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Recurrent bursts of toroidicity-induced Alfven eigenmodes (TAE) are studied using a self-consistent simulation model. Bursts of beam ion losses observed in the neutral beam injection experiment at the Tokamak Fusion Test Reactor [K. L. Wong et al., Phys. Rev. Lett. 66, 1874 (1991)] are reproduced using experimental parameters. It is found that synchronized TAE bursts take place at regular time intervals of 2.9 ms, which is close to the experimental value of 2.2 ms. The stored beam energy saturates at about 40% of that of the classical slowing down distribution. The stored beam energy drop associated with each burst has a modulation depth of 10%, which is also close to the inferred experimental value of 7%. Surface of section plots demonstrate that both the resonance overlap of different eigenmodes and the disappearance of KAM surfaces in phase space due to overlap of higher-order islands created by a single eigenmode lead to particle loss. Only co-injected beam ions build up to a significant stored energy even though their distribution is flattened in the plasma center. However, they are not directly lost, as their orbits extend beyond the outer plasma edge when the core plasma leans on a high field side limiter. The saturation amplitude is deltaB/B~2×10^?2, which is larger than would appear to be compatible with experiment. Physical arguments are presented for why the stored energetic particle response observed in the simulation is still plausible.

The driving and damping mechanism of plasma flow is an important issue because flow shear has a significant impact on turbulence in a plasma, which determines the transport in the magnetized plasma. Here we report clear evidence of the flow damping due to stochastization of the magnetic field. Abrupt damping of the toroidal flow associated with a transition from a nested magnetic flux surface to a stochastic magnetic field is observed when the magnetic shear at the rational surface decreases to 0.5 in the large helical device. This flow damping and resulting profile flattening are much stronger than expected from the Rechester–Rosenbluth model. The toroidal flow shear shows a linear decay, while the ion temperature gradient shows an exponential decay. This observation suggests that the flow damping is due to the change in the non-diffusive term of momentum transport., Understanding the transport of ions, electrons and heat in magnetized plasmas is important to the development of fusion power as well as our understanding of the behaviour of astrophysical objects. Ida et al. find that stochastization of magnetic field lines in a plasma damps plasma flow more strongly than expected.

Characteristics of the MHD instabilities for high beta LHD (large helical device) plasmas in the inward shifted configurations have been investigated by numerical simulations. On the condition that the magnetic Reynolds number is lower than the experimental value, the time evolution of the MHD instabilities is as follows: (1) resistive ballooning modes, the toroidal mode number of which is higher than the LHD's toroidal pitch (), are destabilized in the plasma peripheral region; (2) low toroidal modes typified by are destabilized by the nonlinear mode coupling of the resistive ballooning modes the toroidal mode number of which is adjacent to each other where n is the toroidal mode number. In particular, the velocity of the mode is finite at the magnetic axis so that there is a large velocity directed to the magnetic axis; and (3) when the high n modes are saturated, the destabilized low n modes, which have a global mode structure and shift the magnetic axis, also begin to be saturated. The self mode coupling of the low n modes induces the core crush and transports the plasma from the core region to the peripheral region. Since the nonlinear MHD phenomena are dominated by the resistive modes, the MHD phenomena for the experimental high magnetic Reynolds number are considered to be milder than our numerical results. Thus, when the experimental high magnetic Reynolds number is taken in the simulation, the core crush may be suppressed so that the numerical results are expected to become close to the experimental results where the stable high beta plasmas are obtained.

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, Ti and Te, 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 $\left\langle \beta \right\rangle $ . The high $\left\langle \beta \right\rangle $ 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.

