Gyrokinetic turbulent transport simulations on steady burning condition in D-T-He plasmas
National Institute for Fusion Science, National Institutes of Natural Sciences（国立研究开发法人 国立科学研究所 核聚变科学研究所）；The Graduate University for Advanced Studies（高等研究院）；PRESTO, Japan Science and Technology Agency（日本科学技术振兴机构 PRESTO项目）；Graduate School of Engineering, Kyoto University（京都大学 工学研究科）
Ion temperature gradient(ITG) and trapped electron modes(TEM) driven turbulent transport in an ITER-like plasma is investigated by means of multi-species gyrokinetic Vlasov simulations with D, T, He, and real-mass kinetic electrons including their inter-species collisions. Beyond the conventional zero-dimensional power balance analysis presuming the global energy and particle confinement times, gyrokinetic-simulation-based evaluation of a steady burning condition with He-ash exhaust and D-T fuel inward pinch is demonstrated. It is clarified that a significant imbalance appears in the turbulent particle flux for the fuel ions of D and T, depending on the D-T density ratio and the He-ash accumulation. Then several profile regimes to satisfy Reiter's steady burning condition are, for the first time, identified by the gyrokinetic simulation. Also, the impacts of zonal flows and nonthermal He-ash on the optimal profile regimes are examined.
Adopting the theoretical framework for the generalized fishbonelike dispersion relation, an extended hybrid magnetohydrodynamics gyrokinetic simulation model has been derived analytically by taking into account both thermal ion compressibility and diamagnetic effects in addition to energetic particle kinetic behaviors. The extended model has been used for implementing an eXtended version of Hybrid Magnetohydrodynamics Gyrokinetic Code (XHMGC) to study thermal ion kinetic effects on Alfvénic modes driven by energetic particles, such as kinetic beta induced Alfvén eigenmodes in tokamak fusion pl…
Recently, the electrostatic gyrokinetic Hamiltonian and change of coordinates have been computed to order $ε^2$ in general magnetic geometry. Here $ε$ is the gyrokinetic expansion parameter, the gyroradius over the macroscopic scale length. Starting from these results, the long-wavelength limit of the gyrokinetic Fokker-Planck and quasineutrality equations is taken for tokamak geometry. Employing the set of equations derived in the present article, it is possible to calculate the long-wavelength components of the distribution functions and of the poloidal electric field to order $ε^2$. These h…
In this work, we highlight an issue that may reduce the accuracy of many local nonlinear gyrokinetic simulations - turbulent self-interaction through the parallel boundary condition. Given a sufficiently long parallel correlation length, individual turbulent eddies can span the full domain and "bite their own tails," thereby altering their statistical properties. Such self-interaction is only modeled accurately when the simulation domain corresponds to a full flux surface, otherwise it is artificially strong. For Cyclone Base Case parameters and typical domain sizes, we find that this mechanis…
AI-Accelerated Gyrokinetic Predictions of Turbulent Transport for Stellarator Design Optimization and Experimental Planning
Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）；University of Maryland, College Park（马里兰大学帕克分校）；Oak Ridge National Laboratory（橡树岭国家实验室）；Type One Energy；California Institute of Technology（加州理工学院）；Argonne National Laboratory（阿贡国家实验室）；Princeton University（普林斯顿大学）；University of Wisconsin, Madison（威斯康星大学麦迪逊分校）
We present a new method for formulating closures that learn from kinetic simulation data. We apply this method to phase mixing in a simple gyrokinetic turbulent system - temperature gradient driven turbulence in an unsheared slab. The closure, called the learned multi-mode (LMM) closure, is constructed by, first, extracting an optimal basis from a nonlinear kinetic simulation using singular value decomposition (SVD). Subsequent nonlinear fluid simulations are projected onto this basis and the results are used to formulate the closure. We compare the closure with other closures schemes over a b…
We demonstrate that cross-field transport in the scrape-off layer (SOL) can be moderately increased by electromagnetic effects in high-beta regimes, resulting in a broader electron heat-flux width on the endplates. This conclusion is taken from full-$f$ electromagnetic gyrokinetic simulations of a helical SOL model that roughly approximates the SOL of the National Spherical Torus Experiment (NSTX). The simulations have been performed with the Gkeyll code, which recently became the first code to demonstrate the capability to simulate electromagnetic gyrokinetic turbulence on open magnetic field…
Transport barrier formation and its relation to sheared flows in fluids and plasmas are of fundamental interest in various natural and laboratory observations and of critical importance in achieving an economical energy production in a magnetic fusion device. Here we report the first observation of an edge transport barrier formation event in a gyrokinetic simulation carried out in a realistic tokamak edge geometry. The results show that turbulent Reynolds stress driven sheared ExB flows act in concert with neoclassical orbit loss to quench turbulent transport and form a transport barrier just…
