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To aim at the realization of a helical fusion reactor, we study multi-objective optimization of coil shapes, which satisfy various requirements. In the magnetic field configuration created by these coils, several unfavorable examples are found: some of them have magnetic islands or doublet configurations. In order to automatically and quickly exclude such cases that hinder the optimization, we have developed a new method to detect unfavorable magnetic surfaces by using image recognition. Binarization and erosion are performed as preprocessing, and then blanks of magnetic islands and doublets are extracted as recognition targets. Consequently, we have developed a classifier with high performance. Using this trained classifier, we have shown that almost all cases with unfavorable magnetic surfaces in various magnetic configurations can be excluded in a short time and with high precision., source:https://doi.org/10.1585/pfr.18.1403018

We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs., source:https://doi.org/10.1103/PhysRevLett.127.225001, identifier:0000-0001-9585-5201

We develop a new simulation code for solving the Poisson equation, based on Monte Carlo methods. When static resonant magnetic perturbations (RMPs) are used in tokamak plasma to mitigate or suppress edge-localized modes, the RMPs generate an electric field in the ergodized edge region. The electrostatic potential should be calculated only in the edge region to reduce the computational cost of solving the Poisson equation in the complicated three-dimensional magnetic structure, which is assumed to be fixed in time. In this study, we propose a basic idea for evaluating an electrostatic potential given by the Poisson equation in only a part of the domain in curvilinear coordinates. This Poisson solver allows for the boundary condition to be set not only inside the selected region in which the potential is evaluated, but also outside the selected region. Several benchmarks for the developed code are also presented., source:https://doi.org/10.1585/pfr.17.1403029, identifier:0000-0002-1642-1235

Self-organized structure formation in magnetically confined plasmas is one of the most attractive subjects in modern experimental physics. Nonequilibrium media are known to often exhibit phenomena that cannot be predicted by superposition of linear theories. One representative example of such phenomena is the hydrogen isotope effect in fusion plasmas, where the larger the mass of the hydrogen isotope fuel is the better the plasma confinement becomes, contrary to what simple scaling models anticipate. In this article, threshold condition of a plasma structure formation is shown to have a strong hydrogen isotope effect. To investigate the underlying mechanism of this isotope effect, the electrostatic potential is directly measured by a heavy ion beam probe. It is elucidated that the core electrostatic potential transition occurs with less input power normalized by plasma density in plasmas with larger isotope mass across the structure formation. This observation is suggestive of the isotope effect in the radial electric field structure formation., source:https://doi.org/10.1038/s41598-022-09526-w, identifier:0000-0001-5669-1937

A heating source with off-axis electron cyclotron heating (ECH) alone produced a plasma with a quasi-steady-state hollow electron-temperature profile in the Large Helical Device. The clear formation of this quasi-steady-state hollow electron-temperature profile can be explained by adding the outward heat convection term to the diffusion term, as a simple model to describe the electron heat flux, using the energy conservation equation. In addition, we directly observed the non-locality of the non-diffusive (convective) contribution in transient electron thermal transport in the condition that power-modulated on-axis ECH was applied to the plasma sustained by off-axis ECH. The experimentally evaluated flux-gradient relation shows two different positive values of the electron heat flux at zero temperature gradient by going back and forth between positive and negative temperature gradient regions in the transport hysteresis phenomenon., source:Physics of Plasmas 29, 032504 (2022); https://doi.org/10.1063/5.0074351, source:https://doi.org/10.1063/5.0074351, identifier:0000-0002-2983-5920

