Engineering topics

Terry, P. W.

Publications and source records attributed to Terry, P. W..

13 records

DOE OSTI2025

Suppressing trapped-electron-mode-driven turbulence via optimization of three-dimensional shaping

Abstract Turbulent transport driven by trapped electron modes (TEMs) is believed to drive significant heat and particle transport in quasihelically symmetric stellarators. Two three-dimensionally-shaped magnetic configurations with suppressed TEM-driven turbulence were generated through optimization that targeted quasihelical symmetry and the available energy of trapped electrons. Initial equilibria have flux surface shapes with a helically rotating negative triangularity (NT) and positive triangularity (PT). In gyrokinetic simulations, TEMs are suppressed in the reduced-TEM NT and PT configurations, showing that NT does not have the same beneficial turbulence properties over PT as seen in tokamaks. Heat fluxes from TEMs are also suppressed. Without temperature gradients and with a strong density gradient, the most unstable modes at low k y were consistent with toroidal universal instabilities (UIs) in the NT case and slab UIs in the PT case. Nonlinear simulations show that UIs drive substantial heat flux in both the NT and PT configurations. A moderate increase in β halves the heat flux in the NT configuration, while suppressing the heat flux in the PT geometry. Based on the present work, future optimizations aimed at reducing electrostatic drift wave-driven turbulent transport will need to consider UIs if β is sufficiently small.

Duff, J. M. (ORCID:0000000153086694)↗

DOE OSTI2022

Near-cancellation of up- and down-gradient momentum transport in forced magnetized shear-flow turbulence

Visco-resistive magnetohydrodynamic turbulence, driven by a two-dimensional unstable shear layer that is maintained by an imposed body force, is examined by decomposing it into dissipationless linear eigenmodes of the initial profiles. The down-gradient momentum flux, as expected, originates from the large-scale instability. However, continual up-gradient momentum transport by large-scale linearly stable but nonlinearly excited eigenmodes is identified and found to nearly cancel the down-gradient transport by unstable modes. The stable modes effectuate this by depleting the large-scale turbulent fluctuations via energy transfer to the mean flow. This establishes a physical mechanism underlying the long-known observation that coherent vortices formed from nonlinear saturation of the instability reduce turbulent transport and fluctuations, as such vortices are composed of both the stable and unstable modes, which are nearly equal in their amplitudes. The impact of magnetic fields on the nonlinearly excited stable modes is then quantified. Furthermore, even when imposing a strong magnetic field that almost completely suppresses the instability, the up-gradient transport by the stable modes is at least two-thirds of the down-gradient transport by the unstable modes, whereas for weaker fields, this fraction reaches up to 98%. These effects are persistent with variations in magnetic Prandtl number and forcing strength. Finally, continuum modes are shown to be energetically less important, but essential for capturing the magnetic fluctuations and Maxwell stress. A simple analytical scaling law is derived for their saturated turbulent amplitudes. It predicts the falloff rate as the inverse of the Fourier wavenumber, a property which is confirmed in numerical simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Improving the stellarator through advances in plasma theory

Improvements to the stellarator concept can be realized through advancements in theoretical and computational plasma physics. Herein, recent advances are reported in the topical areas of: (1) improved energetic ion confinement, (2) the impact of three-dimensional (3D) shaping on turbulent transport, (3) reducing coil complexity, (4) novel optimization and design methods, and (5) computational magnetohydrodynamic tools. Furthermore, these advances enable the development of new stellarator configurations with improved confinement properties.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Effect of triangularity on ion-temperature-gradient-driven turbulence

The linear and nonlinear properties of ion-temperature-gradient-driven turbulence with adiabatic electrons are modeled for axisymmetric configurations for a broad range of triangularities δ, both negative and positive. Peak linear growth rates decrease with negative δ but increase and shift toward a finite radial wavenumber kx with positive δ. The growth-rate spectrum broadens as a function of kx with negative δ and significantly narrows with positive δ. Here, the effect of triangularity on linear instability properties can be explained through its impact on magnetic polarization and curvature. Nonlinear heat flux is weakly dependent on triangularity for |δ|≤0.5, decreasing significantly with extreme δ, regardless of sign. Zonal modes play an important role in nonlinear saturation in the configurations studied, and artificially suppressing zonal modes increased nonlinear heat flux by a factor of about four for negative δ, increasing with positive δ by almost a factor of 20. Proxies for zonal-flow damping and drive suggest that zonal flows are enhanced with increasing positive δ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Saturation physics of threshold heat-flux reduction