Alfven eigenmodes (AEs) destabilized by the neutral beam injection (NBI) in a Large Helical Device experiment are investigated using multi-phase magnetohydrodynamic (MHD) hybrid simulation, which is a combination of classical and MHD hybrid simulations for fast ions. The fast ion distribution is simulated with NBI, collisions, and losses in the equilibrium magnetic field in the classical simulation, while the MHD hybrid simulation takes account of the interaction between fast ions and an MHD fluid, in addition to the classical dynamics. It is found in the multi-phase hybrid simulation that the stored fast ion energy is saturated due to the interaction with AEs at a lower level than that of the classical simulation. Two groups of AEs with frequencies close to those observed in the experiment are destabilized alternately at each hybrid simulation. Firstly destabilized are two toroidal Alfven eigenmodes whose frequency is close to the local minimum of the upper Alfven continuous spectrum. Secondly destabilized is a global Alfven eigenmode whose frequency is located well inside the Alfven continuous spectrum gap. In addition, two AEs whose frequencies are close to that of the ellipticity-induced Alfven eigenmode are observed with a lower amplitude. When the hybrid simulation is run continuously, the interchange mode grows more slowly than the AEs, but becomes dominant in the long time scale. The interchange mode oscillates with a constant amplitude and a frequency of ∼1 kHz. The interchange mode reduces the stored fast ion energy to a lower level than that of the AEs.

Kinetic-MagnetoHydroDynamic hybrid simulations are carried out to investigate fishbone modes excited by fast ions on the Experimental Advanced Superconducting Tokamak. The simulations use realistic equilibrium reconstructed from experiment data with the constraint of the q = 1 surface location (q is the safety factor). Anisotropic slowing down distribution is used to model the distribution of the fast ions from neutral beam injection. The resonance condition is used to identify the interaction between the fishbone mode and the fast ions, which shows that the fishbone mode is simultaneously in resonance with the bounce motion of the trapped particles and the transit motion of the passing particles. Both the passing and trapped particles are important in destabilizing the fishbone mode. The simulations show that the mode frequency chirps down as the mode reaches the nonlinear stage, during which there is a substantial flattening of the perpendicular pressure of fast ions, compared with that of the parallel pressure. For passing particles, the resonance remains within the q = 1 surface, while, for trapped particles, the resonant location moves out radially during the nonlinear evolution. In addition, parameter scanning is performed to examine the dependence of the linear frequency and growth rate of fishbones on the pressure and injection velocity of fast ions.

© 2014 IAEA. A multi-phase simulation that is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid is developed to simulate the nonlinear dynamics on the slowing down time scale of the energetic particles. The hybrid simulation code is extended with realistic beam deposition profile, collisions and losses, and is used for both the classical and hybrid phases. The code is run without MHD perturbations in the classical phase, while the interaction between the energetic particles and the MHD fluid is simulated in the hybrid phase. In a multi-phase simulation of DIII-D discharge #142111, the stored beam ion energy is saturated due to Alfvén eigenmodes (AE modes) at a level lower than in the classical simulation. After the stored fast ion energy is saturated, the hybrid simulation is run continuously. It is demonstrated that the fast ion spatial profile is significantly flattened due to the interaction with the multiple AE modes with amplitude v/vA∼ δB/B ∼ O(10-4). The dominant AE modes are toroidal Alfvén eigenmodes (TAE modes), which is consistent with the experimental observation at the simulated moment. The amplitude of the temperature fluctuations brought about by the TAE modes is of the order of 1% of the equilibrium temperature. This is also comparable with electron cyclotron emission measurements in the experiment.

Recurrent bursts of toroidicity induced Alfven eigenmodes (TAEs) are reproduced with a Fokker-Planck-MHD simulation where a fast ion source and slowing down are incorporated self-consistently. The bursts take place at regular time intervals and the behaviours of all the TAEs are synchronized. The fast ion transport due to TAE activity spatially broadens the classical fast ion distribution and significantly reduces its peak value. Only a small change of the distribution takes place with each burst, leading to loss of a small fraction of the fast ions. The system stays close to the marginal stability state established through the interplay of the fast ion source, slowing down and TAE activity.

