Gyrokinetic Simulations Research Articles

Prediction of performance and turbulence in ITER burning plasmas via nonlinear gyrokinetic profile prediction

Abstract Burning plasma performance, transport, and the effect of hydrogen isotope (H, D, D-T fuel mix) on confinement has been predicted for ITER baseline scenario (IBS) conditions using nonlinear gyrokinetic profile predictions. Accelerated by surrogate modeling (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), high fidelity, nonlinear gyrokinetic simulations performed with the CGYRO code (Candy et al 2016 J. Comput. Phys. 324 73), were used to predict profiles of Ti , Te , and ne while including the effects of alpha heating, auxiliary power (NBI + ECH), collisional energy exchange, and radiation losses inside of r / a = 0.9. Predicted profiles and resulting energy confinement are found to produce fusion power and gain that are approximately consistent with mission goals ( P fusion = 500 MW at Q = 10) for the baseline scenario and exhibit energy confinement that is within 1σ of the H-mode energy confinement scaling. The power of the surrogate modeling technique is demonstrated through the prediction of alternative ITER scenarios with reduced computational cost. These scenarios include conditions with maximized fusion gain and an investigation of potential resonant magnetic perturbation (RMP) effects on performance with a minimal number of gyrokinetic profile iterations required (3–6). These predictions highlight the stiff ITG nature of the core turbulence predicted in the ITER baseline and demonstrate that Q > 17 conditions may be accessible by reducing auxiliary input power while operating in IBS conditions. Prediction of full kinetic profiles allowed for the projection of hydrogen isotope effects around ITER baseline conditions. The gyrokinetic fuel ion species was varied from H, D, and 50/50 D-T and kinetic profiles were predicted. Results indicate that a weak or negligible isotope effect will be observed to arise from core turbulence in IBS conditions. The resulting energy confinement, turbulence, and density peaking, and the implications for ITER operations will be discussed.

Plasma self-driven current in tokamaks with magnetic islands

Abstract Magnetic island perturbations may cause a reduction in plasma self-driven current that is needed for tokamak operation.
 A novel effect on tokamak self-driven current revealed by global gyrokinetic simulations is due to magnetic-island-induced
3D electric potential structures, which have the same dominant mode numbers as that of the magnetic island,
whereas centered at both the inner and outer edge of the island. The non-resonant potential islands
are shown to drive a current through an efficient nonlinear parallel acceleration of electrons.
In large aspect ratio (large-A) tokamak devices, this new effect can result in a significant
global reduction of the electron bootstrap current when the island size is sufficiently large,
in addition to the local current loss across the island region due to the pressure profile flattening.
It is shown that there exists a critical magnetic island width for large-A tokamaks beyond which
the electron bootstrap current loss is global and increases rapidly with the island size.
As such, this process may introduce a size limit for tolerable magnetic islands in large-A tokamak
devices in the context of steady state operation. On the other hand, the current loss caused by magnetic islands in
low-A tokamaks such as spherical tokamak (ST) NSTX/U is minor.
The reduction of the axisymmetric current by magnetic islands scales with the square of island width.
However, the loss of the current is mainly local to the island region, and the pace of current
loss as the island size increases is substantially slower compared to large-A tokamaks.
In particular, the bootstrap current reduction in STs is even smaller in the reactor-relevant
high-$\beta_p$ regime where neoclassical tearing modes are more likely to develop.

Numerical study of turbulent eddy self-interaction in tokamaks with low magnetic shear. Part II: Nonlinear simulations.

Abstract Using local nonlinear gyrokinetic simulations and building up on linear results from a companion paper (Vol\v{c}okas, 2024), we demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns in tokamaks with weak or zero magnetic shear $\hat{s}$. We observe that this parallel eddy length scales inversely with magnetic shear and at $\hat{s}=0$ is limited by the thermal speed of electrons $v_{th,e}$. We examine the consequences of these ``ultra long" eddies on turbulent transport, in particular, how field line topology mediates strong parallel self-interaction. Our investigation reveals that, through this process, field line topology can strongly affect transport. It can cause transitions between different turbulent instabilities and in some cases triple the logarithmic gradient needed to drive a given amount of heat flux. We also extensively study a novel ``eddy squeezing" effect introduced in (Vol\v{c}okas, 2023), which reduces the perpendicular size of eddies and their ability to transport energy, thus representing a novel approach to improve confinement. Finally, we investigate the triggering mechanism of Internal Transport Barriers (ITBs) using low magnetic shear simulations, shedding light on why ITBs are often easier to trigger where the safety factor has a low-order rational value.

