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At least 91 records · Page 5
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DOE OSTI2024

Saturation of Fishbone Instability by Self-Generated Zonal Flows in Tokamak Plasmas

Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Gyrokinetic analysis of inter-edge localized mode transport mechanisms in a DIII-D pedestal

In this study, gyrokinetic simulations are used to study pedestal fluctuations for DIII-D discharge 174082 using the GENE code. Nonlinear local simulations indicate that electron heat flux has contributions from electron temperature gradient-driven transport but at levels insufficient to satisfy power balance. We show that microtearing modes (MTM) and neoclassical transport are likely to account for the remaining observed energy losses in the electron and ion channels, respectively. The MTM instabilities found in the simulations are consistent with the high-frequency fluctuations identified in the magnetic fluctuation data from Mirnov coils. The fluctuation data in this discharge also exhibit a low-frequency band of fluctuations. By modifying the equilibrium profiles and plasma β, simulations produce MHD modes, which may be responsible for these observed low-frequency fluctuations. We compare several metrics involving ratios of fluctuation amplitudes and transport quantities for both MTMs and MHD modes. This analysis suggests that the available data are consistent with the simultaneous activity of both MHD modes and MTMs provided that the former is limited largely to the particle transport channel.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

The role of toroidal rotation in the very high energy confinement quality observed in super H-mode experiments on DIII-D

In this paper, we report the key role that toroidal rotation and the related ExB shear physics played in the very high energy confinement quality (H98y2>1.5) of super H-mode experiments on DIII-D. Experiments show that the energy confinement quality decreases when toroidal rotation decreases due to the decreased externally controlled torque per particle. Meanwhile, the total pedestal pressure in the experiments remains very high during the rotation and confinement quality change. TGYRO transport modeling suggests the contribution from rotation in the ExB shear is responsible for the confinement quality in excess of standard H-mode (H98y2~1). CGYRO gyrokinetic simulations reveal the governing physics in the core plasma of super H-modes: significant up-shift of nonlinear the ITG critical gradient is observed when applying ExB shear physics in the modeling based on experimental data. The effects of other physical parameters and contribution from pedestal height, which may play minor roles in this study, are also discussed.

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 OSTI2025

Understanding plasma turbulence through exact coherent structures

Plasma turbulence is a key challenge in understanding transport phenomena in magnetically confined plasmas. This work presents a generalized framework to analyze plasma turbulence that utilizes periodic orbit theory. In periodic orbit theory, doubly periodic solutions (coherent structures) of the governing equation(s) serve as building blocks of the considered turbulent dynamics. To illustrate the concept and method, the particularly simple Kuramoto–Sivashinsky (referred to here as LMRT for the original authors: LaQuey, Mahajan, Rutherford, and Tang) trapped-ion mode toy model is used. By applying numerical optimization techniques to the LMRT equation, we extract coherent spacetime patterns that represent the library of allowable fundamental structures of the equation. These structures provide a framework to systematically describe turbulence as a composition of recurrent solutions, revealing an underlying order within chaotic plasma motion. Although illustrated here using the simplified LMRT model for clarity, this framework provides a general strategy that can be extended to more complex and realistic models of plasma turbulence, including gyrokinetic systems. This offers a new method for predicting and potentially controlling transport processes in fusion plasmas by providing a bridge between nonlinear dynamical systems theory and plasma physics in the form of a generalized framework with which to analyze and understand spatially extended nonlinear partial differential equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Regulation of Alfvén Eigenmodes by Microturbulence in Fusion Plasmas

Global gyrokinetic simulations of mesoscale reversed shear Alfven eigenmodes (RSAE) excited by energetic particles (EP) in fusion plasmas find that RSAE amplitude and EP transport are much higher than experimental levels at nonlinear saturation, but quickly diminish to very low levels after the saturation when background microturbulence is artificially suppressed. In contrast, in simulations coupling micro-meso scales, the RSAE amplitude and EP transport decrease drastically at the initial saturation but later increases to the experimental levels in the quasi-steady state with bursty dynamics due to regulation by thermal ion temperature gradient (ITG) microturbulence. The quasi-steady state EP transport is larger for a stronger microturbulence. Here, the RSAE amplitude in the quasi-steady state ITG-RSAE turbulence from gyrokinetic simulations, for the first time, agrees very well with experimental measurements.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Gyrokinetic and extended-MHD simulations of a flow shear stabilized Z-pinch experiment

