SEARCH · Engineering Papers

Results for “Numerical approximation & analysis”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2025

Sensitivity of the Shallow‐To‐Deep Convective Transition to Moisture and Wind Shear in the Amazon

Deep convection is the primary influence on weather and climate in tropical regions. However, understanding and simulating the shallow‐to‐deep (STD) convective transition has long been challenging. Here, we conduct high‐resolution numerical simulations to assess the environmental controls on the evolution of isolated convection in the Amazon during the wet season. The large‐scale forcing derived through a constrained variational analysis approach for the GoAmazon2014/5 Experiment is used in the simulations. Through sensitivity experiments, we examine the relative importance of moisture and wind shear in controlling the shallow‐to‐deep convective transition for isolated convective events. Convection exhibits the greatest sensitivity to humidity within the lowest 1.5 km, where a 4 mm reduction in column water vapor nearly suppresses ice water formation on deep convective days. In contrast, a reduction in column water vapor in the free troposphere by a factor of two or more is necessary to produce a comparable impact on convection. Increasing low‐level wind speed from 6 to 9 m s -1 enhances afternoon deep convection, raising the cloud ice mixing ratio by approximately 25%. Conversely, upper‐level wind shear reveals the weakest correlation with daytime convection in our simulations. Our results help characterize the role of moisture and wind shear on the STD transition and our understanding of the underlying mechanisms.

environmental controls↗

DOE OSTI2020

Quantum state reduction: Generalized bipartitions from algebras of observables

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by tracing out part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state is reduced given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. One of our main technical results is a general, not inherently numeric, algorithm for finding irreducible representations of matrix algebras. In our work, we demonstrate the viability of this approach with two examples of limited-resolution observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the one-dimensional Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Investigating uncertainties in human adaptation and their impacts on water scarcity in the Colorado river Basin, United States

The Colorado River Basin (CRB) supports the water supply for seven states and forty million people in the Western United States (US) and has been suffering an extensive drought for more than two decades. As climate change continues to reshape water resources distribution in the CRB, its impact can differ in intensity and location, resulting in variations in human adaptation behaviors. The feedback from human systems in response to the environmental changes and the associated uncertainty is critical to water resources management, especially for water-stressed basins. This paper investigates how human adaptation affects water scarcity uncertainty in the CRB and highlights the uncertainties in human behavior modeling. Our focus is on agricultural water consumption, as approximately 80% of the water consumption in the CRB is used in agriculture. We adopted a coupled agent-based and water resources modeling approach for exploring human-water system dynamics, in which an agent is a human behavior model that simulates a farmer’s water consumption decisions. We examined uncertainties at the system, agent, and parameter levels through uncertainty, clustering, and sensitivity analyses. The uncertainty analysis results suggest that the CRB water system may experience 13 to 30 years of water shortage during the 2019–2060 simulation period, depending on the paths of farmers’ adaptation. The clustering analysis identified three decision-making classes: bold, prudent, and forward-looking, and quantified the probabilities of an agent belonging to each class. The sensitivity analysis results indicated agents whose decision-making models require further investigation and the parameters with the higher uncertainty reduction potentials. Here, by conducting numerical experiments with the coupled model, this paper presents quantitative and qualitative information about farmers’ adaptation, water scarcity uncertainties, and future research directions for improving human behavior modeling.

Agent-based modeling↗

DOE OSTI2025

Analysis of fast-ion losses measured in MAST-U via infrared thermography and a Fast Ion Loss Detector

