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NASA NTRS2018

Quantification of Dynamic Model Validation Metrics Using Uncertainty Propagation from Requirements

The Space Launch System, NASA's new large launch vehicle for long range space exploration, is presently in the final design and construction phases, with the first launch scheduled for 2019. A dynamic model of the system has been created and is critical for calculation of interface loads and natural frequencies and mode shapes for guidance, navigation, and control (GNC). Because of the program and schedule constraints, a single modal test of the SLS will be performed while bolted down to the Mobile Launch Pad just before the first launch. A Monte Carlo and optimization scheme will be performed to create thousands of possible models based on given dispersions in model properties and to determine which model best fits the natural frequencies and mode shapes from modal test. However, the question still remains as to whether this model is acceptable for the loads and GNC requirements. An uncertainty propagation and quantification (UP and UQ) technique to develop a quantitative set of validation metrics that is based on the flight requirements has therefore been developed and is discussed in this paper. There has been considerable research on UQ and UP and validation in the literature, but very little on propagating the uncertainties from requirements, so most validation metrics are "rules-of-thumb;" this research seeks to come up with more reason-based metrics. One of the main assumptions used to achieve this task is that the uncertainty in the modeling of the fixed boundary condition is accurate, so therefore that same uncertainty can be used in propagating the fixed-test configuration to the free-free actual configuration. The second main technique applied here is the usage of the limit-state formulation to quantify the final probabilistic parameters and to compare them with the requirements. These techniques are explored with a simple lumped spring-mass system and a simplified SLS model. When completed, it is anticipated that this requirements-based validation metric will provide a quantified confidence and probability of success for the final SLS dynamics model, which will be critical for a successful launch program, and can be applied in the many other industries where an accurate dynamic model is required.

Brown, Andrew M.↗

DOE OSTI2020

Nucleation and growth of voids in shock loaded copper bicrystals

Understanding the evolution of damage and deformation due to spall at grain boundaries can provide a basis for connecting micro- to macroscale failure behavior in metals under extreme conditions. Copper bicrystal samples were shock loaded using flyer-plate impacts in a light gas gun with shock stresses ranging from 3 to 6 GPa. Pulse duration as well as crystal orientation along the shock direction were varied for a fixed boundary misorientation to determine their effects on void nucleation and coalescence. Samples were soft recovered and cross-sectioned to characterize damage using electron backscattering diffraction and scanning electron microscopy to gather information on damage characteristics at and around the GB, with emphasis on growth of boundary and bulk voids. Chemistry and composition analysis were also performed on samples to determine if trace elements present in a sample affected the threshold for void nucleation. Results show that the kinetics of damage growth at the boundary are strongly affected by stress level and impurities. It was found that the boundary selected had a similar or even lower tendency to show damage than the bulk at low pulse durations and amplitudes. As pulse duration and amplitude increased damage localized at the boundary, which was found to consist of many small voids, indicating that the boundary experienced rapid void nucleation and coalescence. Furthermore, the presence of impurities correlated strongly with scatter on damage evolution.

36 MATERIALS SCIENCE↗

NASA NTRS2004

Ballistic Impact of Braided Composites With a Soft Projectile

Impact tests using a soft gelatin projectile were performed to identify failure modes that occur at high strain energy density during impact loading. Use of a soft projectile allows a large amount of kinetic energy to be transferred into strain energy in the target before penetration occurs. Failure modes were identified for flat aluminum plates and for flat composite plates made from a triaxial braid having a quasi-isotropic fiber architecture with fibers in the 0 and +/- 60 deg. directions. For the aluminum plates, a large hole formed as a result of crack propagation from the initiation site at the center of the plate to the fixed boundaries. For the composite plates, fiber tensile failure occurred in the back ply at the center of the plate. Cracks then propagated from this site along the +/- 60 deg. fiber directions until triangular flaps opened to allow the projectile to pass through the plate. The damage size was only slightly larger than the initial impact area. It was difficult to avoid slipping of the fixed edges of the plates during impact, and slipping was shown to have a large effect on the penetration threshold. Failure modes were also identified for composite half-rings fabricated with the 0 deg. fibers aligned circumferentially. Slipping of the edges was not a problem in the half-ring tests. For the composite half-rings, fiber tensile failure also occurred in the back ply. However, cracks initially propagated from this site in a direction transverse to the 0 deg. fibers. The cracks then turned to follow the +/- 60 deg. fibers for a short distance before turning again to follow 0 deg. fibers until two approximately rectangular flaps opened to allow the projectile to pass through the plate. The damage size in the composite half-rings was also only slightly larger than the initial impact area. Cracks did not propagate to the boundaries, and no delamination was observed. The damage tolerance demonstrated by the quasi-isotropic triaxial braid composites indicate that composites of this type can reasonably be considered as a lightweight alternative to metals for fan cases in commercial jet engines.

