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Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows.
Understanding the relevant turbulent transport mechanisms at the edge of a high-performance tokamak is essential for predicting and optimizing the H-mode pedestal structure in future burning plasma devices. Global electromagnetic gyrokinetic simulations will be performed based on representative experimental pedestal scenarios in order to clarify which instabilities are most important for each of the particle and heat transport channels. Edge transport modeling will be performed in order to estimate and bound the particle and heat sources—e.g., the ionization density source and the atomic energy loss channels due to ionization, charge exchange, and radiation. Comparisons will be made with data from the DIII-D, JET, C-Mod and NSTX or MAST experiments.
Microturbulence can produce stationary fine-scale radial corrugations on the plasma density and temperature gradients in magnetic confinement fusion devices. We show that these structures play a significant role in regulating turbulent transport. We focus on the pedestal, studying electron-temperature-gradient (ETG) mode destabilisation and saturation in the presence of radial corrugations on the electron temperature gradient that could result from microtearing turbulence. A linear dispersion relation is derived for a shearless slab case, which indicates that in the presence of a sinusoidal background corrugation, each ETG mode splits into three distinct eigenvalues, with one being the original, one being more unstable and one being less unstable. However, despite the presence of more unstable linear modes, nonlinear gyrokinetic simulations of ETG with corrugated background electron temperature show a reduction of fluxes. Our investigation reveals a radial variation of the phase velocity of the modes that is proportional to the diamagnetic drift velocity and the local pressure gradient. The associated profile shearing breaks the turbulent eddies apart, reducing the transport level. This profile shearing resulting from fine-scale pressure corrugations could be a ubiquitous turbulence saturation mechanism not just in Fusion plasmas, but in Astrophysics and other areas.
In this paper, we report the key role that toroidal rotation and the related ExB shear physics played in the very high energy confinement quality (H98y2>1.5) of super H-mode experiments on DIII-D. Experiments show that the energy confinement quality decreases when toroidal rotation decreases due to the decreased externally controlled torque per particle. Meanwhile, the total pedestal pressure in the experiments remains very high during the rotation and confinement quality change. TGYRO transport modeling suggests the contribution from rotation in the ExB shear is responsible for the confinement quality in excess of standard H-mode (H98y2~1). CGYRO gyrokinetic simulations reveal the governing physics in the core plasma of super H-modes: significant up-shift of nonlinear the ITG critical gradient is observed when applying ExB shear physics in the modeling based on experimental data. The effects of other physical parameters and contribution from pedestal height, which may play minor roles in this study, are also discussed.
The saturated state of turbulence driven by the ion-temperature-gradient instability is investigated using a two-dimensional long-wavelength fluid model that describes the perturbed electrostatic potential and perturbed ion temperature in a magnetic field with constant curvature (a $Z$ -pinch) and an equilibrium temperature gradient. Numerical simulations reveal a well-defined transition between a finite-amplitude saturated state dominated by strong zonal-flow and zonal temperature perturbations, and a blow-up state that fails to saturate on a box-independent scale. We argue that this transition is equivalent to the Dimits transition from a low-transport to a high-transport state seen in gyrokinetic numerical simulations (Dimits et al. , Phys. Plasmas , vol. 7, 2000, 969). A quasi-static staircase-like structure of the temperature gradient intertwined with zonal flows, which have patch-wise constant shear, emerges near the Dimits threshold. The turbulent heat flux in the low-collisionality near-marginal state is dominated by turbulent bursts, triggered by coherent long-lived structures closely resembling those found in gyrokinetic simulations with imposed equilibrium flow shear (van Wyk et al. , J. Plasma Phys. , vol. 82, 2016, 905820609). The breakup of the low-transport Dimits regime is linked to a competition between the two different sources of poloidal momentum in the system – the Reynolds stress and the advection of the diamagnetic flow by the $\boldsymbol {E}\times \boldsymbol {B}$ flow. By analysing the linear ion-temperature-gradient modes, we obtain a semi-analytic model for the Dimits threshold at large collisionality.
