S. Leerink

Anomalous transport and multi-scale drift turbulence dynamics in tokamak ohmic discharge as measured by high resolution diagnostics and modeled by full-f gyrokinetic code

Quantitative reproduction of selected micro-, meso- and macro-scale transport phenomena as measured in the FT-2 tokamak is reached by Elmfire global full-f nonlinear gyrokinetic particle-in-cell simulation predictions. A detailed agreement with mean equilibrium flows, oscillating fine-scale zonal flows and turbulence radial correlation length observed by a set of sophisticated microwave backscattering techniques, as well as a good fit of the thermal diffusivity data in the central and gradient region of discharge are demonstrated. Both the shift and the broadening of the power spectrum of synthetic and experimental Doppler reflectometry diagnostics have been found to overlap perfectly at various radial positions, indicating similar rotation and spreading of the selected density fluctuations. At the same time similar radial electric field dynamics, spatial structure and outward geodesic acoustic mode (GAM) propagation have been observed by comparisons of the probability distribution function, the dominant frequency, the coherence and the cross-phase of the simulated and experimentally measured radial electric field fluctuations, identifying the turbulent driven GAM as a key contributor to the observed strong temporal variation of the radial electric field affected by impurity ions.

The isotope effect in turbulent transport control by GAMs. Observation and gyrokinetic modeling

A comparative investigation of the isotope effect in multi-scale anomalous transport phenomena is performed both experimentally by highly localized turbulence diagnostics in comparable hydrogen and deuterium FT-2 tokamak discharges and theoretically with the help of global gyrokinetic modeling. Substantial excess of the geodesic acoustic mode (GAM) amplitude, radial wavelength and correlation length in a wide spatial region of deuterium discharge resulting in stronger modulation of drift-wave turbulence level is demonstrated by both approaches. A larger turbulence radial correlation length is found at LFS in D-discharge in experiment and a stronger modulation of gyrokinetic particles and energy fluxes is shown there by the gyrokinetic code. The gyrokinetic modeling demonstrated comparable levels of drift wave density and electric field fluctuations in hydrogen and deuterium discharges. Nevertheless, the mean value of the ion energy and particle anomalous flux provided by modeling shows the systematic isotope effect at all radii.

Gyrokinetic full-torus simulations of ohmic tokamak plasmas in circular limiter configuration

Abstract The gyrokinetic full 5D particle distribution code ELMFIRE has been extended to simulate circular tokamak plasmas from the magnetic axis to the limiter scrape-off-layer. The predictive power of the code in the full-torus configuration is tested via its ability to reproduce experimental steady-state profiles in FT-2 ohmic L-mode plasmas. The results show that the experimental profile solution is not reproduced numerically due to the difficulty of obtaining global power balance. This is verified by cross-comparison of ELMFIRE code versions, which shows also the impact of boundary conditions and grid resolution on turbulent transport.

Poloidal inhomogeneity of turbulence in the FT-2 tokamak by radial correlation Doppler reflectometry and gyrokinetic modelling

The poloidal dependence of the drift-wave turbulence characteristics is investigated at the FT-2 tokamak by radial correlation Doppler reflectometry (RCDR) technique and using the full distribution function global gyrokinetic modelling by ELMFIRE code. The poloidal variation of the turbulence radial correlation length from 0.2–0.55 cm is demonstrated both by measurement and computation. The turbulence correlation length rapidly decreases from the top of the poloidal cross-section to the high field side and then steadily grows in the poloidal direction. A well-pronounced excess of the turbulence radial correlation length in deuterium over its value in hydrogen discharges is demonstrated.

Interpolation for momentum conservation in 3D toroidal gyrokinetic particle simulation of plasmas

Abstract A linear momentum conserving interpolation for the electric field in a three-dimensional toroidal particle-in-cell gyrokinetic plasma simulation in a tokamak configuration is found unstable due to the false divergence of E → × B → flow of particles. A paradigm 8-point finite difference for interpolation of the radial electric field on the poloidal plane is proposed which stabilizes the simulation.