Fast-ion losses need to be monitored to avoid damage to plasma facing components. In existing experimental devices, the scintillator-based fast-ion loss detector (FILD) is the most advanced diagnostic for measuring fast-ion losses. However, FILDs provide only local information about the losses. Infrared (IR) thermography can be used as a complementary tool for more global monitoring of the deposition of fast-ion losses on the wall, at the expense of no velocity-space resolution. IR cameras measure the temperature of the plasma facing components. This measurement, determined by a combined effect of the thermal plasma, radiation, neutrons and fast-ion losses, can be decomposed to infer the fast-ion load on the tokamak wall. In this manuscript, a workflow to estimate fast-ion losses via IR thermography is applied to the MAST-U spherical tokamak, using a 1D approximation to extract the experimental heat flux on the FILD front face from IR data. To numerically estimate the different contributions to this total heat flux, the field-line tracing environment SMITER is used to calculate the thermal plasma contribution, the orbit-following Monte-Carlo code ASCOT to estimate the fast-ion losses, and bolometry measurements for the radiation. To validate the workflow, two discharges, L-mode plasmas with low MHD activity, were executed using on and off-axis beams, respectively. The experimentally and numerically estimated heat flux are of the same order of magnitude for the on-axis heated scenario, with a strong dependence of the estimated fast-ion losses contribution on the fit to the kinetic profiles used as input. This is also true for the off-axis heated scenario, where the total numerically estimated heat flux is 2.1 or 1.3 times higher than the maximum experimentally estimated heat flux, depending on the ASCOT input used.

FILD↗

DOE OSTI2024

Development of a neural network model for peeling–ballooning stability analysis in the KSTAR tokamak pedestals

The neural network model, MISHKA-NN is developed to mitigate the computational burden associated with the linear ideal magnetohydrodynamic (MHD) stability analysis of the pedestal based on the peeling–ballooning (P–B) model. By utilizing both 1D plasma profiles (current density, pressure gradient, and safety factor) and 0D parameters (plasma geometry, total current, and toroidal mode number), the model predicts linear growth rate of edge-localized ideal MHD instability in a given equilibrium state. By enabling the prediction of each instability within a second, the model reduces the time required for plotting a pedestal P–B stability diagram (j - α diagram) from approximately 100 CPU hours to a few CPU minutes. Notably, even with the utilization of parametric pressure and current profiles and plasma boundary shapes for the training dataset, the model shows a satisfactory level of performance in benchmarking the j - α diagram for the reconstructed equilibrium from a KSTAR tokamak experiment. We anticipate the model to serve as a versatile alternative to 2D linear MHD stability codes, alleviating numerical costs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

On the Departure from Monin–Obukhov Surface Similarity and Transition to the Convective Mixed Layer

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients Φ for wind speed and air temperature generally align with Monin–Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in Φ to first-order approximation, yielding improved similarity from approximately 0.05z i to above 0.3z i , where z i is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin–Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1 z i .

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Evaluating large scale aqueous organic redox flow battery performance with a hybrid numerical and machine learning framework

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low-capacity degradation in 10 cm$^2$ cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier to commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm$^2$ DHP-based AORFB by combining a physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. Such combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

DOE OSTI2025

A hybrid numerical and machine learning framework for evaluating the performance of a 780 cm 2 aqueous organic redox flow battery

Aqueous organic redox flow battery (AORFB) is a promising cost-competitive technology for large-scale energy storage. Among existing work, the dihydroxyphenazine (DHP)-based AORFB has demonstrated high energy density and low capacity degradation in 10 cm2 cells during lab tests. However, its commercial-scale performance in more complex environments remains unknown, posing a barrier for commercialization. To address this gap, this work presents a comprehensive performance evaluation of a 780 cm 2 DHP-based AORFB by combining physics-based numerical model, machine learning (ML)-based surrogate models, and ML-derived sensitivity quantification. Specifically, we first select 12 key battery parameters that include 10 physicochemical quantities and 2 operation quantities, then select 6 performance metrics that include energy efficiency (EE), discharging capacity, charging energy, and power losses due to concentration, activation, and ohmic over-potentials. With such selection, 12800 combinations of the 12 parameters are subsequently generated using the Latin Hypercube Sampling method. These combinations, together with 38 pre-defined State of Charge, are then integrated to a validated AORFB model developed in COMSOL to compute the performance metrics. With both input parameters and performance metrics, 60 deep neural network (DNN) surrogate models are then trained to approximate the relationship between the 10 physicochemical quantities and 6 performance metrics at each flow rate and current density. Sensitivity scores are then calculated based on the DNN models. Two additional sensitivity analysis tools, i.e., MARS, and SHAP, are also used to cross-validate the sensitivity scores from the DNN. The results demonstrate that 1) the standard potential ranks the first in controlling EE and charging energy, 2) the membrane conductivity is most critical for power loss and EE, and 3) specific area and reaction rate control activation power loss.