Roberts, Gary D.↗

NASA NTRS1994

Effect of high-latitude ionospheric convection on Sun-aligned polar caps

A coupled magnetospheric-ionospheric (M-I) magnetohydrodynamic (MHD) model has been used to simulate the formation of Sun-aligned polar cap arcs for a variety of interplanetary magnetic field (IMF) dependent polar cap convection fields. The formation process involves launching an Alfven shear wave from the magnetosphere to the ionosphere where the ionospheric conductance can react self-consistently to changes in the upward currents. We assume that the initial Alfven shear wave is the result of solar wind-magnetosphere interactions. The simulations show how the E region density is affected by the changes in the electron precipitation that are associated with the upward currents. These changes in conductance lead to both a modified Alfven wave reflection at the ionosphere and the generation of secondary Alfven waves in the ionosphere. The ensuing bouncing of the Alfven waves between the ionosphere and magnetosphere is followed until an asymptotic solution is obtained. At the magnetosphere the Alfven waves reflect at a fixed boundary. The coupled M-I Sun-aligned polar cap arc model of Zhu et al.(1993a) is used to carry out the simulations. This study focuses on the dependence of the polar cap arc formation on the background (global) convection pattern. Since the polar cap arcs occur for northward and strong B(sub y) IMF conditions, a variety of background convection patterns can exist when the arcs are present. The study shows that polar cap arcs can be formed for all these convection patterns; however, the arc features are dramatically different for the different patterns. For weak sunward convection a relatively confined single pair of current sheets is associated with the imposed Alfven shear wave structure. However, when the electric field exceeds a threshold, the arc structure intensifies, and the conductance increases as does the local Joule heating rate. These increases are faster than a linear dependence on the background electric field strength. Furthermore, above the threshold, the single current sheet pair splits into multiple current sheet pairs. For the fixed initial ionospheric and magnetospheric conditions used in this study, the separation distance between the current pairs was found to be almost independent of the background electric field strength. For either three-cell or distorted two-cell background convection patterns the arc formation favored the positive B(sub y) case in the northern hemisphere.

Sojka, J. J.↗

DOE OSTI2025

Self-consistent equilibrium and transport simulations for NSTX-U plasmas enhanced via machine learning surrogate models

The Control-Oriented Transport SIMulator (COTSIM) is an advanced equilibrium and transport code designed for simulating tokamak discharges at computational speeds suitable for control applications. COTSIM’s modular framework enables users to select models that balance accuracy with speed according to specific needs, allowing the code to operate from fast to faster-than-real-time performance levels. This work presents recent enhancements to COTSIM’s predictive accuracy for NSTX-U scenarios, achieved by integrating neural-network-based surrogate models and self-consistent equilibrium calculations. To improve source deposition predictions, a surrogate model for NUBEAM has been incorporated. Additionally, a surrogate model for the Multi-Mode Module (MMM) now supports predictions of anomalous thermal, momentum, and particle diffusivities—key factors for modeling the evolution of temperature and rotation. Each surrogate model was specifically trained for the NSTX-U operational regime to enhance COTSIM’s accuracy while maintaining computational efficiency. Moreover, COTSIM now couples fixed-boundary equilibrium solvers with its transport solvers, enabling self-consistent predictions of plasma profiles and equilibrium evolution over the discharge. Simulation results demonstrate strong agreement between COTSIM and TRANSP predictions for NSTX-U discharges. These substantial advancements expand COTSIM’s utility in model-based control applications for NSTX-U. Potential applications include simultaneous optimization of equilibrium and transport scenarios, integration into digital twins, real-time profile estimation (e.g., temperature and rotation) from limited or noisy measurements, and advanced feedback-based scenario control.

