied the overfitting issue for both the discriminator and the generator, and we found that overfitting occurs also in the generator in addition to the discriminator as previously reported. Subsequently, we considered the solution of elliptic SDEs requiring approximations of three stochastic processes, namely the solution, the forcing, and the diffusion coefficient. Here again, we assumed data collected from simultaneous reads at a limited number of sensors for the multiple stochastic processes. Furthermore, three generators were used for the PI-GANs: two of them were feed forward deep neural networks (DNNs), while the other one was the neural network induced by the SDE. For the case where we have one group of data, we employed one feed forward DNN as the discriminator, while for the case of multiple groups of data we employed multiple discriminators in PI-GANs. We solved forward, inverse, and mixed problems without changing the framework of PI-GANs, obtaining both the means and the standard deviations of the stochastic solution and the diffusion coefficient in good agreement with benchmarks. In this work, we have demonstrated the effectiveness of PI-GANs in solving SDEs for about 120 dimensions. In principle, PI-GANs could tackle very high dimensional problems given more sensor data with low-polynomial growth in computational cost.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Effect of TiN coating on suppressing Ce-Fe interaction under irradiation

Advanced cladding is critical for fast reactors with the adequate thermal conductivity, mechanical stability and radiation tolerance of the cladding base material, corrosion resistance and high temperature coolant compatibility of the cladding surface, and chemical stability of the cladding inner wall against fuel cladding chemical interaction (FCCI). The preliminary results of recent ion irradiation studies of two diffusion-couple samples of cerium (Ce)/oxide-dispersion strengthened steel (ODS) and Ce/TiN/ODS, irradiated with 80 MeV xenon (Xe) ions to 100 displacements per atom (dpa) at 500°C, are summarized. Significant Ce-Fe interaction occurred in the Ce/ODS sample, and no noticeable Ce-Fe interaction was found in the Ce/TiN/ODS sample. It shows the effectiveness of 1-µm TiN diffusion barrier coated by the pulsed laser deposition on suppressing Ce-Fe interaction, a major contributor to FCCI in cladding. Here, density function theory (DFT) calculations of the impurity diffusivities of Ce and Fe within the Ti sublattice of TiN were performed to assist a mechanistic understanding of the experimental results.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2023

Modeling the Effects of Drift Orbit Bifurcation on the Magnetopause Shadowing Loss of Radiation Belt Electrons

Abstract Last closed drift shell (LCDS) has been identified as a crucial parameter for investigating the magnetopause shadowing loss of radiation belt electrons. However, drift orbit bifurcation (DOB) effects have not been physically incorporated into the LCDS calculation. Here we calculate event‐specific LCDS using different approaches to dealing with the DOB effects, that is, tracing field lines ignoring DOB, tracing test particles rejecting field lines with DOB, and tracing particles including field lines with DOB, and then incorporate them into a radial diffusion model to simulate the fast electron dropout observed by Van Allen Probes in May 2017. The model effectively captures the fast dropout at high L* and exhibits the best agreement with data when LCDS is calculated by tracing test particles with DOB more physically included. This study represents the first quantitative modeling of the DOB effects on radiation belt magnetopause shadowing loss via a more physical specification of LCDS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

The Sonora Substellar Atmosphere Models. II. Cholla: A Grid of Cloud-free, Solar Metallicity Models in Chemical Disequilibrium for the JWST Era

