The purpose of this article is to study turbulent transport for laboratory plasmas in toroidal devices by gyrokinetic analyses. Linear analysis is performed to clarify the dominant mode for tokamak plasmas. The dissipative trapped electron mode (d-TEM) and the ion temperature gradient (ITG) mode are predicted using the Sugama collision model operator [Sugama et al., Phys. Plasmas 16, 112503 (2009)]. Nonlinear gyrokinetic analysis is used to quantify turbulent transport. The nonlinear simulation results show the levels of particle and energy transport, where the d-TEM and ITG mode are unstable. The effect of zonal flows is studied by the linear and nonlinear simulation results. The results of the analysis are compared when two types of model collision operator, which are the Sugama and Lenard–Bernstein [Phys. Rev. 112, 1456 (1958)] collision model operators, are used. In this study, the simulation results using the Sugama collision operator show a stronger effect of the zonal flows on the turbulent transport than those using the Lenard–Bernstein collision operator, as predicted by the linear simulation result such as the zonal flow decay time.

Maintaining the high-temperature and high-pressure conditions that are essential to sustained nuclear fusion reactions is a challenge due to the turbulent transport that naturally occurs in the plasma. It is crucial to construct a reliable model for turbulent transport to make progress in fusion research and development. This study proposes multi-fidelity modeling for the improved accuracy of regression models for turbulent transport in magnetic fusion plasma. Multi-fidelity modeling combines low-fidelity data, which have low accuracy but many data points, with high-fidelity data, which are highly accurate but have few data points or small parameter ranges, to enhance the overall predictive accuracy of a model. We used a multi-fidelity information fusion technique, Nonlinear AutoRegressive Gaussian Process regression (NARGP), to solve the regression problems associated with turbulent transport in plasma. We applied NARGP to (i) merge the low-resolution and high-resolution simulation results, (ii) apply regression of turbulence diffusivity to the experimental dataset using linear analyses, and (iii) adapt the quasilinear transport model to nonlinear simulation results of a particular discharge. We demonstrated that NARGP improved the prediction accuracy of the plasma turbulent transport model. NARGP successfully corrected errors in low-fidelity model predictions by using high-fidelity datasets, and this produced high-accuracy predictions for the related discharges. NARGP offers a robust and versatile method for integrating multi-fidelity data, and its broad applicability may contribute to optimizing fusion reactor design and operation.

Maintaining the high-temperature and pressure conditions required for sustained nuclear fusion is challenging due to the turbulent transport that naturally occurs in the plasma. Developing reliable models for turbulent transport is essential for progress in fusion research and development. This study proposes multi-fidelity modeling for the improved accuracy of regression models for turbulent transport in magnetic fusion plasma. Multi-fidelity modeling combines low-fidelity data, which have low accuracy but many data points, with high-fidelity data, which are highly accurate but have few data points or small parameter ranges, to enhance the overall predictive accuracy of a model. We used a multi-fidelity information fusion technique, Nonlinear AutoRegressive Gaussian Process regression (NARGP), to solve the regression problems associated with turbulent transport in plasma. We applied NARGP to (i) merge the low-resolution and high-resolution simulation results, (ii) apply regression of turbulence diffusivity to the experimental dataset using linear analyses, and (iii) adapt the quasi-linear transport model to nonlinear simulation results of a particular discharge. We demonstrated that NARGP improved the prediction accuracy of the plasma turbulent transport model. NARGP offers a robust and versatile method for integrating multi-fidelity data, and its broad applicability may contribute to optimizing fusion reactor design and operation.

The understanding of nature has been developed by separating and connecting elements in a reductive manner. For example, a spatio-temporal scale can provide us a clear picture of elemental separations. In biology, a function also gives us a useful picture to understand biological nature. Furthermore, a physical model also improves the outlook for understanding physical nature. These divided or connected elements, namely, scales, functions, and models form hierarchical structures in nature. On the other hand, fusion science explores various multi-scale and multi-physics phenomena, spreading over spatio-temporal scales from the microscopic to the macroscopic. In particular, collective motion causes structural formations not only in core plasmas but also material-facing ones. Therefore, fusion science has been an excellent subject for the application of the hierarchical approach. However, some problems have emerged with the progress of experimental and numerical research in fusion science. We often encounter phenomena that cannot be well understood by hierarchical separation. For these phenomena, beyond the conventional approaches for hierarchical systems, it is necessary to reconsider them with meta-perspectives, i.e., meta-hierarchy dynamics.