核融合プラズマにおけるアルヴェン固有モードの非線形時間発展, 藤堂泰［核融合科学研究所］＊所属は当時のものを記載

We have developed a 2½-dimensional open boundary particle simulation model and have studied the current-driven electrostatic ion-cyclotron instability and related d.c. potential difference. Fresh streaming electrons are injected smoothly from the boundaries at each time step, avoiding unphysical accumulation of charged particles in front of the boundaries. As a current-driven electrostatic ion cyclotron instability grows, a d.c. potential difference along the magnetic field lines is created.

This article describes recent progress in nonlinear simulation studies of Alfven eigenmodes, especially of the toroidicity-induced Alfven eigenmode (TAE). Early simulations showed clearly that wave-particle trapping saturates the growth of TAE, but experimental results such as recurrent bursts and steady saturation remain unexplained. Recent simulations, which take account of particle source and collisions, can solve the mystery of these qualitatively different behaviors.

Linear and nonlinear particle-magnetohydrodynamic (MHD) simulation codes are developed to study interactions between energetic ions and MHD modes. Energetic alpha particles with the slowing-down distribution are considered and the behavior of n = 2 toroidal Alfv?n eigenmodes (TAE modes) is investigated with the parameters pertinent to the present large tokamaks. The linear simulation reveals the resonance condition between alpha particles and TAE mode. In the nonlinear simulation, two n = 2 TAE modes are destabilized and alpha particle losses induced thereby are observed. Counterpassing particles are lost when they cross the passing-trapped boundary. They are the major part of lost particles, but trapped particles are also lost appreciably.

A particle algorithm for linear kinetic analysis in tokamak plasmas is developed. Linear kinetic stability of a tokamak plasma is analyzed as an initial value problem. Particles are used to sample plasma elements along equilibrium characteristics in 4-dimensional phase space (R,z,v?, ?). Each particle is accompanied with a weight which is a function of the toroidal angle. Integrals in the phase space are evaluated through the weight function and the particle location in the 4-dimensional space. Destabilization of ann=2 toroidal Alfven eigenmode is investigated as a test of the algorithm, and convergence in number of used particles is assessed.

Nonlinear frequency chirping of the energetic-particle-driven geodesic acoustic mode (EGAM) is investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic fluid. It is demonstrated in the simulation result that both frequency chirping up and chirping down take place in the nonlinear evolution of the EGAM. It is found that two hole-clump pairs are formed in the energetic particle distribution function in two-dimensional velocity space of pitch angle variable and energy. One pair is formed in the phase space region that destabilizes the instability, while the other is formed in the stabilizing region. The transit frequency of the hole (clump) in the destabilizing region chirps up (down), while in the stabilizing region the hole (clump) chirps down (up). The transit frequencies of particles in the holes and clumps are in good agreement with the chirping EGAM frequency indicating that the particles are kept resonant with the EGAM during the nonlinear frequency chirping. Continuous energy transfer takes place from the destabilizing phase space region to the stabilizing region during the spontaneous frequency chirping of the wave.

We have developed an electrostatic macro-scale implicit particle simulation code which enables us to simulate low-frequency plasma wave phenomena with large spatial scale length. Specifically, the Poisson equation with the implicit susceptibility term is accurately solved in our scheme with the “strict differencing” and “the consistent filtering.” Linear properties of the simulation scheme, such as the linear stability and the dispersion relation, are examined. We have also applied our simulation code to the excitation and nonlinear saturation of the ion temperature gradient (ITG) drift instability in a system with a shearless slab geometry. The linear properties of the excited ITG mode are compared with the theoretical prediction to find a good agreement.

A central theme of ‘‘Complexity’’ is the question of the creation of ordered structure in nature (self‐organization). The assertion is made that self‐organization is governed by three key processes, i.e., energy pumping, entropy expulsion and nonlinearity. Extensive efforts have been done to confirm this assertion through computer simulations of plasmas. A system exhibits markedly different features in self‐organization, depending on whether the energy pumping is instantaneous or continuous, or whether the produced entropy is expulsed or reserved. The nonlinearity acts to bring a nonequilibrium state into a bifurcation, thus resulting in a new structure along with an anomalous entropy production. As a practical application of our grand view of self‐organization a preferential generation of a dipole magnetic field is successfully demonstrated.