Linear and nonlinear dynamics of self-consistent collisionless tearing modes in toroidal gyrokinetic simulations

We investigate tearing modes (TM) driven by current density gradient in collisionless tokamak plasmas by using the electromagnetic gyrokinetic simulation code ORB5. We elucidate the TM width by simulations for flat profiles, as the absence of background diamagnetic flows implies a small rotation speed, while finite gradients are included to investigate the TM rotation. For flat profiles, the initial saturation width of nonlinearly driven magnetic islands is related to the TM linear growth rate; however, large islands in the initial saturation phase are prone to current density redistribution that reduces the island width in the following evolution. Island-induced E×B and diamagnetic sheared flows develop at the separatrix, able to destabilize the Kelvin–Helmholtz instability (KHI). The KHI turbulence enhances a strong quadrupole vortex flow that reinforces the island decay, resulting in a strong reduction of the island width in an eventual steady state. This process is enhanced by trapped electrons. For finite gradients profile, the TM usually rotates in the electron diamagnetic direction but can change direction when the ion temperature gradient dominates the other gradients. The reduced growth of the TM by diamagnetic effects results in a moderate island size, which remains almost unchanged after the initial saturation. At steady state, strong zonal flows are nonlinearly excited and dominate the island rotation, as expected from previous theoretical and numerical studies. When β is increased, the TM mode is suppressed and a mode with the same helicity but with twisting parity, coupled with the neighboring poloidal harmonics, is destabilized, similar to the kinetic ballooning mode.

Gyrokinetic flux-driven simulations in mixed TEM/ITG regime using a delta-f PIC scheme with evolving background

In the context of global gyrokinetic simulations of turbulence using a particle-in-cell framework, verifying the delta-f assumption with a fixed background distribution becomes challenging when determining quasi-steady state profiles corresponding to given sources over long time scales, where plasma profiles can evolve significantly. The advantage of low relative sampling noise afforded by the delta-f scheme is shown to be retained by considering the background as a time-evolving Maxwellian with time-dependent density and temperature profiles. Implementation of this adaptive scheme to simulate electrostatic collisionless flux-driven turbulence in tokamak plasmas show small and nonincreasing sampling noise levels, which would otherwise increase indefinitely with a stationary background scheme. The adaptive scheme furthermore allows one to reach numerically converged results of quasi-steady state with much lower marker numbers.

Verification of electromagnetic simulation capabilities in global gyrokinetic particle-in-cell code GTS

Recently, the numerical scheme presented by Mishchenko et al. [Phys. Plasmas 21, 052113 (2014); 21, 092110 (2014)] enabled explicit gyrokinetic simulations of low-frequency electromagnetic instabilities in tokamaks at experimentally relevant values of plasma β. This scheme resolved the long-standing cancellation problem that previously hindered gyrokinetic particle-in-cell code simulations of magnetohydrodynamic phenomena with inherently small parallel electric fields. Moreover, the scheme did not employ approximations that eliminate critical tearing-type instabilities. Here, we report on the implementation of this numerical scheme in the global gyrokinetic particle-in-cell code GTS. This implementation allows for a more complete and accurate picture of interaction between small scale turbulence and MHD modes in tokamaks. Additionally, we present a comprehensive set of verification simulations of numerous electromagnetic instabilities relevant to present-day tokamaks. These simulations encompass the kinetic ballooning mode, the internal kink mode, the tearing mode, the micro-tearing mode, and the toroidal Alfven eigenmode destabilized by energetic ions, which are all instrumental in understanding tokamak physics. We will also showcase the preliminary nonlinear simulations of kinetic ballooning instabilities and (2,1) island formation due to tearing mode instability. These simulations validate the accuracy of the scheme implementation and pave the way for studying how these instabilities affect plasma confinement and performance.

Gyrokinetic prediction of core tungsten peaking in a WEST plasma with nitrogen impurities

Abstract Tungsten peaking is predicted in the core of a WEST plasma with total-f gyrokinetic simulations, including both collisional and turbulent transport. This prediction is validated with a synthetic diagnostic of the bolometry. Although nitrogen impurities are shown to reduce the neoclassical peaking of tungsten on-axis, the overall tungsten peaking increases when nitrogen impurities are present, as they reduce the turbulence screening off-axis. This finding is important for the plasma current ramp-up phase of ITER, where light impurities seeding will be desirable to achieve low temperatures at the plasma-facing components and reduce tungsten sputtering. It provides further argument for applying early ECRH heating to maintain margins on the core power balance. The neoclassical peaking factor is cross-verified between XGC and FACIT. The heat flux at separatrix and the heat load width are modeled by XGC and compared to WEST data.

