Session GI01: MFE: Core Transport Modeling and Characterization

On the direct use of core nonlinear gyrokinetic profile predictions for the planning of burning plasma experiments

Surrogate-based optimization techniques in PORTALS [P. Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036] greatly reduce the cost of determining plasma profiles consistent with turbulent transport as predicted by high-fidelity, nonlinear gyrokinetics. Leveraging the capability of PORTALS to scan input parameters at a much-reduced cost thanks to surrogate pre-training, the operational space of SPARC L-modes has been scoped with ion-scale, nonlinear CGYRO and NEO simulations. Profile predictions and the associated performance were evaluated for conditions that span anticipated density ranges of operation (1.0-2.5x10²⁰m^-3) and input power (5-15 MW), with a range of boundary conditions (T₉₅=0.9-2.3 keV). This first-of-a-kind database was possible only due to the use of GPU-accelerated CGYRO, coupled with PORTALS techniques. These predictions are used to help plan the first SPARC campaigns, with the goal of maximizing the probability of reaching breakeven in pre-H-mode operations. The simulations agree closely with empirical scalings of density peaking, and it is found that the ion heat flux is always greater than the electron heat flux, which could be favorable for accessing high edge temperature gradients (such as in I-mode). The high sensitivity of fusion power to edge conditions reveals that the attainment of high edge temperatures (r/a=0.95) could be important to achieve performance milestones in early SPARC campaigns.   

Characterization of Predicted Confinement and Transport in an ARC-class Tokamak Power Plant

We present the results of an INFUSE-funded project aimed at characterizing the microturbulence dynamics expected in a future ARC-class power plant, and the extent to which these same dynamics will be observed in SPARC. Here, the phrase ARC-class is used to denote a compact, high-field tokamak power plant capable of producing several hundred MW of fusion power at large Q_fus, with minimal extrapolation required from SPARC parameters and operational conditions. We focus on inductive scenarios consistent with the ARC V1C parameters presented at the 2021 APS-DPP meeting (R₀ = 3.65 m, a = 1.02, B_T = 11.6 T, I_p = 10.5 MA, κ =1.7, δ = 0.54, β_N = 1.2, /n_G = 0.6, H_98y,2 = 1.0, P_fus = 500 MW). To do so, we first calculate self-consistent 1.5D transport solutions using the OMFIT STEP workflow, combining pedestal stability predictions made with EPED and core transport solutions made using TGYRO and TGLF-SAT2. This workflow predicts solutions quite similar to what was previously predicted for SPARC, as well as the ITER baseline scenario and other inductive burning plasmas. At the predicted confinement factor H_98,y2 ~ 1 (achieved using only central radio frequency-like heating, without core fueling or torque) the plasma is well-coupled, with significant ion thermal transport driven by ion temperature gradient (ITG) modes. Temperature profile shapes and scale lengths are quite close across all three devices, with the largest uncertainty coming from the amount of density peaking achieved. Furthermore, the first nonlinear gyrokinetic profile predictions of an ARC-class device have been performed using the CGYRO code in combination with a newly-developed surrogate model-based transport code (P. Rodriguez-Fernandez et al, Nuclear Fusion 62 076036 (2022)), and are in excellent agreement with the TGLF predictions. Comparisons to analogous SPARC and ITER profile predictions made with both TGLF and direct gyrokinetic simulations will be discussed.   

Scale resolved multi-field gyrokinetic code validation

Achieving high values of density, ion temperature, and energy confinement times is crucial for future fusion reactors. These cannot be reached in today’s magnetic fusion devices. The values are limited, besides the geometry, mainly by turbulent transport. To design turbulence optimized devices, simulation codes need to be validated by experiments.

Validation work has already been done for a single or a small number of turbulence observables, where individual observables were reproduced by the simulation codes within the error bars of the measured quantities. A comprehensive validation should involve as many observables as possible at the same time - a challenging goal for both experiment and theory, which is tackled in this contribution.

We present a study, where a large set of experimental turbulence data is collected at ASDEX Upgrade in two plasma scenarios with varying electron temperature gradient lengths through ECRH. It includes wavenumber spectra, density and temperature fluctuation amplitudes, radial correlation lengths, and the cross-phase between density and temperature fluctuations. These quantities are measured using Doppler reflectometers and an electron cyclotron emission radiometer. They are compared to gyrokinetic turbulence simulations from the GENE code. To account for diagnostic effects in the measurement, sophisticated synthetic diagnostic modeling is applied.

The work shows the encouraging example of code validation, where a remarkable number of measured physics quantities are successfully reproduced by the code. We emphasize the simultaneous agreement between all experimental measurements and simulated turbulence quantities.

These findings provide a sound scientific justification for using codes such as GENE in the design of future fusion reactors.   

Experimental validation of momentum transport theory in the core of a tokamak plasma

Accurate prediction of plasma rotation profiles in future fusion devices requires a comprehensive understanding of momentum transport. This is crucial as plasma rotation affects neoclassical and impurity transport, MHD stability, turbulence, and confinement.

