S. Murakami

Neoclassical transport optimization of LHD

Neoclassical transport is studied for large helical device (LHD) configurations in which the magnetic axis has been shifted radially by determining the mono-energetic transport coefficient and the effective helical ripple. With respect to the transport in the long mean-free-path collisionality region—the so-called 1/ν transport—the optimum configuration is found when the magnetic axis has a major radius of 3.53 m, which is 0.22 m inward shifted from the `standard configuration of LHD. In the optimized case, the effective helical ripple is very small, remaining below 2% inside (4/5) of the plasma radius. This indicates that a strong inward shift of the magnetic axis in the LHD can diminish the neoclassical transport to a level typical of so-called `advanced stellarators.

Core electron-root confinement (CERC) in helical plasmas

The improvement of core electron heat confinement has been realized in a wide range of helical devices such as CHS, LHD, TJ-II and W7-AS. Strongly peaked electron temperature profiles and large positive radial electric field, Er, in the core region are common features for this improved confinement. Such observations are consistent with a transition to the electron-root solution of the ambipolarity condition for Er in the context of neoclassical transport, which is unique to non-axisymmetric configurations. Based on this background, this improved confinement has been collectively dubbed core electron-root confinement (CERC). The thresholds for CERC establishment are found for the collisionality and electron cyclotron heating power. The magnetic configuration properties (e.g. effective ripple and magnetic islands/rational surfaces) play important roles for CERC establishment.

Neoclassical transport simulations for stellarators

The benchmarking of the thermal neoclassical transport coefficients is described using examples of the Large Helical Device (LHD) and TJ-II stellarators. The thermal coefficients are evaluated by energy convolution of the monoenergetic coefficients obtained by direct interpolation or neural network techniques from the databases precalculated by different codes. The temperature profiles are calculated by a predictive transport code from the energy balance equations with the ambipolar radial electric field estimated from a diffusion equation to guarantee a unique and smooth solution, although several solutions of the ambipolarity condition may exist when root-finding is invoked; the density profiles are fixed. The thermal transport coefficients as well as the ambipolar radial electric field are compared and very reasonable agreement is found for both configurations. Together with an additional W7-X case, these configurations represent very different degrees of neoclassical confinement at low collisionalities. The impact of the neoclassical optimization on the energy confinement time is evaluated and the confinement times for different devices predicted by transport modeling are compared with the standard scaling for stellarators. Finally, all configurations are scaled to the same volume for a direct comparison of the volume-averaged pressure and the neoclassical degree of optimization.

A global simulation study of ICRF heating in the LHD

ICRF heating in the Large Helical Device is studied applying two global simulation codes; a drift kinetic equation solver, GNET, and a wave field solver, TASK/WM. Characteristics of energetic ion distributions in the phase space are investigated changing the resonance heating position; i.e. the on-axis and off-axis heating cases. A clear peak of the energetic ion distribution can be seen in the off-axis heating case because of the stable orbit of resonant energetic ions. The simulation results are also compared with experimental results evaluating the count number of the neutral particle analyzer and a relatively good agreement is obtained.

Fast ion charge exchange spectroscopy measurement using a radially injected neutral beam on the large helical device

An experimental technique to investigate fast ion confinement based on charge exchange spectroscopy of H(alpha)-light was applied to evaluate the confinement property of perpendicular fast ions in large helical device (LHD). Sensitivities of the H(alpha) spectra to the pitch angles of injected neutral beams (NBs) and these to the angle between the sight line of the measurement and NB injection path are examined. The energy dependence of the charge exchange cross section significantly affects the observed spectra since the driving NB is injected perpendicular to the magnetic field lines in the geometry of LHD. The measured spectra are compared to the spectra of GNET simulation results and the simulated spectra agreed well with the experimental measurement when we take into account the contribution of halo neutrals. Although it is difficult to obtain the fast ion distribution functions directly, this technique provides useful experimental data in benchmarking simulation codes.

