S. Satake

Non-local neoclassical transport simulation of geodesic acoustic mode

Neoclassical transport simulation code (FORTEC-3D) applicable to both axisymmetric and non-axisymmetric configurations is developed to investigate non-local effects on neoclassical transport phenomena. The time evolution of the radial electric field is simulated in the full volume of the confinement region of tokamak and helical model plasmas. It is found that the damping rate of the geodesic-acoustic-mode (GAM) oscillation becomes faster than that predicted from a single-surface transport analysis. The time evolution of the radial electric field towards the ambipolar state shows a non-local behaviour, which indicates a coupling of GAM oscillation between the neighbouring two flux surfaces because of the finite-orbit-width effect.

Benchmark test of drift-kinetic and gyrokinetic codes through neoclassical transport simulations

Abstract Two simulation codes that solve the drift-kinetic or gyrokinetic equation in toroidal plasmas are benchmarked by comparing the simulation results of neoclassical transport. The two codes are the drift-kinetic δf Monte Carlo code (FORTEC-3D) and the gyrokinetic full- f Vlasov code (GT5D), both of which solve radially-global, five-dimensional kinetic equation with including the linear Fokker–Planck collision operator. In a tokamak configuration, neoclassical radial heat flux and the parallel flow relation, which relates the parallel mean flow with radial electric field and temperature gradient, are compared between these two codes, and their results are also compared with the local neoclassical transport theory. It is found that the simulation results of the two codes coincide very well in a wide rage of plasma collisionality parameter ν ∗ = 0.01 ∼ 10 and also agree with the theoretical estimations. The time evolution of radial electric field and particle flux, and the radial profile of the geodesic acoustic mode frequency also coincide very well. These facts guarantee the capability of GT5D to simulate plasma turbulence transport with including proper neoclassical effects of collisional diffusion and equilibrium radial electric field.

Potential fluctuation associated with the energetic-particle-induced geodesic acoustic mode in the Large Helical Device

Geodesic acoustic modes (GAM) driven by energetic particles are observed in the Large Helical Device (LHD) by a heavy ion beam probe. The GAM localizes near the magnetic axis. It is confirmed that the energetic-particle-induced GAM is accompanied by an electrostatic potential fluctuation and radial electric field fluctuation. The amplitude of the potential fluctuation is several hundred volts, and it is much larger than the potential fluctuation associated with turbulence-induced GAMs observed in the edge region in tokamak plasmas. The energetic-particle-induced GAM modulates the amplitude of the density fluctuation in a high-frequency range. The observed GAM frequency is constant at the predicted GAM frequency in plasmas with reversed magnetic shear. On the other hand, it shifts upwards from the predicted GAM frequency in plasmas with monotonic magnetic shear.

Physics analyses on the core plasma properties in the helical fusion DEMO reactor FFHR-d1

Physics assessments on magnetohydrodynamics equilibrium, neoclassical transport and alpha particle confinement have been carried out for the helical fusion DEMO reactor FFHR-d1, using radial profiles extrapolated from the Large Helical Device. Large Shafranov shift is foreseen in FFHR-d1 due to its high-beta property. This leads to deterioration in neoclassical transport and alpha particle confinement. Plasma position control using vertical magnetic field has been examined and shown to be effective for Shafranov shift mitigation. In particular, in the high-aspect-ratio configuration, it is possible to keep the magnetic surfaces similar to those in vacuum with high central beta of ~8% by applying a proper vertical magnetic field. As long as the Shafranov shift is mitigated, the neoclassical heat loss can be kept at a level compatible with the alpha heating power. The alpha particle loss can also be kept at a low level if the loss boundary of alpha particles is on the blanket surface and the plasma position control is properly applied. The lost positions of alpha particles are localized around the divertor region that is located behind the blanket in FFHR-d1.

Calculation of neoclassical toroidal viscosity in tokamaks with broken toroidal symmetry

A new numerical simulation to evaluate neoclassical toroidal viscosity (NTV) in tokamak configurations with a small perturbation field is developed using the ?f Monte Carlo method. The numerical scheme solves the guiding-centre distribution function in non-axisymmetric plasmas according to the drift-kinetic equation, and evaluates the NTV directly from the pressure anisotropy by utilizing the Fourier spectrum expression of the magnetic field in Boozer coordinates. As a first benchmark, the accuracy of the viscosity calculation is demonstrated in a helical configuration of LHD. The convergence of the calculation and dependence of the viscosity on perturbation field amplitude are also tested in a simple tokamak configuration with model perturbation field, which proves the reliability of the simulation. Next, the basic properties of NTV as dependence of the viscosity on collision frequency and magnetic shear are investigated in a multi-helicity perturbation model field and compared with a bounce-averaged analytic formula. It is found that the clear 1/? and superbanana-plateau dependences cannot be seen in the FORTEC-3D simulation, and the toroidicity of the magnetic field makes a toroidal coupling effect, which enhances NTV if the perturbation has (m, n) and (m ? 1, n) Fourier components simultaneously, where m and n are the poloidal and toroidal numbers of the perturbation field. Local magnetic shear is also found to affect the amplitude of the viscosity.