25 ENERGY STORAGE↗

DOE OSTI2024

Galaxy bispectrum in the spherical Fourier-Bessel basis

The bispectrum, the three-point correlation in Fourier space, is a crucial statistic for studying many effects targeted by the next-generation galaxy surveys, such as primordial non-Gaussianity (PNG) and general relativistic (GR) effects on large scales. In this work we develop a formalism for the bispectrum in the spherical Fourier-Bessel (SFB) basis—a natural basis for computing correlation functions on the curved sky, as it diagonalizes the Laplacian operator in spherical coordinates. Working in the SFB basis allows for line-of-sight effects such as redshift space distortions and GR to be accounted for exactly, i.e., without having to resort to perturbative expansions to go beyond the plane-parallel approximation. Only analytic results for the SFB bispectrum exist in the literature given the intensive computations needed. We numerically calculate the SFB bispectrum for the first time, enabled by a few techniques: We implement a template decomposition of the redshift-space kernel Z 2 into Legendre polynomials, and separately treat the PNG and velocity-divergence terms. We derive an identity to integrate a product of three spherical harmonics connected by a Dirac delta function as a simple sum and use it to investigate the limit of a homogeneous and isotropic Universe. Furthermore, we present a formalism for convolving the signal with separable window functions and use a toy spherically symmetric window to demonstrate the computation and give insights into the properties of the observed bispectrum signal. While our implementation remains computationally challenging, it is a step toward a feasible full extraction of information on large scales via a SFB bispectrum analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Analytic Thermal Model of an Optical Fiber Based Gamma Thermometer and its Application in a University Research Reactor

This paper describes and validates, by comparison with numerical modeling results, an analytical model of thermal transport in an optical fiber based gamma thermometer (OFBGT) that is appropriate for use in university research reactors. The maximum temperature difference between the thermal mass and the outer sheath ( Δ T ) for the OFBGT design that we have considered is approximately 50 ∘ C , for the OFBGT in the Central Irradiation Facility of the Ohio State University Research Reactor (OSURR) with the reactor operating at full power (450 kW). The maximum value of Δ T that is predicted by the analytic model for the OFBGT design is smaller by approximately 1.1 °C than the value of Δ T which is predicted by the numerical model, for the same OFBGT design, but including all the details of the design. We have used the analytical model of thermal transport in an OFBGT to determine a normalized Modulation Transfer Function M T F ′ ( k ) ) for the OFBGT. We conclude that MTF ′ ( k OSU ) > 0.99 , where k OSU is the spatial frequency for the axial dependence of the reactor power distribution in the

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

Multi-resolution, Multi-scale Modeling for Scalable Macroalgae Production

Macroalgae harvested along coastlines and in the open ocean has traditionally been used as food for human consumption, animal feed, and fertilizer. The U.S. ARPA-E MARINER Program estimates that the nation has suitable conditions and geography to produce at least 500 million dry metric tons of macroalgae per year, yielding approximately 2.7 quadrillion BTUs of energy in the form of liquid fuel, which is roughly 10% of the nation’s annual transportation energy demand. Adverse environmental effects of nutrient overload and ocean acidification may also be reduced by large-scale macroalgae cultivation in many coastal ocean regions. However, the successful deployment of large-scale marine macroalgae farms for fuel production depends on ambient hydrodynamic conditions and nutrient availability, as well as their interactions with macroalgae farm structures. Pacific Northwest National Laboratory led an ARPA-E MARINER project to develop a set of numerical modeling tools capable of simulating ocean hydrodynamic and biogeochemical processes, macroalgae trajectories for free-floating systems, macroalgae growth and biomass yields, and hydrodynamic load on macroalgae canopies and farm structures using a multi-resolution and multi-scale approach. This set of modeling tools provides a suite of information essential for system design, optimal project siting, risk analysis, and management of macroalgae production systems in the ocean. Better clarity can also help macroalgae system developers reduce deployment costs, operational risk, and potential impacts on the local marine environment.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