We use the global gyrokinetic stellarator code XGC-S to look at turbulence physics in geometry of the proposed quasi-axisymmetric stellarator, QUASAR. In this article, the XGC-S code is first verified for nonlinear simulations of ion temperature gradient-driven turbulence by a successful benchmark with the established nonlinear tokamak code XGC1 in a CYCLONE-like tokamak case. We then apply the XGC-S code to QUASAR for nonlinear turbulence physics. We find that the highly poloidally localized linear mode gives way to a more evenly distributed nonlinear turbulent structure. Furthermore, the radial extent of the mode increases and occupies a large fraction of the volume, despite the initially localized temperature profile, as the profiles relax.
Magnetic reconnection is believed to be one of the most fundamental physical processes in laboratory and space plasmas. Fundamental physics of collisionless reconnection under general conditions of finite guide magnetic field, realistic electron-to-ion mass ratio, and in 3D geometries is still not adequately understood. The major goal of this project is to study the physics of collisionless magnetic reconnection in a current sheet under a finite guide field and with a realistic ion-to-electron mass ratio mi/me. Under the support of this DoE grant, we have made significant progress in (1) the investigation of linear and nonlinear current sheet instabilities under a wide range of guide field using the 3-D gyro kinetic electron and fully kinetic ion (GeFi) particle simulation model and (2) the investigation of fully nonlinear reconnection process with a strong guide field with the GeFi simulations. Furthermore, (3) we have extended the study to the realistic geometry of the magnetopause using 3D global hybrid simulations. This study, from local to global scales and for 3-D physics at plasma boundaries, has provides advanced theoretical understanding of the fundamental physics of magnetic reconnection in laboratory and space plasma regimes on multi-scales.
Axisymmetric (m = 0) gyrokinetic and extended-MHD simulations of a sheared-flow Z-pinch plasma are performed with the high-order finite volume code COGENT. The present gyrokinetic model solves the long-wavelength limit of the gyrokinetic equation for both ion and electron species coupled to the electrostatic gyro-Poisson equation for the electrostatic potential. The extended-MHD model is electromagnetic and includes the effects of the gyro-viscous pressure tensor, diamagnetic electron and ion heat fluxes, and generalized Ohm's law. Additionally, a prominent feature of this work is that the radial profiles for the plasma density and temperature are taken from the fusion Z-pinch experiment (FuZE), and the magnetic field profile is obtained as a solution of the MHD force balance equation. Such an approach allows to address realistic plasma parameters and provide insights into the current and planned experiments. In particular, it is demonstrated that the radial profiles play an important role in stabilization, as the embedded guiding center (E×B ) drift has a strong radial shear, which can contribute to the Z-pinch stabilization even in the absence of the fluid flow shear. The results of simulations for the FuZE plasma parameters show a decrease in the linear growth rate with an increase in the flow shear; however, full stabilization in the linear regime is not observed even for large (comparable to the Alfvén velocity) radial variations of the axial flow. Nonlinear stability properties of the FuZE plasmas are also studied, and it is found that profile broadening can have a pronounced stabilizing effect in the nonlinear regime.
Here, verification and linear validation of the internal kink instability in tokamak have been performed for both gyrokinetic (GTC) and kinetic-MHD codes (GAM-solver, M3D-C1-K, NOVA, XTOR-K). Using realistic magnetic geometry and plasma profiles from the same equilibrium reconstruction of the DIII-D shot #141216, these codes exhibit excellent agreement for the growth rate and mode structure of the internal kink mode when all kinetic effects are suppressed. The simulated radial mode structures, obtained from linear simulations, are in reasonable agreement with the normalised electron cyclotron emission measurement after adjusting, within the experimental uncertainty, the safety factor q = 1 flux-surface location in the equilibrium reconstruction. Compressible magnetic perturbations strongly destabilize the kink, while poloidal variations of the equilibrium current density reduce the growth rate of the kink. Furthermore, kinetic effects of thermal ions are found to decrease the kink growth rate in kinetic-MHD simulations, but increase the kink growth rate in gyrokinetic simulations, due to the additional drive of the ion temperature gradient and parallel electric field. Kinetic thermal electrons are found to have negligible effects on the internal kink instability.
