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The effect of magnetic field ripple on tokamak plasma without turbulence is studied numerically and augmented with a reduced analytical model that includes neoclassical processes in the presence of non-axisymmetric perturbation and stochastic transport. For this study, a magnetic field ripple perturbation has been implemented in the GYSELA gyrokinetic code. This implementation has been verified thanks to a test of toroidal angular momentum conservation. The GYSELA code was then successfully benchmarked against the NEO code, which solves the drift kinetic equation, and against the reduced model in the collisionality range ν ⋆ ∈ [0.05–0.5] for several amplitudes of the magnetic ripple. An observation, shared by the model, the NEO code and GYSELA simulations is that the thermal drive of the mean poloidal velocity—measured by the k V P coefficient—decreases sharply for large yet experimentally relevant magnetic ripple amplitudes, and may even change sign.

Neoclassical transport is caused by the non-equilibrium distribution function produced by the driving forces due to quasi-steady but non-uniform plasma state parameters and electromagnetic fields as well as by the Coulomb interactions. In this article, we present a method to evaluate the impact of each driving force on neoclassical transport by a single global drift-kinetic simulation. This method can be used to evaluate the impacts of each driving force not only in one-dimensional forms as transport coefficients, but also in multidimensional forms as how the impacts of each driving force are distributed over the phase space. As an application of the method, we investigate the impacts of each driving force on particle density variations in an impurity hole plasma and demonstrate that the impact of the outward driving force of the temperature gradient on the radial impurity flux becomes as large as the impact of the inward driving force of the negative ambipolar radial electric field. Further, we show that the variation of electrostatic potential on each flux surface, Φ1, which is involved in several factors in a drift-kinetic equation, affects the density variations specifically through the radial E × B drift.

Line emissions from both silicon (Si) and boron (B) impurity ions introduced by a single tracer-encapsulated solid pellet (TESPEL) containing silicon hexaboride (SiB6) powders were successfully observed using the extreme ultraviolet (EUV) spectrometer and charge-exchange spectroscopy (CXS) technique in the Large Helical Device. The CXS diagnostic shows clearly that a hollow radial profile of fully ionized B impurities was created immediately after the TESPEL injection, and such a hollow profile was relaxed with time. At the same time, Li-like emissions from the highly ionized Si impurities were also observed with the EUV spectrometer, SOXMOS. Therefore, the decay times of these impurities could be estimated under the same plasma conditions. The estimated decay time of the Si impurities, τSi = 0.12 ± 0.01 s, was found to be slightly longer than that of the B impurities, τB = 0.09 ± 0.01 s

An impurity hole observed in the Large Helical Device (LHD) is a hollow density profile of an impurity ion species formed in the core plasma where the negative (inward-pointing) ambipolar radial electric field ($E_r$) exists. Although local neoclassical models have predicted the sign of $E_r$ in impurity hole plasmas is negative for the entire minor radius, an experimental measurement of an impurity hole plasma has shown that the $E_r$ changes the sign from negative to positive along the minor radius. In the present work, we investigate neoclassical impurity transport in an impurity hole plasma using a global neoclassical simulation code FORTEC-3D. The variation of electrostatic potential on flux surface ($\Phi_1$) is evaluated from the quasi-neutrality condition in multi-ion-species plasma by the global simulation. The ambipolar $E_r$ and neoclassical fluxes are determined in solving a global drift-kinetic equation including the effect of $\Phi_1$. By the global simulation, we show that an $E_r$ which changes the sign along the radius is obtained as a solution of the ambipolar condition and with such an $E_r$, impurity carbon flux can be outwardly directed even where $E_r

The effect of the pitch modulation of the helical coils on the core plasma performance of the LHD-type helical fusion reactor has been examined. The analysis of the MHD stability and neoclassical transport for the pitch modulation α = 0.0 and 0.1 has been conducted based on the finite-beta equilibrium calculated by the HINT code. It was found that the MHD stability is clearly improved without deteriorating the energy transport property by changing the pitch modulation α from 0.1 to 0.0. The reachable operation region expands to the higher density and the expected fusion gain can increase from ∼10 to ∼20. Because the change of the pitch modulation α from 0.1 to 0.0 requires only a slight change in the shape of the helical coils, the engineering design including the maintenance method that has been examined for the reactor with α = 0.1 can be applied without a major modification.