Axisymmetric (m = 0) gyrokinetic and extended-MHD simulations of a sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The extended-MHD model is electromagnetic and includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. Additionally, a prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the fusion Z-pinch experiment (FuZE), and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center (E×B ) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease in the linear growth rate with an increase in the flow shear; however, full stabilization in the linear regime is not observed even for large (comparable to the Alfvén velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied, and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Effects of zonal flows on ion temperature gradient instability in the scrape-off layer of a field-reversed configuration

Gyrokinetic simulations of long wavelength ion temperature gradient (ITG) turbulence in the scrape-off layer (SOL) of a field-reversed configuration (FRC) find that zonal flows are nonlinearly generated and are the dominant mechanism for the nonlinear saturation of the ITG instability. After the ITG saturation, zonal flows remain undamped and gradually suppress the turbulent transport to a very low level. In the simulations with collisions, collisional damping gradually reduces zonal flow amplitude to a lower level, which allows finite ITG turbulence intensity and ion heat transport in the SOL. The steady state turbulence intensity and ion heat transport are found to be proportional to the collision frequency. Furthermore, this favorable scaling suggests that minimizing collisions (e.g. increasing temperature, reducing impurity content, etc) and preserving toroidal symmetry could improve plasma confinement in the FRC.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Nonlinear dynamics of small-scale Alfvén waves

Herein we study the nonlinear evolution of very oblique small-scale Alfvén waves with k ⊥ d i ≳1. At these scales, the waves become significantly compressive, unlike in magnetohydrodynamics, due to the Hall term in the equations. We demonstrate that when frequencies are small compared to the ion gyrofrequency and amplitudes are small compared to unity, no new nonlinear interaction appears due to the Hall term alone at the lowest non-trivial order, even when k ⊥ d i ~1. However, at the second non-trivial order, we discover that the Hall physics leads to a slow but resonant nonlinear interaction between co-propagating Alfvén waves, an inherently three-dimensional effect. Including the effects of finite temperature, finite frequency, and electron inertia, the two-fluid Alfvén wave also becomes dispersive once one or more of k ⊥ ρ s , k ⊥ d e , or k ∥ d i becomes significant: for oblique waves at low β as studied here, this can be at a much smaller scale than d i . We show that the timescale for one-dimensional steepening of two-fluid Alfvén waves is only significant at these smaller dispersive scales, and also derive an expression for the amplitude of driven harmonics of a primary wave. Importantly, both new effects are absent in gyrokinetics and other commonly used reduced two-fluid models. Our calculations have relevance for the interpretation of laboratory Alfvén wave experiments, as well as shedding light on the physics of turbulence in the solar corona and inner solar wind, where the dominant nonlinear interaction between counter-propagating waves is suppressed, allowing these new effects to become important.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A learned closure method applied to phase mixing in a turbulent gradient-driven gyrokinetic system in simple geometry

We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system – temperature-gradient-driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition. Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a broad range of the relevant two-dimensional parameter space (collisionality and gradient drive). We find that the turbulent kinetic system produces phase-mixing rates much lower than the linear expectations, which the LMM closure is capable of capturing. We also compare radial heat fluxes. A Hammett–Perkins closure, generalized to include collisional effects, is quite successful throughout the parameter space, producing ${\sim }14\,\%$ root-mean-square (r.m.s.) error. The LMM closure is also very effective: when trained at three (two) points (in a 35 point parameter grid), the LMM closure produces $8\,\%$ ( $12\,\%$ ) r.m.s. errors. The LMM procedure can be readily generalized to other closure problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Explicit structure-preserving geometric particle-in-cell algorithm in curvilinear orthogonal coordinate systems and its applications to whole-device 6D kinetic simulations of tokamak physics

Explicit structure-preserving geometric particle-in-cell (PIC) algorithm in curvilinear orthogonal coordinate systems is developed. The work reported represents a further development of the structure-preserving geometric PIC algorithm achieving the goal of practical applications in magnetic fusion research. The algorithm is constructed by discretizing the field theory for the system of charged particles and electromagnetic field using Whitney forms, discrete exterior calculus, and explicit non-canonical symplectic integration. In addition to the truncated infinitely dimensional symplectic structure, the algorithm preserves exactly many important physical symmetries and conservation laws, such as local energy conservation, gauge symmetry and the corresponding local charge conservation. As a result, the algorithm possesses the long-term accuracy and fidelity required for first-principles-based simulations of the multiscale tokamak physics. The algorithm has been implemented in the SymPIC code, which is designed for high-efficiency massively-parallel PIC simulations in modern clusters. The code has been applied to carry out whole-device 6D kinetic simulation studies of tokamak physics. A self-consistent kinetic steady state for fusion plasma in the tokamak geometry is numerically found with a predominately diagonal and anisotropic pressure tensor. The state also admits a steady-state sub-sonic ion flow in the range of 10 km s -1 , agreeing with experimental observations and analytical calculations Kinetic ballooning instability in the self-consistent kinetic steady state is simulated. It is shown that high-n ballooning modes have larger growth rates than low-n global modes, and in the nonlinear phase the modes saturate approximately in 5 ion transit times at the 2% level by the E × B flow generated by the instability. These results are consistent with early and recent electromagnetic gyrokinetic simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Gyrokinetic simulations of the effects of magnetic islands on microturbulence in KSTAR

