Study of Finite-Orbit-Width Effect on Neoclassical Transport in Tokamak Core Region

Neoclassical transport simulation using the δ f Monte-Carlo method is carried out to investigate the finite-orbitwidth (FOW) effect on the transport near the magnetic axis. The time evolution of the radial electric field to maintain the ambipolarity of the flux is calculated simultaneously. It is found that, in the near-axis region, the ion heat flux decreases from the value predicted by the standard neoclassical theory both in the banana and plateau regimes. Though the radial transport shows a strong dependence on the FOW effect, the ambipolar electric field profile at the steady state is similar to that calculated in the small-orbit-width limit approximation

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

The Eulerian variational formulation of the gyrokinetic system in general spatial coordinates

The Eulerian variational formulation of the gyrokinetic system with electrostatic turbulence is presented in general spatial coordinates by extending our previous work [H. Sugama et al., Phys. Plasmas 25, 102506 (2018)]. The invariance of the Lagrangian of the system under an arbitrary spatial coordinate transformation is used to derive the local momentum balance equation satisfied by the gyrocenter distribution functions and the turbulent potential, which are given as solutions of the governing equations. In the symmetric background magnetic field, the derived local momentum balance equation gives rise to the local momentum conservation law in the direction of symmetry. This derivation is in contrast to the conventional method using the spatial translation in which the asymmetric canonical pressure tensor generally enters the momentum balance equation. In the present study, the variation of the Lagrangian density with respect to the metric tensor is taken to directly obtain the symmetric pressure tensor, which includes the effect of turbulence on the momentum transport. In addition, it is shown in this work how the momentum balance is modified when the collision and/or external source terms are added to the gyrokinetic equation. The results obtained here are considered useful for global gyrokinetic simulations investigating both neoclassical and turbulent transport processes even in general non-axisymmetric toroidal systems

Radially local approximation of the drift kinetic equation

A novel radially local approximation of the drift kinetic equation is presented. The new drift kinetic equation that includes both E×B and tangential magnetic drift terms is written in the conservative form and it has favorable properties for numerical simulation that any additional terms for particle and energy sources are unnecessary for obtaining stationary solutions under the radially local approximation. These solutions satisfy the intrinsic ambipolarity condition for neoclassical particle fluxes in the presence of quasisymmetry of the magnetic field strength. Also, another radially local drift kinetic equation is presented, from which the positive definiteness of entropy production due to neoclassical transport and Onsager symmetry of neoclassical transport coefficients are derived while it sacrifices the ambipolarity condition for neoclassical particle fluxes in axisymmetric and quasi-symmetric systems

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

Improved linearized model collision operator for the highly collisional regime

The linearized model collision operator for multiple species plasmas given by Sugama et al. [Phys. Plasmas 16, 112503 (2009)] is improved to be properly applicable up to the highly collisional regime. The improved linearized model operator retains the conservation laws of particles, momentum, and energy, and it reproduces the same friction-flow relations as derived by the linearized Landau operator so that this model can be used to correctly evaluate neoclassical transport fluxes in all collisionality regimes. The adjointness relations and Boltzmann’s H-theorem are exactly satisfied by the improved operator except in the case of collisions between unlike particle species with unequal temperatureswhere these relations and H-theorem still hold approximately because there is a large difference between the masses of the two species with significantly different temperatures. Even in the unequal-temperature case, the improved operator can also be modified so as to exactly satisfy the adjointness relations, while it causes the values of the friction coefficients to deviate from those given by the Landau operator. In addition, for application to gyrokinetic simulations of turbulent transport, the improved operator is transformed into the gyrophaseaveraged form by keeping the finite gyroradius effect

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