Quasilinear Transport Model Research Articles

Time-dependent full-radius integrated modeling of the DTT tokamak main plasma scenarios

Abstract We use an integrated modeling workflow with the transport code ASTRA coupled with the quasi-linear transport model TGLF-SAT2, the neoclassical model NCLASS, the FACIT model for the neoclassical impurity transport and the IMEP routines for the pedestal calculations, in order to predict the evolution of the plasma profiles for the DTT tokamak main scenarios. The simulations cover the whole confined plasma radius, up to the separatrix, and the time evolution of the plasma including the early phase in limiter configuration, the whole current ramp-up phase in L-mode divertor configuration, the L-H transition and part of the stationary H-mode phase. Six fields are predicted, i.e. the ion and electron temperatures, the electron density, two impurity densities and the plasma current. The simulations indicate that the main DTT scenarios are within the technical capabilities of the machine. They also indicate that the DTT full power, full current, full field scenario will be able to operate in H-mode with a duration of the flat-top phase of the order of \sim30 seconds, and plasma parameters allowing a core-edge integrated study of the power exhaust, which is the main mission of the device. The simulations show also a strong flexibility of the DTT plasmas, that allows DTT to study reactor-relevant conditions unexplored by existing tokamaks.

Overview of multiscale turbulence studies covering ion-to-electron scales in magnetically confined fusion plasma

Turbulent transport in magnetically confined fusion plasma has conventionally been analyzed at the ion gyroradius scale based on the microturbulence theory. However, ion-scale turbulence analysis sometimes fails to predict the turbulent transport flux observed experimentally. Microturbulence at the electron gyroradius scale and cross-scale interactions between disparate-scale turbulences are possible mechanisms to resolve this issue. This overview discusses the recent progress in multiscale turbulence studies and presents future perspectives from recent experimental, theoretical, and numerical investigations. The following aspects are highlighted: (1) the importance of electron-scale effects in experiments, (2) the physical mechanisms of cross-scale interactions, (3) modeling electron-scale effects in quasilinear transport models, and (4) the impacts of cross-scale interactions on burning plasmas. Understanding multiscale turbulence is necessary to improve performance prediction and explore optimal operations for future burning plasmas.

Prediction of transport in the JET DTE2 discharges with TGLF and NEO models using the TGYRO transport code

The JET Deuterium-Tritium-Experiment Campaign 2 (DTE2) has demonstrated the highest-ever fusion energy production. To forecast the transport dynamics within these discharges, the TGLF and NEO models within the TGYRO transport code were employed. A critical development in this study is the new quasilinear transport model, TGLF-SAT2, specifically designed to resolve discrepancies identified in JET deuterium discharges. This model accurately describes the saturated three-dimensional (3D) fluctuation spectrum, aligning closely with a database of nonlinear CGYRO turbulence simulations, thereby enhancing the predictive accuracy of TGYRO simulations. In validating against the JET DTE2 discharges across two primary operating scenarios, TGYRO effectively predicted the temperature profiles within a broad radial window (ρ ∼ 0.2–0.85), though with minor ion temperature discrepancies near the core. However, a consistent underprediction of electron density profiles by 20% across the simulation domain was noted, indicating areas for future refinement. To achieve a self-consistent steady-state solution based on the JET DTE2 discharges, an integrated modeling workflow TGYRO-STEP within the OMFIT framework was introduced. This workflow iterates among the core transport, the pedestal pressure and the MHD equilibrium, ultimately yielding a converged solution that significantly reduces dependence on experimental boundary conditions for temperature and density profiles. The integrated simulation results show negligible differences in electron density and temperature profiles compared to standalone TGYRO modeling, while the ion temperature profile is lower due to the updated boundary condition in TGYRO-STEP. The application of the TGYRO-STEP workflow to JET DTE2 discharges serves as a crucial test to validate its robustness and highlights its limitations, providing valuable insights for its potential future application in ITER and Fusion Power Plant deuterium and tritium prediction modeling.