International audience; Trace impurity transport is studied with the flux-driven gyrokinetic GYSELA code [V. Grandgirard et al., $Comp.\ Phys.\ Commun.$\ 207, 35 (2016)]. A reduced and linearized multi-species collision operator has been recently implemented, so that both neoclassical and turbulent transport channels can be treated self-consistently on an equal footing. In the Pfirsch-Schlüter regime likely relevant for tungsten, the standard expression of the neoclassical impurity flux is shown to be recovered from gyrokinetics with the employed collision operator. Purely neoclassical simulations of deuterium plasma with trace impurities of helium, carbon and tungsten lead to impurity diffusion coefficients, inward pinch velocities due to density peaking, and thermo-diffusion terms which quantitatively agree with neoclassical predictions and NEO simulations [E. Belli et al., $Plasma\ Phys.\ Control.\ Fusion$ 54, 015015 (2012)]. The thermal screening factor appears to be less than predicted analytically in the Pfirsch-Schlüter regime, which can be detrimental to fusion performance. Finally, self-consistent nonlinear simulations have revealed that the tungsten impurity flux is not the sum of turbulent and neoclassical fluxes computed separately, as usually assumed. The synergy mostly results from the turbulence-driven in-out poloidal asymmetry of tungsten density. This result puts forward the need for self-consistent simulations of impurity transport, i.e. including both turbulence and neoclassical physics, in view of quantitative predictions for ITER.

Modifications of the drift-kinetic transport code XGC0 to include the transport, ionization, and recombination of individual charge states, as well as the associated radiation, are described. The code is first applied to a simulation of an NSTX H-mode discharge with carbon impurity to demonstrate the approach to coronal equilibrium. The effects of neoclassical phenomena on the radiated power profile are examined sequentially through the activation of individual physics modules in the code. Orbit squeezing and the neoclassical inward pinch result in increased radiation for temperatures above a few hundred eV and changes to the ratios of charge state emissions at a given electron temperature. Analogous simulations with a neon impurity yield qualitatively similar results. Keywords: Neoclassical transport, Impurity radiation, Coronal equilibrium, Kinetic simulation, Particle-in-cell, Spherical torus

Since the observation of impurity hole in LHD, which contradicts the prediction of the conventional neoclassical transport theory, several attempts have been made to explain the mechanism behind the phenomenon. Consideration of the impact of electrostatic potential variation within the flux surface, Φ1, is one of those attempts. However, all of the numerical studies that have investigated the effect of Φ1 to date have been conducted with local simulation codes, and no global calculation has been performed yet. Here, a global neoclassical simulation code FORTEC-3D is applied to evaluate Φ1, including the global effects, for the first time. The global simulation result for a high-temperature low-density plasma, which corresponds to an impurity hole plasma, shows significant difference from the local simulation results in the Φ1 profile. This indicates that consideration of the global effects is essential for quantitative evaluation of impurity neoclassical transport in an impurity hole plasma.

Particle confinement processes are studied in detail on the Large Helical Device (LHD). Diffusion coefficients (D) and convection velocities (V) are estimated from density modulation experiments. T...

Integrated physics analysis of plasma operation scenario of the compact helical reactor FFHR-c1 has been conducted. The DPE method, which predicts radial profiles in a reactor by direct extrapolation from the reference experimental data, has been extended to implement the equipartition effect. Close investigation of the plasma operation regime has been conducted and a candidate plasma operation point of FFHR-c1 has been identified within the parameter regime that has already been confirmed in LHD experiment in view of MHD equilibrium, MHD stability and neoclassical transport.

イオン温度分布計測とイオン加熱を主目的とした垂直中性粒子ヒ?ーム入射装置(NBI)か?大型ヘリカル装置 (LHD)て?稼働を始め,ヘリカル系のイオン加熱実験およひ?イオン熱輸送の研究か?進展している.LHD における イオン系内部輸送障壁(イオン ITB)形成フ?ラス?マの熱輸送特性に関する最新の成果を紹介する.イオン系内部 輸送障壁か?形成されると,輸送障壁の領域のイオン熱拡散は新古典輸送レヘ?ルまて?低減する.このとき,不純物はフ?ラス?マコアから排出され,ヘリカル系特有の不純物ホールを形成する.

The neoclassical transport database, DCOM/NNW, is improved to evaluate the neoclassical transport flux more accurately in high-temperature plasma in LHD. GSRAKE code, which solves the ripple-averaged drift kinetic equation, is also used to extend the database to the further collisionless regime. Finally we construct a neoclassical transport database DCOM-GSRAKE/NNW for LHD (DGN/LHD). The neoclassical transport analyses of high temperature LHD plasma are performed using DGN/LHD. Also DGN/LHD is implemented as a neoclassical transport analysis module in the TASK3D, the integrated simulation code for a helical plasma (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An assessment of alpha particle confinement is performed in the European DEMO reference design. 3D MHD equilibria with nested flux-surfaces and single magnetic axis are obtained with the VMEC free-boundary code, thereby including the plasma response to the magnetic ripple created by the finite number of TF coils. Populations of fusion alphas that are consistent with the equilibrium profiles are evolved until slowing-down with the VENUS-LEVIS orbit code in the guiding-centre approximation. Fast ion losses through the last-closed flux-surface are numerically evaluated with two ripple models: (1) using the 3D equilibrium and (2) algebraically adding the non-axisymmetric ripple perturbation to the 2D equilibrium. By virtue of the small ripple field and its non-resonant nature, both models quantitatively agree. Differences are however noted in the toroidal location of particles losses on the last-closed flux-surface, which in the first case is 3D and in the second not. Superbanana transport, i.e. ripple-well trapping and separatrix crossing, is expected to be the dominant loss mechanism, the strongest effect on alphas being between 100–200 KeV. Above this, stochastic ripple diffusion is responsible for a rather weak loss rate, as the stochastisation threshold is observed numerically to be higher than analytic estimates. The level of ripple in the current 18 TF coil design of the European DEMO is not found to be detrimental to fusion alpha confinement.

