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DOE OSTI2023

Physics-Based Real-time Analysis and Control to Achieve Transient-Free Operations for the ITER Era (Final Report)

This is the final report for the early career award for Prof. Egemen Kolemen that aimed to develop the physics and technical basis of real-time transient – i.e. disruptions and Edge Localized Modes (ELMs) – avoidance and feedback control at the DIII-D nuclear fusion facility for the ITER era. During this project, we reconstructed high quality real-time DIII-D equilibria using kinetic information from the motional Stark effect (MSE), Thomson Scattering (TS), and Charge Exchange Recombination (CER) spectroscopy. These equilibria were analyzed in real-time to determine the low-n ideal MHD stability and the pedestal stability thresholds, and to obtain plasma response models. These calculations were used to understand which physical process evolves to lead to the onset of disruption in ITER-relevant scenarios at DIII-D, and how disruption can be predicted using stability analysis as opposed to the current methods of correlation of various signals, which are descriptive but lack predictive power. In the disruption studies, we focused on tearing modes, since these constitute the vast majority of disruptions in this regime. With this knowledge, real-time disruption avoidance algorithms were developed and tested. The enhanced situation awareness and physics insight were used in advanced real-time feedback control of pedestal and core profiles, which allowed the pursuit and sustainment of transient-free high-confinement regimes that cannot be achieved via feed-forward design based on in-between shot analysis.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Improving an Acoustic Vehicle Detector Using an Iterative Self-Supervision Procedure

In many non-canonical data science scenarios, obtaining, detecting, attributing, and annotating enough high-quality training data is the primary barrier to developing highly effective models. Moreover, in many problems that are not sufficiently defined or constrained, manually developing a training dataset can often overlook interesting phenomena that should be included. To this end, we have developed and demonstrated an iterative self-supervised learning procedure, whereby models are successfully trained and applied to new data to extract new training examples that are added to the corpus of training data. Successive generations of classifiers are then trained on this augmented corpus. Using low-frequency acoustic data collected by a network of infrasound sensors deployed around the High Flux Isotope Reactor and Radiochemical Engineering Development Center at Oak Ridge National Laboratory, we test the viability of our proposed approach to develop a powerful classifier with the goal of identifying vehicles from continuously streamed data and differentiating these from other sources of noise such as tools, people, airplanes, and wind. Using a small collection of exhaustively manually labeled data, we test several implementation details of the procedure and demonstrate its success regardless of the fidelity of the initial model used to seed the iterative procedure. Finally, we demonstrate the method’s ability to update a model to accommodate changes in the data-generating distribution encountered during long-term persistent data collection.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Implementation of a 9-point stencil in SOLPS-ITER and implications for Alcator C-Mod divertor plasma simulations

The SOLPS-ITER code suite is used worldwide for plasma edge modeling, the interpretation of experiments, as well as for the design of the ITER divertor. The numerical scheme of the plasma solver of the code, B2.5, is based on the assumption of perfectly ﬁeld-aligned grids, while in practice grids are often strongly distorted to match divertor target shapes. Neglecting these grid distortion leads to qualitatively and quantitatively incorrect results for ﬂuid neutral simulations, and may affect results in cold (detached) divertors even when using kinetic neutral simulations. In this contribution, we present the ﬁrst results of a newly implemented 9-point stencil in B2.5 to properly handle misaligned grids. The new scheme is then applied to ﬂuid neutral simulations of a well-diagnosed and previously modeled Alcator C-Mod discharge. Results are compared with the original 5-point scheme neglecting grid distortion effects, as well as with simulations including a full kinetic neutral model. We conclude that the 9-point stencil is essential to correctly model the transport of ﬂuid neutrals on distorted grids, and to capture the effects of divertor closure on the ﬂuid neutral behavior.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2018

The effect of electron cyclotron heating on density fluctuations at ion and electron scales in ITER baseline scenario discharges on the DIII-D tokamak