Remarkable progress has been made in diagnosing energetic particle instabilities on present-day machines and in establishing a theoretical framework for describing them. This overview describes the much improved diagnostics of Alfven instabilities and modelling tools developed world-wide, and discusses progress in interpreting the observed phenomena. A multi-machine comparison is presented giving information on the performance of both diagnostics and modelling tools for different plasma conditions outlining expectations for ITER based on our present knowledge., 37 pages, 20 figures

Recurring bursts of chirping Alfvén modes that were observed in JT-60U tokamak plasmas driven by negative-ion-based neutral beams (N-NB) are reproduced in first-principle simulations performed with an extended version of the hybrid code MEGA. This code simulates the interactions between gyrokinetic fast ions and magnetohydrodynamic (MHD) modes in the presence of a realistic fast ion source and collisions, so that it self-consistently captures dynamics across a wide range of time scales (0.01–100 ms). The simulation confirms that the experimentally observed phenomena known as 'fast frequency sweeping (fast FS) modes' are caused by bursts of energetic particle modes (EPM) with dominant toroidal mode number n = 1. On the long time scale (1–10 ms), the simulation reproduces the chirping range (40–60 kHz), the burst duration (few ms) and intervals (5–10 ms). On the short time scale (0.01–0.1 ms), it reproduces pulsations and phase jumps, which we interpret as the result of beating between multiple resonant wave packets. Having reproduced at multiple levels of detail the dynamics of low-amplitude long-wavelength Alfvén modes driven by N-NB ions, the next goal is to reproduce and explain abrupt large-amplitude events (ALE) that were seen in the same experiments at longer time intervals (10–100 ms).

A new simulation method has been developed to investigate the excitation and saturation processes of toroidal Alfv?n eigenmodes (TAE modes). The background plasma is described by a magnetohydrodynamic (MHD) fluid model, while the kinetic evolution of energetic alpha particles is followed by the drift kinetic equation. The magnetic fluctuation of n=2 mode develops and saturates at the level of 1.8×10?3 of the equilibrium field when the initial beta of alpha particles is 2% at the magnetic axis. After saturation, the TAE mode amplitude shows an oscillatory behavior with a frequency corresponding to the bounce frequency of the alpha particles trapped by the TAE mode. The decrease of the power transfer rate from the alpha particles to the TAE mode, which is due to the trapped particle effect of a finite-amplitude wave, causes the saturation. From the linear growth rate the saturation level can be estimated.

The sensitivity of the growth and nonlinear evolution of fast-ion-driven modes is examined with respect to the choice of particle boundary conditions, diffusion coefficients, fast ion gyroradii and bulk compressibility. The primary purpose of this work is to justify the choice of parameters to be used in the self-consistent long-time simulations of fast ion dynamics using global MHD-kinetic hybrid codes that include fast ion sources and collisions. The present study is conducted for a scenario based on the N-NB-driven JT-60U shot E039672, which is subject to abrupt large events (ALE). We use realistic geometry, a realistic fast ion distribution, and focus on experimentally observed harmonics with low toroidal mode numbers n = 1, 2, 3. The use of realistic boundary conditions and finite Larmor radii for the fast ions is shown to be essential. The usual values μ 0 η = ν = χ ∼ 10 − 6 v A 0 R 0 used for resistivity, viscosity and thermal diffusivity, and Γ = 5 / 3 used for the specific heat ratio (controlling the effect of compressibility) are shown to be reasonable choices. Our method for performing the parameter scans around the threshold for the onset of convective amplification is proposed as a strategy for nonlinear benchmark studies.