The importance of the parallel momentum balance on the bootstrap current evaluation in non-axisymmetric systems is demonstrated by the benchmarks among the local drift-kinetic equation solvers, i.e., the Zero-Orbit-width (ZOW) model, DKES, and PENTA. The ZOW model is extended to include the ion parallel mean flow effect on the electron-ion parallel friction. Compared to DKES code in which only the pitch-angle-scattering term is included in the collision operator, PENTA code employs the Sugama-Nishimura method to correct the momentum balance. The ZOW model and PENTA codes, both of which conserve the parallel momentum in like-species collisoins and include the electron-ion parallel frictions, agree each other well on the calculations of the bootstrap current. The DKES results without the parallel momentum conservation deviates significantly from those from the ZOW model and PENTA. This work verifies the reliability of the bootstrap current calculation with the ZOW model and PENTA for the helical plasmas.

Achieving impurity and helium ash control is a crucial issue in the path towards fusion-grade magnetic confinement devices, and this is particularly the case of helical reactors, whose low-collisionality ion-root operation scenarios usually display a negative radial electric field which is expected to cause inwards impurity pinch. In this work we discuss, based on experimental measurements and standard predictions of neoclassical theory, how plasmas of very low ion collisionality, similar to those observed in the impurity hole of the large helical device (Yoshinuma et al and The LHD Experimental Group 2009 Nucl. Fusion 49 062002, Ida et al and The LHD Experimental Group 2009 Phys. Plasmas 16 056111 and Yokoyama et al and LHD Experimental Group 2002 Nucl. Fusion 42 143), can be an exception to this general rule, and how a negative radial electric field can coexist with an outward impurity flux. This interpretation is supported by comparison with documented discharges available in the International Stellarator-Heliotron Profile Database, and it can be extrapolated to show that achievement of high ion temperature in the core of helical devices is not fundamentally incompatible with low core impurity content.

Neoclassical transport properties are studied in the TJ-II stellarator, taking effective ripple and plateau factor as the figures of merit. Using the DKES code run by grid computing techniques, these two quantities have been estimated as functions of rotational transform and plasma volume. The effective helical ripple increases with plasma volume and rotational transform. These findings suggest the degradation of confinement with iota or volume, which contradicts the scaling laws of energy confinement and the TJ-II experimental results. The plateau factor is almost constant with volume, but it increases following an almost quadratic law with rotational transform. This indicates that the improvement in confinement with iota cannot be explained by neoclassical transport in TJ-II

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.

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.

For the application of the nuclear fusion of hydrogen as a heat source for electricity generation understanding of the magnetic fuel confinement is crucial. Most of the cross-field transport in modern-day tokamaks is carried by turbulence driven by steep pressure gradients. Background neoclassical transport, however, provides a steady level of cross-field flux even in cases when turbulence becomes weak or suppressed. The goal of this work is to quantify how neoclassical (NC) effects and turbulence can influence each other. For this purpose the nonlinear gyrokinetic turbulence code GENE is employed. Firstly, its ability to self-consistently calculate the NC radial electric field is successfully benchmarked against the radial force balance equation and NC transport in the plasma region close to the center of a tokamak is studied. In the next step a model system where a long-wavelength external potential is imposed on ion temperature gradient-driven (ITG) turbulence is investigated. It is found that the self-generated shear flow pattern of the turbulence adapts to the imposed pattern and a small external shear is sufficient to notably reduce turbulent transport. Motivated by this global ITG simulations with fixed pressure gradient profiles are performed with and without inclusion of NC effects. Their comparison reveals that the NC field enhances turbulent transport by 20-30 % for a ratio of ion gyroradius and device radius larger than 1/300. An explanation is that the NC field aligns a region of low shear with the maximum of the gradient profile where the turbulent drive is strongest. Further investigation reveals that NC effects also change the dependence of the system on collisionality or safety factor. Finally, in physically more comprehensive simulations with fixed power input and a self-consistently evolving temperature profile, the additional NC transport channel is found to reduce the frequency and amplitude of intermittent turbulent transport bursts.