Search NASA⌕ Search

SEARCH · Search NASA

Results for “rotational transform”

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.

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

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Importance of the Rotational Transform for L–H Transitions in the TJ-II Stellarator

We study the effect of the rotational transform profile on the L–H confinement transitions in the neutral beam-heated plasmas in the TJ-II stellarator. The rotational transform profile in the vacuum is determined by the external coil currents but is modified by the plasma current, Ip. We find that L–H confinement transitions systematically occur when the configuration and plasma current are such that a low-order rational is placed in the plasma edge region, with a distribution centered around ρ=0.8±0.05. It is suggested that magnetohydrodynamic turbulence plays an important role in triggering the L–H transitions at TJ-II.

van Milligen, Boudewijn Philip (ORCID:000000015344↗
DOE OSTI2025

Application of Lagrangian techniques for calculating the on-axis rotational transform

The Floquet exponents of periodic field lines are studied through the variations of the magnetic action on the magnetic axis, which is assumed to be elliptical. The near-axis formalism developed by Mercier, Solov'ev and Shafranov is combined with a Lagrangian approach. The on-axis Floquet exponent is shown to coincide with the on-axis rotational transform. A discrete solution suitable for numerical implementation is introduced, which gives the Floquet exponents as solutions to an eigenvalue problem. This discrete formalism expresses the exponents as the eigenvalues of a $6$ X $6$ matrix.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Modeling of frequency-sweeping Alfvén modes in the TJ-II stellarator

Alfvénic activity has been observed in the TJ-II stellarator which resembles the frequency sweeping demonstrated by Alfvén cascade modes in tokamaks. A numerical validation study was conducted using a reduced magnetohydrodynamic (MHD) model to show that such modes could only have been observed in discharges where the rotational transform profile was non-monotonic. During experiments, coil current was varied which resulted in shifting of the minimum value of the rotational transform profile. To mimic this effect, we study the Alfvénic activity predicted by the reduced MHD model for a set of input rotational transform profiles with varying minima. A mode is found whose toroidal and poloidal mode numbers match those predicted in experiments which sweeps downward/upward in frequency as the minimum value of the rotational transform profile is increased/decreased. The results serve as a demonstration of the validity and utility of MHD spectroscopy.

Alfvén cascades↗
DOE OSTI2022

Rational surfaces, flows and radial structure in the TJ-II stellarator

Abstract In this work, we report on the results obtained by measuring several turbulent quantities well inside the plasma edge by means of a Langmuir probe during dynamical rotational transform scans in the TJ-II stellarator, while applying a radial electric field to the edge plasma using a biasing probe. By calculating the intermittence parameter from floating potential measurements, we are able to identify a major low order rational surface and hence relate the probe measurements to the local value of the rotational transform. Based on the former, we are able to show that the poloidal plasma velocity (and hence radial electric field) has a significant radial structure that is clearly related to the rotational transform profile and in particular the lowest order rational surfaces in the range studied. The poloidal velocity is also affected by the edge biasing. The particle flux Γ was also found to exhibit a radial pattern, as did the flow shear suppression term ω E × B , but the relation of the former to the low-order rational surfaces was less clear. We surmise that this lack of direct correspondence is due to an unknown term in the turbulence evolution equation: the instability growth rate, γ . We make use of a reduced Magnetohydrodynamic turbulence model to interpret the results. Overall, a picture is obtained in which the plasma self-organizes towards a state with a clear radial pattern of the radial electric field, in line with expectations from some numerical studies describing the spontaneous formation of an ‘ E × B staircase’, consisting of alternating layers with fast and slow radial transport. In this state, the radial profiles of various quantities (density, temperature, pressure) will not be smooth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Magnetic configuration scans during divertor operation of Wendelstein 7-X

Wendelstein 7-X (W7-X) (Greifswald, Germany) is an advanced stellarator, which uses the modular coil concept to realize a magnetic configuration optimized for fusion-relevant plasma properties. The magnet system of the machine allows a variation of the rotational transform (iota) at the boundary. In the latest W7-X operational phase a dedicated configuration scan has been performed varying the rotational transform between magnetic configurations with iota = 5/4 and iota = 5/5 at the boundary. This paper presents an overview of the experiments and of the main results with respect to confinement and stability. The main observation is an increase of the plasma energy in several intermediate configurations of the scan when the 5/5-islands are close to the plasma boundary but still inside the last-closed-flux-surface. In addition, these configurations showed marked MHD-activity with a crashing behavior related to the 5/5-islands. The corresponding mode amplitude was correlated with the size of the internal 5/5 islands.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Near-axis expansion of stellarator equilibrium at arbitrary order in the distance to the axis