Fast ion pressure profiles flattened by multiple Alfvén eigenmodes (AEs) are investigated for various neutral beam deposition powers in a multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic fluid. Monotonic degradation of fast ion confinement and fast ion profile stiffness is found with increasing beam deposition power. The confinement degradation and profile stiffness are caused by a sudden increase in fast ion transport flux brought about by AEs for fast ion pressure gradients above a critical value. The critical pressure gradient and the corresponding beam deposition power depend on the radial location. The fast ion pressure gradient stays moderately above the critical value, and the profiles of the fast ion pressure and fast ion transport flux spread radially outward from the inner region, where the beam is injected. It is found that the square root of the MHD fluctuation energy is proportional to the beam deposition power. Analysis of the time evolutions of the fast ion energy flux profiles reveals that intermittent avalanches take place with contributions from the multiple eigenmodes. Surface of section plots demonstrate that the resonance overlap of multiple eigenmodes accounts for the sudden increase in fast ion transport with increasing beam power. The critical gradient and critical beam power for the profile stiffness are substantially higher than the marginal stability threshold.

A computer simulation of a magnetohydrodynamic dynamo in a rapidly rotating spherical shell is performed. Extensive parameter runs are carried out changing electrical resistivity. When resistivity is sufficiently small, total magnetic energy can grow more than ten times larger than total kinetic energy of convection motion which is driven by an unlimited external energy source. When resistivity is relatively large and magnetic energy is comparable or smaller than kinetic energy, the convection motion maintains its well‐organized structure. However, when resistivity is small and magnetic energy becomes larger than kinetic energy, the well‐organized convection motion is highly irregular. The magnetic field is organized in two ways. One is the concentration of component parallel to the rotation axis and the other is the concentration of perpendicular component. The parallel component tends to be confined inside anticyclonic columnar convection cells, while the perpendicular component is confined outside convection cells.

Effects of poloidal shear flow on the stability of interchange modes in a Large Helical Device (LHD) configuration are numerically studied. Three-dimensional (3D) numerical codes are utilized for the equilibrium and stability calculations. A static equilibrium is employed and a model poloidal flow as a flux function is incorporated in the initial perturbation. The results show that the initially applied flow can suppress the growth of the interchange mode if the flow is sufficiently large.

High-frequency energetic particle driven geodesic acoustic modes (EGAM) observed in the large helical device plasmas are investigated using a hybrid simulation code for energetic particles and magnetohydrodynamics (MHD). Energetic particle inertia is incorporated in the MHD momentum equation for the simulation where the beam ion density is comparable to the bulk plasma density. Bump-on-tail type beam ion velocity distribution created by slowing down and charge exchange is considered. It is demonstrated that EGAMs have frequencies higher than the geodesic acoustic modes and the dependence on bulk plasma temperature is weak if (1) energetic particle density is comparable to the bulk plasma density and (2) charge exchange time (τcx ) is sufficiently shorter than the slowing down time (τs ) to create a bump-on-tail type distribution. The frequency of high-frequency EGAM rises as the energetic particle pressure increases under the condition of high energetic particle pressure. The frequency also increases as the energetic particle pitch angle distribution shifts to higher transit frequency. It is found that there are two kinds of particles resonant with EGAM: (1) trapped particles and (2) passing particles with transit frequency close to the mode frequency. The EGAMs investigated in this work are destabilized primarily by the passing particles whose transit frequencies are close to the EGAM frequency.

A multi-phase simulation, which is a combination of classical simulation and hybrid simulation for energetic particles interacting with a magnetohydrodynamic (MHD) fluid including neutral beam injection, slowing-down, and pitch angle scattering, is applied to DIII-D discharge #142111 where the fast ion spatial profile is significantly flattened due to multiple Alfven eigenmodes (AEs). The large fast ion pressure profile flattening observed experimentally is successfully reproduced by these first of a kind comprehensive simulations. Temperature fluctuations due to three of the dominant toroidal Alfven eigenmodes in the simulation results are compared in detail with electron cyclotron emission measurements in the experiment. It is demonstrated that the temperature fluctuation profile and the phase profile are in very good agreement with the measurement, and the amplitude is also in agreement within a factor of two. This level of agreement validates the multi-phase hybrid simulation for the prediction of AE activity and alpha particle transport in burning plasmas.