Gaussian process regression models for the properties of micro-tearing modes in spherical tokamaks

Spherical tokamaks have many desirable features that make them an attractive choice for a future fusion power plant. Power-plant viability is intrinsically related to plasma heat and particle confinement, and this is often determined by the level of micro-instability-driven turbulence. Accurate calculation of the properties of turbulent microinstabilities is therefore critical for tokamak design; however, the evaluation of these properties is computationally expensive. The considerable number of geometric and thermodynamic parameters and the high resolutions required to accurately resolve these instabilities make repeated use of direct numerical simulations in integrated modeling workflows extremely computationally challenging and create the need for fast, accurate, reduced-order models. This paper outlines the development of a data-driven reduced-order model, often termed a surrogate model for the properties of micro-tearing modes (MTMs) across a spherical tokamak reactor-relevant parameter space utilizing Gaussian process regression and classification, techniques from machine learning. These two components are used in an active learning loop to maximize the efficiency of data acquisition, thus minimizing computational cost. The high-fidelity gyrokinetic code GS2 is used to calculate the linear properties of the MTMs: the mode growth rate, frequency, and normalized electron heat flux, and core components of a quasi-linear transport model. Data cross-validation and direct validation on unseen data are used to ascertain the performance of the resulting surrogate models.

A flexible gyro-fluid system of equations

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 velocity space moments compared to the number of velocity quadrature points in gyrokinetic codes. However, none of the published gyro-Landau-fluid closure schemes considers the Onsager symmetries of the resulting quasi-linear fluxes as a constraint. Onsager symmetry guarantees that the matrix of diffusivities is positive definite, an important property for the numerical stability of a transport solver. A two parameter real closure for improving the accuracy of low resolution gyro-fluid equations, which preserves the Onsager symmetry and allows higher velocity space moments, is presented in this paper. The new linear gyro-fluid system (GFS) is used to extend the TGLF quasi-linear transport model so that it can compute the energy and momentum fluxes due to parallel magnetic fluctuations, completing the transport matrix. The GFS equations do not use a bounce average approximation. The GFS equations are fully electromagnetic with general flux surface magnetic geometry, pitch angle scattering for electron collisions, and subsonic equilibrium toroidal rotation. Using GFS eigenmodes in the quasi-linear TGLF model will be shown to yield a more accurate match to fluxes computed by CGYRO turbulence simulations. Prospects for future applications of a quasi-linear theory to new plasma transport regimes and magnetic confinement devices in addition to tokamaks are opened by the flexibility of the GFS eigensolver.

Core integrated simulations for the Divertor Tokamak Test facility scenarios towards consistent core-pedestal-SOL modelling

Deuterium plasma discharges of the Divertor Tokamak Test facility (DTT) in different operational scenarios have been predicted by a comprehensive first-principle based integrated modelling activity using state-of-art quasi-linear transport models. The results of this work refer to the updated DTT configuration, which includes a device size optimisation (enlargement to m and a = 0.70 m) and upgrades in the heating systems. The focus of this paper is on the core modelling, but special attention was paid to the consistency with the scrape-off layer parameters required to achieve divertor plasma detachment. The compatibility of these physics-based predicted scenarios with the electromagnetic coil system capabilities was then verified. In addition, first estimates of DTT sawteeth and of DTT edge localised modes were achieved.

Upgrade and benchmark of quasi-linear transport model EDWM

The verification of a new saturation rule applied to the quasi-linear fluid model EDWM (extended drift wave model) and the calibration of several other features are presented. As one of the computationally fastest first-principle-based core transport models, EDWM can include an arbitrary number of ions and charge states. This feature is especially important for experimental devices with plasma-facing components made of heavy elements, such as the upcoming ITER device. As a quasi-linear model, EDWM solves a linear dispersion relation to obtain the instabilities driving the turbulence and combines the linear description with an estimation of the saturation level of the electrostatic potential to determine the fluxes. A new saturation rule at the characteristic length combined with a spectral filter for the poloidal wavenumber dependency is developed. The shape of the filter has been fitted against the poloidal wavenumber dependency of the electrostatic potential from non-linear gyrokinetic simulations. Additionally, EDWM's collision frequency and safety factor dependencies, as well as the electron heat flux level, have been calibrated against gyrokinetic and gyrofluid results. Finally, the saturation level has been normalized against non-linear gyrokinetic simulations and later validated against experimental measured fluxes from 12 discharges at JET.