A direct construction of equilibrium magnetic fields with toroidal topology at arbitrary order in the distance from the magnetic axis is carried out, yielding an analytical framework able to explore the landscape of possible magnetic flux surfaces in the vicinity of the axis. This framework can provide meaningful analytical insight into the character of high-aspect-ratio stellarator shapes, such as the dependence of the rotational transform and the plasma beta limit on geometrical properties of the resulting flux surfaces. The approach developed here is based on an asymptotic expansion on the inverse aspect ratio of the ideal magnetohydrodynamics equation. The analysis is simplified by using an orthogonal coordinate system relative to the Frenet–Serret frame at the magnetic axis. The magnetic field vector, the toroidal magnetic flux, the current density, the field line label and the rotational transform are derived at arbitrary order in the expansion parameter. Moreover, a comparison with a near-axis expansion formalism employing an inverse coordinate method based on Boozer coordinates (the so-called Garren–Boozer construction) is made, where both methods are shown to agree at lowest order. Finally, as a practical example, a numerical solution using a W7-X equilibrium is presented, and a comparison between the lowest-order solution and the W7-X magnetic field is performed.

Physics↗
DOE OSTI2023

Protein model quality assessment using rotation–equivariant transformations on point clouds

Machine learning research concerning protein structure has seen a surge in popularity over the last years with promising advances for basic science and drug discovery. Working with macromolecular structure in a machine learning context requires an adequate numerical representation, and researchers have extensively studied representations such as graphs, discretized 3D grids, and distance maps. As part of CASP14, we explored a new and conceptually simple representation in a blind experiment: atoms as points in 3D, each with associated features. These features—initially just the basic element type of each atom—are updated through a series of neural network layers featuring rotation-equivariant convolutions. Starting from all atoms, we further aggregate information at the level of alpha carbons before making a prediction at the level of the entire protein structure. We find that this approach yields competitive results in protein model quality assessment despite its simplicity and despite the fact that it incorporates minimal prior information and is trained on relatively little data. As a result, its performance and generality are particularly noteworthy in an era where highly complex, customized machine learning methods such as AlphaFold 2 have come to dominate protein structure prediction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Stellarator coil optimization supporting multiple magnetic configurations

Abstract We present a technique that can be used to design stellarators with a high degree of experimental flexibility. For our purposes, flexibility is defined by the range of values the rotational transform can take on the magnetic axis of the vacuum field while maintaining satisfactory quasisymmetry. We show that accounting for configuration flexibility during the modular coil design improves flexibility beyond that attained by previous methods. Careful placement of planar control coils and the incorporation of an integrability objective enhance the quasisymmetry and nested flux surface volume of each configuration. We show that it is possible to achieve flexibility, quasisymmetry, and nested flux surface volume to reasonable degrees with a relatively simple coil set through an NCSX-like example. This example coil design is optimized to achieve three rotational transform targets and nested flux surface volumes in each magnetic configuration larger than the NCSX design plasma volume. Our work suggests that there is a tradeoff between flexibility, quasisymmetry, and volume of nested flux surfaces.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Statistical Analysis of the Limiting Dynamics of Two dimensional Boussinesq Turbulent Systems

In the current study, we investigate rotational and stratified turbulent systems within the framework of the Boussinesq equations. The effects of rotation and stratification give rise to a variety of dynamical regimes in atmospheric and oceanic turbulence. To develop a better understanding of the fundamental flow properties through a more straightforward mathematical framework, we commence our research with a simplified two-dimensional Boussinesq model that incorporates rotation and stratification effects. We explore two distinct limiting dynamics, considering pure rotation and pure stratification separately. We examine these intriguing dynamics through numerical investigations, applying the exact solution theory of Boussinesq equations and examining small-scale perturbations to the exact solution under rotation and stratification. We conduct an analysis of statistical quantities associated with the turbulent state variables. The results indicate that, under weak rotation at the equilibrium statistical state, the flow field exhibits vortex flow. However, strong rotation transforms the flow into vertical shear flow. We observe both downscale and upscale energy transfers with a decay rate of k −3 in the absence of external forcing and dissipation. Furthermore, we delve into the study of internal gravity wave mode interactions in the simplified two-dimensional Boussinesq system, which is a crucial aspect of geophysical turbulence due to gravity. Our findings reveal that the time series of the mode coefficients exhibit wave-like interactions between wave modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Single-stage gradient-based stellarator coil design: Optimization for near-axis quasi-symmetry