A novel scheme to predict the turbulent transport of ion heat of magnetic confined plasmas is developed by combining mathematical optimization techniques employed in data analysis approaches and first-principle gyrokinetic simulations. Gyrokinetic simulation, as a first-principle approach, is a reliable way to predict turbulent transport. However, in terms of the flux-matching [Candy et al., Phys. Plasmas 16, 060704 (2009)], quantitative transport estimates by gyrokinetic simulations incur extremely heavy computational costs. In order to reduce the costs of quantitative transport prediction based on the gyrokinetic simulations, we develop a scheme with the aid of a reduced transport model. In the scheme, optimization techniques are applied to find relevant input parameters for nonlinear gyrokinetic simulations, which should be performed to obtain relevant transport fluxes and to optimize the reduced transport model for a target plasma. The developed scheme can reduce the numbers of the gyrokinetic simulations to perform the quantitative estimate of the turbulent transport levels and plasma profiles. Utilizing the scheme, the predictions for the turbulent transport can be realized by performing the first-principle simulations once for each radial position.

Transport simulation is performed by integrated code using reduced transport models (Toda S et al 2019 Phys. Plasmas 26 012510) in a kinetic electron condition for turbulent heat transport including the effect of zonal flows in helical plasmas. A reduced model can be formulated for the heat diffusivity using only the linear properties, or can be constructed by considering the expression of the quasilinear flux. These reduced models reproduce nonlinear gyrokinetic simulation results for ion temperature gradient mode turbulence by a linear growth rate and zonal flow decay time. Temperature profiles can be obtained when the turbulent heat transport is evaluated by reduced models at each time step in the evolution of integrated simulation. Computational cost using the reduced models where linear gyrokinetic simulation is performed at each time step in the integrated simulation is about two orders of magnitude lower than that using nonlinear gyrokinetic simulation. Stationary temperature profiles are predicted by simulation, in which, the linear simulation is performed at each time step in the integrated simulation for steady heating power. The density profile and the edge temperature are needed in this simulation.

The turbulent transport of magnetic confinement plasmas including multi-ion-particle-species in helical systems such as the Large Helical Device (LHD) [Takeiri et al., Nucl. Fusion 57, 102023 (2017)] and their plasma profile sensitivities are investigated by local flux-tube gyrokinetic simulations. In the multi-ion-species plasmas, while the heat transport of each particle species has slightly different sensitivity towards the plasma temperature gradients and the density gradients, there exist quite different dependencies in the particle transport on the radial gradient profiles of the plasma temperatures and densities between each particle species. Furthermore, in the LHD plasma with the carbon impurity hole structure [Ida et al., Plasma Phys. 16, 056111 (2009)], the turbulent particle transport flux of the impurity carbon ion remains radially inward-directed robustly within the wide ranges of radial gradient profiles of the plasma temperatures and densities.

Using transport models, the impacts of trapped electrons on zonal flows and turbulence in helical field configurations are studied. The effect of the trapped electrons on the characteristic quantities of the linear response for zonal flows is investigated for two different field configurations in the Large Helical Device. The turbulent potential fluctuation, zonal flow potential fluctuation and ion energy transport are quickly predicted by the reduced models for which the linear and nonlinear simulation results are used to determine dimensionless parameters related to turbulent saturation levels and typical zonal flow wavenumbers. The effects of zonal flows on the turbulent transport for the case of the kinetic electron response are much smaller than or comparable to those in an adiabatic electron condition for the two different field configurations. It is clarified that the effect of zonal flows on the turbulent transport due to the trapped electrons changes, depending on the field configurations.

The particle and heat transport driven by the ion temperature gradient instability in helical plasmas is investigated by the gyrokinetic analysis taking into account the kinetic electron response. High and low ion temperature plasma cases for the discharge in the Large Helical Device (LHD) are studied. Two types of transport models with a lower computational cost to reproduce the nonlinear gyrokinetic simulation results within allowable errors are presented for application in quick transport analyses. The turbulent electron and ion heat diffusivity models are given in terms of the linear growth rate and the characteristic quantity for the linear response of zonal flows, while the model of the effective particle diffusivity is not obtained for the flattened density profile observed in the LHD. The quasilinear flux model is also shown for the heat transport. The quasilinear flux models for the energy fluxes are found to reproduce the nonlinear simulation results at the accuracy similar to that of the heat diffusivity models. In addition, the quasilinear particle flux model, which is applicable to the transport analysis for LHD plasmas, is constructed. These turbulent reduced models enable coupling to the other simulation in the integrated codes for the LHD.