The effect of neutral interactions on scrape-off layer (SOL) turbulence is investigated in a continuum gyrokinetic code that has been coupled to a continuum kinetic model of neutral transport. This extends the work of a previous paper, which compared two NSTX SOL simulations in simple helical geometry, one with neutrals and one without. The former included electron-impact ionization, charge exchange, and wall recycling. Here, the case with neutrals is compared to a gyrokinetic-only simulation that includes an effective ionization source to separate the effect of sourcing from charge exchange collisions. It is observed that sourcing accounts for many features of the simulated SOL with neutrals, including density and temperature magnitudes and reduced normalized density fluctuations, but differences persist. In particular, a flatter density profile results due to changes in parallel transport when neutral collisions are included, illustrating the importance of neutral drag on global plasma properties. An analysis of coherent turbulent structures, or blobs, in these simulations demonstrates the case with neutrals has slower and larger blobs. Here, a series of seeded blob simulations corroborates the blob velocity observation. In general, the blob motion does not contribute significantly to radial transport in these simulations.
We present ContourNet, a deep learning approach to identify salient local isocontours as blobs in large-scale 5D gyrokinetic tokamak simulation data. Blobs-regions of high turbulence that run along the edge wall down toward the diverter and can damage the tokamak-are non-well-defined features but have been empirically localized by isocontours in 2D normalized fluctuating density fields. The key of our study is to train ContourNet to follow the empirical rules to detect blobs over the time-varying simulation data. The architecture of ContourNet is a convolutional neural segmentation network: the inputs are the density field and a rasterized isocontour; the output is a set of isocontour encircling blobs. At the training stage, we feed the network with manually identified isocontours and propagated labels. At the inference stage, we extract isocontours from the segmented blob regions. Results show that our approach can achieve both high accuracy and performance, which enables scientists to understand the blob dynamics influencing the confinement of the plasma.
The evolution of the particle weight in a δf particle-in-cell simulation depends on the marker distribution that can evolve in a turbulent field due to turbulent diffusion. When Monte Carlo methods are used to implement the test particle collision operator, or when the particle motion is not strictly Hamiltonian in a collisionless simulation, the marker distribution will evolve along the particle trajectory and, in general, cannot be known exactly. A two-dimensional numerical marker distribution is proposed as an approximation. It is shown to be advantageous over other common methods for evaluating the marker distribution in long-time turbulence simulations. A generalized two-weight δf-method is proposed to mitigate the marker evolution problem.
Extensive linear and nonlinear simulations to study electron temperature gradient (ETG) stability and thermal transport in National Spherical Torus Experiment (NSTX) and NSTX-U plasmas were performed using the fully electromagnetic gyrokinetic code CGYRO. Linear simulations were performed to determine ETG thresholds in different discharges, showing that ETG modes in spherical tokamaks can present different scalings compared to conventional aspect-ratio tokamaks. Nonlinear gyrokinetic simulations were conducted for selected cases to calculate electron thermal transport and compare to experimental values. Results are also compared with those of ETG modes in the multi-mode model and the Trapped-Gyro-Landau-Fluid reduced model codes, to better understand their applicability in spherical tokamaks.
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We derive the E × B shearing rate associated with vortex flow inside a macroscopic magnetic island (MI) in axisymmetric toroidal geometry. Due to the elongation of the MI and incompressibility of the E × B flow, the shearing rate near X-points is much lower than that near the mid-plane (x-axis of the local Cartesian coordinate) of the MI on the same flux surface. Furthermore, the rate formally vanishes at the X-points where the local poloidal magnetic field associated with the MI stagnates. Here, this calculation of E × B shearing profile and, in particular, minimal E × B shear near the X-points is consistent with the recent experimental finding that turbulence tends to spread into an MI through regions around the X-points and can contribute to more thorough quantitative interpretation of the results from experiments and simulations.
