Ion Temperature Gradient Simulations Research Articles

Size convergence of the E×B staircase pattern in flux tube simulations of ion temperature gradient-driven turbulence

The radial size convergence of the E×B staircase pattern is addressed in local gradient-driven flux tube simulations of ion temperature gradient (ITG)-driven turbulence. It is shown that a mesoscale pattern size of ∼57–76 ρ is inherent to ITG-driven turbulence with Cyclone Base Case parameters in the local limit.

Global gyrokinetic simulations of electrostatic microturbulent transport using kinetic electrons in LHD stellarator

Global gyrokinetic simulations of ion temperature gradient (ITG) and trapped electron mode (TEM) in the LHD stellarator are carried out using the gyrokinetic toroidal code (GTC) with kinetic electrons. ITG simulations show that kinetic electron effects increase the growth rate by more than 50% and more than double the turbulent transport levels compared with simulations using adiabatic electrons. Zonal flow dominates the saturation mechanism in the ITG turbulence. Nonlinear simulations of the TEM turbulence show that the main saturation mechanism is not the zonal flow but the inverse cascade of high to low toroidal harmonics. Further nonlinear simulations with various pressure profiles indicate that the ITG turbulence is more effective in driving heat conductivity whereas the TEM turbulence is more effective for particle diffusivity.

Effects of magnetic island on profile formation in flux-driven ITG turbulence

Full-f gyrokinetic simulations of ion temperature gradient (ITG) turbulence in the presence of a magnetic island are performed. A newly developed method for evaluating the flux-surface average is implemented to treat adiabatic electrons inside the magnetic island precisely. A neoclassical simulation below the threshold for linear ITG instability shows that the density profile does not relax at the O-point, although the ion temperature profile is flattened there. This results from the force balance in the direction of the magnetic field between the pressure gradient related to ion parallel motion and the mean radial electric field. A flux-driven ITG turbulence simulation shows a quasi-periodic transport reduction due to interaction between the background temperature profile and the vortex mode, which is a nonlinearly generated mesoscale structure with the same mode numbers as the magnetic island. These results indicate that not only the parallel streaming but also the equilibrium electric field and turbulence contribute significantly to profile formation around a magnetic island.

Effects of light impurities on zonal flow activities and turbulent thermal transport

Nonlinear effects of light impurities on the zonal flow activities and electrostatic ITG (ion temperature gradient) mode are investigated with gyrokinetic simulations. For the investigation, a new multiple-ion-species gyrokinetic Poisson solver is implemented numerically. Benchmark tests for the new solver show good agreements with theoretical and previous simulation results. Nonlinear ITG simulations with and without light impurities are compared. To isolate nonlinear effects of impurities on ITG, simulation parameters are set to exhibit approximately identical spectra of linear growth rates for the admixed and pure deuterium cases (i.e., the cases with and without the impurities). With an intermediate safety factor (∼1.4), the admixed case shows smaller heat transport and more robust E × B staircase structures than the pure deuterium case. The locations of the transport suppression and staircases are strongly correlated, which indicate that light impurities have stabilizing effects on ITG by enhancing the staircase-like E × B shearing. Especially, the radial correlation length of the fluctuations is significantly reduced for the admixed case. On the other hand, the stabilizing effect of impurities is weakened with a high safety factor (∼5). In those cases, strong geodesic acoustic mode activity is observed, and the electric field is dominated by oscillating components instead of stationary staircases.

Global gyrokinetic simulation of neoclassical ambipolar electric field and its effects on microturbulence in W7-X stellarator

Global neoclassical simulations of a model equilibrium of the W7-X stellarator find an ambipolar electric field with either an ion root or an electron root solution depending on the temperature ratio between electrons and ions. The ambipolar electric field is then used as an equilibrium field in the turbulence simulations of ion temperature gradient (ITG) instability. The shear of the ambipolar electric field has modest effects on the ITG linear instability, nonlinear saturation amplitude, and turbulent transport in the ion root case. However, in the electron root case, the ambipolar electric field significantly reduces the linear ITG growth rate, turbulence intensity, and radial correlation length, resulting in an ion heat conductivity comparable to the neoclassical transport level in the strong shear region.