First principle-based multi-channel integrated modelling in support of the design of the Divertor Tokamak Test facility

An intensive integrated modelling work of the main scenarios of the new Divertor Tokamak Test (DTT) facility with a single null divertor configuration has been performed using first principle quasi-linear transport models, in support of the design of the device and of the definition of its scientific work programme. First results of this integrated modelling work on DTT (R 0 = 2.14 m, a = 0.65 m) are presented here along with outcome of the gyrokinetic simulations used to validate the reduced models in the DTT range of parameters. As a result of this work, the heating mix has been defined, the size of device has been increased to R 0 = 2.19 m and a = 0.70 m, the use of pellets for fuelling has been recommended and reference profiles for diagnostic design, estimates of neutron yields and fast particle losses have been made available.

Verification of a quasi-linear model for gyrokinetic turbulent transport

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper (Staebler et al 2020 Plasma Phys. Control. Fusion 63 015013), a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium E × B velocity shear (Staebler et al 2013 Phys. Rev. Lett. 110 055003) and the zonal flow mixing model for electron-scale turbulence (Staebler et al 2016 Phys. Plasmas 23 062518) are both revised to be compatible with this new model. The models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations (Staebler et al 2005 Phys. Plasmas 12 102508) are also changed to improve the linear eigenmodes.

Validation of quasi-linear turbulent transport models against plasmas with dominant electron heating for the prediction of ITER PFPO-1 plasmas

Kinetic profile predictions of ITER PFPO-1 plasmas require high accuracy in the central electron temperatures to be applied to the calculation of third harmonic electron cyclotron absorption. Correctly predicting the transition from L-mode to H-mode further requires precise estimates of the ion heat flux in the periphery of the plasma. Recent versions of the quasi-linear transport models TGLF and QuaLiKiz were tested against an extensive set of experimental results from ASDEX Upgrade (AUG) and JET-ILW, where the focus was put on AUG plasmas heated by ECRH. Spectra obtained from TGLF are compared to a set of linear gyrokinetic simulations performed with GKW. Electron and ion temperature profiles obtained with TGLF-SAT1geo show good agreement with the experimental profiles, but there is a slight tendency to underpredict central T e and T i at high ratios T e/T i. QuaLiKiz yields reasonable results for T e and T i profiles in plasmas where the ion temperature gradient mode is dominant, but predicts a significantly too weak transport in the presence of dominant trapped electron modes in conditions of strong central electron heating.

Evidence and modeling of turbulence bifurcation in L-mode confinement transitions on Alcator C-Mod

Analysis and modeling of rotation reversal hysteresis experiments show that a single turbulent bifurcation is responsible for the Linear to Saturated Ohmic Confinement (LOC/SOC) transition and concomitant intrinsic rotation reversal on Alcator C-Mod. Plasmas on either side of the reversal exhibit different toroidal rotation profiles and therefore different turbulence characteristics despite the profiles of density and temperature, which are indistinguishable within measurement uncertainty. Elements of this bifurcation are also shown to persist for auxiliary heated L-modes. The deactivation of subdominant (in the linear growth rate and contribution to heat transport) ion temperature gradient and trapped electron mode instabilities is identified as the only possible change in turbulence within a reduced quasilinear transport model across the reversal, which is consistent with the measured profiles and inferred heat and particle fluxes. Experimental constraints on a possible change from strong to weak turbulence, outside the description of the quasilinear model, are also discussed. These results indicate an explanation for the LOC/SOC transition that provides a mechanism for the hysteresis through the dynamics of subdominant modes and changes in their relative populations and does not involve a change in the most linearly unstable ion-scale drift-wave instability.

Role of Microtearing Turbulence in DIII-D High Bootstrap Current Fraction Plasmas.

We report on the first direct comparisons of microtearing turbulence simulations to experimental measurements in a representative high bootstrap current fraction (f_{BS}) plasma. Previous studies of high f_{BS} plasmas carried out in DIII-D with large radius internal transport barriers (ITBs) have found that, while the ion energy transport is accurately reproduced by neoclassical theory, the electron transport remains anomalous and not well described by existing quasilinear transport models. A key feature of these plasmas is the large value of the normalized pressure gradient, which is shown to completely stabilize conventional drift-wave and kinetic ballooning mode instabilities in the ITB, but destabilizes the microtearing mode. Nonlinear gyrokinetic simulations of the ITB region performed with the cgyro code demonstrate that the microtearing modes are robustly unstable and capable of driving electron energy transport levels comparable to experimental levels for input parameters consistent with the experimental measurements. These simulations uniformly predict that the microtearing mode fluctuation and flux spectra extend to significantly shorter wavelengths than the range of linear instability, representing significantly different nonlinear dynamics and saturation mechanisms than conventional drift-wave turbulence, which is also consistent with the fundamental tearing nature of the instability. The predicted transport levels are found to be most sensitive to the magnetic shear, rather than the temperature gradients more typically identified as driving turbulent plasma transport.

