
Jeff CandyGeneral Atomics · Theory and Computational Science
Jeff Candy
Doctor of Philosophy
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Publications (346)
The Fusion Synthesis Engine (FUSE) is a state-of-the-art software suite designed to revolutionize fusion power plant design. FUSE integrates first-principle models, machine learning, and reduced models into a unified framework, enabling comprehensive simulations that go beyond traditional 0D systems studies. FUSE's modular structure supports a hier...
The DIII-D tokamak has elucidated crucial physics and developed projectable solutions for ITER and fusion power plants in the key areas of core performance, boundary heat and particle transport, and integrated scenario operation, with closing the core-edge integration knowledge gap being the overarching mission. New experimental validation of high-...
This work presents the PORTALS framework (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), which leverages surrogate modeling and optimization techniques to enable the prediction of core plasma profiles and performance with nonlinear gyrokinetic simulations at significantly reduced cost, with no loss of accuracy. The efficiency of PORTALS is...
This work characterizes the core transport physics of SPARC early-campaign plasmas using the PORTALS-CGYRO framework. Empirical modeling of SPARC plasmas with L-mode confinement indicates an ample window of breakeven (Q > 1) without the need of H-mode operation. Extensive modeling of multi-channel (electron energy, ion energy, and electron particle...
The objectives of NSTX-U research are to reinforce the advantages of STs while addressing the challenges. To extend confinement physics of low-A, high beta plasmas to lower collisionality levels, understanding of the transport mechanisms that set confinement performance and pedestal profiles is being advanced through gyrokinetic simulations, reduce...
Experimental conditions obtained on the DIII-D tokamak in the ITER Similar Shape (ISS) have been compared extensively with nonlinear gyrokinetic simulation using the CGYRO code [Candy et al., J. Comput. Phys. 324, 73–93 (2016)] with comparisons spanning ion and electron heat fluxes, electron and impurity particle transport, and turbulent fluctuatio...
Gyro-fluid equations are velocity space moments of the gyrokinetic equations. Special gyro-Landau-fluid closures have been developed that include the damping due to kinetic resonances by fitting to the collisionless local plasma response functions. This damping allows for accurate linear eigenmodes to be computed with a relatively low number of vel...
The STEP (Stability, Transport, Equilibrium, and Pedestal) integrated-modeling tool has been developed in OMFIT to predict stable, tokamak equilibria self-consistently with core-transport and pedestal calculations. STEP couples theory-based codes to integrate a variety of physics, including magnetohydrodynamic stability, transport, equilibrium, ped...
We have developed an innovative workflow, Stability, Transport, Equilibrium, and Pedestal (STEP)-zero-dimensional (0D), within the OMFIT integrated modeling framework. Through systematic validation against the International Tokamak Physics Activity global H-mode confinement database, we demonstrated that STEP-0D, on average, predicts the energy con...
The STEP (Stability, Transport, Equilibrium, and Pedestal) integrated-modeling tool has been developed in OMFIT to predict stable, tokamak equilibria self-consistently with core-transport and pedestal calculations. STEP couples theory-based codes to integrate a variety of physics, including MHD stability, transport, equilibrium, pedestal formation,...
Investigation of linear gyrokinetic ion-scale modes ([Formula: see text]) finds that a transition from ion temperature gradient to microtearing mode (MTM) dominance occurs as the density is increased near the pedestal region of a parameterized DIII-D sized tokamak. H-modes profile densities, temperatures, and equilibria are parameterized utilizing...
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)...
New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by...
DIII-D physics research addresses critical challenges for the operation of ITER and the next generation of fusion energy devices. This is done through a focus on innovations to provide solutions for high performance long pulse operation, coupled with fundamental plasma physics understanding and model validation, to drive scenario development by int...
A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al 2007 Plasma Phys. Control. Fusion 49 1019) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal wave...
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 (ETG)-driven transport, but at levels insufficient to satisfy power balance. We show that Microtearing modes...
The accumulation of tungsten impurities measured in a KSTAR experiment was analyzed theoretically using a drift-kinetic code, NEO, to determine the contribution of neoclassical transport. According to the NEO simulation results, there is a certain value of impurity toroidal rotation speed maximizing the neoclassical inward convection. The inward co...