Gyrokinetic simulations have greatly improved our theoretical understanding of turbulent transport in fusion devices. Most gyrokinetic models in use are delta-f simulations in which the slowly varying radial profiles of density and temperature are assumed to be constant for turbulence saturation times, and only the turbulent electromagnetic fluctuations are calculated. New massive simulations are being built to self-consistently determine the radial profiles of density and temperature. However, these new codes have failed to realize that modern gyrokinetic formulations, composed of a gyrokinet…
A novel methodology to analyze non-Gaussian probability distribution functions (PDFs) of intermittent turbulent transport in global full-f gyrokinetic simulations is presented. In this work, the Auto-Regressive Integrated Moving Average (ARIMA) model is applied to time series data of intermittent turbulent heat transport to separate noise and oscillatory trends, allowing for the extraction of non-Gaussian features of the PDFs. It was shown that non-Gaussian tails of the PDFs from first principles based gyrokinetic simulations agree with an analytical estimation based on a two fluid model.
A set of flux tube gyrokinetic equations that includes the effect of the spatial variation of the density, temperature and rotation gradients on the turbulence is derived. This new set of equations uses periodic boundary conditions. In the limit $l_\bot/L \ll 1$, where $l_\bot$ is the characteristic perpendicular length of turbulent structures and $L$ is the characteristic size of the device, this new set of flux tube gyrokinetic equations is shown to be equivalent to the traditional global $δf$ gyrokinetic equations to an order higher in $l_\bot/L$ than the usual flux tube formulations.
The SOL width is a parameter of paramount importance in modern tokamaks as it controls the power density deposited at the divertor plates, critical for plasma-facing material survivability. An understanding of the parameters controlling it has consequently long been sought (Connor et al. 1999 NF 39 2). Prior to Chang et al.(2017 NF 57 11), studies of the tokamak edge have been mostly confined to reduced fluid models and simplified geometries, leaving out important pieces of physics. Here, we analyze the results of a DIII-D simulation performed with the full-f gyrokinetic code XGC1 which includ…
The Large Eddy Simulation (LES) approach - solving numerically the large scales of a turbulent system and accounting for the small-scale influence through a model - is applied to nonlinear gyrokinetic systems that are driven by a number of different microinstabilities. Comparisons between modeled, lower resolution, and higher resolution simulations are performed for an experimental measurable quantity, the electron density fluctuation spectrum. Moreover, the validation and applicability of LES is demonstrated through a series of diagnostics based on the free energetics of the system.
Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the po…
Understanding turbulent transport physics in the tokamak edge and scrape-off layer (SOL) is critical to developing a successful fusion reactor. The dynamics in these regions plays a key role in achieving high fusion performance by determining the edge pedestal that suppresses turbulence in H-mode. Additionally, the survivability of a reactor is set by the heat load to the vessel walls, making it important to understand turbulent spreading of heat as it flows along open magnetic field lines in the SOL. Large-amplitude fluctuations, magnetic X-point geometry, and plasma interactions with materia…
A key uncertainty in the design and development of magnetic confinement fusion energy reactors is predicting edge plasma turbulence. An essential step in overcoming this uncertainty is the validation in accuracy of reduced turbulent transport models. Drift-reduced Braginskii two-fluid theory is one such set of reduced equations that has for decades simulated boundary plasmas in experiment, but significant questions exist regarding its predictive ability. To this end, using a novel physics-informed deep learning framework, we demonstrate the first ever direct quantitative comparisons of turbule…
Differential rotation is induced in tokamak plasmas when an underlying symmetry of the governing gyrokinetic-Maxwell system of equations is broken. One such symmetry-breaking mechanism is considered here: the turbulent acceleration of particles along the mean magnetic field. This effect, often referred to as the `parallel nonlinearity', has been implemented in the $δf$ gyrokinetic code $\texttt{stella}$ and used to study the dependence of turbulent momentum transport on the plasma size and on the strength of the turbulence drive. For JET-like parameters with a wide range of driving temperature…