Magnetic reconnection in W7-X is studied by means of global numerical simulations in a series of models of increasing complexity. The magnetic geometry ranges from that of a cylinder to the full three-dimensional field of W7-X, and the equations solved range from ideal magnetohydrodynamics (MHD) to gyrokinetics. We simulate plasmas from the first operation phase with electron cyclotron current drive (ECCD). These are characterized by an equilibrium magnetic field featuring an ECCD-distorted 'humped' profile of the rotational transform ι, with ι = 1 in two radial locations. Such plasmas generally show sawtooth activity, hence motivating the present study. We pay particular attention to the role of equilibrium current density gradients in the destabilization of reconnecting modes. When the equilibrium temperature and density gradients are artificially suppressed (to eliminate the pressure gradient drive), the perturbed electrostatic potential is radially localized between the locations at which ι = 1. This is shown with a purely collisionless gyrokinetic model, in cylindrical geometry. In the real toroidal geometry of W7-X, for a non-ideal MHD model including a uniform resistivity, electron inertia and (numerical) viscosity, the same qualitative behaviour is observed. In particular, even if a resonant (m, n) = (1, -1) perturbation is initialized, the most unstable mode is the (m, n) = (-4, 4), where m and n are the poloidal and toroidal mode numbers, respectively. Other modes are destabilized due to geometric coupling. The growth rate of this instability scales as η 1/3 , where η is the plasma resistivity, thus suggesting that ECCD drives ideal MHD stable W7-X plasmas towards non-ideal marginality. An ideal magnetohydrodynamic analysis confirms the result. A fluid-kinetic hybrid version of the EUTERPE code shows that gyrokinetic ions have a stabilizing effect on these modes. For W7-X relevant collisionalities, the growth rate scales linearly with the electron skin depth, d e . Implications of our results for sawtoothing W7-X operation are discussed.
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 compute exact fluxes by a quasilinear method is determined using linear eigenmodes computed with the gyrokinetic code. A model of this non-linear intensity is constructed using the linear eigenmode properties and the geometry shape functions obtained from the 3D intensity spectrum. The model computes the poloidal wavenumber spectrum of the electron and ion energy fluxes with unprecedented accuracy. In conclusion, new insights are gained into the way zonal flow mixing saturates ion-scale turbulence by controlling the radial wavenumber width of the turbulence spectrum.
Pair plasmas, collections of both matter and antimatter particles of equal mass, represent a paradigm for the study of basic plasma science, and many open questions exist regarding these unique systems. They are found in many astrophysical settings, such as gamma-ray bursts, and have recently also been produced in carefully designed laboratory experiments. A central research topic in plasma physics is instability; however, unlike their more common ion–electron siblings, pair plasmas are generally thought to be stable to cross field pressure gradients in homogeneous magnetic fields. It is shown here by means of kinetic full-f simulations that, when a pressure gradient is first established, the Gradient-driven Drift Coupling mode is destabilized and becomes turbulent. Force balance is eventually achieved by a combination of flattened pressure profiles due to turbulent transport and establishment of a magnetic field gradient, saturating the growth. During the unstable phase, key physics can be captured by a δf gyrokinetic description, where it is shown analytically and numerically that parallel particle motion results in a coupling of all electromagnetic field components. A fluid model derived therefrom accurately predicts linear eigenmodes and is used to resolve global profile effects. For laser-based electron–positron plasma experiments, prompt instability is predicted with growth times much shorter than plasma lifetimes. Similarly, growth rates are calculated for the planned APEX experiment as well as gamma-ray burst scenarios, suggesting that the instability may contribute to the early evolution of these systems.