Exoplanet and brown dwarf atmospheres commonly show signs of disequilibrium chemistry. In the James Webb Space Telescope (JWST) era, high-resolution spectra of directly imaged exoplanets will allow the characterization of their atmospheres in more detail, and allow systematic tests for the presence of chemical species that deviate from thermochemical equilibrium in these atmospheres. Constraining the presence of disequilibrium chemistry in these atmospheres as a function of parameters such as their effective temperature and surface gravity will allow us to place better constraints on the physics governing these atmospheres. This paper is part of a series of works presenting the Sonora grid of atmosphere models. In this paper, we present a grid of cloud-free, solar metallicity atmospheres for brown dwarfs and wide-separation giant planets with key molecular species such as CH 4 , H 2 O, CO, and NH 3 in disequilibrium. Our grid covers atmospheres with T eff ∈ [500 K, 1300 K], log g ∈ [3.0, 5.5] (cgs) and an eddy diffusion parameter of logK zz = 2,4 and 7 (cgs). We study the effect of different parameters within the grid on the temperature and composition profiles of our atmospheres. We discuss their effect on the near-infrared colors of our model atmospheres and the detectability of CH 4 , H 2 O, CO, and NH 3 using the JWST. We compare our models against existing MKO and Spitzer observations of brown dwarfs and verify the importance of disequilibrium chemistry for T dwarf atmospheres. Finally, we discuss how our models can help constrain the vertical structure and chemical composition of these atmospheres.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Dynamic Mixing Behaviors of Ionically Tethered Polymer Canopy of Nanoscale Hybrid Materials in Fluids of Varying Physical and Chemical Properties

An emerging area of sustainable energy and environmental research is focused on the development of novel electrolytes that can increase the solubility of target species and improve subsequent reaction performance. Electrolytes with chemical and structural tunability have allowed for significant advancements in flow batteries and CO 2 conversion integrated with CO 2 capture. Liquid-like nanoparticle organic hybrid materials (NOHMs) are nanoscale fluids that are composed of inorganic nanocores and an ionically tethered polymeric canopy. NOHMs have been shown to exhibit enhanced conductivity making them promising for electrolyte applications, though they are often challenged by high viscosity in the neat state. In this study, a series of binary mixtures of NOHM-I-HPE with five different secondary fluids, water, chloroform, toluene, acetonitrile, and ethyl acetate, were prepared to reduce the fluid viscosity and investigate the effects of secondary fluid properties (e.g., hydrogen bonding ability, polarity, and molar volume) on their transport behaviors, including viscosity and diffusivity. We report our results revealed that the molecular ratio of secondary fluid to the ether groups of Jeffamine M2070 ($λ_{\text{SF}}$) was able to describe the effect that secondary fluid has on transport properties. Our findings also suggest that in solution, the Jeffamine M2070 molecules exist in different nanoscale environments, where some are more strongly associated with the nanoparticle surface than others, and the conformation of the polymer canopy was dependent on the secondary fluid. This understanding of the polymer conformation in NOHMs can allow for the better design of an electrolyte capable of capturing and releasing small gaseous or ionic species.

25 ENERGY STORAGE↗

DOE OSTI2020

Phase Transition in a Memristive Suspended MoS 2 Monolayer Probed by Opto- and Electro-Mechanics

Semiconducting monolayers of a 2D material are able to concatenate multiple interesting properties into a single component. Here, by combining opto-mechanical and electronic measurements, we demonstrate the presence of a partial 2H–1T' phase transition in a suspended 2D monolayer membrane of MoS 2 . Electronic transport shows unexpected memristive properties in the MoS 2 membrane, in the absence of any external dopants. A strong mechanical softening of the membrane is measured concurrently and may only be related to the 2H–1T' phase transition, which imposes a 3% directional elongation of the topological 1T' phase with respect to the semiconducting 2H. We note that only a few percent 2H–1T' phase switching is sufficient to observe measurable memristive effects. Our experimental results combined with first-principles total energy calculations indicate that sulfur vacancy diffusion plays a key role in the initial nucleation of the phase transition. Our study clearly shows that nanomechanics represents an ultrasensitive technique to probe the crystal phase transition in 2D materials or thin membranes. Lastly, a better control of the microscopic mechanisms responsible for the observed memristive effect in MoS 2 is important for the implementation of future devices.