Equilibrium and transport modeling↗

DOE OSTI2023

Modeling and optimization of steady flow of natural gas and hydrogen mixtures in pipeline networks

Here, we extend the canonical problems of simulation and optimization of steady-state gas flows in pipeline networks with compressors to the transport of mixtures of highly heterogeneous gases injected throughout a network. Our study is motivated by proposed projects to blend hydrogen generated using clean energy into existing natural gas pipeline systems as part of efforts to reduce the reliance of energy systems on fossil fuels. Flow in a pipe is related to endpoint pressures by a basic Weymouth equation model, with an ideal gas equation of state, where the wave speed depends on the hydrogen concentration. At vertices, in addition to mass balance, we also consider mixing of incoming flows of varying hydrogen concentrations. The problems of interest are the heterogeneous gas flow simulation (HGFS), which determines system pressures and flows given fixed boundary conditions and compressor settings, as well as the heterogeneous gas flow optimization (HGFO), which extremizes an objective by determining optimal boundary conditions and compressor settings. We examine conditions for uniqueness of solutions to the HGFS, as well as compare and contrast mixed-integer and continuous nonlinear programming formulations for the HGFO. We develop computational methods to solve both problems, and examine their performance using four test networks of increasing complexity.

08 HYDROGEN↗

DOE OSTI2021

Geometric electrostatic particle-in-cell algorithm on unstructured meshes

We present a geometric particle-in-cell (PIC) algorithm on unstructured meshes for studying electrostatic perturbations with frequency lower than electron gyrofrequency in magnetized plasmas. In this method, ions are treated as fully kinetic particles and electrons are described by the adiabatic response. The PIC method is derived from a discrete variational principle on unstructured meshes. To preserve the geometric structure of the system, the discrete variational principle requires that the electric field is interpolated using Whitney 1-forms, the charge is deposited using Whitney 0-forms and the electric field is computed by discrete exterior calculus. The algorithm has been applied to study the ion Bernstein wave (IBW) in two-dimensional magnetized plasmas. The simulated dispersion relations of the IBW in a rectangular region agree well with theoretical results. In a two-dimensional circular region with fixed boundary condition, the spectrum and eigenmode structures of the IBW are obtained from simulations. We compare the energy conservation property of the geometric PIC algorithm derived from the discrete variational principle with that of previous PIC methods on unstructured meshes. The comparison shows that the new PIC algorithm significantly improves the energy conservation property.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

The DESC stellarator code suite Part 3: Quasi-symmetry optimization

The DESC stellarator optimization code takes advantage of advanced numerical methods to search the full parameter space much faster than conventional tools. Only a single equilibrium solution is needed at each optimization step thanks to automatic differentiation, which efficiently provides exact derivative information. A Gauss–Newton trust-region optimization method uses second-order derivative information to take large steps in parameter space and converges rapidly. With just-in-time compilation and GPU portability, high-dimensional stellarator optimization runs take orders of magnitude less computation time with DESC compared to other approaches. This paper presents the theory of the DESC fixed-boundary local optimization algorithm along with demonstrations of how to easily implement it in the code. Example quasi-symmetry optimizations are shown and compared to results from conventional tools. Three different forms of quasi-symmetry objectives are available in DESC, and their relative advantages are discussed in detail. In the examples presented, the triple product formulation yields the best optimization results in terms of minimized computation time and particle transport. This paper concludes with an explanation of how the modular code suite can be extended to accommodate other types of optimization problems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Narrow operator models of stellarator equilibria in Fourier Zernike basis

Numerical computation of the ideal magnetohydrodynamic (MHD) equilibrium magnetic field is at the base of stellarator optimisation and provides the starting point for solving more sophisticated partial differential equations like transport or turbulence models. Conventional approaches solve for a single stationary point of the ideal MHD equations, which is fully defined by three invariants and the numerical scheme employed by the solver. We present the first numerical approach that can solve for a continuous distribution of equilibria with fixed boundary and rotational transform, varying only the pressure invariant. This approach minimises the force residual by optimising parameters of multilayer perceptrons that map from a scalar pressure multiplier to the Fourier Zernike basis as implemented in the modern stellarator equilibrium solver DESC.