The advanced momentum transport analysis framework presented herein can uniquely, separately, and concomitantly determine the contributions of diffusion, convection, and intrinsic torque to the momentum transport within the core plasma from torque modulation experiments. The analysis, self-consistently, incorporates the time dependencies of all transport mechanisms, which is essential to compensate for changes in the transport synchronous with the torque perturbation, to separate the momentum fluxes and closely match experiment. The transport coefficients inferred from ASDEX Upgrade experiments show quantitative agreement with gyrokinetic predictions for the Prandtl and pinch number, providing an unprecedented degree of validation. Scaling laws derived from a database of gyrokinetic calculations are also compared to the experimental results.

Of particular interest is the intrinsic torque, which remains the largest uncertainty in predicting the rotation of future fusion devices. This work demonstrates that the intrinsic torque is co-current directed and mainly originates at the edge of the plasma in discharges dominated by ITG according to gyrokinetic calculations. Furthermore, the magnitude of this edge intrinsic torque correlates with the plasma pressure gradient in the pedestal. The intrinsic torque in the plasma core, conversely, correlates most strongly with local turbulence properties. This work generates novel experimental opportunities for validating momentum transport theory and holds the potential to provide the first consistent, physics-based, and validated predictions of momentum transport for future reactor scenarios.   

New measurements of H-mode core density fluctuation wavenumber spectra and tests of quasilinear turbulence modeling

Measurements of the density fluctuation wavenumber spectrum, δn_e(k), obtained with Doppler backscattering (DBS) in ECH-heated H-mode DIII-D plasmas, are reported and used to test predictions from the TGLF code. Remarkable agreement is found between DBS measurements and our novel synthetic DBS diagnostic using measured profiles. The back-scattered power spectrum, P_s(k), was directly measured with DBS over a broad wavenumber range, 0.5 ≤ k ≤ 16 cm^-1 in electron-heated H-mode plasmas possessing low collisionality (ν^*_e < 1), T_e/T_i > 1, and zero injected torque – a regime expected to be relevant for future devices. Measurements reveal a nonuniform spectrum with weak decay (k^-0.6) at low wavenumbers increasing to rapid decay (k^-9.4) at high-k. Starting with the SCOTTY beam tracing code, a novel synthetic DBS diagnostic was developed that allows us to calculate the back-scattered power, P_s, using the TGLF model δn_e(k). TGLF predicts that R/L_Te-driven modes (TEM/ETG) dominate the transport spectra in this plasma regime. Parameter scans with TGLF predict the P_s(k) spectrum is sensitive to small changes in R/L_Te at low and intermediate-k. Interestingly, +10% R/L_Te destabilizes electron modes near k_θρ_s = 1.0, nonlinearly increasing electron thermal and particle fluxes. With +10% R/L_Te, the synthetic DBS diagnostic predicts the formation of a peak near k_θρ_s = 1.0 in the P_s(k) spectrum – which was not observed experimentally. These TGLF predictions, combined with DBS measurements, suggest the mid-radius of this plasma is in a state of mixed ion-electron turbulence. Our results, fluctuation wavenumber spectrum measurements and a novel synthetic diagnostic, allow for significantly improved tests of both reduced turbulence/transport models and nonlinear gyrokinetic simulations (currently underway).   

Thermodynamic bounds on gyrokinetic instabilities and turbulence

For over half a century, an enormous effort has been devoted to the study of microinstabilities in magnetically confined plasmas through gyrokinetic theory. Thousands of papers and millions of lines of code have been devoted to this subject. Most of the results are of highly specialized nature, e.g. the study of particular modes (ITG, ETG, TEM, KBM, RBM, MTM,…) in specific magnetic geometries, but little is known in general about gyrokinetic microinstaiblities, despite the great effort devoted to their study.

This talk will describe how rigorous upper bounds can be derived on the growth of any electrostatic or electromagnetic instability in gyrokinetics, regardless of the magnetic geometry, number of particle species, plasma pressure, and collisions. These bounds are valid not only for linear instability growth, but also for nonlinear turbulence. The reason why they are so general is that they result from thermodynamic considerations of energy and entropy balance. They reflect the fastest possible instantaneous growth of gyrokinetic fluctuation energy, which is much easier to calculate than conventional eigenmodes. In fact, the calculation can be completed, once and for all, for all gyrokinetic instabilities by solving a low-dimensional matrix eigenvalue problem. Comparisons with numerical simulations will be shown, indicating that the upper bounds are usually close to the maximum growth rate that can be achieved in a theta pinch, which, in turn, is a few times larger than that in a typical tokamak or stellarator. Methods of deriving less general but increasingly stringent bounds will also be described, the overall strategy being to study gyrokinetics by proceeding from general properties to more specific ones rather than the other way around.