Here we present a new coil design paradigm for magnetic confinement in stellarators. Our approach directly optimizes coil shapes and coil currents to produce a vacuum quasi-symmetric magnetic field with a target rotational transform on the magnetic axis. This approach differs from the traditional two-stage approach in which first a magnetic configuration with desirable physics properties is found, and then coils to approximately realize this magnetic configuration are designed. The proposed single-stage approach allows us to find a compromise between confinement and engineering requirements, i.e., find easy-to-build coils with good confinement properties. Using forward and adjoint sensitivities, we derive derivatives of the physical quantities in the objective, which is constrained by a nonlinear periodic differential equation. In two numerical examples, we compare different gradient-based descent algorithms and find that incorporating approximate second-order derivative information through a quasi-Newton method is crucial for convergence. We also explore the optimization landscape in the neighborhood of a minimizer and find many directions in which the objective is mostly flat, indicating ample freedom to find simple and thus easy-to-build coils.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Gradient-based optimization of 3D MHD equilibria

Using recently developed adjoint methods for computing the shape derivatives of functions that depend on magnetohydrodynamic (MHD) equilibria (Antonsen et al. , J. Plasma Phys. , vol. 85, issue 2, 2019; Paul et al. , J. Plasma Phys. , vol. 86, issue 1, 2020), we present the first example of analytic gradient-based optimization of fixed-boundary stellarator equilibria. We take advantage of gradient information to optimize figures of merit of relevance for stellarator design, including the rotational transform, magnetic well and quasi-symmetry near the axis. With the application of the adjoint method, we reduce the number of equilibrium evaluations by the dimension of the optimization space ( ${\sim }50\text {--}500$ ) in comparison with a finite-difference gradient-based method. We discuss regularization objectives of relevance for fixed-boundary optimization, including a novel method that prevents self-intersection of the plasma boundary. We present several optimized equilibria, including a vacuum field with very low magnetic shear throughout the volume.

Physics↗
DOE OSTI2022

Adjoint methods for quasi-symmetry of vacuum fields on a surface

Adjoint methods can speed up stellarator optimisation by providing gradient information more efficiently compared with finite-difference evaluations. Adjoint methods are herein applied to vacuum magnetic fields, with objective functions targeting quasi-symmetry and a rotational transform value on a surface. Here to measure quasi-symmetry, a novel way of evaluating approximate flux coordinates on a single flux surface without the assumption of a neighbourhood of flux surfaces is proposed. The shape gradients obtained from the adjoint formalism are evaluated numerically and verified against finite-difference evaluations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Direct computation of magnetic surfaces in Boozer coordinates and coil optimization for quasisymmetry

We propose a new method to compute magnetic surfaces that are parametrized in Boozer coordinates for vacuum magnetic fields. We also propose a measure for quasisymmetry on the computed surfaces and use it to design coils that generate a magnetic field that is quasisymmetric on those surfaces. The rotational transform of the field and complexity measures for the coils are also controlled in the design problem. Using an adjoint approach, we are able to obtain analytic derivatives for this optimization problem, yielding an efficient gradient-based algorithm. Starting from an initial coil set that presents nested magnetic surfaces for a large fraction of the volume, our method converges rapidly to coil systems generating fields with excellent quasisymmetry and low particle losses. In particular for low complexity coils, we are able to significantly improve the performance compared with coils obtained from the standard two-stage approach, e.g. reduce losses of fusion-produced alpha particles born at half-radius from $17.7\,\%$ to $6.6\,\%$ . We also demonstrate 16-coil configurations with alpha loss ${<}1\,\%$ and neoclassical transport magnitude $\epsilon _{\text {eff}}^{3/2}$ less than approximately $5\times 10^{-9}$ .