fusion plasma↗

DOE OSTI2023

Delamination-Assisted Ultrafast Wrinkle Formation in a Freestanding Film

Freestanding films provide a versatile platform for materials engineering thanks to additional structural motifs not found in films with a substrate. A ubiquitous example is wrinkles, yet little is known about how they can develop over as fast as a few picoseconds due to a lack of experimental probes to visualize their dynamics in real time on the nanoscopic scale. Here, we use time-resolved electron diffraction to directly observe light-activated wrinkling formation in freestanding La 2/3 Ca 1/3 MnO 3 films. Via a “lock-in” analysis of oscillations in the diffraction peak position, intensity, and width, we quantitatively reconstructed how wrinkles develop on the time scale of lattice vibration. Contrary to the common assumption of fixed boundary conditions, we found that wrinkle development is associated with ultrafast delamination at the film boundaries. Finally, our work provides a generic protocol to quantify wrinkling dynamics in freestanding films and highlights the importance of the film–substrate interaction in determining the properties of freestanding structures.

36 MATERIALS SCIENCE↗

DOE OSTI2020

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Stellarator optimization for good magnetic surfaces at the same time as quasisymmetry

A method is demonstrated to optimize a stellarator's geometry to eliminate magnetic islands and achieve other desired physics properties at the same time. For many physics quantities that have been used in stellarator optimization, including quasisymmetry, neoclassical transport, and magnetohydrodynamic stability, it is convenient to use a magnetic equilibrium representation that assures the existence of magnetic surfaces. However, this representation hides the possible presence of magnetic islands, which are typically undesirable. To include both surface-based objectives and island widths in a single optimization, two fixed-boundary equilibrium calculations are run at each iteration of the optimization: one that enforces the existence of magnetic surfaces (the Variational Moments Equilibrium Code) [S. P. Hirshman and J. C. Whitson, Phys. Fluids 26, 3553 (1983)] and one that does not (the Stepped Pressure Equilibrium Code) [Hudson et al., Phys. Plasmas 19, 112502 (2012)]. By penalizing the island residues in the objective function, the two magnetic field representations are brought into agreement during the optimization. Here, an example is presented in which, particularly on the surface where quasisymmetry was targeted, quasisymmetry is achieved more accurately than in previously published examples.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Fueling limits in a cylindrical viscosity-limited reactor

Recently, a method to achieve a “natural hot-ion mode” was suggested by utilizing ion viscous heating in a rotating plasma with a fixed boundary. We explore the steady-state solution to the Braginskii equations and find the parameter regime in which a significant temperature difference between ions and electrons can be sustained in a driven steady state. Here, the threshold for this effect occurs at ρ i ≳ 0.1R. An analytic, leading order low flow solution is obtained, and a numerical, moderate Mach number M ≲ 2 is investigated. The limitation is found to be at moderate Mach numbers.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Radial coordinate maps, radial vectors, and binormal vectors for 5/6, 5/5 and 5/4 edge island domains in W7-X

Abstract The edge island domain in Wendelstein 7-X consists of divertor islands whose position coincide with the location of rational values of the rotational transform - ι ≈ ( 5 / 6 , 5 / 5 , 5 / 4 ) and surround the main confinement volume (the ‘main plasma’), providing the magnetic topology for an island divertor. The 5/5 edge consists of five individual islands that are unconnected. In contrast, a single island connects onto itself after 6 or 4 toroidal transits in the 5/6 or 5/4 edge, respectively. Many interesting phenomena are related to these islands and diagnostic analyses require a mapping from ‘laboratory’ or real space coordinates to the island coordinate system (ICS). A procedure is described here to calculate several scalar and vector quantities for closed island structures which can be utilized in fast interpolation schemes for inverse maps. For the 5/5 edge, a fixed-boundary vacuum (zero beta) magneto-hydrodynamic solution of the 5/5 island is found with the Variational Moments Equilibrium Code, VMEC. The solution is compatible with already existing routines which determine the radial and binormal vectors of VMEC solutions at arbitrary laboratory coordinates. VMEC does not support solutions for the 5/4 and 5/6 islands, but the radial and binormal vectors are available in a local 2D Fourier ICS.