In the framework of the flux-matching method, which is a useful way for the validation of the gyrokinetic turbulence simulations, it is strongly demanded to evaluate the plasma profile sensitivity of the transport coefficients obtained in the employed simulation model within the profile gradient ranges estimated from the experimental observations. The sensitivity causes the plasma profile stiffness for wide ranges of the transport fluxes. In the nonlinear gyrokinetic simulations for the ion temperature gradient (ITG) turbulence in the Large Helical Device (LHD) [Takeiri et al., Nucl. Fusion 57, 102023 (2017)], it is found that the temperature gradients around the experimental nominal observations are slightly larger than the threshold of the instability, and the ion heat diffusivities are quite sensitive to the temperature gradient. The growth rates of the instability, the generations of the zonal flows, and the sensitivities of the transport coefficients to the temperature profiles depend on the radial locations, the employed simulation models, and the field configurations. Specifically, in the optimized LHD field configuration, the sensitivities are relaxed in the outer radial region due to the enhancement of the zonal flows and the reduction of the ITG instability. In order to estimate the range of the temperature gradients possible given the experimentally obtained data of the temperature with errorbars, the statistical technique, Akaike's Information Criterion [H. Akaike, in Proceedings of the 2nd International Symposium on Information Theory, edited by B. N. Petrov and F. Caski (Akadimiai Kiado, Budapest, 1973), pp. 267–281] is applied. Against the range of the temperature gradients, the flux-matching method to predict the temperature gradient in helical plasmas is demonstrated.

In magnetic confined systems, the transport of particles and heat of multi-species plasmas are demanded to be accurately predicted for understandings of the burning plasma in the ITER, future reactors, and also stellarators such as the Large Helical Device (LHD) [1]. For the purposes, large scale numerical simulations based on the first principle of the kinetic frameworks are extremely powerful. Indeed, by means of the flux-matchings, it becomes able to validate the kinetic simulation results against the experimental observations for the plasma temperature and density profiles with the experimental errors taken into account [2, 3]. In LHD experiments, we often observe the extremely hollow impurity density profiles called impurity hole [4] in high ion temperature plasma heated by neutral beam injection (NBI). The hollow profile has a great advantage to avoid impurity accumulation which deteriorates the performances of the confinement. Therefore, the clarification of its generation mechanism is one of the critical issues for high performance of magnetically confined plasmas. In these plasmas which consist of multi-species, the particle transport fluxes of each species should be quantitatively evaluated by kinetic simulations for the neoclassical and anomalous contributions, where the particle balances for each species should be determined by the total particle transport fluxes including the both contributions. In the micro-instability analyses for the LHD impurity hole plasma, it was found that the ion temperature gradient (ITG) mode is the dominant instability mode, and the nonlinear gyrokinetic turbulence simulations are performed to evaluate anomalous contributions. Figure 1 shows the impurity carbon density gradient dependences of the turbulent contributions of the radial transport fluxes of particles for all species satisfying the ambipolar conditions. It is newly found that there are quite different dependencies between each species while the main ion (hydrogen) density gradient has little effects on the fluxes. Furthermore, the impurity carbon particle flux remains the negative (radially inward directed) for wide ranges of the gradients. Therefore, if the system is in the steady state with negligible auxiliary particle sources or sinks, the outward neoclassical carbon particle flux should be expected for balancing with the inward turbulent flux. On the other hand, in order to evaluate the neoclassical contributions, we solve the drift-kinetic equation and evaluate the ambipolar radial electric field by the neoclassical simulations. Since the neoclassical particle fluxes can be affected by the external momentum torque by NBI heating through the radial electric field (Er) generation, co-injected external torque can cause not only negative Er but also positive one. Although the negative Er is often observed in the core region of the LHD plasmas, if there exists the positive one, the neoclassical particle flux of carbon can be outward directed which is consistent with the expectation that the outward directed neoclassical particle fluxes for balancing with turbulent one. In addition, if there exist sufficient direct inward contributions of the injected beam to the total ion particle flux, the carbon particle fluxes can be outward directed because each ion particle flux should be shifted outward due to the additional contribution for satisfying ambipolar condition.

A transition of the radial structure of the electric field is studied by the one-dimensional diffusive transport model in helical plasmas. At first, the model for the anomalous diffusivity including a numerical factor is used to reproduce the experimental results. The Maxwell's construction is found to be satisfied at the radial point for the electric field transition. Next, the dynamical transport simulation is carried out to reproduce the electric field pulsation, which is observed in helical devices. The limited parameter region near the boundary between the different radial electric field states is clarified to give the self-generated oscillation. A reduced model based on the gyrokinetic simulation, which does not include the numerical factor, is also derived and is used for the transport simulation. The computational cost becomes much lower to obtain the plasma profile, which is compared with the experimental results.