A collisionless plasma possesses a certain amount of "available energy", which is that part of the thermal energy that can be converted into field energy. Here, a calculation is presented of the available energy carried by trapped electrons in a slender non-omnigenous flux tube of plasma. This quantity is compared with gyrokinetic simulations of the nonlinear saturated radial energy flux resulting from turbulence driven by collisionless trapped-electron modes in various stellarator and a tokamak. The numerical calculation of available energy is extremely fast and shows a strong correlation wit…
Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases consid…
A set of equations is derived describing the macroscopic transport of particles and energy in a thermonuclear plasma on the energy confinement time. The equations thus derived allow studying collisional and turbulent transport self-consistently, retaining the effect of magnetic field geometry without postulating any scale separation between the reference state and fluctuations. Previously, assuming scale separation, transport equations have been derived from kinetic equations by means of multiple-scale perturbation analysis and spatio-temporal averaging. In this work, the evolution equations f…
Understanding the multi-scale neoclassical and turbulence physics in the edge region (pedestal + scrape-off layer) is required in order to reliably predict performance in future fusion devices. We explore turbulent characteristics in the edge region from a multiscale neoclassical and turbulent XGC1 gyrokinetic simulation in a DIII-D like tokamak geometry, here excluding neutrals and collisions. For an H-mode type plasma with steep pedestal, it is found that the electron density fluctuations increase towards the separatrix, and stay high well into the SOL, reaching a maximum value of $δn_e / \b…
3D2V continuum gyrokinetic simulations of electrostatic plasma turbulence in a straight, open-field-line geometry have been performed using the full-$f$ discontinuous-Galerkin code Gkeyll. These simulations include the basic elements of a fusion-device scrape-off layer: localized sources to model plasma outflow from the core, cross-field turbulent transport, parallel flow along magnetic field lines, and parallel losses at the limiter or divertor with sheath model boundary conditions. The set of sheath boundary conditions used in the model allows currents to flow through the walls. In addition …
In magnetized plasma turbulence, the couplings of perpendicular spatial scales that arise due to the nonlinear interactions are analyzed from the perspective of the free-energy exchanges. The plasmas considered here, with appropriate ion or electron adiabatic electro-neutrality responses, are described by the gyrokinetic formalism in a toroidal magnetic geometry. Turbulence develops due to the electrostatic fluctuations driven by temperature gradient instabilities, either ion temperature gradient (ITG) or electron temperature gradient (ETG). The analysis consists in decomposing the system into…
Detecting Shearless Phase-Space Transport Barriers in Global Gyrokinetic Turbulence Simulations with Test Particle Map Models
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Zhejiang University（浙江大学）；Princeton University（普林斯顿大学）；University of São Paulo（圣保罗大学）；Princeton Plasma Physics Laboratory（普林斯顿等离子体物理实验室）
Magnetic confinement fusion reactors suffer severely from heat and particle losses through turbulent transport, which has inspired the construction of ever larger and more expensive reactors. Numerical simulations are vital to their design and operation, but particle collisions are too infrequent for fluid descriptions to be valid. Instead, strongly magnetised fusion plasmas are described by the gyrokinetic equations, a nonlinear integro-differential system for evolving the particle distribution functions in a five-dimensional position and velocity space, and the consequent electromagnetic fie…
We analyze plasma heating in weakly collisional kinetic Alfvén wave (KAW) turbulence using high resolution gyrokinetic simulations spanning the range of scales between the ion and the electron gyroradii. Real space structures that have a higher than average heating rate are shown not to be confined to current sheets. This novel result is at odds with previous studies, which use the electromagnetic work in the local electron fluid frame, i.e. $\mathbf{J} \!\cdot\! (\mathbf{E} + \mathbf{v}_e\times\mathbf{B})$, as a proxy for turbulent dissipation to argue that heating follows the intermittent sp…
The theoretical investigation of relevant turbulent transport mechanisms in H-mode pedestals is a great scientific and numerical challenge. In this study, we address this challenge by global, nonlinear gyrokinetic simulations of a full pedestal up to the separatrix, supported by a detailed characterisation of gyrokinetic instabilities from just inside the pedestal top to pedestal centre and foot. We present ASDEX Upgrade pedestal simulations using an upgraded version of the gyrokinetic, Eulerian, delta-f code GENE (genecode.org) that enables stable global simulations at experimental plasma bet…
