Transport In Toroidal Plasmas Research Articles

Role of wave-particle resonance in turbulent transport in toroidal plasmas

A clear understanding of wave-particle interaction and associated transport mechanisms of different particle species in the drift wave instabilities is important for accurate modeling and predictions of plasma confinement properties in tokamaks. In particular, the roles of linear resonance and nonlinear scattering in turbulent transport need to be delineated when constructing reduced transport models. First-principle, global gyrokinetic simulations find that electron particle and heat transport decreases to a very low level, while ion heat transport level has no dramatic change when wave-particle resonance is suppressed in the collisionless trapped electron mode (CTEM) turbulence. On the other hand, ion heat transport in the self-consistent ion temperature gradient (ITG) turbulence simulation is qualitatively similar to that in the test-particle simulation using the static ITG turbulence fields. These simulation results show that electron transport is primarily driven by the wave-particle resonance in the CTEM turbulence, and the ion transport is mostly driven by the nonlinear wave-particle scattering in both the CTEM and ITG turbulence.

ASTI: Data assimilation system for particle and heat transport in toroidal plasmas

ASTI, a data assimilation system for integrated transport simulation of fusion plasma, has been developed to predict and control the fusion plasma behavior. ASTI employs the ensemble Kalman filter (EnKF) and smoother (EnKS) as data assimilation methods and the integrated transport simulation code for helical fusion plasma, TASK3D, as the system model. ASTI assimilates the time-series data of measured temperature and density radial profiles into the particle and heat transport simulation. In this study, we consider the uncertainties included in the density, temperature, transport model, neutral beam injection (NBI) heating model, and particle source model. We apply ASTI to 12 experimental data sets of the NBI-heated plasma in Large Helical Device (LHD) and investigate the validity of estimation and the prediction performance of ASTI. The obtained radial profile and time evolution of density, electron temperature, and ion temperature agree well with the experimental data sets. Faster and more accurate integrated transport simulation is realized byASTI than the previous integrated simulation of fusion plasmas.

Flux-surface averaged radial transport in toroidal plasmas with magnetic islands

In toroidal magnetic confinement fusion research, one-dimensional (1D) transport models rely on one radial coordinate that labels nested toroidal flux surfaces. The presence of magnetic islands in the magnetic geometry does not impede making 1D transport calculations if the island regions are excluded and then, if necessary, treated separately. In this work, we show a simple way to modify the flux-surface coordinate and corresponding metric coefficients when an island region is excluded. Comparisons with the metric obtained from Poincaré plots are shown, as well as applications to two types of plasma: heliac (TJ-II, CIEMAT, Spain), where the geometrical effects alone cannot explain the experimental results when islands move throughout the minor radius; and heliotron (LHD, NIFS, Japan), where we estimate the effect of an island heat sink in flux-gradient relations.

New Paradigm for Turbulent Transport Across a Steep Gradient in Toroidal Plasmas.

First principles gyrokinetic simulation of the edge turbulent transport in toroidal plasmas finds a reverse trend in the turbulent transport coefficients under strong gradients. It is found that there exist both linear and nonlinear critical gradients for the nonmonotonicity of transport characteristics. The discontinuity of the transport flux slope around the turning gradient shows features of a second order phase transition. Under a strong gradient the most unstable modes are in nonground eigenstates with unconventional mode structures, which significantly reduces the effective correlation length and thus reverse the transport trend. Our results suggest a completely new mechanism for the low to high confinement mode transition without invoking shear flow or zonal flow.

On the interplay between neoclassical tearing modes and nonlocal transport in toroidal plasmas.

This Letter presents the first observation on the interplay between nonlocal transport and neoclassical tearing modes (NTMs) during transient nonlocal heat transport events in the HL-2A tokamak. The nonlocality is triggered by edge cooling and large-scale, inward propagating avalanches. These lead to a locally enhanced pressure gradient at the q = 3/2 (or 2/1) rational surface and hence the onset of the NTM in relatively low β plasmas (βN < 1). The NTM, in return, regulates the nonlocal transport by truncation of avalanches by local sheared toroidal flows which develop near the magnetic island. These findings have direct implications for understanding the dynamic interaction between turbulence and large-scale mode structures in fusion plasmas.

Analysis of TJ-II experimental data with neoclassical formulations of the radial electric field

Neoclassical theory provides usable expressions for studying transport in toroidal plasmas and computing the associated radial electric field. An algebraic and three semi-analytical models are used here to study the radial electric field in TJ-II plasmas and compare it with experimental data from a heavy ion beam probe (HIBP) and with DKES calculations. Good qualitative agreement as well as reasonable quantitative agreement is found which allows us to validate the models for describing TJ-II radial electric fields. Furthermore, a simple algebraic formulation (2005 Plasma Phys. Rep. 31 14) provides physical insight for the interpretation of experimental data from the TJ-II heliac in spite of its complicated geometry, like the place of the transition from the electron to the ion root of the radial electric field, which occurs at the maximum value of collisionality, for example.