Physics↗

DOE OSTI2022

Energetic particle optimization of quasi-axisymmetric stellarator equilibria

Abstract An important goal of stellarator optimization is to achieve good confinement of energetic particles such as, in the case of a reactor, alphas created by deuterium–tritium fusion. In this work, a fixed-boundary stellarator equilibrium was re-optimized for energetic particle confinement via a two-step process: first, by minimizing deviations from quasi-axisymmetry (QA) on a single flux surface near the mid-radius, and secondly by maintaining this improved QA while minimizing the analytical quantity Γ C , which represents the angle between magnetic flux surfaces and contours of J | | , the second adiabatic invariant. This was performed multiple times, resulting in a group of equilibria with significantly reduced energetic particle losses, as evaluated by Monte Carlo simulations of alpha particles in scaled-up versions of the equilibria. This is the first time that energetic particle losses in a QA stellarator have successfully been reduced by optimizing Γ C . The relationship between energetic particle losses and metrics such as QA error ( E q a ) and Γ C in this set of equilibria were examined via statistical methods and a nearly linear relationship between volume-averaged Γ C and prompt particle losses was found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Dimensionless parameters for cloudy Rayleigh-Bénard convection: Supersaturation, Damköhler, and Nusselt numbers

In steady-state Rayleigh-Bénard convection, heat is transported by turbulent thermal convection from the bottom, hot surface to the top, cold surface, leading to a height-independent sensible heat flux. When water vapor is present and cloud formation occurs, there is also an additional latent heat flux. Heat transport in cloudy Rayleigh-Bénard convection depends on turbulent flow as well as the microphysical state of the clouds: specifically, whether substantial supersaturations exist and whether cloud liquid water is removed through sedimentation/precipitation. In this article we bridge between the Rayleigh-Bénard convection literature and the atmospheric literature. We express the governing equations for cloudy convection in dimensionless form, thereby explicitly identifying the governing parameters relevant to the cloudy case, including Schmidt, Damköhler, supersaturation, and sedimentation numbers. We further connect to the atmospheric literature by obtaining a Nusselt number (dimensionless heat flux) for a cloud-convection system, directly from the conservation equations for temperature and water vapor. This flux has the same form as that identified by Zhang et al. [L. Zhang, K. L. Chong, and K.-Q. Xia, J. Fluid Mech. 874, 1041 (2019)] for convection with water vapor, but is extended to the cloudy case. For equal thermal and water vapor diffusivities, the flux corresponds to the widely used atmospheric quantities equivalent temperature and moist static energy. Using large eddy simulation (LES) of an idealized cloudy Rayleigh-Bénard convection system with fixed boundary conditions, we find that the equivalent heat flux (Nusselt number) is only weakly dependent on the microphysical details of the system, such as liquid water mixing ratio and cloud droplet number concentration. Finally, from the results, we show the vertical profiles of sensible and latent heat fluxes depend on the liquid water content, whereas the equivalent heat flux remains a constant throughout the height of the chamber.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Neural-Network-Enhanced COTSIM: Advancing Predictive Capabilities for Fast DIII-D Simulations