Construction of neoclassical transport database for large helical device plasma applying neural network method

A neoclassical transport database for the large helical device (LHD) plasma, DCOM/NNW, is constructed using the neural network method. Monoenergetic neoclassical transport coefficients evaluated by the Monte Carlo code, DCOM, are used as training data of the neural network. The databases for two typical magnetic field configurations in LHD, namely, standard and inward-shifted configurations, are constructed and transport coefficients for thermal plasma are evaluated. The plasma parameter dependencies and the ambipolar radial electric field are investigated.

A convergence study for the Laguerre expansion in the moment equation method for neoclassical transport in general toroidal plasmas

The dependence of neoclassical parallel flow calculations on the maximum order of Laguerre polynomial expansions is investigated in a magnetic configuration of the Large Helical Device [S. Murakami, A. Wakasa, H. Maassberg, et al., Nucl. Fusion 42, L19 (2002)] using the monoenergetic coefficient database obtained by an international collaboration. On the basis of a previous generalization (the so-called Sugama-Nishimura method [H. Sugama and S. Nishimura, Phys. Plasmas 15, 042502 (2008)]) to an arbitrary order of the expansion, the 13 M, 21 M, and 29 M approximations are compared. In a previous comparison, only the ion distribution function in the banana collisionality regime of single-ion-species plasmas in tokamak configurations was investigated. In this paper, the dependence of the problems including electrons and impurities in the general collisionality regime in an actual nonsymmetric toroidal configuration is reported. In particular, qualities of approximations for the electron distribution function are investigated in detail.

Effect of neoclassical transport optimization on electron heat transport in low-collisionality LHD plasmas

Abstract Electron heat transport in the low-collisonality electron cyclotron heating plasma is investigated to clarify the effect of neoclassical transport optimization on the thermal plasma transport in the Large Helical Device (LHD). Five configurations are realized by shifting the magnetic axis position in major radius: 3.45, 3.53, 3.6, 3.75, and 3.9 m. A clear effective helical ripple (which is a quantitative measure of the neoclassical transport optimization) dependency on the enhancement factor of the global energy confinement relative to ISS95 is observed. Local heat transport analyses show a higher electron temperature and a lower heat transport in the neoclassical transport optimized configuration at half the minor radius. The comparisons of the experimental total heat fluxes with that of the neoclassical transport by DCOM/NNW suggest that the neoclassical transport plays a significant role in the heat transport and that the neoclassical transport optimization is effective in improving the plasma confinement in the low-collisionality LHD plasma.

Shape effect of the outermost flux surface on effective helical ripple and zonal flow response in an L = 2 heliotron

We calculate two indicators for neoclassical and anomalous transport in the low collisional regime, effective helical ripple eeff and zonal flow response , in an L = 2 heliotron with various shapes of the outermost flux surface. The eeff has a minimum as a function of a parameter representing plasma column twisting, δb. The time average of the damped zonal flow, , shows a similar dependence on δb. We can thus find the optimum configuration for both these indicators in an arbitrary L = 2 heliotron, by choosing the optimum value of δb, together with inherent toroidicity and main helicity of the outermost flux surface. The existence of the optimum is due to the most effective cancellation of the radial drifts of the particles trapped in each helical ripple, rather than the magnetic field symmetry in a whole surface.

NUMERICAL ANALYSES OF ENERGETIC PARTICLES IN LHD

Abstract The confinement of energetic ions generated by neutral beam injection (NBI) and ion cyclotron resonance frequency heating is studied using GNET simulation code, in which the drift kinetic equation is solved in five-dimensional phase-space. The steady-state distributions of the energetic ions are obtained, and characteristics of the energetic-ion distribution depending on the plasma heating method are shown. The magnetic configuration effect on the energetic-ion confinement is also investigated, and it is found that the energetic-ion confinement is improved by a strong inward shift of the magnetic axis position in the major radius direction. The interaction between energetic particles and Alfvén eigenmodes are investigated using the MEGA code and the AE3D code. A reduced version of the MEGA code has been developed to simulate the Alfvén eigenmode (AE) evolution in the Large Helical Device (LHD) plasma with NBI and collisions taken into account. The spatial profile and frequency of the AE modes in the LHD plasma are analyzed with the AE3D code. The evolution of energetic particles and AE mode amplitude and phase are followed in a self-consistent way, while the AE spatial profiles are assumed to be constant. It is demonstrated that the AE bursts can be simulated with the new code.