Experiments simulating the ITER Baseline Scenario on the DIII-D tokamak show that torque-free pure electron heating, when coupled to plasmas subject to a net co-current beam torque, affects density fluctuations at electron scales on a sub-confinement time scale, whereas fluctuations at ion scales change only after profiles have evolved to a new stationary state. Modifications to the density fluctuations measured by the Phase Contrast Imaging diagnostic (PCI) are assessed by analyzing the time evolution following the switch-off of Electron Cyclotron Heating (ECH), thus going from mixed beam/ECH to pure neutral beam heating at fixed β N . Within 20 ms after turning off ECH, the intensity of fluctuations is observed to increase at frequencies higher than 200 kHz; in contrast, fluctuations at lower frequency are seen to decrease in intensity on a longer time scale, after other equilibrium quantities have evolved. Non-linear gyro-kinetic modeling at ion and electron scales scales suggest that, while the low frequency response of the diagnostic is consistent with the dominant ITG modes being weakened by the slow-time increase in flow shear, the high frequency response is due to prompt changes to the electron temperature profile that enhance electron modes and generate a larger heat flux and an inward particle pinch. These results suggest that electron heated regimes in ITER will feature multi-scale fluctuations that might affect fusion performance via modifications to profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

L-H transition trigger physics in ITER-similar plasmas with applied n = 3 magnetic perturbations

The L–H transition power threshold PLH is observed to increase with applied n = 3 resonant magnetic perturbations (RMP) in ITER-similar-shape plasmas with balanced neutral beam torque injection in DIII-D. The increase is most pronounced with added electron–cyclotron heating: PLH increases with decreasing edge plasma collisionality as PLH/PLH-08 ~ (ν*)−0.5, where PLH-08 is the 2008 ITPA multi-machine power threshold scaling. This result raises concerns for H-mode access at low edge collisionality in ITER, where RMP may have to be applied before the L–H transition to safely suppress the first edge-localized mode. Non-axisymmetric modifications with RMP include a simultaneous reduction of the radial electric field (Er) well depth and E × B shear. This can be attributed to increasing edge toroidal co-current rotation, and is consistent with substantially increased local long-wavelength turbulence (measured via beam emission spectroscopy). At high RMP perturbation strength the edge electric field Er reverses sign locally (becomes positive), with changes in dominant turbulence modes. Edge magnetic stochasticity provides an attractive explanation of the observed modifications, and the observed changes in toroidal rotation and Er are consistent with a simple fluid model describing radial electron current flow along stochastic fieldlines. The observed collisionality dependence of the L-mode edge electric field with applied RMP is also qualitatively consistent with this model. Reflectometry data indicate a significant reduction of the normalized L-mode radial density gradient a/Ln at high RMP field with simultaneous increase in radial particle flux and electron thermal flux from power balance analysis. We conjecture that the increase of PLH with RMP results from the combined effects of reduced E × B flow shear (increasing turbulent transport levels) and toroidal/poloidal flow modulation due to edge stochasticity. Initial experiments indicate that non-resonant n = 3 magnetic perturbations lead only to relatively small changes in Er, E × B shear and fluctuation characteristics, and have less impact on the L–H transition power threshold. This motivates further exploration of the RMP spectrum dependence of PLH for possible mitigation of the observed threshold increase.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Alcator C-Mod: Research in support of ITER and steps beyond

This paper presents an overview of recent highlights from research on Alcator C-Mod. Significant progress has been made across all research areas over the last two years, with particular emphasis on divertor physics and power handling, plasma-material-interaction studies, ELM-suppressed pedestal dynamics, core transport and turbulence, and RF heating and current drive utilizing Ion Cyclotron and Lower Hybrid tools. Specific results of particular relevance to ITER include: inner wall SOL transport studies that have led, together with results from other experiments, to the change of the detailed shape of the inner wall in ITER; runaway electron studies showing that the critical electric field required for runaway generation is much higher than predicted from collisional theory; core tungsten impurity transport studies reveal that tungsten accumulation is naturally avoided in typical C-Mod conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1965

Computer modification reduces time of performing iterative division

Time reduction in performing iterative division results from using a serial-by-parallel divider employing a look-ahead feature that predetermines the sign relationships of several iterations before the computer cycle begins. This method can be employed in any data handling system performing high-speed division.