The effects of misalignment of modular coils on various physical properties in the Chinese first quasi-axisymmetric Stellarator (CFQS) are discussed in this study. To estimate the effects quantitatively, simple assumptions are made regarding the structure of coil displacement. We consider the following three cases: displacement in radial direction (Case A), displacement in the vertical direction (Case B), and displacement by tilting (Case C). In all cases, we assume that the displacement structure has a stellarator symmetry. These assumptions are employed to calculate the change in the magnetic surfaces, rotational transform profile, magnetic well depth profile, and the effective helical ripple. Calculation results show that if the magnitude of displacement is less than 10 mm, the effects on these physical properties are small, and the good neoclassical transport property is retained., source:https://doi.org/10.1585/pfr.14.3403151, identifier:0000-0003-3764-3184

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., source:https://doi.org/10.1585/pfr.12.1203004

A numerical code has been developed in order to investigate the applicability of the permanent magnet method to vertically-stacked multiple high-temperature superconducting (HTS) tapes. The permanent magnet method was proposed to simply and contactlessly measure the critical current density in the HTS tape. By this method, the critical current density is estimated from the proportional relation between the critical current density and the Lorentz force working on the permanent magnet. The Maxwell equation, coupled with the superconductivity characteristics, is solved by the edge-based finite element method to investigate the effect of the number of HTS tapes on the Lorentz force. As a result, it is clear that the permanent magnet method can be applied to measurement of the critical current density in the multiple HTS tapes although there is an upper limit of the number of HTS tapes in which the critical current density can be measured. In addition, by using stronger magnet, the permanent magnet method can measure the critical current density when more number of HTS tapes are stacked., source:https://doi.org/10.1585/pfr.17.2405035, identifier:0000-0003-4355-8293

We present initial results in the development of a gyrokinetic particle-in-cell code for the whole-volume modeling of stellarators. This is achieved through two modifications to the X-point Gyrokinetic Code (XGC), originally developed for tokamaks. One is an extension to three-dimensional geometries with an interface to Variational Moments Equilibrium Code (VMEC) data. The other is a connection between core and edge regions that have quite different field-line structures. The VMEC equilibrium is smoothly extended to the edge region by using a virtual casing method. Non-axisymmetric triangular meshes in which triangle nodes follow magnetic field lines in the toroidal direction are generated for field calculation using a finite-element method in the entire region of the extended VMEC equilibrium. These schemes are validated by basic benchmark tests relevant to each part of the calculation cycle, that is, particle push, particle-mesh interpolation, and field solver in a magnetic field equilibrium of Large Helical Device including the edge region. The developed code also demonstrates collisionless damping of geodesic acoustic modes and steady states with residual zonal flow in the core region., source:Plasma 2019, 2(2), 179-200; https://doi.org/10.3390/plasma2020014, source:https://doi.org/10.3390/plasma2020014, identifier:0000-0003-2513-0453

The magnetic island in the large helical device (LHD) shows the dynamic behaviour of the healing/growth transition withthe 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., source:https://iopscience.iop.org/article/10.1088/0029-5515/55/7/073004

Conceptual design of a compact large helical device (LHD)-type helical fusion reactor FFHR-c1 has been conducted. This design focuses on a year-long electric power generation with as small a reactor size as possible by adopting the operation with auxiliary heating and innovative ideas for the design of the superconducting magnet, divertor and blanket system. The primary design parameters, which have been selected by extrapolation from the previous design FFHR-d1B using simple scalings, has been examined by the systems code and the 1D integrated physics analysis code from the viewpoint of plant power balance and the achievable plasma operation regime. The design feasibility of the proposed design point has been confirmed with the physics parameters that are consistent with the LHD experiment. Further improvement of the plasma performance is expected by the optimisation of the helical coil winding law. Although intensive R&D is needed to realise the innovative ideas of the engineering design, this design ensures the path to helical commercial power plants and provides more options and increases the probability of solving critical issues of fusion reactors., source:T. Goto et al 2019 Nucl. Fusion 59 076030, source:https://doi.org/10.1088/1741-4326/ab15c3, identifier:0000-0001-6028-8980

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., source:T Goto et al 2018 Plasma Phys. Control. Fusion 60 074001, source:https://doi.org/10.1088/1361-6587/aabd51, identifier:0000-0001-6028-8980

