Yasuhiro Idomura

Gyrokinetic simulations of turbulent transport

This overview is an assessment of the gyrokinetic framework and simulations to compute turbulent transport in fusion plasmas. It covers an introduction to the gyrokinetic theory, the principal numerical techniques which are being used to solve the gyrokinetic equations, fundamentals in gyrokinetic turbulence and the main results which have been brought by simulations with regard to transport in fusion devices and fluctuation measurements.

Overview of toroidal momentum transport

Toroidal momentum transport mechanisms are reviewed and put in a broader perspective. The generation of a finite momentum flux is closely related to the breaking of symmetry (parity) along the field. The symmetry argument allows for the systematic identification of possible transport mechanisms. Those that appear to lowest order in the normalized Larmor radius (the diagonal part, Coriolis pinch, E x B shearing, particle flux, and up-down asymmetric equilibria) are reasonably well understood. At higher order, expected to be of importance in the plasma edge, the theory is still under development.

Consequences of profile shearing on toroidal momentum transport

Turbulent transport of toroidal momentum is investigated in global linear gyrokinetic simulations. The poloidal tilt of the global mode structure arising from the radial variation of the equilibrium (profile shearing) is shown to induce non-diagonal non-pinch momentum transport (residual stress). Local simulations performed at finite radial wave vector show that the effect is mainly due to the antisymmetric radial component of the magnetic drift. The residual stress resulting from profile shearing enhances co-current rotation for ion temperature gradient turbulence and counter-current rotation for trapped electron mode turbulence. (Some figures in this article are in colour only in the electronic version)

Plasma size scaling of avalanche-like heat transport in tokamaks

The influence of plasma size on global ion temperature gradient turbulence is studied with the full-f Eulerian code GT5D (Idomura et al 2009 Nucl. Fusion 49 065029). The gyrokinetic model includes a consistent neoclassical electric field as well as a fixed-power source operator, enabling long-time simulations with self-consistent turbulent transport and equilibrium profiles. The effects of plasma size (from ρ* = 1/100 to ρ* = 1/225) are studied by scaling the minor radius a and the input power. For the first time, worse-than-Bohm scaling is observed under experimentally realistic conditions. For all plasma sizes, avalanches propagate over significant radii but their propagation depends on the radial electric shear. It is found that this quantity does not scale with ρ* due to the building up of intrinsic momentum. Such a dependence can be inferred from a force balance relation, which remains approximately valid in nonlinear simulations. An adaptive parallel momentum source has been implemented in GT5D to damp the parallel momentum profile. The new scan then reveals that the radial electric shear scales with ρ* while the transport is globally higher. These simulations therefore suggest that intrinsic momentum reduces heat transport. This work also addresses another important issue in gyrokinetics: it is shown that for fixed initial physical parameters the turbulent quasi-steady-state is statistically independent of the initial conditions.

Full-f gyrokinetic simulation over a confinement time

A long time ion temperature gradient driven turbulence simulation over a confinement time is performed using the full-f gyrokinetic Eulerian code GT5D. The convergence of steady temperature and rotation profiles is examined, and it is shown that the profile relaxation can be significantly accelerated when the simulation is initialized with linearly unstable temperature profiles. In the steady state, the temperature profile and the ion heat diffusivity are self-consistently determined by the power balance condition, while the intrinsic rotation profile is sustained by complicated momentum transport processes without momentum input. The steady turbulent momentum transport is characterized by bursty non-diffusive fluxes, and the resulting turbulent residual stress is consistent with the profile shear stress theory [Y. Camenen et al., “Consequences of profile shearing on toroidal momentum transport,” Nucl. Fusion 51, 073039 (2011)] in which the residual stress depends not only on the profile shear and the rad...

Accuracy of momentum transport calculations in full-f gyrokinetic simulations

Accuracy of momentum transport calculations in gyrokinetic simulations are studied using the full-f gyrokinetic Eulerian code GT5D. Toroidal angular momentum conservation is examined both in the axisymmetric limit without turbulent fluctuations and in turbulent tokamaks. As shown by Scott and Smirnov (2010 Phys. Plasmas 17 112302), the toroidal angular momentum is conserved when the simulation is based on modern gyrokinetic theory with an energetic consistency. The convergence of turbulent heat and momentum fluxes is examined by implementing higher-order drift and polarization terms. The results support the correctness of the turbulent momentum transport computed using conventional first-order gyrokinetics.

Spectroscopic determination of kinetic parameters for frequency sweeping Alfvén eigenmodes

A method for analyzing fundamental kinetic plasma parameters, such as linear drive and external damping rate, based on experimental observations of chirping Alfven eigenmodes, is presented. The method, which relies on new semiempirical laws for nonlinear chirping characteristics, consists of fitting procedures between the so-called Berk-Breizman model and the experiment in a quasiperiodic chirping regime. This approach is applied to the toroidicity induced Alfven eigenmode (TAE) on JT-60 Upgrade (JT-60U) [N. Oyama et al., Nucl. Fusion 49, 104007 (2009)], which yields an estimation of the kinetic parameters and suggests the existence of TAEs far from marginal stability. Two collision models are considered, and it is shown that dynamical friction and velocity-space diffusion are essential to reproduce nonlinear features observed in experiments. The results are validated by recovering measured growth and decay of perturbation amplitude and by estimating collision frequencies from experimental equilibrium data.

Plasma size and power scaling of ion temperature gradient driven turbulence

The transport scaling with respect to plasma size and heating power is studied for ion temperature gradient driven turbulence using a fixed-flux full-f gyrokinetic Eulerian code. It is found that when heating power is scaled with plasma size, the ion heat diffusivity increases with plasma size in a local limit regime, where fixed-gradient δf simulations predict a gyro-Bohm scaling. In the local limit regime, the transport scaling is strongly affected by the stiffness of ion temperature profiles, which is related to the power degradation of confinement.

Performance evaluations of gyrokinetic Eulerian code GT5D on massively parallel multi-core platforms

A gyrokinetic toroidal five dimensional Eulerian code GT5D [Y.Idomura et. al., Comput. Phys. Commun 179, 391 (2008)] is ported on five advanced massively parallel plat- forms and comprehensive benchmark tests are performed. Sustained performances of the GT5D kernel and their dependency on the memory bandwidth are discussed. By using a novel multi-layer hybrid parallelization model, the size of MPI communicators can be suppressed below ~ 100 up to ~ 107 cores, and the scalability is improved on multi-core platforms. In strong scaling tests, a good scalability is confirmed up to several thousands cores on every platforms, and the maximum sustained performance of ~ 19.4 Tflops (the peak ratio of ~ 10.1%) is achieved using 16384 cores of BX900.