Energetic particles, Shafranov shift and finite $β$ effects on TAE, KBM and ITG instabilities in global electromagnetic gyrokinetic simulations
Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Max-Planck-Institut für Plasmaphysik（马克斯·普朗克等离子体物理研究所）；Université de Lorraine（洛林大学）；De Vinci Higher Education（德文奇高等教育）；University of Warwick（华威大学）
Spherical tokamaks (STs) have been shown to possess properties desirable for a fusion power plant such as achieving high plasma ? and having increased vertical stability. To understand the confinement properties that might be expected in the conceptual design for a high $β$ ST fusion reactor, a 1GW ST plasma equilibrium was analysed using local linear gyrokinetics to determine the type of micro-instabilities that arise. Kinetic ballooning modes (KBMs) and micro-tearing modes (MTMs) are found to be the dominant instabilities. The parametric dependence of these linear modes was determined and fr…
Local nonlinear gyrokinetic simulations of tokamak plasmas demonstrate that turbulent eddies can extend along magnetic field lines for hundreds of poloidal turns when the magnetic shear is very small. By accurately modeling different field line topologies (e.g. low-order, almost rational, or irrational safety factor), we show that the parallel self-interaction of such "ultra long" eddies can dramatically reduce heat transport. This reveals novel strategies to improve confinement, constitutes experimentally testable predictions, and illuminates past observations of internal transport barriers.
Self-consistent simulations of neoclassical and electrostatic turbulent transport in a DIII-D H-mode edge plasma under resonant magnetic perturbations (RMPs) have been performed using the global total-f gyrokinetic particle-in-cell code XGC, in order to study density-pump out and electron heat confinement. The RMP field is imported from the extended magneto-hydrodynamics (MHD) code M3D-C1, taking into account the linear two-fluid plasma response. With both neoclassical and turbulence physics considered together, the XGC simulation reproduces two key features of experimentally observed edge tra…
Long global gyrokinetic turbulence simulations are particularly challenging in situations where the system deviates strongly from its initial state and when fluctuation level are high e.g. in strong gradient regions. For Particle-in-Cell simulations, statistical sampling noise accumulation from large marker weights due to large deviations from the control variate of a delta-f scheme make such simulations often impractical. An adaptive control variate in the form of a flux-surface-averaged Maxwellian with a time-dependent temperature profile is introduced in an attempt to alleviate the former p…
The gyrokinetic particle simulation serves as a powerful tool for the studies of transport, nonlinear phenomenon, and energetic particle physics in tokamak plasmas. While most gyrokinetic simulations make use of the scalar and vector potentials, a new model (GK-E&B) has been developed by using the E and B field in a general and comprehensive form and has been implemented in simulating kinetic Alfvén waves in uniform plasma [Chen et al, Science China Phys. Mechanics & Astronomy 64 (2021)]. In our work, the Chen et al. GK-E&B model has been expressed in general tokamak geometry explicitly using …
Two symmetries of the local nonlinear delta-f gyrokinetic system of equations in tokamaks in the high flow regime are presented. The turbulent transport of toroidal angular momentum changes sign under an up-down reflection of the tokamak and a sign change of both the rotation and the rotation shear. Thus, the turbulent transport of toroidal angular momentum must vanish for up-down symmetric tokamaks in the absence of both rotation and rotation shear. This has important implications for the modeling of spontaneous rotation.
Turbulence is shown to be critical to the onset and evolution of the neoclassical tearing mode, affecting both its growth and rotation. The interaction is here studied for the first time in the three dimensional, toroidal gyrokinetic framework. Turbulent fluctuations do not destroy the growing island early in its development, which maintains a coherent form as it grows, in fact the island is seeded and its rotation frequency determined, by nonlinear interaction. This process provides an initial structure that is of the order of an ion gyro-radius wide, allowing the island to rapidly reach a la…
The nonlinear dynamics of beta-induced Alfvén Eigenmodes (BAE) driven by energetic particles (EP) in the presence of ion-temperature-gradient (ITG) turbulence is investigated, by means of selfconsistent global gyrokinetic simulations and analytical theory. A tokamak magnetic equilibrium with large aspect ratio and reversed shear is considered. A previous study of this configuration has shown that the electron species plays an important role in determining the nonlinear saturation level of a BAE in the absence of turbulence [A. Biancalani, et al., J. Plasma Phys. (2020)]. Here, we extend the st…
Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behavior of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measureme…
