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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A comparative study of internal kink stability in EU DEMO designs with negative and positive triangularity

Abstract Internal kink (IK) instability is investigated for European demonstration fusion reactor (EU DEMO) plasmas in both negative triangularity (NT) and positive triangularity (PT) configurations. For NT plasmas, the IK becomes more unstable as an ideal conformal wall moves away from the plasma boundary, with the mode growth rate saturating at the wall radial location of about b / a = 1.5 , where a is the plasma minor radius and b the wall radial location. The plasma resistivity destabilizes the IK mode. The effect of sub-sonic toroidal plasma flow is sufficiently weak and can thus be ignored for these EU DEMO equilibria. These results are consistent with those for PT plasmas, albeit with larger mode growth rate in the NT configuration. Both perturbative and self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid calculations predict (partial) stabilization of the IK modes in both NT and PT configurations, with inclusion of various kinetic contributions. Precessional drift motion of trapped fusion-born alphas in EU DEMO produces weak stabilization to the IK mode. Stronger stabilization occurs with the toroidal precession of trapped thermal particles (ions and electrons) and the bounce-transit motion of thermal ions. The stabilization is similar between the NT and PT configurations, due to the similarity of the mode eigenfunction (occupying a nearly circular region in the plasma core) despite the sign difference in the triangularity. The non-perturbative MHD-kinetic hybrid model predicts much less stabilization of the mode than the perturbative model, primarily due to the self-consistent determination of the mode eigenvalue in the former. Generally, no significant difference in the IK mode stability is found between the NT and PT plasmas in EU DEMO.

Physics↗
DOE OSTI2021

Numerical investigation of active control of tearing mode by magnetic coils and the role of Δ'

Magnetic feedback stabilization of the tearing mode (TM) is numerically investigated, utilizing the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) for toroidal tokamak equilibria. With control coil configurations assumed in this study, magnetic feedback partially or fully stabilizes the TM, with either vanishing or finite equilibrium pressure. The best control is achieved by the combination of internal active coils and internal poloidal sensors. The internal and external tearing indices are evaluated for the close-loop system, based on the MARS-F computed mode eigenvalue and eigenfunction, respectively. In the absence of the favorable curvature effect, these two indices are real-valued and quantitatively agree well with each other. For the equilibrium with finite pressure gradient at the mode rational surface, the favorable average curvature effect becomes important and the close-loop tearing index also becomes complex-valued, partly due to interaction of the feedback system with the dissipative wall eddy current response. Isolating the inner layer and outer region response to magnetic feedback, with either proportional or proportional-derivative actions, allows to establish that feedback stabilization of the TM occurs mainly due to modification of the behavior of the external ideal solution, further confirming the analytic result reported in He et al 2021 Phys. Plasmas 28 012504.

Physics↗
DOE OSTI2022

Fast calculation of the tokamak vertical instability

There has been recent interest in fast calculations of the tokamak axisymmetric vertical instability for real time feedback control purposes. It is shown that the maximum eigenvalue for the basic rigid version of this stability problem can be obtained by finding the positive root to a simple scalar function. This function can be generalized to include plasma mass and has complexity linear in the number of conductive elements. The formulation is based on standard matrix decompositions of the fixed-geometry part of the eigenproblem. The calculation bottleneck is the summary of mutual inductances from the reconstructed equilibrium current density. The with-mass spectrum can be made fully real-valued by the addition of a critical amount of damping with negligible effect on the vertical growth rate. Furthermore, the calculation has been implemented in the plasma control system at the DIII-D tokamak and used in experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

A non-orthogonal variational quantum eigensolver

Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for the systematic improvement of a logical wavefunction ansatz without a significant increase in circuit complexity. To minimize the circuit complexity of this approach, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. This strategy doubles the size of the state preparation circuits but not their depth, while adding a small number of additional two-qubit gates relative to standard variational quantum eigensolver. We also propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of the matrix elements. We explain how this Monte Carlo procedure can be extended to adaptively schedule the required measurements, reducing the number of circuit executions necessary for a given accuracy. We apply these ideas to two model strongly correlated systems, a square configuration of H4 and the π-system of hexatriene (C6H8).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quantum simulation of excited states from parallel contracted quantum eigensolvers