SUHMO: an adaptive mesh refinement SUbglacial Hydrology MOdel v1.0

Abstract. Water flowing under ice sheets and glaciers can have a strong influence on ice dynamics, particularly through pressure changes, suggesting that a comprehensive ice sheet model should include the effect of basal hydrology. Modeling subglacial hydrology remains a challenge, however, mainly due to the range of spatial and temporal scales involved – from subglacial channels to vast subglacial lakes. Additionally, networks of subglacial drainage channels dynamically evolve over time. To address some of these challenges, we have developed an adaptive mesh refinement (AMR) model based on the Chombo software framework. We extend the model proposed by Sommers et al. (2018) with a small but significant change to accommodate the transition from unresolved to resolved flow features. We handle the strong nonlinearities present in the equations by resorting to an efficient nonlinear full approximation scheme multigrid (FAS-MG) algorithm. We outline the details of the algorithm and present convergence analysis results demonstrating its good performance. Additionally, we present results validating our approach, using test cases from the Subglacial Hydrology Model Intercomparison Project (SHMIP) (de Fleurian et al., 2018). We finish by presenting a more complex, 100 km-by-100 km synthetic test case with peaks and valleys that we use to investigate the effective pressure distribution as the number of AMR levels increases. These preliminary results suggest that a minimum spatial resolution is needed to properly capture channel features, but additional work is required to precisely quantify this and its impact on accurately modeling the coupled ice sheet–hydrology system. The efficiency of our approach, relying on localized refinement, is also demonstrated. Future work will include coupling the SUbglacial Hydrology MOdel (SUHMO) with the BISICLES AMR ice sheet model (Cornford et al., 2013), both built on the same numerical framework.

58 GEOSCIENCES↗

DOE OSTI2020

Molecular bond stabilization in the strong-field dissociation of O 2 +

We theoretically examine the rotational and vibrational dynamics of O 2 + molecular ions exposed to intense, short laser pulses for conditions realized in contemporary pump-probe experiments. We solve the time-dependent Schrödinger equation within the Born-Oppenheimer approximation for an initial distribution of randomly aligned molecular ions. For fixed peak intensities, our numerical results show that total, angle-integrated O 2 + → O( 3 P) + O + ( 4 S 0 ) dissociation yields do not monotonically increase with increasing infrared-probe pulse duration. We find this pulse-duration-dependent stabilization to be consistent with the transient trapping of nuclear probability density in a light-induced (bond-hardening) potential-energy surface and robust against rotational excitation. We analyze this stabilization effect and its underlying bond-hardening mechanism (i) in the time domain, by following the evolution of partial nuclear probability densities associated with the dipole-coupled O 2 + (a 4 Π u ) and O 2 + (f 4 Π g ) cationic states, and (ii) in the frequency domain, by examining rovibrational quantum-beat spectra for the evolution of the partial nuclear probability densities associated with these states. In this work, our analysis reveals the characteristic timescale for the bond-hardening mechanism in O 2 + and explains the onset of bond stabilization for sufficiently long pulse durations.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

Efficient phase-factor evaluation in quantum signal processing

Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in principle be obtained for a range of tasks, such as Hamiltonian simulation and the quantum linear system problem. A further benefit of QSP is that it uses a minimal number of ancilla qubits, which facilitates its implementation on near-to-intermediate term quantum architectures. However, there is so far no classically stable algorithm allowing computation of the phase factors that are needed to build QSP circuits. Existing methods require the use of variable precision arithmetic and can only be applied to polynomials of a relatively low degree. We present here an optimization-based method that can accurately compute the phase factors using standard double precision arithmetic operations. We demonstrate the performance of this approach with applications to Hamiltonian simulation, eigenvalue filtering, and quantum linear system problems. Furthermore, our numerical results show that the optimization algorithm can find phase factors to accurately approximate polynomials of a degree larger than 10000 with errors below 10 -12 .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Dynamic modeling studies of basin-scale pressure interference and CO 2 plume evolution in multi-well geologic CO 2 storage

This research employs numerical modeling to analyze how CO 2 plumes and pressure fronts evolve when CO 2 is injected into a single storage formation from multiple projects located in proximity. Here, this analysis also evaluates the extent to which injection well spacing alleviates pressure buildup in the absence of active pressure management tactics. The simulation approach was based on a single, homogenous saline aquifer in which CO 2 injection occurs under a one-injector baseline case and several multi-well cases where well spacing varies. Analysis results show that the extent of pressure buildup is in the range of tens or a few hundreds of kilometers and contingent upon the defining pressure buildup demarcating the front edge. For the geological setting evaluated in this paper, our analysis suggests that without active basin pressure management strategies, commercial-scale projects would likely need to be sited far apart to avoid pressure interference from one another. Analysis results show the radius of CO 2 plume varies approximately from 2 to 3 km from injection wells (each injecting 1 Mt/year for 30 years) depending on cases and modeling parameters assumed. Given the pressure interference, this paper thus draws attention to the importance of greater coordination among storage operators and regulatory stakeholders. Because this analysis assumes a very specific geologic setting, this exploratory analysis bears further investigations across other geologic scenarios.