The saturation physics of ion-temperature-gradient-driven turbulence is examined in relation to the temperature-gradient variation of the heat flux, which can exhibit an upshift of the critical gradient for significant flux relative to the linear instability threshold. Gyrokinetic measurements of saturation properties and spectral energy transfer, which will be defined in Sec. II, are presented, indicating that the physics of saturation is fundamentally unchanged on either side of the upshifted gradient. To analyze heat transport below and above the upshifted critical gradient, a fluid model for toroidal ion-temperature-gradient turbulence is modified to include the kinetic instability threshold. The model and the heat flux are rendered in the eigenmode decomposition to track the dominant mode-coupling channel of zonal-flow-catalyzed transfer to a conjugate stable mode. Given linear and nonlinear symmetries, the stable mode level and the cross-correlation of the unstable and stable mode amplitudes are related to the unstable mode level via linear physics. Here, the heat flux can then be written in terms of the unstable-mode level, which through a nonlinear balance depends on the eigenmode-dependent coupling coefficients and the triplet correlation time of the dominant coupled modes. Resonance in these quantities leads to suppressed heat flux above the linear threshold, with a nonlinear upshift of the critical gradient set by the resonance broadening of a finite perpendicular wavenumber and collisionality.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Electromagnetic turbulence in increased β plasmas in the Large Plasma Device

The variation of pressure-gradient-driven turbulence with plasma $\beta$ (up to $\beta \approx 15\,\%$ ) is investigated in linear, magnetized plasma. The magnitude of magnetic fluctuations is observed to increase substantially with increasing $\beta$ . More importantly, parallel magnetic fluctuations are observed to dominate at higher $\beta$ values, with $\delta B_\parallel / \delta B_\perp \approx 2$ and $\delta B / B_0 \approx 1\,\%$ . Parallel magnetic fluctuations are strongly correlated with density fluctuations and the two are observed to be out of phase. The relative magnitude of and cross-phase between density and parallel magnetic field fluctuations are consistent with the dynamic pressure balance ( $P+{B_{0}^2}/{2\mu _0} = \textrm {constant}$ ). A local slab model theory for electromagnetic, modified drift Alfvén waves, including parallel magnetic fluctuations, shows partial agreement with experimental observations.

Physics↗

DOE OSTI2021

Dissipation in the magnetic turbulence of reversed field pinch plasmas

Reversed field pinch plasmas are subject to tearing instability that creates a broad spectrum of magnetic fluctuations. The dominant fluctuations have poloidal and toroidal mode numbers (m,n) = (1,6 - 10) and can grow to 2 - 3% of the mean magnetic field. Through non-linear coupling this growth culminates in a strong reconnection event and broadening of the magnetic spectrum extending to the ion gyroradius scale. Multiple developments occur during the reconnection stage: ions and electrons are energized, magnetic fluctuation amplitudes increase, plasma flow is halted, and the toroidal magnetic flux increases in a sawtooth-like fashion as the RFP dynamo becomes stronger. Magnetic fluctuations are measured in the plasma edge at multiple radial locations from r/a = 0.75 to 0.96 to assess and characterize the magnetic turbulence. The measured spectrum perpendicular to the mean field, S(k ⊥ ), can be fit to a model spectrum consisting of power law and exponential component with one free parameter that characterizes dissipation. The measured dissipation is much larger than estimated from classical viscous or resistive dissipation, but it is consistent with a flow damping measurement of anomalous viscosity. The measurements show an evolution of the spectrum during which fluctuation power builds up in the smallest wavenumbers and cascades to the larger wavenumber due to the non-linear coupling between the linear (m,n) = (1, > 6) and the non-linear (m,n) = (0, 1) tearing mo

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Kinetic-ballooning-mode turbulence in low-average-magnetic-shear equilibria

In this work, kinetic-ballooning-mode (KBM) turbulence is studied via gyrokinetic flux-tube simulations in three magnetic equilibria that exhibit small average magnetic shear: the Helically Symmetric eXperiment (HSX), the helical-axis Heliotron-J and a circular tokamak geometry. For HSX, the onset of KBM being the dominant instability at low wavenumber occurs at a critical value of normalized plasma pressure $\beta ^{\rm KBM}_{\rm crit}$ that is an order of magnitude smaller than the magnetohydrodynamic (MHD) ballooning limit $\beta ^{\rm MHD}_{\rm crit}$ when a strong ion temperature gradient (ITG) is present. However, $\beta ^{\rm KBM}_{\rm crit}$ increases and approaches the MHD ballooning limit as the ITG tends to zero. For these configurations, $\beta ^{\rm KBM}_{\rm crit}$ also increases as the magnitude of the average magnetic shear increases, regardless of the sign of the normalized magnetic shear. Simulations of Heliotron-J and a circular axisymmetric geometry display behaviour similar to HSX with respect to $\beta ^{\rm KBM}_{\rm crit}$ . Despite large KBM growth rates at long wavelengths in HSX, saturation of KBM turbulence with $\beta > \beta _{\rm crit}^{\rm KBM}$ is achievable in HSX and results in lower heat transport relative to the electrostatic limit by a factor of roughly five. Nonlinear simulations also show that KBM transport dominates the dynamics when KBMs are destabilized linearly, even if KBM growth rates are subdominant to ITG growth rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Predicting the critical gradient of ITG turbulence in fusion plasmas