Physics of GAM-initiated L–H transition in a tokamak

Based on experimental observations using the TUMAN-3M and FT-2 tokamaks, and the results of gyrokinetic modeling of the interplay between turbulence and the geodesic acoustic mode (GAM) in these installations, a simple model is proposed for the analysis of the conditions required for L–H transition triggering by a burst of radial electric field oscillations in a tokamak. In the framework of this model, one-dimensional density evolution is considered to be governed by an anomalous diffusion coefficient dependent on radial electric field shear. The radial electric field is taken as the sum of the oscillating term and the quasi-stationary one determined by density and ion temperature gradients through a neoclassical formula. If the oscillating field parameters (amplitude, frequency, etc) are properly adjusted, a transport barrier forms at the plasma periphery and sustains after the oscillations are switched off, manifesting a transition into the high confinement mode with a strong inhomogeneous radial electric field and suppressed transport at the plasma edge. The electric field oscillation parameters required for L–H transition triggering are compared with the GAM parameters observed at the TUMAN-3M (in the discharges with ohmic L–H transition) and FT-2 tokamaks (where no clear L–H transition was observed). It is concluded based on this comparison that the GAM may act as a trigger for the L–H transition, provided that certain conditions for GAM oscillation and tokamak discharge are met.

Turbulence and anomalous tokamak transport control by Geodesic Acoustic Mode

The elementary process of turbulence control by Geodesic Acoustic Modes (GAMs) leading to modulation of its level at the GAM frequency is for the first time supported by experimental observations at the FT-2 tokamak. The modulation effect is confirmed by the global total-distribution-function gyrokinetic modelling of the tokamak discharge, predicting strong modulation of the electron thermal diffusivity induced by GAMs, which propagates inward and possesses the GAM temporal and spatial structure.

Comparison of gyrokinetic simulations of parallel plasma conductivity with analytical models

A full f gyrokinetic particle-in-cell simulation including Coulomb collisions is shown to reproduce the results from analytic estimates for parallel plasma conductivity in the collisional parameter regime, with reasonably good agreement, when varying the temperature and impurity content of the plasma. Differences between the models are discussed.

Numerically stable method for kinetic electrons in gyrokinetic particle-in-cell simulation of toroidal plasmas

The direct implicit method with a second-order implicit integration scheme is formulated for and applied to the electron parallel nonlinearity in global electrostatic gyrokinetic particle-in-cell simulations of toroidal fusion plasmas. The method shows improved numerical accuracy and stability properties compared to the direct implicit method with a first-order integration scheme. The conservation of total energy and toroidal angular momentum are analyzed by both techniques and the results are presented.

Fast synthetic X-mode Doppler reflectometry diagnostics for the full-f global gyrokinetic modeling of the FT-2 tokamak

The fast linear (Born approximation) version of the X-mode Doppler reflectometry (DR) synthetic diagnostics is developed in the framework of the ELMFIRE global gyrokinetic modeling of the FT-2 tokamak ohmic discharge. The DR signal frequency spectra and the dependence of their frequency shift and shape on the probing antenna position are computed and shown to be similar to those measured in the high magnetic field side probing DR experiment at the FT-2 tokamak. The fluctuation poloidal velocities are determined using the DR experiment and synthetic diagnostics and shown to be within 15%. However, the computed and measured dependences of the DR signal power on the antenna position appear to be different presumably due to underestimation of the small-scale trapped electron mode turbulence component in the measurement region by the code.The fast linear (Born approximation) version of the X-mode Doppler reflectometry (DR) synthetic diagnostics is developed in the framework of the ELMFIRE global gyrokinetic modeling of the FT-2 tokamak ohmic discharge. The DR signal frequency spectra and the dependence of their frequency shift and shape on the probing antenna position are computed and shown to be similar to those measured in the high magnetic field side probing DR experiment at the FT-2 tokamak. The fluctuation poloidal velocities are determined using the DR experiment and synthetic diagnostics and shown to be within 15%. However, the computed and measured dependences of the DR signal power on the antenna position appear to be different presumably due to underestimation of the small-scale trapped electron mode turbulence component in the measurement region by the code.