42 ENGINEERING↗

DOE OSTI2023

Field Laboratory for Emerging Stacked Unconventional Plays in Central Appalachia

The goal of the Field Laboratory for Emerging Stacked Unconventional Plays (ESUP) in Central Appalachia project was to investigate and characterize the resource potential for multi-play production of emerging unconventional reservoirs in Central Appalachia. Project activities included drilling, logging and coring of a vertical characterization well drilled to basement to approximately 15,000 feet in depth. The data from drilling and well logs as well recovered core samples were used by the research team to support characterization of the geology and potential pay zones within the Nora Gas Field of southwestern Virginia and the greater Central Appalachian Basin. This project was led by Dr. Nino Ripepi of the Virginia Center for Coal and Energy Research (VCCER) in close collaboration with EnerVest Operating LLC (EnerVest). VCCER is housed in the Department of Mining and Minerals Engineering at Virginia Tech and was created by an Act of the Virginia General Assembly on March 30, 1977, as an interdisciplinary study, research, information, and resource facility for the Commonwealth of Virginia. EnerVest is a top tier, low-cost oil and natural gas company with a long history of traditional operating relationships with institutional investors as well as public and private companies. This report summarizes two major research activities: 1) Log and Core Analysis and 2) Numerical Modeling. Core analysis comprises the characterization efforts of the ESUP Field Laboratory and includes a discussion of the well logs run in the deep characterization wells, an initial analysis of those, the number, size and location of cores recovered, core testing and analysis done to date as well as plans for future analysis. Numerical modeling is comprised of seven major modeling efforts, including (1) Multiphysics shale transport modeling work, (2) the developed in-house compositional simulator studies, (3) reservoir modeling studies using GEM software, (4) fracture modeling work using EFRAC3D software and (5) numerical modeling efforts with ABAQUS software, (6) Numerical modeling efforts using FLAC3D and PFC3D, and (7) Automatic Machine Learning (AutoML) Studies.

02 PETROLEUM↗

DOE OSTI2025

Stage-local partitioned two-step runge-kutta methods for large systems of ordinary differential equations

We introduce stage-local partitioned two-step Runge-Kutta methods are an extension of standard two-step Runge-Kutta methods, which are an alternative to the standard additive two-step Runge-Kutta methods currently existing in the literature. Furthermore, these new schemes are designed with an eye towards truly N-partitioned systems and leverage local stage approximations to make several computationally interesting approximations viable. Specifically, the focus on local stage approximations makes possible the construction of truly asynchronous schemes, in the parallel sense, possible. In addition, we show that an implicit-explicit approach to these schemes can lead to methods that require the inversion of only local nonlinear systems.

Applied Dynamical Systems↗

DOE OSTI2025

ThinCurr: An open-source 3D thin-wall eddy current modeling code for the analysis of large-scale systems of conducting structures

In this paper we present a new thin-wall eddy current modeling code, ThinCurr, for studying inductively-coupled currents in 3D conducting structures -- with primary application focused on the interaction between currents flowing in coils, plasma, and conducting structures of magnetically-confined plasma devices. The code utilizes a boundary finite element method on an unstructured, triangular grid to accurately capture device structures. The new code, part of the broader Open FUSION Toolkit, is open-source and designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. Scalability to large models is enabled through use of hierarchical off-diagonal low-rank compression of the inductance matrix, which is otherwise dense. Ease of handling large models of complicated geometry is further supported by automatic determination of supplemental elements through a greedy homology approach. Here, a detailed description of the numerical methods of the code and verification of the implementation of those methods using cross-code comparisons against the VALEN code and Ansys commercial analysis software is shown.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