Sustaining fusion reactions in tokamaks requires heating plasma to thermonuclear temperatures while maintaining confinement and stability. Neutral beam injection (NBI) provides heating, current drive, torque, and fueling, while electron cyclotron (EC) waves are widely used for heating and current drive; together, these actuators shape the plasma current, temperature, and density profiles. The control-oriented tokamak simulator (COTSIM), a predictive, control-oriented code, has been enhanced with neural-network surrogates for transport and sources. Turbulent transport is predicted by MMMnet—a neural-network version of the updated multimode model (MMM 9.0.10)—with significantly reduced computation time relative to MMM; neoclassical transport follows the Chang–Hinton model. NUBEAMnet, a surrogate of the Monte Carlo NUBEAM module, predicts beam-driven heating, current, and torque. EC heating and current drive use a control-oriented, empirically scaled source model; plasma resistivity follows the Spitzer formulation; bootstrap current uses the Sauter model. Equilibrium is computed using both prescribed and fixed-boundary solvers (FBSs), and the pedestal structure is modeled with an empirical pedestal model. For a representative DIII-D discharge, COTSIM predicts electron and ion temperature and safety-factor profiles in close agreement with TRANSP predictive and interpretive simulations while extending predictions through the pedestal region to the plasma edge (versus 80% of the minor radius in TRANSP). Furthermore, the equivalent COTSIM simulation runs in under 3 min compared to about 2 h for TRANSP, enabling rapid scenario planning, optimization of tokamak operation, and between-pulse control design.

Control-oriented tokamak simulator (COTSIM)↗

DOE OSTI2022

High Performance Equilibrium Solvers for Integrated Magnetic Fusion Simulations

With the funding provided by this award, we developed numerical codes for the study of magnetically confined plasmas for fusion applications. Accordingly, our work can be divided into two separate categories: 1) the design and analysis of novel numerical methods providing high accuracy and high efficiency; 2) the study of the equilibrium and stability of magnetically confined plasmas with some of these numerical codes, as well as the study of the nature of the turbulent behavior which may arise in the presence of instabilities. We first developed new numerical schemes based on integral equation methods for the computation of steady-state magnetic configurations in fusion experiments, providing high accuracy for the magnetic field and its derivatives, which are required for stability and turbulence calculations. We employed different integral formulations depending on the application of interest: axisymmetric or non-axisymmetric equilibria, force-free or magnetohydrodynamic equilibria, fixed-boundary equilibria or free-boundary equilibria. While efficient, these methods do not yet apply to plasma boundaries which are not smooth, a situation which is fairly common in magnetic confinement experiments. To address this temporary weakness, we also constructed a new steady-state solver based on the Hybridizable Discontinuous Galerkin (HDG) method, which provides full geometric flexibility. In addition to these numerical tools focused on steady-states, we also contributed to the improvement of the speed and accuracy of codes simulating the plasma dynamics of fusion plasmas, by developing a novel velocity space representation for the efficient solution of kinetic equations, which most accurately describe the time evolution of hot plasmas in fusion experiments. Using the tools discussed above, we studied several questions pertaining to the equilibrium and stability of magnetically confined plasmas. In particular, we derived a new simple model for axisymmetric devices called tokamaks, to predict how elongated a fusion plasma can be before it becomes unstable and collapses. We also looked at the effect of the shape of the outer plasma surface on key properties of the steady-state magnetic configurations, and how these properties impact turbulence in fusion plasmas, and the corresponding transport of momentum. Likewise, we studied the role of large localized flows on the steady-state magnetic configurations, and how they may influence plasma stability and turbulence. Non-axisymmetric steady-state magnetic configurations are inherently more complex than axisymmetric steady-state configurations, and the subject of ongoing controversies regarding the regularity of the equations determining such steady-states, and their solutions. Implementing an existing NYU code in a new geometry, we studied the nature of the singularity of the solutions observed in the code, and methods to eliminate them. Our main conclusion is that by appropriately tailoring the plasma boundary, it is possible to eliminate the singularities otherwise appearing in our simulations, and to obtain steady-states which appear to be smooth. To gain further insights on incompletely understood turbulence phenomena, we proposed a new reduced model capturing most of these phenomena, which is simple enough to not require expensive numerical simulations on massive supercomputers to investigate them. We demonstrated the strong similarity between our simulations and published results obtained from computationally expensive simulations, and plan to rely on our reduced model to identify the key mechanisms determining the evolution and strength turbulent driven transport in fusion plasmas. Finally, we proposed a new framework for tokamak reactor design studies, enabling us to consider the relative merits of steady-state versus pulsed fusion reactors. We found that pulsed fusion reactors may benefit most from recent advances in magnet technology, and the availability of very high field magnets. As such, they may become more desirable than steady-state tokamak reactors for cost efficient electricity generation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