Effects of zonal fields on energetic-particle excitations of reversed shear Alfvén eigenmode: Simulation and theory

Abstract Employing both nonlinear gyrokinetic simulation and analytical theory, we have investigated the effects of zonal (electromagnetic) fields on the energetic particle's drive of reversed shear Alfv'en eigenmodes in tokamak plasmas. Contrary to the conventional expectation, simulations with zonal fields turned on and off in the energetic particle dynamics while keeping the full nonlinear dynamics
of the thermal plasma indicate that zonal fields further enhance the instability drive and lead, thus, to a higher saturation level. These puzzling simulation results can be understood analytically in terms of the general fishbone-like dispersion relation with the correspondingly different energetic-particle phase-space structures induced by the zonal fields. Analytical expressions for the zonal fields beat driven by the reversed shear Alfv'en eigenmodes are also derived, and shown to be in good agreement with the simulation results.

Impurity convection reversal caused by edge localized turbulence for generating a stationary edge radiative layer in the HL-2A tokamak

Abstract Effect of impurity on edge turbulence was investigated on the HL-2A tokamak by using Neon supersonic molecular beam injection (SMBI). For the first time, a stationary radiative layer accompanied by edge localized turbulence lasting more than 100ms is observed at the edge region ρ=0.7-0.9. This duration is much longer than the SMBI pulse length (1.2ms), indicating that the impurity diffusion is on the whole cancelled out by the impurity convection without spreading of the localized turbulence during this period. This implies that the impurity convection is reversed from positive to negative impurity density gradient region. This reversal could be explained by the parallel impurity compression mechanism. The observed turbulence is a broadband electrostatic turbulence (25-70 kHz) propagating in the electron diamagnetic drift direction with normalized poloidal wavenumber of 0.1≤ kθρs≤0.4. It has been found that the excitation of the edge localized turbulence strongly depends on the local collisionality. This feature is qualitatively predicted by the spectral multiscale gyrokinetic turbulence simulation, which suggests that the turbulence could be a dissipative trapped electron mode (DTEM). This experiment demonstrates that mutual interaction between externally injected impurity ions and edge turbulence can generate a stationary edge radiative layer and avoid impurity core accumulation. These results could provide a potential approach for the formation of a stable impurity radiative layer by impurity injection in tokamaks.

Turbulent transport mechanisms and their impact on the pedestal top of JET plasmas with small-ELMs

Abstract Understanding the transport mechanisms that regulate the H-mode pedestal structure is crucial for developing regimes with edge dynamics that are compatible with the thermal and particle load constraints of plasma facing components. In this regard, at the JET tokamak, H-mode plasma regimes featuring small-ELM (BSE) dynamics have been developed, expelling less plasma energy per ELM compared to the standard type-I ELM. The pedestal of these new regimes remains stable against peeling-ballooning modes, leaving its structure unexplained.
In this study, three baseline H-mode JET discharges, a reference with type-I ELM and two BSE regimes, are selected to investigate the turbulent transport mechanisms occurring in pedestals with different structures. The turbulence analysis is conducted using local gyrokinetic simulations around the pedestal top position. The results show that at ion-scales, while hybrid ITG-KBM and KBM are destabilized in the type-I ELM discharge, the BSE regimes are dominated by hybrid ITG-TEM, suggesting a different role of turbulent transport in the two cases. At electron-scales, both regimes are dominated by toroidal and slab ETG, the latter extending up to very small scales. Simulations of turbulence driven by hybrid ITG-TEM focuses on the impact and competition of electromagnetic (EM) effects and equilibrium $\vb*{E}\times\vb*{B}$ shearing. A strong EM stabilization mechanism is found, resulting in a saturated turbulence regime with spectra different from those in the electrostatic limit (ES$_l$). Additionally, while increasing $\vb*{E}\times\vb*{B}$ shearing reduces transport in ES$_l$ simulations, it is observed to have the opposite effect in the EM regime. Finally, stiff ETG transport is also shown to produce transport levels compatible with experimental observations.
The findings of this study suggest the EM stabilization and its competition with $\vb*{E}\times\vb*{B}$ shearing as new key elements determining the nature of the turbulent transport mechanisms around the pedestal top, which need to be considered in reduced models for pedestal limits.