The influence of the ion diamagnetic flow on the resistive interchange mode including dissipation in the Large Helical Device (LHD) plasmas is investigated with three-dimensional (3D) magnetohydrodynamic (MHD) codes. The contribution on the interchange mode stability depends on the difference between the ideal growth rate γI and the single fluid growth rate including resistivity and dissipation γD. When γD is close to γI, the ion diamagnetic effects are stabilizing. In this case the stabilization can be approximated by an analytic formula by analogy with the case without dissipation. When γD is far from γI the ion diamagnetic effects are destabilizing.

This conference report summarizes the contributions to, and discussions at, the 4th Asia-Pacific Transport Working Group Meeting held at Kyushu University, Japan, during 10–13 June 2014. The topics of the meeting were organized under five main headings: turbulence suppression and transport barrier formation, effect of magnetic topology on MHD activity and transport, non-diffusive contribution of momentum and particle transport, non-local transport and turbulence spreading and coupling, energetic particles and instability. The Young Researchers' Forum which was held in this meeting is also described in this report.

Dynamics of fast ions and shear Alfven waves are simulated using MEGA, a global nonlinear hybrid code. The scenario considered is based on JT-60U shot E039672, driven by strong negative-ion-based neutral beams (N-NB), just before the onset of a so-called abrupt large event (ALE). It is found that modes with toroidal mode numbers n = 2, 3, 4 can be destabilized, besides the n = 1 mode studied previously. The properties of the modes with n > 1 are sensitive to the value of the plasma beta and the form of the fast ion distribution, so simulation conditions are set up as realistically as presently possible. When the fast ion drive exceeds a certain threshold, the n = 3 mode is enhanced through a convective amplification process while following fast ions were displaced either by the n = 3 mode itself or by the n = 1 mode. The fast ion transport in several cases, simulated with single- or multiple-n modes, is analysed and implications of the results for the explanation of ALEs are discussed.

Magnetohydrodynamic (MHD) instabilities driven by energetic alpha particles and beam deuterium particles are investigated for ITER operation scenarios using a hybrid simulation code for energetic particles interacting with an MHD fluid. The particle simulation method with finite Larmor radius effects is applied to both alpha and beam deuterium particles. For the steady-state scenario with 9 MA plasma current, beta-induced Alfv?n eigenmodes (BAE modes) with low toroidal mode number (n = 3, 5) were found to become dominant in the nonlinear phase although many toroidal Alfv?n eigenmodes (TAE modes) with n ? 15 are most unstable in the linear phase. The redistribution of energetic particles with δβα ? δβbeam ? 0.07%, which respectively correspond to 6% and 8% of the central values, occurs in the nonlinear phase. When the toroidal mode number of the fluctuations is restricted to n ? 8, the redistribution is substantially reduced, thus, suggesting that the resonance overlap between the n ? 15 TAE and low-n BAE modes enhances the energetic particle transport in the run with full toroidal mode numbers. For the ITER scenario with 15 MA plasma current, an MHD instability with n = 3 that peaks around the q = 1 (q is the safety factor) magnetic surfaces is driven by bulk plasma current and bulk pressure, and results in significant redistribution of alpha particles with δβα ? 0.3%. For the equilibrium profile with the safety factor profile uniformly raised by 0.1 to remove the q = 1 surfaces, only a benign MHD instability occurs and the energetic particle transport is negligible.

Property of pressure driven modes in Large Helical Device (LHD) plasmas with a resonant magnetic perturbation (RMP) is numerically studied. Particularly, we analyze three-dimensional (3D) RMP effects on the linear magnetohydrodynamic (MHD) stability of the modes. For this purpose, 3D numerical codes are utilized for both calculations of an equilibrium including an RMP generating an m = 1/n = 1 magnetic island and the stability of the perturbations resonant at the ι = 1 surface. Here, m and n are the poloidal and the toroidal mode numbers, respectively, and ι denotes rotational transform. Owing to the RMP, the pressure driven mode is localized around the X-point of the island. The type of the mode structure changes from the interchange type to the ballooning type. This property is attributed to the fact that the equilibrium pressure gradient is larger at the X-point than at the O-point.