Abstract Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

Physics↗
DOE OSTI2024

Superconductor to exciton condensate transition in a model copper-oxide material

Abstract Superconductivity and exciton condensation are fundamental phenomena in condensed matter physics, associated with the condensation of electron–electron and electron–hole pairs, respectively, into coherent quantum states. In this study, we present evidence of a superconductor to exciton condensate transition within the context of the three-band Hubbard model of copper-oxide-like materials. As the electron–electron repulsion increases, the superconducting phase is superseded by exciton condensation. In support of theoretical predictions—not yet realized experimentally—we observe the coexistence of the two condensates in the vicinity of the transition where the quantum states become a superposition of electron–electron and electron–hole condensates. Coexistence is rigorously computed from large eigenvalues and their eigenvectors in both the two-electron reduced density matrix (2-RDM) and the particle-hole RDM, which we obtain from a direct variational ground-state energy minimization with respect to the 2-RDM by semidefinite programming. We further discern that adjacent d orbitals and intervening p orbitals facilitate electron–electron pairing between copper orbitals, thereby supporting the superexchange mechanism for superconductivity. These observations suggest the feasibility of witnessing a superconductor to exciton condensate transition in copper-oxide analogs, bearing significant implications for identifying materials conducive to efficient transport processes.

Schouten, Anna O. (ORCID:0000000264255219)↗
DOE OSTI2023

A solvable model of a nonlinear extension of quantum mechanics

We introduce a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics problem. Here, we hope that this simple example will elucidate some of the issues of interpreting nonlinear generalization of quantum mechanics that have been put forth to resolve questions about quantum measurement theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Simulation of MHD instabilities with fluid runaway electron model in M3D- C 1

Runaway electrons are generated in a tokamak during the start up, during normal operation and during a plasma disruption. During a disruption, runaway electrons can be accelerated to high energies, potentially damaging the first wall. To predict the consequences of runaway generation during a disruption, it is necessary to consider resonant interactions of runaways with the bulk plasma. Here we consider the interactions of runaways on low mode number tearing modes. We have developed a fluid runaway electron model for the 3D MHD code M3D-C1[Jardin,et al. J Comput. Sci Discovery 6 014002 (2012)]. To benchmark, we have reproduced the MHD linear tearing mode results (with runaway electrons) in a circular cylinder presented in previous analytic studies[[Helander, P., et al, Phys. Plasmas 14 144102 (2007)] and extended here with a numerical eigenvalue calculation. Furthermore, we find that the low mode number tearing mode has a rotation caused by the MHD - runaways interaction, and the toroidal current scale length is much smaller with runaways than that for without and decreases as the runaway speed increases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

On the role of mode resonances in regulating zonal-flow-moderated plasma microturbulence

Abstract The onset of turbulent heat transport at a higher temperature gradient than the critical gradient of linear instability, known as the Dimits shift, is a recurring feature of nonlinear simulations for magnetically confined fusion plasmas. Resonance in the nonlinear coupling between the modes that dominate energy transfer can lead to suppression of turbulence and transport above the linear critical gradient. As an expression of this resonance, gyrokinetic simulations show a quasi-coherent interaction between streamers and sidebands coupled through the zonal flow within the Dimits regime. This mechanism is further confirmed by use of artificial complex frequencies which break the resonance. By incorporating corresponding saturation physics, the standard quasilinear model for rapid head flux prediction is improved, which can now predict reduced heat flux in the Dimits regime. In particular, the triplet correlation time, the lifetime of the nonlinear interaction, is shown to be well-approximated by combinations of linear eigenvalues, and yields good representations of the heat flux variation both in and above the Dimits regime. Thus, a reduced but predictive model for transport near the critical gradient of zonal-flow saturated turbulence now exists.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Real time detection of multiple stable MHD eigenmode growth rates towards kink/tearing modes avoidance in DIII-D tokamak plasmas

