Polarization and magnetization in collisional and turbulent transport processes

Expressions of polarization and magnetization in magnetically confined plasmas are derived, which include full expansions in the gyroradius to treat effects of both equilibrium and microscopic electromagnetic turbulence. Using the obtained expressions, densities and flows of particles are related to those of gyrocenters. To the first order in the normalized gyroradius expansion, the mean part of the particle flow is given by the sum of the gyrocenter flow and the magnetization flow, which corresponds to the so-called magnetization law in drift kinetics, while the turbulent part contains the polarization flow as well. Collisions make an additional contribution to the second-order particle flow. The mean particle flux across the magnetic surface is of the second-order, and it contains classical, neoclassical, and turbulent transport processes. The Lagrangian variational principle is used to derive the gyrokinetic Poisson and Ampère equations, which properly include mean and turbulent parts so as to be useful for full-f global electromagnetic gyrokinetic simulations. It is found that the second-order Lagrangian term given by the inner product of the turbulent vector potential and the drift velocity consisting of the curvature drift and the ∇B drift should be retained in order for the derived Ampère equation to correctly include the diamagnetic current, which is necessary especially for the full-f high-beta plasma simulations. The turbulent parts of these gyrokinetic Poisson and Ampère equations are confirmed to agree with the results derived from the WKB representation in earlier works

Kinetic Simulations of Neoclassical and Anomalous Transport Processes in Helical Systems

Drift kinetic and gyrokinetic theories and simulations are powerful means for quantitative predictions of neoclassical and anomalous transport fluxes in helical systems such as the Large Helical Device (LHD). The δf Monte Carlo particle simulation code, FORTEC-3D, is used to predict radial profiles of the neoclassical particle and heat transport fluxes and the radial electric field in helical systems. The radial electric field profiles in the LHD plasmas are calculated from the ambipolarity condition for the neoclassical particle fluxes obtained by the global simulations using the FORTEC-3D code, in which effects of ion or electron finite orbit widths are included. Gyrokinetic Vlasov simulations using the GKV code verify the theoretical prediction that the neoclassical optimization of helical magnetic configuration enhances the zonal flow generation which leads to the reduction of the turbulent heat diffusivity χi due to the ion temperature gradient (ITG) turbulence. Comparisons between results for the high ion temperature LHD experiment and the gyrokinetic simulations using the GKV-X code show that the χi profile and the poloidal wave number spectrum of the density fluctuation obtained from the simulations are in reasonable agreements with the experimental results. It is predicted theoretically and confirmed by the linear GKV simulations that the E × B rotation due to the background radial electric field Er can enhance the zonal-flow response to a given source. Thus, in helical systems, the turbulent transport is linked to the neoclassical transport through Er which is determined from the ambipolar condition for neoclassical particle fluxes and influences the zonal flow generation leading to reduction of the turbulent transport. In order to investigate the Er effect on the regulation of the turbulent transport by the zonal flow generation, the flux-tube bundle model is proposed as a new method for multiscale gyrokinetic simulations

Development of a Drift-Kinetic Simulation Code for Estimating Collisional Transport Affected by RMPs and Radial Electric Field

A drift-kinetic δf simulation code is developed for estimating collisional transport in a quasi-steady state of toroidal plasma affected by resonant magnetic perturbations and radial electric field. In this paper, validity of the code is confirmed through several test calculations. It is found that radial electron flux is reduced by positive radial-electric field, although radial diffusion of electron is strongly affected by chaotic field-lines under an assumption of zero electric field

Nonlinear functional relation covering near- and far-marginal stability in ion temperature gradient driven turbulence

A novel nonlinear functional relation of turbulence potential intensity, zonal flow potential intensity, and ion thermal diffusivity that accurately reproduces nonlinear gyrokinetic simulations of toroidal ion temperature gradient (ITG) driven turbulence is proposed. Applying mathematical optimization techniques to find extremal solutions in high-dimensional parameter space, the optimal regression parameters in the functional form are determined to be valid for both near- and far-marginal regime of the ITG stability including the Dimits-shift. Then, the regression error of ∼5% is accomplished. In addition, it is clarified that the intensity ratio of the zonal flow and turbulence potential intensity is a crucial factor to determine the reproduction accuracy

Electron heat diffusivity in radially-bounded ergodic region of toroidal plasma

Drift-kineticδ f simulations are performed to investigate effect of ergodic field lines caused by resonant magnetic perturbations (RMPs) on radial heat diffusivity of electrons in the edge region of toroidal plasma of collisionality V* 〜0:1. The following is assumed in the simulations. The ergodic region is bounded radially on both sides by closed magnetic surfaces. The pressure gradient remains nonzero in the ergodic region because of an incomplete flattening of the pressure profile, and the characteristic scale length of the pressure gradient is of larger order than the overlapping width of the neighbouring magnetic islands. It is found in the quasi-steady state of δf that the electron heat diffusivity is of smaller order than the theoretical estimate derived by the Rechester-Rosenbluth model (Rechester A.B. and Rosenbluth M.N. 1978Phys.Rev. Lett.4038). The radial heat conduction is dominated not only by parallelmotions along the ergodic field lines but also by trapped particle motions generated by the RMP field. The contribution of the trapped particles reduces the radial heat conduction enhanced by the parallel motions

Benchmark of a new multi-ion-species collision operator for δf Monte Carlo neoclassical simulation

A numerical method to implement a linearized Coulomb collision operator in the two-weight Monte Carlo method for multi-ion-species neoclassical transport simulation is developed. The conservation properties and the self-adjoint property of the operator in the collisions between two particle species with different temperatures are verified. The linearized operator in a Monte Carlo code is benchmarked with other two kinetic simulations, a continuum gyrokinetic code with the same linearized collision operator and a full-f PIC code with Nanbu collision operator. The benchmark simulations of the equilibration process of plasma flow and temperature fluctuation among several particle species show very good agreement between Monte Carlo code and the other two codes. An error in the H-theorem in the two-weight Monte Carlo method is found, which is caused by the weight spreading phenomenon inherent in the two-weight method. It is demonstrated that the weight averaging method serves to restoring the H-theorem without causing side effect

Development of a Gyrokinetic Particle-in-Cell Code for Whole-Volume Modeling of Stellarators

We present initial results in the development of a gyrokinetic particle-in-cell code for the whole-volume modeling of stellarators. This is achieved through two modifications to the X-point Gyrokinetic Code (XGC), originally developed for tokamaks. One is an extension to three-dimensional geometries with an interface to Variational Moments Equilibrium Code (VMEC) data. The other is a connection between core and edge regions that have quite different field-line structures. The VMEC equilibrium is smoothly extended to the edge region by using a virtual casing method. Non-axisymmetric triangular meshes in which triangle nodes follow magnetic field lines in the toroidal direction are generated for field calculation using a finite-element method in the entire region of the extended VMEC equilibrium. These schemes are validated by basic benchmark tests relevant to each part of the calculation cycle, that is, particle push, particle-mesh interpolation, and field solver in a magnetic field equilibrium of Large Helical Device including the edge region. The developed code also demonstrates collisionless damping of geodesic acoustic modes and steady states with residual zonal flow in the core region