Source record↗

NASA NTRS1975

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

A technique is described for the efficient numerical solution of nonlinear partial differential equations by rapid iteration. In particular, a special approach is described for applying the Aitken acceleration formula (a simple Pade approximant) for accelerating the iterative convergence. The method finds the most appropriate successive approximations, which are in a most nearly geometric sequence, for use in the Aitken formula. Simple examples are given to illustrate the use of the method. The method is then applied to the mixed elliptic-hyperbolic problem of steady, inviscid, transonic flow over an airfoil in a subsonic free stream.

Martin, E. D.↗

NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1976

A technique for accelerating iterative convergence in numerical integration, with application in transonic aerodynamics

Martin, E. D.↗

NASA NTRS1976

Computer assisted expansion of 1/Delta series with Newton iteration

The Newton iteration method has been widely applied to the solution of various equations such as Kepler's equation. In this study it is used in planetary and satellite theory as a general procedure for Fourier series inversion. The method is used for the construction of the 1/Delta series either in literal form or in numerical form with small eccentricities and inclinations substituted in advance. This usually results in very compact series. With the Newton iteration procedure and a computerized series manipulation technique, the Fourier series of 1/Delta of the mutual perturbations among most natural satellites can be easily constructed.

Chao, C. C.↗

NASA NTRS1978

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Desideri, J. A.↗

NASA NTRS1977

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of the nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The continuous cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and symptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗

NASA NTRS1980

Modified Iterative Extended Hueckel. 1: Theory

Iterative Extended Huekel is modified by inclusion of explicit effective internuclear and electronic interactions. The one electron energies are shown to obey a variational principle because of the form of the effective electronic interactions. The modifications permit mimicking of aspects of valence bond theory with the additional feature that the energies associated with valence bond type structures are explicitly calculated. In turn, a hybrid molecular, orbital valence, bond scheme is introduced which incorporates variant total molecular electronic density distributions similar to the way that Iterative Extended Hueckel incorporates atoms.

Aronowitz, S.↗

NASA NTRS1980

Incorporation of star measurements for the determination of orbit and attitude parameters of a geosynchronous satellite: An iterative application of linear regression

Currently on NOAA/NESS's VIRGS system at the World Weather Building star images are being ingested on a daily basis. The image coordinates of the star locations are measured and stored. Subsequently, the information is used to determine the attitude, the misalignment angles between the spin axis and the principal axis of the satellite, and the precession rate and direction. This is done for both the 'East' and 'West' operational geosynchronous satellites. This orientation information is then combined with image measurements of earth based landmarks to determine the orbit of each satellite. The method for determining the orbit is simple. For each landmark measurement one determines a nominal position vector for the satellite by extending a ray from the landmark's position towards the satellite and intersecting the ray with a sphere with center coinciding with the Earth's center and with radius equal to the nominal height for a geosynchronous satellite. The apparent motion of the satellite around the Earth's center is then approximated with a Keplerian model. In turn the variations of the satellite's height, as a function of time found by using this model, are used to redetermine the successive satellite positions by again using the Earth based landmark measurements and intersecting rays from these landmarks with the newly determined spheres. This process is performed iteratively until convergence is achieved. Only three iterations are required.

Phillips, D.↗

NASA NTRS1980

Iterative methods based upon residual averaging

Iterative methods for solving boundary value problems for systems of nonlinear partial differential equations are discussed. The methods involve subtracting an average of residuals from one approximation in order to arrive at a subsequent approximation. Two abstract methods in Hilbert space are given and application of these methods to quasilinear systems to give numerical schemes for such problems is demonstrated. Potential theoretic matters related to the iteration schemes are discussed.

Neuberger, J. W.↗

NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗

NASA NTRS1983

Minimizing inner product data dependencies in conjugate gradient iteration

The amount of concurrency available in conjugate gradient iteration is limited by the summations required in the inner product computations. The inner product of two vectors of length N requires time c log(N), if N or more processors are available. This paper describes an algebraic restructuring of the conjugate gradient algorithm which minimizes data dependencies due to inner product calculations. After an initial start up, the new algorithm can perform a conjugate gradient iteration in time c*log(log(N)).

Vanrosendale, J.↗