The power balance ion heat flux in the pedestal region on DIII-D increases and becomes increasingly anomalous (above conventional neoclassical) in experiments with higher temperature and lower density pedestals where the ion collisionality (𝜈∗𝑖) is lowered toward values expected on ITER. Direct measurements of the main-ion temperature are shown to...
A linear response, local model for the DBS amplitude applied to gyrokinetic simulations shows that radial correlation Doppler reflectometry measurements (RCDR, Schirmer et al., Plasma Phys. Control. Fusion 49 1019 (2007)) are not sensitive to the average turbulence radial correlation length, but to a correlation length that depends on the binormal...
The turbulence and transport expected in the SPARC tokamak Primary Reference Discharge (PRD) [P. Rodriguez-Fernandez et al., J. Plasma Phys. 86, 865860503 (2020)] have been investigated with the gyrokinetic code CGYRO [J. Candy et al., J. Comput. Phys. 324, 73–93 (2016)]. Linear and nonlinear simulations that focus on ion ( k θ ρ s < 1.0) and elect...
The asymmetry between deuterium (D) and tritium (T) turbulent particle fluxes in mixed D–T plasmas is studied with numerical simulations of nonlinear gyrokinetic turbulence in ion temperature gradient-dominated and trapped electron mode-dominated regimes. At 50–50 D–T concentration, the asymmetry, or flow separation, between D and T fluxes is such...
A new pseudolocal tomography algorithm is developed for soft X-ray(SXR) imaging measurements of the turbulent electron temperature fluctuations (δ Te) in tokamaks and stellarators. The algorithm overcomes the constraints of limited viewing ports on the vessel wall (viewing angle) and limited number of lines of sight (LOS). This is accomplished by i...
Excellent confinement has been routinely observed in DIII-D (J. L. Luxon, Nucl. Fusion 2002) high β p discharges, which are characterized by a strong large-radius internal transport barrier (ITB) in almost all kinetic channels. Typically, the ion thermal transport is neoclassical with conventional long-wavelength turbulence instabilities suppressed...
We propose a novel flux-surface parameterization suitable for local MHD equilibrium calculations with strongly-shaped flux surfaces. The method is based on a systematic expansion in a small number of intuitive shape parameters, and reduces to the well-known Miller D-shaped parameterization in the limit where some of the coefficients are set to zero...
The findings of an investigation into the properties of the three dimensional (3D) saturated fluctuation intensity of the electric potential in gyrokinetic turbulence simulations is presented. Scans in flux surface elongation and Shafranov shift are used to isolate the tokamak geometric dependencies. The potential intensity required in order to com...
An extensive validation effort performed for a modest-beta NSTX NBI-heated H-mode discharge predicts that electron thermal transport can be entirely explained by electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in conditions of strong and weak ETG turbulence drive. Thermal power-balance estimates c...
An integrated modeling workflow capable of finding the steady-state plasma solution with self-consistent core transport, pedestal structure, current profile, and plasma equilibrium physics has been developed and tested against a DIII-D discharge. Key features of the achieved core-pedestal coupled workflow are its ability to account for the transpor...
The role of nonadiabatic electrons in regulating the hydrogenic isotope-mass scaling of gyrokinetic turbulence in tokamak fusion plasmas is assessed in the transition from ion-dominated core transport regimes to electron-dominated edge transport regimes. We propose a new isotope-mass scaling law that describes the electron-to-ion mass-ratio depende...
Using a novel wavenumber-advection algorithm, we show that profile curvature (shear in the profile gradient) can be implemented with spectral accuracy in gyrokinetic turbulence simulations. This approach enables a global simulation capability with the relatively low cost and high accuracy of local simulations. Using this new algorithm, we show that...
We report on the first direct comparisons of microtearing turbulence simulations to experimental measurements in a representative high bootstrap current fraction (fBS) plasma. Previous studies of high fBS plasmas carried out in DIII-D with large radius internal transport barriers (ITBs) have found that, while the ion energy transport is accurately...
We observe the formation of a high-pressure staircase pedestal (≈16–20 kPa) in the DIII-D tokamak when large amplitude edge localized modes are suppressed using resonant magnetic perturbations. The staircase pedestal is characterized by a flattening of the density and temperature profiles in midpedestal creating a two-step staircase pedestal struct...