The quasilinear mixing-length approach to efficient prediction of transport in fusion devices is improved to account for the ‘Dimits’ upshift between linear and nonlinear critical pressure gradients in zonal-flow-saturated turbulence regimes. This modification uses the frequency mismatch between modes interacting turbulently to track changes in saturation efficiency. Near criticality, energy is transferred exclusively to stable eigenmodes, rapidly increasing the efficacy of the nonlinearity. Finally, the modified quasilinear model is able to predict below-threshold turbulent ion-temperature-gradient-driven transport accurately and also yields significantly improved predictions for trapped-electron-mode transport.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

The impact of magnetic fields on momentum transport and saturation of shear-flow instability by stable modes

The Kelvin–Helmholtz (KH) instability of a shear layer with an initially uniform magnetic field in the direction of flow is studied in the framework of 2D incompressible magnetohydrodynamics with finite resistivity and viscosity using direct numerical simulations. The shear layer evolves freely, with no external forcing, and thus broadens in time as turbulent stresses transport momentum across it. As with hydrodynamic KH, the instability here features a conjugate stable mode for every unstable mode in the absence of dissipation. Stable modes are shown to transport momentum up its gradient, shrinking the layer width whenever they exceed unstable modes in amplitude. In simulations with weak magnetic fields, the linear instability is minimally affected by the field, but enhanced small-scale fluctuations relative to the hydrodynamic case are observed. These enhanced fluctuations coincide with increased energy dissipation and faster layer broadening, with these features more pronounced in simulations with stronger fields. These trends result from the magnetic field reducing the effects of stable modes relative to the transfer of energy to small scales. As field strength increases, stable modes become less excited, thus transporting less momentum against its gradient. Furthermore, the energy that would otherwise transfer back to the driving shear because of the stable modes is instead allowed to cascade to small scales, where it is lost to dissipation. Approximations of the turbulent state in terms of a reduced set of modes are explored. While the Reynolds stress is well-described using just two modes per wavenumber at large scales, the Maxwell stress is not.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Direct measurements of the 3D plasma velocity in single-helical-axis RFP plasmas

The first local velocity measurements of helical equilibrium plasmas in the Reversed Field Pinch (RFP) Single Helical Axis (SHAx) state using a Charge Exchange Recombination Spectroscopy (CHERS) diagnostic are presented. Measurements show strong axisymmetric and non-axisymmetric flow, with n ¼ 5 components of flow related to the ðm; nÞ¼ð1; 5Þ dominant magnetic mode on the order of the axisymmetric flow in certain regions of the plasma, as well as significant n > 5 flow. Flow measurements are compared with NIMROD simulations of visco-resistive, single-fluid MHD in toroidal and cylindrical geometries with limited axial periodicity. Both measurements and the simulation with toroidal geometry show stronger inboard flows relative to the outboard flows, which is attributed to the toroidal geometry of the device. In the experiment, the n ¼ 5 component of flow is phase shifted from the reconnection-like flow pattern observed in the single-fluid simulations, possibly due to decoupling of the ion and electron fluids over much of the plasma. Finally, the strength of the helical angular flow shear relative to the critical shear necessary to disrupt nonlinear coupling between tearing modes is calculated around the helical magnetic axis. The shear in the measured flow is on the order of the theoretical critical threshold needed to nonlinearly decouple modes, but the measurement uncertainty in the gradient of the flow is large.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Threshold Heat-Flux Reduction by Near-Resonant Energy Transfer

Near-resonant energy transfer to large-scale stable modes is shown to reduce transport above the linear critical gradient, contributing to the onset of transport at higher gradients. This is demonstrated for a threshold fluid theory of ion temperature gradient turbulence based on zonal-flow-catalyzed transfer. Furthermore, the heat flux is suppressed above the critical gradient by resonance in the triplet correlation time, a condition enforced by the wave numbers of the interaction of the unstable mode, zonal flow, and stable mode.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Pair plasma instability in homogeneous magnetic guide fields

Pair plasmas, collections of both matter and antimatter particles of equal mass, represent a paradigm for the study of basic plasma science, and many open questions exist regarding these unique systems. They are found in many astrophysical settings, such as gamma-ray bursts, and have recently also been produced in carefully designed laboratory experiments. A central research topic in plasma physics is instability; however, unlike their more common ion–electron siblings, pair plasmas are generally thought to be stable to cross field pressure gradients in homogeneous magnetic fields. It is shown here by means of kinetic full-f simulations that, when a pressure gradient is first established, the Gradient-driven Drift Coupling mode is destabilized and becomes turbulent. Force balance is eventually achieved by a combination of flattened pressure profiles due to turbulent transport and establishment of a magnetic field gradient, saturating the growth. During the unstable phase, key physics can be captured by a δf gyrokinetic description, where it is shown analytically and numerically that parallel particle motion results in a coupling of all electromagnetic field components. A fluid model derived therefrom accurately predicts linear eigenmodes and is used to resolve global profile effects. For laser-based electron–positron plasma experiments, prompt instability is predicted with growth times much shorter than plasma lifetimes. Similarly, growth rates are calculated for the planned APEX experiment as well as gamma-ray burst scenarios, suggesting that the instability may contribute to the early evolution of these systems.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