2D materials↗

DOE OSTI2023

Effects of Mineral Impurities and Heat on Uranium(VI) Sorption onto Bentonite (Final Report)

Most nuclear waste disposal options include compacted bentonite, consisting of montmorillonite clay, as part of a barrier system to minimize contaminant mobility. Uranium (U) is the primary element in spent nuclear fuel, and from an environmental perspective, a potential contaminant of water resources. Furthermore, uranium may control nuclear fuel degradation rates and the consequent release of other radioactive contaminants based on its diffusive transport away from waste canisters. Uranium sorption onto clay and other mineral surfaces is expected to limit U(VI) mobility in these systems. However, at this point a prediction of U(VI) sorption and transport behavior in performance assessment (PA) models is complicated by a series of factors, such as: (1) the presence of various U(VI) solution species with different charges and sorption characteristics; (2) the complex microstructure of montmorillonite clay resulting in two types of clay porosities and multiple sorption sites; (3) the largely unknown effects of bentonite mineral impurities on pore water chemistry, U(VI) sorption and diffusion behavior; and (4) the potential impacts of heat, generated by the decay of spent fuel, on mineralogical and microstructural transformations, and any subsequent effects on radionuclide sorption and mobility. In this project, we investigated the effects of calcite impurities on U(VI) sorption and diffusion onto montmorillonite before and after mineral exposure to heat. Overall, our main goals were to: 1. Gain a mechanistic understanding of the effects of calcite impurities on U(VI) sorption and diffusion in montmorillonite/bentonite at variable chemical conditions, and before and after mineral exposure to heat; and to 2. Work towards the development of new surface complexation and diffusion models to predict U(VI) sorption and mobility in montmorillonite/bentonite while accounting for the impacts of calcite impurities and heat. In order to achieve these goals, we pursued the following research objectives and tasks: 1. Characterize the effects of calcite impurities on U(VI) sorption onto Na-montmorillonite, and evaluate if and how these effects change due to solids’ exposure to heat (Task 1). 2. Characterize U(VI) surface speciation in solid samples from Task 1, with a particular focus on U(VI) precipitates and co-precipitates (Task 2). 3. Test the relevance of observed changes in U(VI) sorption characteristics for U(VI) diffusive transport behavior in bentonite barriers (Task 3). 4. Evaluate the exclusion of anionic U(VI) solution complexes from clay nanopores (Task 4). 5. Building on Tasks 1-4, start the development of new surface complexation and reactive transport models that can simulate and predict U(VI) sorption and diffusion in complex bentonite systems (Task 5). A detailed description of all tasks, and their specific results and conclusions is provided in this report.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2020

Axial magnetic flux amplification in Hall-magnetohydrodynamic simulations of externally magnetized z-pinches

It is shown that externally magnetized gas-puff z-pinches under compression can exhibit robust axial flux amplification under suitable axial boundary conditions. This effect relies upon the Hall term in the generalized Ohm's law to generate azimuthal currents in the presence of a driving axial electric field. Under dynamic compression, the total current tends to flow in a mostly force-free boundary layer, separating the predominately azimuthal field outside the layer and the predominately axial field inside the layer. The effect only appears to occur if the axial boundaries allow for outflow or absorption of electromagnetic energy. The effect is mitigated by imposing either periodic or conducting axial boundary conditions. A semi-analytic equilibrium analysis agrees with steady-state solutions of the time-dependent electron-magnetohydrodynamic equations and provides an estimate of the scaling of the boundary layer as well as suggesting a scenario for the formation of the boundary layer. When operative, the effect can significantly impede plasma compression due to the increase in axial flux that diffuses into the pre-compressed plasma or through the presence of conductors that inhibit movement of the generated axial flux. Several facilities have noted unusual implosion behavior in z-pinch experiments with applied axial fields that does not appear to be explainable within the standard magnetohydrodynamic model. In conclusion, it is suggested that these experiments can be explained by the axial flux amplification and concentration effect

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