Plasma edge and scrape-off layer turbulence in gyrokinetic simulations of negative triangularity plasmas

Abstract Gyrokinetic simulations in the long-wavelength or drift-kinetic limit are carried out of DIII-D inner-wall-limited (IWL) plasmas to investigate the effect of triangularity on edge and scrape-off layer (SOL) turbulence. The effect of neutral interactions and triangularity on plasma blobs is explored due to the impact blobs can have in setting the SOL width or introducing impurities through interactions with plasma-facing components. Seeded blob simulations with neutrals in shaped SOL scenarios demonstrate that increasing elongation, triangularity, or Shafranov shift decreases radial blob velocities, but neutral interactions have a minor effect. Fully turbulent simulations of DIII-D IWL plasmas include both open- and closed-field-line regions. The negative triangularity (NT) simulation has lower average core Te , lower normalized Te fluctuations, and lower fluxes, but a greater number of coherent structures (blobs) identified with increased size and velocity, on average. Density and electron temperature profiles are within a factor of 2 of experimental values. The increased trapped electron particle fraction in NT simulations is consistent with previous studies.

Surprisingly tight Courant–Friedrichs–Lewy condition in explicit high-order Arakawa schemes

The Arakawa scheme, which exactly conserves energy and enstrophy in two-dimensional hydrodynamics, severely reduces the maximum allowable stable time step compared to the Courant–Friedrichs–Lewy condition when combined with a spectral or spectral-like high-order discretization. We calculate the time step restriction by finding the responsible high frequency eigenfunctions and suggest a remedy. The phenomenon has relevance for analogous methods conserving multiple quadratic invariants in gyrokinetic or magnetohydrodynamic simulations.

Gyrokinetic linear simulation of feedback instability in dipole magnetosphere

We perform a novel linear simulation of the feedback instability by applying a gyrokinetic model to the magnetosphere, where the geomagnetic field is modeled by a dipole magnetic field. In order to avoid huge numerical calculation costs, the effect of the fluctuating mirror force is neglected. It is found that kinetic effects, such as the finite Larmor radius effect and the electron Landau damping, strongly stabilize the feedback instability and form a peak in the perpendicular wave number spectrum of the growth rate. During the linear growth, it is observed that electron free energy has a much larger value than the electromagnetic field perturbation energy. Since such large electron free energy may lead to electron heating and acceleration, it is important to understand its generation mechanism. Analyses based on the energy conservation reveal that the coupling of the non-uniformity of the equilibrium fields along the geomagnetic field and the fluctuating electron distribution gives rise to thermodynamic power generating the electron free energy. A fine velocity space structure around an average Alfvén velocity of the fluctuating electron distribution mainly contributes to drive the thermodynamic power.

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Gyrokinetic simulation of the toroidal rotation driven by the ambipolar radial electric field induced by stochastic magnetic perturbations in a tokamak plasma

Full-f gyrokinetic simulations of hydrogen isotope mixing in tokamak plasmas

Hydrogen isotope mixing phenomena in tokamak plasmas are analyzed using global full-f gyrokinetic simulations. Model plasma parameters are chosen based on hydrogen isotope pellet experiments on JET, in which fast hydrogen isotope mixing in the timescale of the energy confinement time τE occurred after injecting deuterium (D) pellets into hydrogen (H) plasmas. Two numerical experiments are conducted using plasma profiles before and after the pellet injection. In both cases, turbulent fluctuations in the plasma core are characterized by ion temperature gradient driven turbulence. In the former case, the density profile of bulk H ions is kept in a quasi-steady state, and the particle confinement time of bulk H ions τH is an order of magnitude longer than τE. In the latter case, the density profiles of bulk H ions and pellet D ions show transient relaxation in the timescale of τE, and both τH and the timescale of particle pinch τD become comparable to τE, indicating the fast hydrogen isotope mixing. In the toroidal angular momentum balance, it is found that the enhanced ion particle transport leading to the fast hydrogen isotope mixing is driven by the toroidal field stress.