Abstract Real time detection of time evolving growth rates of multiple stable magnetohydrodynamic (MHD) eigenmodes has been achieved in DIII-D tokamak experiments via multi-mode three-dimensional (3D) active MHD spectroscopy. The measured evolution of the multi-modes’ growth rates is in good accordance with the variation of the plasma β N . Using experimental equilibria, resistive MARS-F simulations found the two least stable modes to have comparable growth rates to those experimentally measured. Real time and offline calculations of the modes’ growth rates show comparable results and indicate that cleaner system input and output signals will improve the accuracy of the real time stability detection. Moreover, the shortest real time updating time window of multi-mode eigenvalues can be about 2 ms in DIII-D experiments. This real time monitoring of stable, macroscopic kink and tearing modes thus provides an effective tool for avoidance of the most common causes of tokamak disruption.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Gaps labeling theorem for the bubble-diamond self-similar graphs

Abstract Motivated by the appearance of fractals in several areas of physics, especially in solid state physics and the physics of aperiodic order, and in other sciences, including the quantum information theory, we present a detailed spectral analysis for a new class of fractal-type diamond graphs, referred to as bubble-diamond graphs, and provide a gap-labeling theorem in the sense of Bellissard for the corresponding probabilistic graph Laplacians using the technique of spectral decimation. Labeling the gaps in the Cantor set by the normalized eigenvalue counting function, also known as the integrated density of states, we describe the gap labels as orbits of a second dynamical system that reflects the branching parameter of the bubble construction and the decimation structure. The spectrum of the natural Laplacian on limit graphs is shown generically to be pure point supported on a Cantor set, though one particular graph has a mixture of pure point and singularly continuous components.

Physics↗
DOE OSTI2024

Integrating subsystem embedding subalgebras and coupled cluster Green’s function: a theoretical foundation for quantum embedding in excitation manifold

Here, in this study, we introduce a novel approach to coupled-cluster Green's function (CCGF) embedding by seamlessly integrating conventional CCGF theory with the state-of-the-art sub-system embedding sub-algebras coupled cluster (SES-CC) formalism. This integration focuses primarily on delineating the characteristics of the sub-system and the corresponding segments of the Green's function, defined explicitly by active orbitals. Crucially, our work involves the adaptation of the SES-CC paradigm, addressing the left eigenvalue problem through a distinct form of Hamiltonian similarity transformation. This advancement not only facilitates a comprehensive representation of the interaction between the embedded sub-system and its surrounding environment but also paves the way for the quantum mechanical description of multiple embedded domains, particularly by employing the emergent quantum flow algorithms. Our theoretical underpinnings further set the stage for a generalization to multiple embedded sub-systems. This expansion holds significant promise for the exploration and application of non-equilibrium quantum systems, enhancing the understanding of system–environment interactions. In doing so, the research underscores the potential of SES-CC embedding within the realm of quantum computations and multi-scale simulations, promising a good balance between accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Exploiting a derivative discontinuity estimate for accurate G0W0 ionization potentials and electron affinities

Abstract The GW approximation has become an important tool for predicting charged excitations of isolated molecules and condensed systems. Its popularity can be attributed to many factors, including a favorable scaling and relatively good accuracy. In practical applications, the GW is often performed as a one-shot perturbation known as G 0 W 0 . Unfortunately, G 0 W 0 suffers from a strong starting point dependence and is often not as accurate as one would need. Self-consistent GW methodologies alleviate these problems but come with a marked increase in computational cost. In this manuscript, we propose the use of an estimate of the exchange-correlation derivative discontinuity to provide a remarkably good starting point for G 0 W 0 calculations, yielding ionization potentials and electron affinities with eigenvalue self-consistent GW quality at no additional cost. We assess the quality of the resulting methodology with the GW 100 benchmark set and compare its advantages over other similar methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Analog and symbolic computation through the Koopman framework

We develop a Koopman operator framework for studying the computational structure of dynamical systems. Specifically, we show that the resolvent of the Koopman operator provides a natural abstraction of halting, yielding a ‘Koopman halting problem’ that is recursively enumerable in general. For symbolic systems, such as those defined on Cantor space, this operator formulation captures reachability between clopen sets, while for equicontinuous systems we prove that the Koopman halting problem is decidable. Our framework demonstrates that absorbing (halting) states in coarse-grained finite automata correspond to Koopman eigenfunctions with eigenvalue one, while cycles in the transition graph impose spectral constraints associated with periodic dynamics. These results provide a unifying perspective on computation in symbolic and analog systems, showing how computational universality is reflected in operator spectra, invariant subspaces, and algebraic structures. Beyond symbolic dynamics, this operator-theoretic lens opens pathways to analyze the computational properties of a broader class of dynamical systems, including polynomial and analog models, and suggests that computational hardness may admit dynamical signatures in terms of Koopman spectral structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
DOE OSTI2022