This study closely investigates the plasma operation scenario for the LHD-type helical reactor FFHR-d1 in view of MHD equilibrium/stability, neoclassical transport, alpha energy loss and impurity effect. In 1D calculation code that reproduces the typical pellet discharges in LHD experiments, we identify a self-consistent solution of the plasma operation scenario which achieves steady-state sustainment of the burning plasma with a fusion gain of Q ~ 10 was found within the operation regime that has been already confirmed in LHD experiment. The developed calculation tool enables systematic analysis of the operation regime in real time., source:T. Goto et al 2017 Nucl. Fusion 57 066011, source:https://doi.org/10.1088/1741-4326/aa6870, identifier:0000-0001-6028-8980

1D physics analysis of the plasma start-up scenario of the large helical device (LHD)-type helical reactor FFHR-d1 was conducted. The time evolution of the plasma profile is calculated using a simple model based on the LHD experimental observations. A detailed assessment of the magnetohydrodynamic equilibrium and neo-classical energy loss was conducted using the integrated transport analysis code TASK3D. The robust controllability of the fusion power was confirmed by feedback control of the pellet fuelling and a simple staged variation of the external heating power with a small number of simple diagnostics (line-averaged electron density, edge electron density and fusion power). A baseline operation control scenario (plasma start-up and steady-state sustainment) of the FFHR-d1 reactor for both self-ignition and sub-ignition operation modes was demonstrated., source:T. Goto et al 2015 Nucl. Fusion 55 063040, source:https://doi.org/10.1088/0029-5515/55/6/063040, identifier:0000-0001-6028-8980

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., source:https://doi.org/10.1063/1.5115440, identifier:0000-0001-5444-1758

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., source:https://doi.org/10.1063/1.4945618, identifier:0000-0001-5444-1758

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., source:https://aip.scitation.org/doi/abs/10.1063/5.0027905, identifier:0000-0001-5444-1758

The Eulerian variational principle for the Vlasov-Poisson-Ampère system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to obtain the momentum conservation law and the symmetric pressure in a more direct way than using the translational and rotational symmetries of the system. Next, the Eulerian variational principle is given for the collisionless drift kinetic equation, where particles' phase-space trajectories in given electromagnetic fields are described by Littlejohn's guiding center equations [R. G. Littlejohn, J. Plasma Phys. 29, 111 (1983)]. Then, it is shown that, in comparison with the conventional moment method, the invariance under a general spatial coordinate transformation yields a more convenient way to obtain the momentum balance as a three-dimensional vector equation in which the symmetric pressure tensor, the Lorentz force, and the magnetization current are properly expressed. Furthermore, the Eulerian formulation is presented for the extended drift kinetic system, for which, in addition to the drift kinetic equations for the distribution functions of all particle species, the quasineutrality condition and Ampère's law to determine the self-consistent electromagnetic fields are given. Again, the momentum conservation law for the extended system is derived from the invariance under the general spatial coordinate transformation. Besides, the momentum balances are investigated for the cases where the collision and/or external source terms are added to the Vlasov and drift kinetic equations., source:https://aip.scitation.org/doi/abs/10.1063/1.5031155, identifier:0000-0001-5444-1758