Verification of local electrostatic gyrokinetic simulation of driftwave instability in field-reversed configuration

Local linear simulations of ion temperature gradient (ITG) instabilities using a gyrokinetic particle code GKD1D have been verified by comparing with the analytic dispersion relation in the slab geometry and by benchmarking with a global gyrokinetic code GTC-X in a realistic field-reversed configuration (FRC). Results of ITG simulations using either adiabatic or kinetic electrons exhibit excellent agreements between the two codes for linear frequencies, growth rates, and mode structures. The ITG modes in the FRC scrape-off layer region are mostly dominated by the poloidal m=1 harmonic. Kinetic electrons enhance the subdominant m=2 harmonic and the even parity dominates the ITG mode structure. Kinetic electrons increase the growth rates for the low-n modes, but decrease the growth rates for the high-n modes.

Development and testing of an unstructured mesh method for whole plasma gyrokinetic simulations in realistic tokamak geometry

In this work, we have formulated and implemented a mixed unstructured mesh-based finite element–Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented, and a significant speed-up by a factor of ∼30 is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an application, the ion temperature gradient (ITG) mode is simulated using the simplified gyrokinetic Vlasov-Poisson model. Our simulation and that using the ORB5 code for the DIII-D Cyclone case show reasonable agreement. As an additional application, ITG simulations using an ASDEX Upgrade equilibrium have been performed with density and temperature gradient profiles similar to the Cyclone case. Capabilities of the TRIMEG code for simulations with realistic experimental equilibria in the plasma core and in the whole plasma volume with open field lines are demonstrated.

A 5D gyrokinetic full-[formula omitted] global semi-Lagrangian code for flux-driven ion turbulence simulations

This paper addresses non-linear gyrokinetic simulations of ion temperature gradient (ITG) turbulence in tokamak plasmas. The electrostatic Gysela code is one of the few international 5D gyrokinetic codes able to perform global, full-f and flux-driven simulations. Its has also the numerical originality of being based on a semi-Lagrangian (SL) method. This reference paper for the Gysela code presents a complete description of its multi-ion species version including: (i) numerical scheme, (ii) high level of parallelism up to 500k cores and (iii) conservation law properties.

Unraveling Quasiperiodic Relaxations of Transport Barriers with Gyrokinetic Simulations of Tokamak Plasmas

The generation and dynamics of transport barriers governed by sheared poloidal flows are analyzed in flux-driven 5D gyrokinetic simulations of ion temperature gradient driven turbulence in tokamak plasmas. The transport barrier is triggered by a vorticity source that polarizes the system. The chosen source captures characteristic features of some experimental scenarios, namely, the generation of a sheared electric field coupled to anisotropic heating. For sufficiently large shearing rates, turbulent transport is suppressed and a transport barrier builds up, in agreement with the common understanding of transport barriers. The vorticity source also governs a secondary instability--driven by the temperature anisotropy (T(∥)≠T(⊥)). Turbulence and its associated zonal flows are generated in the vicinity of the barrier, destroying the latter due to the screening of the polarization source by the zonal flows. These barrier relaxations occur quasiperiodically, and generically result from the decoupling between the dynamics of the barrier generation, triggered by the source driven sheared flow, and that of the crash, triggered by the secondary instability. This result underlines that barriers triggered by sheared flows are prone to relaxations whenever secondary instabilities come into play.

Global gyrokinetic ion temperature gradient turbulence simulations of ITER

Global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence in an ideal MHD ITER equilibrium plasma are performed with the ORB5 code. The noise control and field-aligned Fourier filtering procedures implemented in ORB5 are essential in obtaining numerically healthy results with a reasonable amount of computational effort: typical simulations require 109 grid points, 109 particles and, despite a particle per cell ratio of unity, achieve a signal to noise ratio larger than 50. As compared with a circular concentric configuration with otherwise similar parameters (same ρ* = 1/720), the effective heat diffusivity is considerably reduced for the ITER MHD equilibrium. A self-organized radial structure appears, with long-lived zonal flows (ZF), modulating turbulence heat transport and resulting in a corrugated temperature gradient profile. The ratio of long-lived ZF to the fluctuating ZF is markedly higher for the ITER MHD equilibrium as compared with circular configurations, thereby producing a more effective ITG turbulence suppression, in spite of a higher linear growth rate. As a result, the nonlinear critical temperature gradient, R/LTcrit,NL, is about twice the linear critical temperature gradient, R/LTcrit,lin. Moreover, the heat transport stiffness above the nonlinear threshold is considerably reduced as compared with circular cases. Plasma elongation is probably one of the essential causes of this behaviour: indeed, undamped ZF residual levels and geodesic acoustic mode damping are both increasing with elongation. Other possible causes of the difference, such as magnetic shear profile effects, are also investigated.