An efficient method to propagate model uncertainty when inverting seismic data for time domain seismic moment tensors

SUMMARY We present a computationally efficient method to approximately propagate uncertainty when linearly inverting seismic data for point source, time variable moment tensor components. The method is based on the assumption that the data residual, given by the difference between the observed seismic data and the data predicated by a linear inversion, contains the effects of both data and model uncertainty. Our method uses a distribution of data residuals, added directly to the data, in a pseudo-Monte Carlo scheme. Using the assumption that the data residual is a stochastic process, we use the well-known Karhunen–Loève (KL) theorem to construct a distribution of data residuals, where the required basis functions are constructed using Fourier series. The Fourier series are scaled by a product of a random variable and the real-valued spectral amplitudes of the original data residual’s spectrum. Thus, the Fourier series and spectral amplitudes are eigenfunction-eigenvalue pairs used in the KL-based construction of data residual distribution. Using tests with synthetic data, we show that our method compares closely with a Finite Difference Monte Carlo (FDMC) method that we presented previously. More importantly, the method presented here is computationally several orders of magnitude faster than our previous FDMC method, and requires no a priori assumptions of model and/or data uncertainty.

Poppeliers, Christian (ORCID:0000000159526849)↗
DOE OSTI2022

Clustering with general photo- z uncertainties: application to Baryon Acoustic Oscillations

ABSTRACT Photometric data can be analysed using the 3D correlation function ξp to extract cosmological information via e.g. measurement of the Baryon Acoustic Oscillations (BAO). Previous studies modeled ξp assuming a Gaussian photo-z approximation. In this work we improve the modeling by incorporating realistic photo-z distribution. We show that the position of the BAO scale in ξp is determined by the photo-z distribution and the Jacobian of the transformation. The latter diverges at the transverse scale of the separation s⊥, and it explains why ξp traces the underlying correlation function at s⊥, rather than s, when the photo-z uncertainty σz/(1+ z) ≳ 0.02. We also obtain the Gaussian covariance for ξp. Due to photo-z mixing, the covariance of ξp shows strong off-diagonal elements. The high correlation of the data causes some issues to the data fitting. None the less, we find that either it can be solved by suppressing the largest eigenvalues of the covariance or it is not directly related to the BAO. We test our BAO fitting pipeline using a set of mock catalogs. The data set is dedicated for Dark Energy Survey Year 3 (DES Y3) BAO analyses and includes realistic photo-z distributions. The theory template is in good agreement with mock measurement. Based on the DES Y3 mocks, ξp statistic is forecast to constrain the BAO shift parameter α to be 1.001 ± 0.023, which is well consistent with the corresponding constraint derived from the angular correlation function measurements. Thus, ξp offers a competitive alternative for the photometric data analyses.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

AlgoSCR: an algorithm for solar contamination removal from radio interferometric data

Hydrogen intensity mapping is a new field in astronomy that promises to make three-dimensional maps of the matter distribution of the Universe using the redshifted 21cm line of neutral hydrogen gas (HI). Several ongoing and upcoming radio interferometers, such as Tianlai, CHIME, HERA, HIRAX, etc., are using this technique. These instruments are designed to map large swaths of the sky by drift scanning over periods of many months. One of the challenges of the observations is that the daytime data are contaminated by strong radio signals from the Sun. In the case of Tianlai, this results in almost half of the measured data being unusable. We try to address this issue by developing an algorithm for solar contamination removal (AlgoSCR) from the radio data. The algorithm is based on an eigenvalue analysis of the visibility matrix and hence is applicable only to interferometers. We apply AlgoSCR to simulated visibilities, as well as real daytime data from the Tianlai dish array. The algorithm can reduce strong solar contamination by about 95 per cent without seriously affecting other weaker sky signals and thus makes the data usable for certain applications.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