A remarkable extension of the high-ion-temperature (high-Ti) regime was obtained in deuterium plasma experiments in the Large Helical Device. In order to clarify transport characteristics in the ion internal transport barrier (ITB) formation with an isotope effect, a dataset of pure deuterium (nD/ne > 0.8) and pure hydrogen (nH/ne > 0.8) plasmas in the high-Ti regime were analyzed, and two mechanisms of transport improvement were characterized. A significant reduction of ion heat transport in the core of both deuterium and hydrogen plasmas was observed, indicating ion ITB formation. The dependence of the ion heat diffusivity on temperature ratio (Te/Ti) and normalized Ti-gradient (R/LTi = −(R/Ti)(dTi/dr)) was investigated in the core region, in which gyrokinetic simulations with the GKV code predict the destabilization of ion temperature gradient (ITG) modes. The Te/Ti dependence shows ITG-like property, while a significant deviation from the ITG-like property is found in the R/ dependence, indicating suppression of the ITG mode in the large R/ regime and resultant ion ITB formation. In the comparison between deuterium plasma and hydrogen plasma, the lower transport in the deuterium plasma is observed in both ion and electron heat diffusivities, indicating a significant isotope effect. It was found with the nonlinear turbulent transport simulation with GKV that the zonal flow enhancement contributes to the ITG suppression in the deuterium plasma., source:K. Nagaoka et al 2019 Nucl. Fusion 59 106002, source:https://doi.org/10.1088/1741-4326/ab2d02, identifier:0000-0002-5892-6047

The integrated transport analysis suite, TASK3D-a (Analysis), has been developed to be capable for routine whole-discharge analyses of plasmas confined in three-dimensional (3D) magnetic configurations such as the LHD. The routine dynamic energy balance analysis for NBI-heated plasmas was made possible in the first version released in September 2012. The suite has been further extended through implementing additional modules for neoclassical transport and ECH deposition for 3D configurations. A module has also been added for creating systematic data for the International Stellarator–Heliotron Confinement and Profile Database. Improvement of neutral beam injection modules for multiple-ion species plasmas and loose coupling with a large-simulation code are also highlights of recent developments., source:M. Yokoyama et al 2017 Nucl. Fusion 57 126016, source:https://doi.org/10.1088/1741-4326/aa800a

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., source:Paper Moderation of neoclassical impurity accumulation in high temperature plasmas of helical devices J.L. Velasco1, I. Calvo1, S. Satake2,3, A. Alonso1, M. Nunami2,3, M. Yokoyama2,3, M. Sato2, T. Estrada1, J.M. Fontdecaba1, M. Liniers1, K.J. McCarthy1, F. Medina1, B. Ph Van Milligen1, M. Ochando1, F. Parra4,5, H. Sugama2, A. Zhezhera6, The LHD Experimental Team2 and The TJ-II Team1Hide full author list Published 27 October 2016 • © 2016 EURATOM Nuclear Fusion, Volume 57, Number 1 Citation J.L. Velasco et al 2017 Nucl. Fusion 57 016016, source:https://doi.org/10.1088/0029-5515/57/1/016016

0000-0001-9585-5201, We assess the magnetic field configuration in modern fusion devices by comparing experiments with the same heating power, between a stellarator and a heliotron. The key role of turbulence is evident in the optimized stellarator, while neoclassical processes largely determine the transport in the heliotron device. Gyrokinetic simulations elucidate the underlying mechanisms promoting stronger ion scale turbulence in the stellarator. Similar plasma performances in these experiments suggests that neoclassical and turbulent transport should both be optimized in next step reactor designs.

0000-0003-2513-0453, We present initial results in the development of a gyrokinetic particle-in-cell code for the whole-volume modeling of stellarators. This is achieved through two modifications to the X-point Gyrokinetic Code (XGC), originally developed for tokamaks. One is an extension to three-dimensional geometries with an interface to Variational Moments Equilibrium Code (VMEC) data. The other is a connection between core and edge regions that have quite different field-line structures. The VMEC equilibrium is smoothly extended to the edge region by using a virtual casing method. Non-axisymmetric triangular meshes in which triangle nodes follow magnetic field lines in the toroidal direction are generated for field calculation using a finite-element method in the entire region of the extended VMEC equilibrium. These schemes are validated by basic benchmark tests relevant to each part of the calculation cycle, that is, particle push, particle-mesh interpolation, and field solver in a magnetic field equilibrium of Large Helical Device including the edge region. The developed code also demonstrates collisionless damping of geodesic acoustic modes and steady states with residual zonal flow in the core region.