Neoclassical transport in toroidal plasmas with nonaxisymmetric flux surfaces

The capability to treat nonaxisymmetric flux surface geometry has been added to the drift-kinetic code NEO (Belli and Candy 2008 Plasma Phys. Control. Fusion 50 095010). Geometric quantities (i.e. metric elements) are supplied by a recently-developed local 3D equilibrium solver, allowing neoclassical transport coefficients to be systematically computed while varying the 3D plasma shape in a simple and intuitive manner. Code verification is accomplished via detailed comparison with 3D Pfirsch–Schlüter theory. A discussion of the various collisionality regimes associated with 3D transport is given, with an emphasis on non-ambipolar particle flux, neoclassical toroidal viscosity, energy flux and bootstrap current. Finally, we compute the transport in the presence of ripple-type perturbations in a DIII-D-like H-mode edge plasma.

Dual Maxwell Construction and Transport Barrier of Helical Plasmas

The interface of transport in toroidal plasmas is studied. The case, in which the gradient-flux relation is a multiple-valued function, is analyzed by use of the statistical theory of confined plasmas. An analytic formula for the determination of the interface of transport is given, taking an example of the transport in toroidal helical plasmas. The formula is given in a form of a dual Maxwell construction (rule of equal area). The location of the interface in stationary state and the access to the stationary state are discussed.

Improved Unlike-Particle Collision Operator for delta-f Drift-Kinetic Particle Simulations

AbstractPlasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for δf particle simulation has been developed to study the nonlocal effects of impurities due to finite ion orbits on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. An improved field-particle operator is designed to exactly enforce conservation of number, momentum and energy.

Unlike-particle collision operator for gyrokinetic particle simulations

Plasmas in modern tokamak experiments contain a significant fraction of impurity ion species in addition to main deuterium background. A new unlike-particle collision operator for δf particle simulation has been developed to self-consistently study the non-local effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for simulation of cross-collisions between different ion species includes test-particle and conserving field-particle operators. The field-particle operator is designed to enforce conservation of number, momentum and energy. It was shown that the new operator correctly simulates the thermal equilibration of different plasma components. It was verified that the ambipolar radial electric field reaches steady state when the total radial guiding center particle current vanishes.

Drift-kinetic simulation of neoclassical transport with impurities in tokamaks

Plasmas in modern tokamak experiments contain a significant fraction of impurity ions in addition to the main deuterium background ions. A new multiple ion-species δf particle simulation capability has been developed to self-consistently study the nonlocal effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for an unlike-particle collision operator, including test-particle and conserving field-particle parts, is described. Effects of the carbon impurity on the main deuterium species heat flux as well as an ambipolar radial electric field in a National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] configuration were studied. A difference between carbon poloidal rotation found from simulation and from conventional theoretical estimates has been investigated and was identified to be a nonlocal finite orbit effect. In the case of large-aspect ratio tokamak configurations with steep toroidal flow profiles, we propose a theoretical model to describe this nonlocal effect. The dominant mechanisms captured by the model are associated with ion parallel velocity modification due to steep toroidal flow and radial electric field profiles. We present simulation results for carbon poloidal velocity in NSTX. Comparisons with neoclassical theory are discussed.

Anomalous parallel momentum transport due to E×B flow shear in a tokamak plasma

Nondiffusive anomalous momentum transport in toroidal plasmas occurs through symmetry breaking mechanisms. In this paper the contribution of sheared E×B flows to parallel momentum transport [R. R. Dominguez and G. M. Staebler, Phys Fluids B 5, 3876 (1993)] is investigated with nonlinear gyrokinetic simulations in toroidal geometry. The background perpendicular shear is treated independently from the parallel velocity shear to isolate a nondiffusive, nonpinch contribution to the parallel momentum flux. It is found that the size of the term depends strongly on the magnetic shear, with the sign reversing for negative magnetic shear. Perpendicular shear flows are responsible for both symmetry breaking and suppression of turbulence, resulting in a shearing rate at which there is a maximum contribution to the momentum transport. The E×B momentum transport is shown to be quenched by increasing flow shear more strongly than the standard linear quench rule for turbulent heat diffusivity.