Saturation and nonlinear electromagnetic stabilization of ITG turbulence

Energy transfer in ion-temperature-gradient-driven (ITG) turbulence and its role in modeling transport are examined for finite normalized plasma pressure β for a number of test cases and experimental discharges. The analysis shows that like the zero-β case, finite-β ITG turbulence saturates by nonlinear energy transfer to stable modes mediated by a zonal flow. Electromagnetic effects reliably increase stable mode amplitudes but affect heat fluxes only at the ≈5% level. The most important change with increased β is an increase in the correlation time of the triplet interaction of the unstable mode, stable mode, and zonal flow, thus providing a heightened nonlinear energy transfer efficiency, which allows the instability to saturate at lower amplitude. The heat flux is examined in connection with nonlinear electromagnetic stabilization, the phenomenon where the flux falloff with β is more pronounced than the falloff predicted by quasilinear transport models. The inclusion of the triplet correlation time in the quasilinear model captures most of the nonlinearly enhanced stabilization for the configurations studied here.

Perturbative transport modeling of cold-pulse dynamics in Alcator C-Mod Ohmic plasmas

Perturbative transport experiments in magnetically confined plasmas have shown, for more than 20 years, that the injection of cold pulses at the plasma edge can trigger the increase of core temperature. Predictive heat transport simulations with the trapped gyro Landau fluid (TGLF) quasilinear transport model demonstrate that the increase of core temperature in some regimes, and lack thereof in other regimes, can be explained by a change in dominant linear micro-instability in Alcator C-Mod. The effect of density and plasma current on the cold pulse are well captured by TGLF, including the relative change in position of the temperature flex point as current density changes. Linear stability analysis of simulated density and current scans reveals a competition between trapped electron and ion temperature gradient modes as the main driver of the core transient response. These results further demonstrate that cold-pulse propagation and associated phenomenology in the cases studied are well explained within the local transport paradigm, without resorting to non-local effects.

Impact of electron-scale turbulence and multi-scale interactions in the JET tokamak

Experimental observations in JET tokamak plasmas and gyrokinetic simulations point to an important role, for electron heat transport, of electron-scale instabilities and of their interaction with ion-scale instabilities. Since these effects are maximized for strong electron heating and ion-scale modes close to marginal stability, these findings are of high relevance for ITER plasmas, featuring both conditions. Gyrokinetic and quasi-linear transport models accounting for multi-scale effects are assessed against JET experimental results.

VITALS: A Surrogate-Based Optimization Framework for the Accelerated Validation of Plasma Transport Codes

Understanding transport in magnetically confined plasmas is critical for developing predictive models for future devices such as ITER. Thanks to recent progress in simulation and theory, along with enhanced computational power and better diagnostic systems, direct and quantitative comparisons between experimental results and models is possible. However, validating transport models using additional constraints and accounting for experimental uncertainties still remains a formidable task. In this work, a new optimization framework is developed to address the issue of constrained validation of transport models. The Validation via Iterative Training of Active Learning Surrogates (VITALS) framework exploits surrogate-based strategies using Gaussian processes and sequential parameter updates to achieve the combination of plasma parameters that matches experimental transport measurements within diagnostic error bars. VITALS is successfully implemented to study L-mode plasmas in the Alcator C-Mod tokamak, and for the first time, additional measurable quantities, such as incremental diffusivity and fluctuation levels, are used during the validation process of the quasi-linear transport models TGLF-SAT1 and TGLF-SAT0. First results indicate that these machine-learning algorithms are very suitable and adaptable as a self-consistent, fast, and comprehensive validation methodology for plasma transport codes.