Linearised Fokker–Planck collision model for gyrokinetic simulations

Abstract We introduce a gyrokinetic, linearised Fokker–Planck collision model that satisfies conservation laws and is accurate at arbitrary collisionalities. The differential test-particle component of the operator is exact; the integral field-particle component is approximated using a spherical harmonic and a modified Laguerre polynomial expansion developed by Hirshman and Sigmar (1976 Phys. Fluids 19 1532). The numerical methods of the implementation in the δf-gyrokinetic code stella (Barnes et al 2019 J. Comput. Phys. 391 365–80) are discussed, and conservation properties of the operator are demonstrated. The collision model is then benchmarked against the collision model of the gyrokinetic solver GS2 in the limiting cases of a reduced test-particle collision operator and energy- and momentum-conserving operator. The accuracy of the full collision model is investigated by solving the parallel Spitzer-Härm problem for the transport coefficients. It is shown that retaining collisional energy flux and higher-order terms in the field-particle operator reduces errors in the transport coefficients from 10%–25% for a simple momentum- and energy-conserving model to under 1%.

Reduction or Enhancement of Stellarator Turbulence by Impurities

A systematic study of the impact of impurities on the turbulent heat fluxes is presented for the stellarator Wendelstein 7-X (W7-X) and, for comparison, the Large Helical Device and ITER. By means of nonlinear multispecies gyrokinetic simulations, it is shown that impurities, depending on the sign of their density gradient, can significantly enhance or reduce turbulent ion heat losses. For the relevant scenario of turbulence reduction, an optimal impurity concentration that minimizes the ion heat diffusivity emerges as a universal feature. This result demonstrates the potential of impurities for controlling turbulence and accessing enhanced confinement regimes in fusion plasmas and, in particular, in W7-X. Published by the American Physical Society 2024

Direct microstability optimization of stellarator devices.

Turbulent transport is regarded as one of the key issues in magnetic confinement nuclear fusion, both for tokamaks and stellarators. In this work, we show that a significant decrease in a microstability-based proxy, as opposed to a geometric one, for the turbulent heat flux, namely the quasilinear heat flux, can be obtained in an efficient manner by coupling stellarator optimization with linear gyrokinetic simulations. This is accomplished by computing the quasilinear heat flux at each step of the optimization process, as well as the deviation from quasisymmetry, and minimizing their sum, leading to a balance between neoclassical and the turbulent transport proxy.

Negative triangularity scenarios: from TCV and AUG experiments to DTT predictions

Abstract Experiments, gyrokinetic simulations and transport predictions were performed to investigate if a negative triangularity (NT) L-mode option for the Divertor Tokamak Test (DTT) full-power scenario would perform similarly to the positive triangularity (PT) H-mode reference scenario, avoiding the harmful edge localized modes (ELMs). The simulations show that a beneficial effect of NT coming from the edge/scrape-off layer (SOL) region ρ tor > 0.9 is needed to allow the actual NT L-mode option to perform like the PT H-mode. Dedicated experiments at TCV and AUG, with DTT-like shapes, show an optimistic picture. In TCV, experiments indicate that even with the relatively small triangularity of the DTT NT scenario, a large beneficial effect of NT comes from the plasma edge and SOL, allowing NT L-modes to outperform PT L-modes with the same power input, reaching the same central pressures as PT H-modes with twice as much applied heating power. For AUG, NT plasmas go into H-mode more easily than for TCV, but always present much smaller pedestals compared with PT plasmas with the same input power, showing a much weaker or absent ELM activity. However, NT has a smaller beneficial effect for AUG than for TCV, with NT pulses outperforming PT pulses with the same input power only for an ECRH-only case with relatively low input power. For the considered AUG cases, PT pulses perform better than NT ones at higher ECRH power or with mixed NBI and ECRH power. Based on this analysis, the NT option is a viable alternative for the DTT full power scenario, providing high performance plasmas with reduced or absent ELMs.

NSTX-U research advancing the physics of spherical tokamaks

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, reduced model development, and comparison to NSTX experiment, as well as improved simulation of RF heating. To develop stable non-inductive scenarios needed for steady-state operation, various performance-limiting modes of instability were studied, including MHD, tearing modes, and energetic particle instabilities. Predictive tools were developed, covering disruptions, runaway electrons, equilibrium reconstruction, and control tools. To develop power and particle handling techniques to optimize plasma exhaust in high performance scenarios, innovative lithium-based solutions are being developed to handle the very high heat flux levels that the increased heating power and compact geometry of NSTX-U will produce, and will be seen in future STs. Predictive capabilities accounting for plasma phenomena, like edge harmonic oscillations, ELMs, and blobs, are being tested and improved. In these ways, NSTX-U researchers are advancing the physics understanding of ST plasmas to maximize the benefit that will be gained from further NSTX-U experiments and to increase confidence in projections to future devices.