Salomon Janhunen

Full f gyrokinetic method for particle simulation of tokamak transport

A gyrokinetic particle-in-cell approach with direct implicit construction of the coefficient matrix of the Poisson equation from ion polarization and electron parallel nonlinearity is described and applied in global electrostatic toroidal plasma transport simulations. The method is applicable for calculation of the evolution of particle distribution function f including as special cases strong plasma pressure profile evolution by transport and formation of neoclassical flows. This is made feasible by full f formulation and by recording the charge density changes due to the ion polarization drift and electron acceleration along the local magnetic field while particles are advanced. The code has been validated against the linear predictions of the unstable ion temperature gradient mode growth rates and frequencies. Convergence and saturation in both turbulent and neoclassical limit of the ion heat conductivity is obtained with numerical noise well suppressed by a sufficiently large number of simulation particles. A first global full f validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. At high Mach number (Mp~1) of the poloidal flow, the radial electric field is significantly enhanced over the standard neoclassical prediction. The neoclassical radial electric field together with the related GAM oscillations is found to regulate the turbulent heat and particle diffusion levels particularly strongly in a large aspect ratio tokamak at low plasma current.

The European turbulence code benchmarking effort: turbulence driven by thermal gradients in magnetically confined plasmas

A cross-comparison and verification of state-of-the-art European codes describing gradient-driven plasma turbulence in the core and edge regions of tokamaks, carried out within the EFDA Task Force on Integrated Tokamak Modelling, is presented. In the case of core ion temperature gradient (ITG) driven turbulence with adiabatic electrons (neglecting trapped particles), good/reasonable agreement is found between various gyrokinetic/gyrofluid codes. The main physical reasons for some deviations observed in nonlocal simulations are discussed. The edge simulations agree very well on collisionality scaling and acceptably well on beta scaling (below the MHD boundary) for cold-ion cases, also in terms of the non-linear mode structure.

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.

Global spectral investigation of plasma turbulence in gyrokinetic simulations

Gyrokinetic global particle-in-cell simulations for a small torus with a large aspect ratio (ϵ−1>∼7) indicate a k⊥−α spectrum for electrostatic turbulence. When electrons are treated kinetically, the simulation results fit α that grows from about 1 at the plasma core to about 3 at the plasma edge for the flux surface component of the wave vector perpendicular to the magnetic field, while for adiabatic electrons α=4 is found for all radii, in agreement with the Hasegawa-Mima model. The relation between spectra and transport is investigated through the formation of an internal transport barrier. The role of flow shear in suppressing turbulence is illustrated by spectral diagnostics. A strong dependence between the presence of small wavenumbers and transport is explicitly observed. The simulated spectra are compared to recent experimental results.

Collisional dynamics of Er in turbulent plasmas in toroidal geometry

The gyrokinetic full f simulation code ELMFIRE has been used to perform the first global self-consistent computational study of the dynamics of the radial electric field in the presence of turbulence in an experimental toroidal configuration. Parameters have been taken from the FT-2 tokamak. Appreciable differences have been found in comparison with the neo-classical analytic estimate of radial electric field, specially in the outer region with higher level of turbulence. Similar differences have previously been observed in experiments. The analysis included in this work does not support the hypothesis of the neo-classical non-ambipolar transport from finite Larmor-radius effects as a source of discrepancies, but qualitatively supports the theory of eddy viscosity producing those deviations from standard neo-classical theory.

Full f gyrokinetic simulation of FT-2 tokamak plasma

A direct implicit ion polarization gyrokinetic full f particle-in-cell approach is implemented with kinetic electrons in global tokamak transport simulations. The method is applicable for calculations of rapid transients and steep gradients in the plasma, which is made feasible by recording the charge density change by the ion polarization drift together with the particle advancing. The code has been successfully validated against the linear and nonlinear predictions of the unstable mode growth rates and frequencies and their turbulent saturation level. A first global validation of the neoclassical radial electric field in the presence of turbulence for a heated collisional tokamak plasma is obtained. The neoclassical radial electric field together with the related geodesic acoustic mode oscillations is found to regulate the turbulence and heat and particle diffusion levels in a large aspect ratio tokamak at low plasma current.

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.

Characteristics of transport barrier generation from gyrokinetic plasma Simulation in a Tokamak

An advanced full f gyrokinetic three-dimensional (3-D) plasma simulation code has been developed, thus making it possible to treat steep plasma gradients, wide particle orbit effects, and rapid dynamic changes in long simulations. The study of a small tokamak plasma heated by lower hybrid waves shows a generation of internal transport barrier which is detected as a simultaneous collapse of heat and particle diffusion coefficients as well as large scale structures in fluctuations inside the barrier.

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.

Gyrokinetic full f analysis of electric field dynamics and poloidal velocity in the FT2-tokamak configuration

The ELMFIRE gyrokinetic simulation code has been used to perform full f simulations of the FT-2 tokamak. The dynamics of the radial electric field and the creation of poloidal velocity in the presence of turbulence are presented.