The influence of kinetic electrons on the isotope scaling of gyrokinetic turbulent energy flux is assessed. A simple framework is used to study the transition from ion-dominated turbulence regimes to regimes where electron and ion transport levels are comparable. In the ion-dominated regime, the turbulent ion energy flux increases as the ion mass i...
This paper develops two non-inductive steady state scenarios for larger size configuration of China Fusion Engineering Test Reactor (CFETR) with integrated modeling simulations. A self-consistent core-pedestal coupled workflow for CFETR is developed under integrated modeling framework OMFIT, which allows more accurate evaluation of CFETR performanc...
We describe the mathematical formulation, outline the numerical discretization, and present performance analysis results for the CGYRO plasma turbulence code. The performance data was collected on 5 current leadership systems (2 KNL-based, 2 hybrid CPU-GPU and 1 Skylake-based). CGYRO is a relatively new gyrokinetic turbulence code, based on the wel...
A new extensive validation study performed for a modest-beta National Spherical Torus eXperiment (NSTX) neutral beam injection-heated H-mode discharge predicts that electron thermal transport can be entirely explained by short-wavelength electron-scale turbulence fluctuations driven by the electron temperature gradient mode (ETG), both in condition...
Plasmas with a negative triangularity shape have been created on the DIII-D tokamak that, despite maintaining standard L-mode edge radial profiles, reach volume averaged pressure levels typical of H-mode scenarios. Within the auxiliary power available for these experiments, plasmas exhibit near-zero power degradation while sustaining βN = 2.7 and H...
A novel method aimed at a kinetic moments closure for a magnetized plasma with arbitrary collisionality is proposed. The intended first application is to a tokamak edge and scrape-off-layer plasma. The velocity distribution function for each species is expanded in 8 Gaussian Radial Basis Functions (GRBFs) which are essentially shifted Maxwellians a...
A numerical method to compute the time-domain response of a loudspeaker or other transducer using contour integration of its frequency response (i.e., transfer function) is presented. The approach, based on Weideman's scheme for inversion of the Laplace transform along a parabolic contour, is applicable to analytic functions that contain isolated s...
The influence of sonic toroidal rotation on gyrokinetic stability and transport is studied, with important implications for heavy impurity dynamics. When centrifugal drifts and electrostatic trapping corrections are included, significant modifications to the calculated transport of heavy impurities are observed. These high-rotation corrections add...
We present a methodology to measure transducers with a dual-added-mass technique in order to extract the motional impedance ZM(ω) and force factor Bℓ from the total impedance. This methodology is suitable for determining moving mass and compliance for motional impedance models that include viscoelasticity and frequency-dependent damping by curve fi...
Sheared E×B flow in a tokamak, driven by external torque from neutral beam injection, is known to have an important stabilizing effect on drift-wave turbulence. In gyrokinetic codes, flow shear can be implemented directly on a radial mesh with nonperiodic boundary conditions. The mesh-based implementation is straightforward, but carries the possibi...
High fidelity, multi-scale gyrokinetic simulations capable of capturing both ion ( k θ ρ s ∼ ( 1.0 ) ) and electron-scale ( k θ ρ e ∼ ( 1.0 ) ) turbulence were performed in the core of an Alcator C-Mod ELM-y H-mode discharge which exhibits reactor-relevant characteristics. These simulations, performed with all experimental inputs and realistic...
Experiments simulating the ITER baseline scenario on the DIII-D tokamak show that torque-free pure electron heating, when coupled to plasmas subject to a net co-current beam torque, affects density fluctuations at electron scales on a sub-confinement time scale, whereas fluctuations at ion scales change only after profiles have evolved to a new sta...
Fusion whole device modeling simulations require comprehensive models that are simultaneously physically accurate, fast, robust, and predictive. In this paper we describe the development of two neural-network (NN) based models as a means to perform a snon-linear multivariate regression of theory-based models for the core turbulent transport fluxes,...
New validation of global, nonlinear, ion-scale gyrokinetic simulations (GYRO) is carried out for L- and I-mode plasmas on Alcator C-Mod, utilizing heat fluxes, profile stiffness, and temperature fluctuations. Previous work at C-Mod found that ITG/TEM-scale GYRO simulations can match both electron and ion heat fluxes within error bars in I-mode [Whi...
A new paradigm of zonal flow mixing as the mechanism by which zonal E × B fluctuations impact the saturation of gyrokinetic turbulence has recently been deduced from the nonlinear 2D spectrum of electric potential fluctuations in gyrokinetic simulations. These state of the art simulations span the physical scales of both ion and electron turbulence...