Turbulence in high-beta ASDEX upgrade advanced scenarios

Recent experiments at ASDEX Upgrade achieve non-inductive operation in full tungsten wall conditions by applying electron cyclotron and neutral beam current drive. These discharges are characterised by a well-measured safety factor profile, which does not drop below one, and a good energy confinement. By reproducing the experimental heat fluxes, nonlinear gyrokinetic simulations suggest that the observed strong peaking of the ion temperature in the core is caused by the stabilising impact of a significant beam ion content, as well as strong electromagnetic effects on turbulent transport. Quasilinear transport models are not yet applicable in this interesting and reactor relevant parameter regime, but available simulation data may serve as a testbed for improvements. As the present plasma is close to the kinetic ballooning (KBM) threshold, elevating the safety factor profile under otherwise identical conditions is proposed to clarify, whether profiles are ultimately limited by KBM turbulence, or by global stability constraints.

Alfvén eigenmode stability and critical gradient energetic particle transport using the Trapped-Gyro-Landau-Fluid model

The Trapped-Gyro-Landau-Fluid (TGLF) transport model is a physically realistic and comprehensive theory based on a local quasilinear transport model fitted to linear and nonlinear GYRO gyrokinetic simulations [Staebler et al., Phys. Plasmas 14, 55909 (2007)]. This work presents the first use of the TGLF model to treat low-n Alfvén eigenmode (AE) stability and energetic particle (EP) transport. TGLF accurately recovers the local GYRO toroidicity-induced AE (TAE) and energetic particle mode (EPM) linear growth and frequency rates for a fusion alpha case. With a very high grid resolution, TGLF can quickly find the critical EP pressure gradient profile for stiff EP transport based on an AE linear threshold given the background thermal plasma profiles in DIII-D. The TGLF critical gradient profile using the recipe γAE = 0, that is the linear AE growth rate without additional driving rates from the background plasma gradients, matches the more expensive linear GYRO results with a single worst toroidal mode number n. TGLF can easily find the minimum critical gradient profile with testing multiple ns. From a database of runs using a newly developed TGLFEP code, a rough but insightful parametric “power law” scaling for critical EP beta is demonstrated. An important toroidal stabilization condition on the EP pressure gradient pEP/LpEP drive is isolated: R/LpEP>CR ∼ 3, where LpEP is the EP pressure gradient length and R is the tokamak major radius. This paper also demonstrates that relaxation of the fixed slowing down EP profile shape approximation often used to find the critical EP density profile has little effect on the resulting EP transport. The single EP species critical gradient model is generalized to handle two EP species.

The role of zonal flows in the saturation of multi-scale gyrokinetic turbulence

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 electron scale turbulence. Instead, it is the mixing rate by the zonal ExB velocity spectrum with the turbulent distribution function that competes with linear growth. A model of this mechanism is shown to be able to capture the suppression of electron-scale turbulence by ion-scale turbulence and the threshold for the increase in electron scale turbulence when the ion-scale turbulence is reduced. The model computes the strength of the zonal flow velocity and the saturated potential spectrum from the linear growth rate spectrum. The model for the saturated electric potential spectrum is applied to a quasilinear transport model and shown to accurately reproduce the electron and ion energy fluxes of the non-linear gyrokinetic multi-scale simulations. The zonal flow mixing saturation model is also shown to reproduce the non-linear upshift in the critical temperature gradient caused by zonal flows in ion-scale gyrokinetic simulations.

Turbulent transport analysis of JET H-mode and hybrid plasmas using QuaLiKiz and Trapped Gyro Landau Fluid

The physical transport processes at the basis of JET typical inductive H-mode scenarios and advanced hybrid regimes, with improved thermal confinement, are analyzed by means of some of the newest and more sophisticated quasi-linear transport models: trapped gyro Landau fluid (TGLF) and QuaLiKiz. The temporal evolution of JET pulses is modelled by CRONOS where the turbulent transport is modelled by either QuaLiKiz or TGLF. Both are first principle models with a more comprehensive physics than the models previously developed and therefore allow the analysis of the physics at the basis of the investigated scenarios. For H-modes, ion temperature gradient (ITG) modes are found to be dominant and the transport models are able to properly reproduce temperature profiles in self-consistent simulations. However, for hybrid regimes, in addition to ITG trapped electron modes (TEM) are also found to be important and different physical mechanisms for turbulence reduction play a decisive role. Whereas E × B flow shear and plasma geometry have a limited impact on turbulence, the presence of a large population of fast ions, quite important in low density regimes, can stabilize core turbulence mainly when the electromagnetic effects are taken into account. The TGLF transport model properly captures these mechanisms and correctly reproduces temperatures.