Neoclassical electron transport calculation by using delta f Monte Carlo method

High electron temperature plasmas with steep temperature gradient in the core are obtained in recent experiments in the Large Helical Device [A. Komori et al., Fusion Sci. Technol. 58, 1 (2010)]. Such plasmas are called core electron-root confinement (CERC) and have attracted much attention. In typical CERC plasmas, the radial electric field shows a transition phenomenon from a small negative value (ion root) to a large positive value (electron root) and the radial electric field in helical plasmas are determined dominantly by the ambipolar condition of neoclassical particle flux. To investigate such plasmas’ neoclassical transport precisely, the numerical neoclassical transport code, FORTEC-3D [S. Satake et al., J. Plasma Fusion Res. 1, 002 (2006)], which solves drift kinetic equation based on δf Monte Carlo method and has been applied for ion species so far, is extended to treat electron neoclassical transport. To check the validity of our new FORTEC-3D code, benchmark calculations are carried out with ...

Experimental study of radial electric field and electrostatic potential fluctuation in the Large Helical Device

A heavy ion beam probe was installed on the Large Helical Device (LHD) to investigate the roles of radial electric fields (Er) in magnetically confined high-temperature plasmas. Two new observations are presented. One is the observation of electrostatic potential profiles during the formation of extremely hollow density profiles of impurities, called the impurity hole (Ida K et al 2009 Phys. Plasmas 16 056111), in the LHD plasmas. The measured Er is negative, and the Er determined by the ambipolarity condition of neoclassical particle fluxes is consistent with this observation. However, the transport analysis indicates that the formation of the extremely hollow profile is not attributable to the impurity fluxes driven by Er and the density and temperature gradients of the impurity. The other new observation is on the geodesic acoustic mode (GAM). The electrostatic potential fluctuation associated with the GAM, which is probably induced by energetic particles, in plasmas with the reversed or weak magnetic shear is identified. The GAM is localized in the core region of the plasma.

Lagrangian neoclassical transport theory applied to the region near the magnetic axis

Neoclassical transport theory around the magnetic axis of a tokamak is studied, in which relatively wide “potato” orbits play an important role in transport. Lagrangian formulation of transport theory, which has been investigated to reflect finiteness of guiding-center orbit widths to transport equations, is developed in order to analyze neoclassical transport near the axis for a low-collisionality plasma. The treatment of self-collision term in Lagrangian formulation is revised to retain momentum conservation property of it. By directly reflecting the orbital properties of all the types of orbits in calculation, the ion thermal conductivity around the axis is found to decrease from that predicted by conventional neoclassical theory. This result supports recent numerical simulations which show the reduction of thermal conductivity near the magnetic axis.

Effects of magnetic drift tangential to magnetic surfaces on neoclassical transport in non-axisymmetric plasmas

In evaluating neoclassical transport by radially local simulations, the magnetic drift tangential to a flux surface is usually ignored in order to keep the phase-space volume conservation. In this paper, effect of the tangential magnetic drift on the local neoclassical transport is investigated. To retain the effect of the tangential magnetic drift in the local treatment of neoclassical transport, a new local formulation for the drift kinetic simulation is developed. The compressibility of the phase-space volume caused by the tangential magnetic drift is regarded as a source term for the drift kinetic equation, which is solved by using a two-weight δf Monte Carlo method for non-Hamiltonian system [G. Hu and J. A. Krommes, Phys. Plasmas 1, 863 (1994)]. It is demonstrated that the effect of the drift is negligible for the neoclassical transport in tokamaks. In non-axisymmetric systems, however, the tangential magnetic drift substantially changes the dependence of the neoclassical transport on the radial ele...

Experimental observation of response to resonant magnetic perturbation and its hysteresis in LHD

The magnetic island in the large helical device (LHD) shows the dynamic behaviour of the healing/growth transition with the hysteretic behaviour. The thresholds of plasma beta and poloidal flow for island healing are larger than that for growth. The threshold of resonant magnetic perturbation (RMP) for healing is smaller than that for growth. Furthermore, thresholds of the amplitude of RMP depend on the magnetic axis position Rax in the LHD. The RMP threshold increases as the magnetic axis position Rax increases. The poloidal viscosity may be considered as a candidate to explain the experimental observation from the viewpoint of the relationship between the electromagnetic torque and the viscous torque.