In this work, we explore both the potential improvements and pitfalls that arise when using advanced collision models in gyrokinetic simulations of plasma microinstabilities. Comparisons are made between the simple-but-standard electron Lorentz operator and specific variations of the advanced Sugama operator. The Sugama operator describes multi-spe...
Nonlinear gyrokinetic simulations using the GENE code have previously predicted a significant nonlinear enhanced electromagnetic stabilization in certain JET discharges with high neutral-beam power and low core magnetic shear (Citrin et al 2013 Phys. Rev. Lett. 111 155001, 2015 Plasma Phys. Control. Fusion 57 014032). This dominates over the impact...
An important problem in plasma physics is the lack of an accurate and complete description of Coulomb collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of th...
We describe a new approach to solve the electromagnetic gyrokinetic equations which is optimized for accurate treatment of multispecies Fokker–Planck collisions including both pitch-angle and energy diffusion. The new algorithm is spectral/pseudospectral in four of the five phase space dimensions, and in the fieldline direction a novel 5th-order co...
Recent experiments on C-mod seeding nitrogen into ohmic plasmas with q 95 = 3.4 found that the seeding greatly reduced long-wavelength (ITG-scale) turbulence. The long-wavelength turbulence that was reduced by the nitrogen seeding was localized to the region of , where the turbulence is well above marginal stability (as evidenced by ). The nonlinea...
It is shown that Ion Temperature Gradient turbulence close to the threshold exhibits a long time behaviour, with smaller heat fluxes at later times. This reduction is connected with the slow growth of long wave length zonal flows, and consequently, the numerical dissipation on these flows must be sufficiently small. Close to the nonlinear threshold...
The 2D spectrum of the saturated electric potential from gyrokinetic turbulence simulations that include both ion and electron scales (multi-scale) in axisymmetric tokamak geometry is analyzed. The paradigm that the turbulence is saturated when the zonal (axisymmetic) ExB flow shearing rate competes with linear growth is shown to not apply to the e...
To better understand the role of cross-scale coupling in experimental conditions, a series of multi-scale gyrokinetic simulations were performed on Alcator C-Mod, L-mode plasmas. These simulations, performed using all experimental inputs and realistic ion to electron mass ratio ((mi/me)1/2 = 60.0), simultaneously capture turbulence at the ion (kθρs...
This paper presents quasi-linear gyrokinetic predictions of the Coriolis momentum pinch for low aspect-ratio National Spherical Torus Experiment (NSTX) H-modes where previous experimental measurements were focused. Local, linear calculations predict that in the region of interest (just outside the mid-radius) of these relatively high-beta plasmas,...
Accurate prediction of fusion performance in present and future tokamaks requires taking into account the strong interplay between core transport, pedestal structure, current profile, and plasma equilibrium. An integrated modeling workflow capable of calculating the steady-state self-consistent solution to this strongly coupled problem has been dev...
A Gyro-Landau-Fluid (GLF) 3 + 1 model has been recently implemented in BOUT++ framework, which contains full Finite-Larmor-Radius effects, Landau damping, and toroidal resonance [Ma et al., Phys. Plasmas 22, 055903 (2015)]. A linear global beta scan has been conducted using the JET-like circular equilibria (cbm18 series), showing that the unstable...
The transport of heat in laboratory and astrophysical plasmas is dominated by the complex nonlinear dynamics of plasma turbulence. In magnetically confined plasmas used for fusion energy research, turbulence is responsible for cross-field transport that limits the performance of tokamak reactors. We report a set of novel gyrokinetic simulations tha...
This paper presents an overview of recent highlights from research on Alcator C-Mod. Significant progress has been made across all research areas over the last two years, with particular emphasis on divertor physics and power handling, plasma-material interaction studies, edge localized mode-suppressed pedestal dynamics, core transport and turbulen...
One modeling framework for integrated tasks (OMFIT) is a comprehensive integrated modeling framework which has been developed to enable physics codes to interact in complicated workflows, and support scientists at all stages of the modeling cycle. The OMFIT development follows a unique bottom-up approach, where the framework design and capabilities...