Analysis and compression of six-dimensional gyrokinetic datasets using higher order singular value decomposition

Higher order singular value decomposition (HOSVD) is explored as a tool for analyzing and compressing gyrokinetic data. An efficient numerical implementation of an HOSVD algorithm is described. HOSVD is used to analyze the full six-dimensional (three spatial, two velocity space, and time dimensions) gyrocenter distribution function from gyrokinetic simulations of ion temperature gradient, electron temperature gradient, and trapped electron mode driven turbulence. The HOSVD eigenvalues for the velocity space coordinates decay very rapidly, indicating that only a few structures in velocity space can capture the most important dynamics. In almost all of the cases studied, HOSVD extracts parallel velocity space structures which are very similar to orthogonal polynomials. HOSVD is also used to compress gyrokinetic datasets, an application in which it is shown to significantly outperform the more commonly used singular value decomposition. It is shown that the effectiveness of the HOSVD compression improves as the dimensionality of the dataset increases.

Turbulent transport of toroidal angular momentum in fusion plasmas

Global nonlinear gyrokinetic simulations of ion temperature gradient (ITG) and collisionless trapped electron mode (CTEM) turbulence find significant spinning up of a plasma in the directions opposite for CTEM and ITG turbulence. The outward momentum convection by the particle flux could be strong enough to overcome the inward momentum pinch and reverse the radial direction of the convective momentum flux. Momentum pinch velocity shows no explicit dependence on background temperature, while it is significantly affected by steepening the background density. Convective momentum fluxes are generally smaller in the CTEM turbulence than the ITG turbulence, while the intrinsic Prandtl number is similar or slightly larger in the CTEM turbulence.

Improvements of the particle-in-cell code EUTERPE for petascaling machines

In the present work we report some performance measures and computational improvements recently carried out using the gyrokinetic code EUTERPE (Jost, 2000 [1] and Jost et al., 1999 [2]), which is based on the general particle-in-cell (PIC) method. The scalability of the code has been studied for up to sixty thousand processing elements and some steps towards a complete hybridization of the code were made. As a numerical example, non-linear simulations of Ion Temperature Gradient (ITG) instabilities have been carried out in screw-pinch geometry and the results are compared with earlier works. A parametric study of the influence of variables (step size of the time integrator, number of markers, grid size) on the quality of the simulation is presented.

Gyrokinetic Vlasov Code Including Full Three-dimensional Geometry of Experiments

A new gyrokinetic Vlasov simulation code, GKV-X, is developed for investigating the turbulent transport in magnetic confinement devices with non-axisymmetric configurations. Effects of the magnetic surface shapes in three-dimensional equilibrium obtained from the VMEC code are accurately incorporated. Linear simulations of ion temperature gradient (ITG) instabilities and zonal flows in the Large Helical Device (LHD) [O. Motojima, N. Oyabu, A. Komori et al., Nucl. Fusion 43, 1674 (2003)] configuration are carried out by the GKV-X code as benchmark tests against the GKV code [T.-H. Watanabe and H. Sugama, Nucl. Fusion 46, 24 (2006)]. For high poloidal wavenumbers, the frequency, growth rate, and mode structure of the ITG instability are influenced by the VMEC geometrical data such as the metric tensor components of the Boozer coordinates, while the difference between the zonal flow responses obtained by the GKV and GKV-X codes is found to be small in the core LHD region.

Avalanchelike bursts in global gyrokinetic simulations

Highly variable flux surface averaged heat fluxes are resolved in gyrokinetic simulations of ion temperature gradient (ITG) turbulence, even in large systems. Radially propagating fronts or avalanches are also seen. Their propagation lengths in gyroradii and relative amplitude remain constant as simulation size is increased, so the avalanches appear to result from local dynamics, rather than global relaxation events. For the Cyclone [Dimits et al., Phys. Plasmas 7, 969 (2000)] case, the avalanche propagation direction is found to depend on the sign of the shearing rate. A mechanism for avalanche propagation based on the advection of turbulence tilted by the shear flows is proposed: The Cyclone linear ITG dispersion relation explains the propagation direction of tilted vortices. It also explains why there is no such preferred direction in a simulation with reduced magnetic shear. The paper explores several models for these bursts. First, certain types of models based on nonlinear heat diffusion equations a...