As the finalization of a hydrogen experiment towards the deuterium phase, the exploration of the best performance of hydrogen plasma was intensively performed in the large helical device. High ion and electron temperatures, T-i and T-e, of more than 6 keV were simultaneously achieved by superimposing high-power electron cyclotron resonance heating onneutral beam injection (NBI) heated plasma. Although flattening of the ion temperature profile in the core region was observed during the discharges, one could avoid degradation by increasing the electron density. Another key parameter to present plasma performance is an averaged beta value . The high regime around 4% was extended to an order of magnitude lower than the earlier collisional regime. Impurity behaviour in hydrogen discharges with NBI heating was also classified with a wide range of edge plasma parameters. The existence of a no impurity accumulation regime, where the high performance plasma is maintained with high power heating > 10 MW, was identified. Wide parameter scan experiments suggest that the toroidal rotation and the turbulence are the candidates for expelling impurities from the core region.

The topological bifurcation of the flow in non-equilibrium magnetized plasmas is demonstrated by a turbulence simulation. A system with two generic sources of turbulence, the gradients of density and parallel flow, is considered. Topological index of the flow is introduced, in order to indicate the chirality of flow pattern. We here report that the turbulence-driven flow forms the structure of co-axial helixes with opposite chirality. By changing the source of plasma particles, which modifies the density gradient, the transition between three turbulent states is obtained. In addition to the two turbulent states, which are dominated by the drift wave and the D'Angelo mode, respectively, the new state is found. In this third state, fluctuations are driven by both of the free energy sources simultaneously, and compete with the others. The result illustrates the generic feature of turbulence flow generation in non-equilibrium magnetized plasmas.

A high ion temperature plasma in the Large Helical Device is examined in the case in which the ion temperature gradient mode is unstable. The nonlinear gyro-kinetic simulation is performed to evaluate the turbulent ion heat diffusivity with the kinetic electron response. It is clarified that the decay time of zonal flows [S. Ferrando-Margalet et al., Phys. Plasmas 14, 122505 (2007)] decreases radially outward due to the trapped electron and the ion energy transport increases outward. To reduce the computational cost for applying to the dynamical transport simulation, an extended transport model for the ion heat diffusivity in terms of the mixing length estimate and the characteristic quantity for the linear response of zonal flows is proposed.

Multiple free energy sources for instabilities coexist in magnetized plasmas with density gradient and velocity shear. Linear stabilities are investigated, and the mutual relation between resistive drift wave, D'Angelo mode and flute mode is systematically clarified. By evaluating the linear growth rates, dominant instability is categorized in a parameter space. The parallel wavenumber spectrum could be used as a guideline for the identification of the instabilities. (C) 2017 The Japan Society of Plasma Science and Nuclear Fusion Research

Particle transport processes of impurity ions in a multi-ion-species plasma in the Large Helical Device are investigated by neoclassical transport simulations. While the quasi-linear gyrokinetic analyses indicate that the anomalous contribution of the impurity particle transport is radially inward-directed, it is found that the external momentum sources can cause the existence of the electron root with positive radial electric field and outward-directed neoclassical particle flux of the impurity ion. (C) 2017 The Japan Society of Plasma Science and Nuclear Fusion Research

The ion scale microinstabilities in the large helical device (LHD) are investigated by the gyrokinetic simulations for the multi-ion-species plasmas including hydrogen, helium, and impurity ions. The observations in the LHD experiments show that the ion temperature increases with the decreases of the ratio of hydrogen density to helium density. It is found from the linear gyrokinetic simulations with the multi-ion-species and real-mass kinetic electrons in the LHD discharges that the growth rates of the ion scale microinstabilities are reduced for the heliumdominated multi-species plasma compared with the hydrogen-dominated one. In addition to the differences of the conditions including the temperature, the density profiles, and the temperature ratio between both plasmas, due to the dependence on the mass number and the electric charge of the mixed ion species, the mixing length estimates obtained from the linear simulations predicts smaller ion thermal diffusivity for the helium-dominated plasma than the hydrogen-dominated one in the hydrogen gyro-Bohm unit, which is consistent with the experimental results.

Transport simulation for the electron and ion temperature profiles is performed in helical plasmas by using the heat diffusivity models and the quasilinear flux models [S. Toda et al., Phys. Plasmas 26, 012510 (2019)] for the electron and ion heat turbulent transport. The turbulent transport for the nonlinear simulation results can be evaluated by these models. The high-Ti and low-Ti plasmas for the discharge in the Large Helical Device (LHD) are studied, where the ion temperature gradient mode is unstable. The electron and the ion temperature profiles of the dynamical simulation results do not contradict with those of the experimental results in the LHD. For the plasmas of the LHD in this study, the transport simulation results by the diffusivity models and the quasilinear flux models for the heat transport to reproduce the nonlinear simulation results in the allowable errors are found to explain the experimental results for the temperature profiles. (C) 2019 The Japan Society of Plasma Science and Nuclear Fusion Research