Gyrokinetic simulations are utilized to study effects of magnetic islands (MIs) on the ion temperature gradient (ITG) turbulence in the KSTAR tokamak with resonant magnetic perturbations. Simulations show that the transport is controlled by the nonlinear interactions between the ITG turbulence and self-generated vortex flows and zonal flows, leading to an anisotropic structure of fluctuation and transport on the poloidal plane and in the toroidal direction. MIs greatly enhance turbulent transport of both particle and heat. The turbulent transport exhibits variations in the toroidal direction, with transport through the resonant layer near the island X-point being enhanced when the X-point is located at the outer mid-plane. A quantitative agreement is shown between simulations and KSTAR experiments in terms of time frequency and perpendicular wavevector spectrum.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Global gyrokinetic simulation of neoclassical ambipolar electric field and its effects on microturbulence in W7-X stellarator

Global neoclassical simulations of a model equilibrium of the W7-X stellarator find an ambipolar electric field with either an ion root or an electron root solution depending on the temperature ratio between electrons and ions. The ambipolar electric field is then used as an equilibrium field in the turbulence simulations of ion temperature gradient (ITG) instability. The shear of the ambipolar electric field has modest effects on the ITG linear instability, nonlinear saturation amplitude, and turbulent transport in the ion root case. However, in the electron root case, the ambipolar electric field significantly reduces the linear ITG growth rate, turbulence intensity, and radial correlation length, resulting in an ion heat conductivity comparable to the neoclassical transport level in the strong shear region.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Gyrokinetic benchmark of the electron temperature-gradient instability in the pedestal region

Transport from turbulence driven by the electron temperature-gradient (ETG) instability is likely a major source of electron heat losses through the pedestal. Due to extreme gradients and strong shaping, ETG instabilities in the pedestal are distinct from those in the core, having, for example, multiple branches (toroidal and slab) in different wavenumber ranges. Due to its importance for pedestal transport, and its rather exotic character, a rigorous multi-code benchmarking exercise is imperative. In this work, we describe such an exercise, wherein we have carried out a detailed comparison of local linear pedestal ETG simulations using three gyrokinetic codes, CGYRO, GEM, and GENE and testing different geometric parameters (such as circular, Miller, and equilibrium EFIT geometry). The resulting linear frequencies, growth rates, and eigenfunctions show very good agreement between the codes in the three types of employed geometries. A nonlinear benchmark between CGYRO and GENE is also described, exhibiting good agreement (a maximum of 20% difference in the heat fluxes computed) at two locations in the pedestal. This lays the foundation for confidently modeling ETG turbulence in the pedestal

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

The role of ion-scale micro-turbulence in pedestal width of the DIII-D wide-pedestal QH mode

The low-edge rotation, intrinsically ELM-free, and improved confinement wide-pedestal quiescent H-mode (QH-mode), discovered in DIII-D tokamak, has pedestal widths exceeding the EPED-kinetic-ballooning mode (KBM) model scaling typically by at least 25%. Ion-scale ($k_yp_s$ < 1) microturbulence and its role in setting the pedestal structure is investigated using the radially local δ$f$ gyrokinetic code CGYRO. The electromagnetic trapped electron mode (TEM) is unstable at the pedestal top, while plasma beta (β$_e$) is ∼60% below the KBM onset threshold and the electron temperature gradient mode is found to be unstable in the peak gradient region. Nonlinear simulation reveals that the ion-scale turbulence could produce electron energy flux consistent with the flux inferred from power balance at the pedestal top, with a reasonable variation of the local shearing rate; and the local neoclassical transport from NEO is dominant over the simulated turbulent transport in the ion energy flux channel. The simulated ion-scale turbulence produces much lower electron energy flux than inferred from experiment in the pedestal peak gradient region. A correction to the EPED-KBM pedestal width scaling is obtained based on the two-dimensional scan of pedestal top plasma beta (β$_e$) and normalized electron density and temperature scale lengths,${a}$/${L_n}_e$, ${a}$/${L_T}_n$using CGYRO linear simulations. Mode transitions among TEM, micro-tearing mode, ion-temperature gradient mode and KBM, are observed in the 2D scan at the pedestal top. A fixed normalized growth rate for these drift-type modes is taken to determine the pedestal width scaling, which shows good consistency with the QH experimental database on pedestal heights and widths. The onset of KBM instabilities and the local E × B shear suppression criterion set the lower and upper limit for the pedestal width of standard QH-mode, wide-pedestal QH-mode and type-I ELMy H mode. A potentially higher and wider pedestal is expected from the new scaling of pedestal width. This work presents an improved understanding of the ion-scale micro-turbulence of wide-pedestal QH-mode and sheds light on a promising scenario for future reactors, including ITER and beyond.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Saturation of fishbone instability through zonal flows driven by energetic particle transport in tokamak plasmas