Nonlinear turbulent transport in magnetic fusion plasmas

For more than a decade, the study of microturbulence driven by ion temperature gradient (ITG) drift instabilities in tokamak devices has been an active area of research in magnetic fusion science for both experimentalists and theorists alike. An important impetus for this avenue of research was the discovery of the radial streamers associated with the ITG modes in the early 1990s using the particle-in-cell (PIC) simulation method. Subsequently, ITG simulations using codes with increasing realism have been made possible by the dramatic increase in computing power. Notable examples were the demonstration of the importance of nonlinearly generated zonal flows in regulating ion thermal transport and the transition from Bohm to gyroBohm scaling with increased device size. In this paper, we will describe an interesting nonlinear physical process, as well as the resulting turbulent transport, that is associated with the interactions between the nonlinear parallel acceleration of the ions and the zonal flow modes. This study was carried out by utilizing a fully parallelized three-dimensional PIC code in global toroidal geometry on the most advanced, modern, massively parallel supercomputers.

Computing ITG turbulence with a full- f semi-Lagrangian code

This paper addresses non-linear global gyrokinetic simulations of ion temperature gradient (ITG) driven turbulence with the G ysela code. The particularity of G ysela code is to use a semi-Lagrangian (SL) scheme for the full distribution function. The 4D non-linear drift-kinetic version of the code already shows the interest in such a SL method which exhibits good properties of energy conservation. The code has been upgrated to run 5D toroidal simulations. Linear benchmarks and non-linear results are presented.

Full radius linear and nonlinear gyrokinetic simulations for tokamaks and stellarators: zonal flows, applied E × B flows, trapped electrons and finite beta

The aim of this paper is to report on recent advances made in global gyrokinetic simulations of ion temperature gradient (ITG) modes and other microinstabilities. The nonlinear development and saturation of ITG modes and the role of E × B zonal flows are studied with a global nonlinear δf formulation that retains parallel nonlinearity and thus allows for a check of the energy conservation property as a means of verifying the quality of the numerical simulation. Due to an optimized loading technique, the conservation property is satisfied with an unprecedented quality well into the nonlinear stage. The zonal component of the perturbation evolves to a quasi-steady state with regions of ITG suppression, strongly reduced radial energy flux and steepened effective temperature profiles alternating with regions of higher ITG mode amplitudes, larger radial energy flux and flattened effective temperature profiles. A semi-Lagrangian approach free of statistical noise is proposed as an alternative to the nonlinear δf formulation. An ASDEX-Upgrade experiment with an internal transport barrier is analysed with a global gyrokinetic code that includes trapped electron dynamics. The weakly destabilizing effect of trapped electron dynamics on ITG modes in an axisymmetric bumpy configuration modelling W7-X is shown in global linear simulations that retain the full electron dynamics. Finite β effects on microinstabilities are investigated with a linear global spectral electromagnetic gyrokinetic formulation. The radial global structure of electromagnetic modes shows a resonant behaviour with rational q values.

Stabilization of ion temperature gradient mode by small-scale zonal flows

Interaction between large-scale turbulence and small-scale sheared flows is a new issue in magnetized plasmas. In this work, the key interaction mechanism is explored by sampling the large-scale ion temperature gradient (ITG) mode and the small-scale zonal flows driven by the electron temperature gradient turbulence. It is analytically found that the small-scale zonal flows lead to a radially nonlocal mode coupling of ITG fluctuations. It can mediate to transfer the fluctuating free energy of an unstable mode in the longer wavelength region to the stable or damped components at shorter wavelengths. Then, the ITG mode is stabilized. Three-dimensional gyrofluid ITG simulations with an initial value code have confirmed the analytical results very well. The spectral analysis also shows a distinctive feature that this kind of interaction can deform the radial decaying spectrum of ITG fluctuation in the short wavelength region. It may be expected to modulate the turbulent ion heat transport in ITG turbulence.

Numerical assessment of ion turbulent thermal transport scaling laws

Numerical simulations of ion temperature gradient driven turbulence are carried out to investigate the parametric dependence of ion thermal transport on the reduced gyroradius and on the local safety factor.Whereas the simulations show a clear proportionality of the conductivityto the gyroradius, the dependence on the safety factor cannot be representedas a simple power law like the one exhibited by the empirical scaling laws.