Test particle simulations for transport in toroidal plasmas

The authors derive the guiding center equations of motion from the phase space Euler–Lagrange formulation for the motion of a charged particle in toroidal magnetic confinement geometry. The guiding center equations are numerically solved together with the Monte Carlo Coulomb collisional pitch angle scattering. The numerically calculated microscopic diffusion coefficients for various values of collisionality ν* in the case of no electrostatic potential agree well with the results of neoclassical theory. The diffusion coefficient is then measured in the presence of a model electrostatic drift wave fluctuation and an equilibrium potential. The diffusion coefficient increases with increasing fluctuation amplitude while the equilibrium potential diminishes the diffusion processes through both the orbit squeezing and the Er×B shear flow of the poloidal velocity.

Structure of short-wavelength drift modes and transport in a toroidal plasma

Short-wavelength fluctuations, such as electron and ion drift waves, may be one cause of anomalous transport in toroidal plasmas. The purpose of this paper is to establish the radial structure of these modes and to clarify some discrepancies in the literature. The conventional form of toroidal drift modes can occur only at isolated plasma radii and are unlikely to be the source of a universal transport. However, a more recently described class of electron and ion drift modes can occur at all plasma radii. They have a structure consistent with an anomalous transport exhibiting the Bohm scaling with magnetic field and decreasing with plasma rotation.

Theory of Anomalous Transport in Toroidal Plasmas

Based on the method of self-sustained turbulence, the anomalous transport coefficient is derived for various toroidal plasmas. The L-mode confinements in the tokamaks, stellarators, H/T systems and RFP are explained by this formula, showing the influence of the magnetic geometry. The mechanism of the confinement improvement is discussed. Associated with the H-mode, the bifurcation physics is described. The catastrophic event at the {beta}-limit is described. 30 refs., 5 figs.

Onsager symmetry of transport in toroidal plasmas

Complete theories of transport contain thermodynamic cross terms, such as a particle flux driven by the temperature gradient. The matrix that relates the forces that drive the transport to the fluxes was shown to be symmetric by Onsager but with the choice of the forces and the fluxes rigidly constrained by thermodynamics. Those constraints for toroidal plasmas are derived and the implications are explored.

Transport processes in magnetically confined plasmas

Intensified studies of plasma transport in toroidal plasmas over the past three to five years have progressed through increased understanding in some areas and changed perceptions about the most important issues in other areas. Recent developments are reviewed for six selected topics: edge fluctuations and transport; L–H mode transition; core fluctuations; modern plasma turbulence theory; transient transport; and global scaling. Some of the developments that are highlighted include: the role of a strongly sheared poloidal flow in edge plasma turbulence, transport and the L–H transition; change of focus from k⊥ ρs ∼ 1 to k⊥ ρs ≪ 1 fluctuations in tokamak plasmas; modern direct-interaction-approximation plasma turbulence and hybrid fluid/kinetic theoretical models; and transient transport experiments that are raising fundamental questions about our conceptions of local transport processes in tokamaks.

Modeling transport in toroidal plasmas: Status and issues

The scope and detail of physics contained in computational models for fluid (density, momentum, energy) transport in toroidal plasmas have steadily increased during the past two decades. There has been considerable success in the development and verification of models for sources and sinks of particles, energy, momentum, and magnetic flux. Transport codes have collectively become very useful tools in interpreting experimental data and in providing guidance for new experiments. However, a more thorough understanding of the fundamental transport processes of magnetically confined plasmas and development of improved computational models are needed to enhance the predictive capabilities of transport codes. It is argued that fluid transport modeling by itself cannot lead to a complete understanding of transport—there must be a very strong collaboration among theory, experiment, and modeling on both the fluid and kinetic levels.

Radio-frequency-induced current and transport in toroidal plasmas

The theory of current generation and transport in toroidal geometry as a result of the absorption of high-frequency waves is developed. The radial particle and heat fluxes as well as the parallel current are given in terms of velocity moments of the rf-induced velocity space particle flux. The radial flux can be separated into classical and neoclassical parts. It is suggested that the absorption of rf can be used to control impurity transport.

Convective cells and transport in toroidal plasmas

The properties of convective cells and the diffusion resulting from such cells are significantly influenced by an inhomogeneity in the external confining magnetic field, such as that in toroidal plasmas. It is shown, first, that the zero-frequency convective cell of the homogeneous medium (vortex) is transformed into the interchange flute mode in the presence of the field inhomogeneity. For stable interchange profiles, this has the effect of reducing the step size of the diffusion process. Second, in an inhomogeneous field, convective motions damp by magnetic pumping at a rate typically much faster than perpendicular viscous damping. This reduces the lifetime of the cell. The convective diffusion in the presence of a field inhomogeneity is estimated. For a thermal background, this diffusion is shown to be substantially smaller than classical diffusion. The influence of the field inhomogeneity is also shown to be significant for nonthermal backgrounds.