Gyrokinetic and kinetic-MHD simulations are performed for the fishbone instability in the DIII-D discharge #178631, chosen for validation of first-principles simulations to predict the energetic particle (EP) transport in an ITER prefusion baseline scenario. Fishbone modes are found to generate zonal flows, which dominate the fishbone saturation. The underlying mechanisms of the two-way fishbone-zonal flows nonlinear interplay are discussed in details. Numerical and analytical analyses identify the fishbone-induced EP redistribution as the dominant generation mechanism for zonal flows. The zonal flows modify the nonlinear dynamics of phase space zonal structures, which reduces the amount of EPs able to resonate with the mode, leading to an early fishbone saturation. Simulation results including zonal flows agree quantitatively with DIII-D experimental measurements of the fishbone saturation amplitude and EP transport, supporting this novel saturation mechanism by self- generated zonal flows. Moreover, the wave-particle mode-locking mechanism is shown to determine quantitatively the fishbone frequency down-chirping, as evident in GTC simulation results in agreement with predictions from analytical theory. Finally, the&#xD;fishbone-induced zonal flows are possibly responsible for the formation of an ion-ITB in the DIII-D discharge. Based on the low EP transport and the large zonal flow shearing rates associated with the fishbone instability in gyrokinetic simulations of the ITER scenario, it is conjectured that high performance scenarios could be designed in ITER burning plasmas through fishbone-induced ITBs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Gyrokinetic electromagnetic particle simulations in triangular meshes with C1 finite elements

The triangular mesh-based gyrokinetic scheme enables comprehensive axis-to-edge studies across the entire plasma volume. Our approach employs triangular finite elements with first-derivative continuity (C1), building on previous work to facilitate gyrokinetic simulations. Additionally, we have adopted the mixed variable/pullback scheme for gyrokinetic electromagnetic particle simulations. The filter-free treatment in the poloidal cross-section with triangular meshes introduces unique features and challenges compared to previous treatments using structured meshes. Our implementation has been validated through benchmarks using ITPA-toroidicity-induced Alfvén eigenmode parameters, showing its capability in moderate to small electron skin depth regimes. Additional examinations using experimental parameters confirm its applicability to realistic plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Directional finite difference method for directly solving 3D gyrokinetic field equations with enhanced accuracy

The gyrokinetic (GK) field equation is a three-dimensional (3D) elliptic equation, but it is often simplified to a set of two-dimensional (2D) equations by assuming that the field does not vary along a specific direction. However, this simplification can introduce inevitable 0th-order numerical errors, as nonlinear mode coupling in toroidal geometry can produce undesirable harmonic modes that violate the assumption. In this work, we propose a novel directional finite difference method (FDM) with a local coordinate transformation to better resolve the target field of interest. The directional FDM can accurately solve 3D GK field equations without simplifications, which can overcome the limitations of conventional methods. The accuracy and efficiency of different FDMs are analyzed in great detail for a variety of geometries, from simple 2D Cartesian coordinates to realistic 3D curvilinear coordinates. The 0th-order numerical errors of simplified 2D GK equations were found to be more problematic for low-harmonic modes and low aspect ratio geometries such as spherical tokamaks. On the other hand, the directional 3D FDM can accurately resolve a much wider range of harmonic modes aligned to the direction of interest, including the low-harmonic modes. In conclusion, we demonstrate that the directional 3D FDM is a highly effective algorithm for solving the 3D GK field equations, achieving accuracy improvements of 10 to 100 times or more, particularly for low-harmonic modes in spherical tokamaks.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