Physics↗
DOE OSTI2022

Power-transfer and fixed-point analysis of sawtooth simulations of a current-carrying stellarator

Power-transfer and fixed-point analysis of previous NIMROD simulations (Roberds et al. , Phys. Plasmas , vol. 23, issue 9, 2016, 092513) improved the understanding of the effect of 3D (non-axisymmetric equilibrium) magnetic fields on sawtooth oscillations in the Compact Toroidal Hybrid (CTH) experiment. Computing the locations of order-1 fixed points, their Greene's residues, and local values for the rotational transform results in a description of CTH sawteeth consistent with Kadomtsev's model. A power-transfer analysis quantifies the distribution of energy among toroidal Fourier modes and their nonlinear interactions. The Lorentz power transfer drives sawtooth growth, and it is unambiguously interpreted as the flow of energy from toroidal mode $n'$ to mode $n$ , catalysed by $\boldsymbol {B}_{n-n'}$ . It has been reported previously that the CTH sawtooth frequency increases with the 3D field strength. This is attributed to an increased growth rate of the internal kink that drives sawtooth oscillations. Here, 3D fields remove energy from the kink, eliminating the possibility that these fields are an additional energy source that drives growth. Instead, 3D fields catalyse energy transfer from large-to-small scales, where magnetic reconnection is stronger. It is proposed that this energy transfer increases the reconnection rate at small scales, which is consistent with the increased growth rate observed at higher 3D field strengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

The DESC stellarator code suite. Part 2. Perturbation and continuation methods

A new perturbation and continuation method is presented for computing and analysing stellarator equilibria. The method is formally derived from a series expansion about the equilibrium condition $\boldsymbol {F} \equiv \boldsymbol {J}\times \boldsymbol {B} - \boldsymbol {\nabla } p = 0$ , and an efficient algorithm for computing solutions to second- and third-order perturbations is developed. The method has been implemented in the DESC stellarator equilibrium code, using automatic differentiation to compute the required derivatives. Examples are shown demonstrating its use for computing complicated equilibria, perturbing a tokamak into a stellarator and performing parameter scans in pressure, rotational transform and boundary shape in a fraction of the time required for a full solution.

Conlin, Rory (ORCID:0000000183662111)↗
DOE OSTI2024

Exploration of the parameter space of quasisymmetric stellarator vacuum fields through adjoint optimisation

Optimising stellarators for quasisymmetry leads to strongly reduced collisional transport and energetic particle losses compared with unoptimised configurations. Although stellarators with precise quasisymmetry have been obtained in the past, it remains unclear how broad the parameter space is where good quasisymmetry may be achieved. We study the range of aspect ratios and rotational transform values for which stellarators with excellent quasisymmetry on the boundary can be obtained. A large number of Fourier harmonics is included in the boundary representation, which is made computationally tractable by the use of adjoint methods to enable fast gradient-based optimisation and by the direct optimisation of vacuum magnetic fields, which converge more robustly compared with solutions from magnetohydrostatics. Several novel configurations are presented, including stellarators with record levels of quasisymmetry on a surface, three field period quasiaxisymmetric stellarators with substantial magnetic shear, and compact quasisymmetric stellarators at low aspect ratios similar to tokamaks.

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

A new approach to the design of surface subsystems of polymeric insulators for HV and MV apparatus under AC voltage

The design of high voltage and medium voltage AC and DC standoff insulators, and, in general, of insulation systems where surface and interface properties are predominant factors, is based on specifications and standards that rely upon long-term experiences and lab testing. Surface insulating properties depend on electrical and thermal stresses, besides environmental factors, and the inception of extrinsic ageing phenomena, such as partial discharges, can be already a cause of reduced reliability and premature failure (for organic insulating materials). An innovative approach, based on field simulation, discharge modelling, and partial discharge inception measurements is presented by the authors, which can establish a solid basis to optimise insulation design for any type of supply voltage waveform. This method, the three-leg approach, is applied here to a cable system under AC sinusoidal voltage, but it can work for any type of insulation system, such as bushings, switch gears, transformers, rotating machines, and power electronics boards.

42 ENGINEERING↗