A new 'Super H-mode' regime is predicted, which enables pedestal height and predicted fusion performance substantially higher than for H-mode operation. This new regime is predicted to exist by the EPED pedestal model, which calculates criticality constraints for peeling-ballooning and kinetic ballooning modes, and combines them to predict the pede...
Main ion dilution has been predicted by gyrokinetic simulations to have a significant effect on ion thermal transport in C-Mod ohmic plasmas. This effect was verified experimentally with a specific set of experiments on C-Mod in which ohmic deuterium plasmas across the linear ohmic confinement (LOC) through the saturated ohmic confinement (SOC) reg...
Intrinsic toroidal rotation in a tokamak can be driven by turbulent momentum transport due to neoclassical flow effects breaking a symmetry of turbulence. In this paper we categorize the contributions due to neoclassical effects to the turbulent momentum transport, and evaluate each contribution using gyrokinetic simulations. We find that the relat...
The first study using multi-scale (coupled ITG/TEM/ETG) gyrokinetic simulations at both reduced and realistic electron mass ratios, μ = (mD/me).5 = 20.0, 40.0 and 60.0, has been performed on a standard, Alcator C-Mod, L-mode discharge. Ion-scale (kθρs ∼ 1.0) and multi-scale (up to kθρe ∼ 0.8) gyrokinetic simulations are compared at different simula...
In this work we outline an approach to the problem of local equilibrium in non-axisymmetric configurations that adheres closely to Miller's original method for axisymmetric plasmas (Miller et al. 1998
Phys. Plasmas
5
, 973). Importantly, this method is novel in that it allows not only specification of 3D shape, but also explicit specification of th...
Peaked density profiles in low-collisionality AUG and JET H-mode
plasmas are probably caused by a turbulently driven particle pinch, and Alcator C-Mod experiments confirmed that collisionality is a critical parameter. Density peaking in reactors could produce a number of important effects, some beneficial, such as enhanced fusion power and transpor...
The capability to treat nonaxisymmetric flux surface geometry has been added to the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010). Geometric quantities (i.e. metric elements) are supplied by a recently-developed local 3D equilibrium solver, allowing neoclassical transport coefficients to be systematically comp...
For the first time, nonlinear
gyrokinetic simulations of I-mode plasmas are performed and compared with experiment. I-mode is a high confinement regime, featuring energy confinement similar to H-mode, but without enhanced particle and impurity particle confinement [D. G. Whyte et al., Nucl. Fusion 50, 105005 (2010)]. As a consequence of the separat...
A fundamental macroscopic description of a magnetized plasma is the Vlasov
equation supplemented by the nonlinear inverse-square force Fokker-Planck
collision operator [Rosenbluth et al., Phys. Rev., 107, 1957]. The Vlasov part
describes advection in a six-dimensional phase space whereas the collision
operator involves friction and diffusion coeffi...
For the first time, nonlinear gyrokinetic simulations spanning both the ion and electron spatio-temporal scales have been performed with realistic electron mass ratio ((m[subscript D] [over m [subscript e])[superscript 1 over 2] = 60.0), realistic geometry, and all experimental inputs, demonstrating the coexistence and synergy of ion (k[subscript θ...
Previous studies of DIII-D L-mode
plasmas have shown that a transport shortfall exists in that our current models of turbulent transport can significantly underestimate the energy transport in the near edge region. In this paper, the Trapped Gyro-Landau-Fluid (TGLF) drift wave transport
model is used to simulate the near edge transport in a DIII-D...
In this work, we extend previous analytic theories for the neoclassical transport of a trace heavy impurity in a rotating plasma in the Pfirsch–Schlüter regime. The complete diffusive and convective components of the ambipolar particle flux are derived. The solution is valid for arbitrary impurity charge and impurity Mach number and for general geo...
Linear and nonlinear gyrokinetic simulations are used to probe turbulent impurity transport in intrinsically rotating tokamak plasmas. For this simulation-based study, experimental input parameters are taken from a pair of ICRF heated Alcator C-Mod discharges exhibiting a change in the sign of the normalized toroidal rotation gradient at mid-radius...
The object of this review is to summarize the achievements of research on the Alcator C-Mod tokamak [Hutchinson et al., Phys. Plasmas
1, 1511 (1994) and Marmar, Fusion Sci. Technol. 51, 261 (2007)] and to place that research in the context of the quest for practical fusion energy. C-Mod is a compact, high-field tokamak, whose unique design and oper...