In Large Helical Device experiments, independent low-order magnetic fluctuations due to the resistive interchange mode are commonly observed; investigating the characteristics of this instability is our ultimate goal. Two new methods for analyzing the single low-order instability in the stochastic region are developed. One method investigates it by constructing the initial single-mode perturbation. The other method investigates it by constructing a reference surface outside the last closed flux surface. The reference surface is necessary for constructing the coordinates that are used to extract the Fourier mode in the stochastic field line structure.

The progress of physical understanding as well as parameter improvement of net-current-free helical plasma is reported for the Large Helical Device since the last Fusion Energy Conference in Daejeon in 2010. The second low-energy neutral beam line was installed, and the central ion temperature has exceeded 7 keV, which was obtained by carbon pellet injection. Transport analysis of the high-T-i plasmas shows that the ion-thermal conductivity and viscosity decreased after the pellet injection although the improvement does not last long. The effort has been focused on the optimization of plasma edge conditions to extend the operation regime towards higher ion temperature and more stable high density and high beta. For this purpose a portion of the open helical divertors are being modified to the baffle-structured closed ones aimed at active control of the edge plasma. It is compared with the open case that the neutral pressure in the closed helical divertor increased by ten times as predicted by modelling. Studies of physics in a three-dimensional geometry are highlighted in the topics related to the response to a resonant magnetic perturbation at the plasma periphery such as edge-localized-mode mitigation and divertor detachment. Novel approaches of non-local and non-diffusive transport have also been advanced.

The interaction between toroidal Alfv?n eigenmode (TAE) and energetic ions in the Large Helical Device (LHD) is investigated using a reduced version of the MEGA code that implements a realistic equilibrium magnetic field with the HINT code and corresponding TAE profile with the AE3D code. In simulations, the linear growth rate of TAE amplitude is proportional to energetic ion density; consequently, the nonlinear saturation level of the TAE amplitude is enhanced by the increase in the energetic ion density. Energy transfer analysis is performed to clarify destabilization and saturation mechanisms of the TAE and to identify resonant energetic ions. An analysis of test particles in the electromagnetic field perturbed by the TAE shows that the magnitude of fluctuations in the energetic ion orbits is proportional to the square root of the TAE amplitude. Our results qualitatively reproduce the radial transport of energetic ions by the TAE in the LHD.

The hybrid code MEGA is used to simulate an abrupt large-amplitude event (ALE) in JT-60U shot E039672 that was strongly driven by a pair of negative-ion-based neutral beams (N-NBs). This configuration is known to be unstable to energetic particle modes (EPMs) with toroidal mode number n = 1. The purpose of this study is to look for a threshold with respect to the on-axis fast ion beta value, βh0, beyond which the EPM undergoes convective amplification (CA) and causes significant fast ion transport. This is motivated by the hypothesis that such a threshold may work as a trigger mechanism for relaxation events, such as ALE. In order to facilitate quantitative comparisons with the experiment, a realistic geometry and bulk pressure is used. Furthermore, MEGA is initialized with a fast ion distribution computed for JT-60U by an orbit-following Monte-Carlo code, and a passive vacuum region allows particles to travel without encountering artificial loss boundaries. Consistently with the experiment, the simulation predicts a burst time of about 0.3 ms and peak magnetic fluctuation levels around δBϑ/B

Linear properties of energetic particle driven geodesic acoustic mode (EGAM) in the large helical device plasmas are investigated using a hybrid simulation code for a magnetohydrodynamics fluid interacting with energetic particles. It is found that the EGAM is a global mode with the spatially uniform oscillation frequency despite the spatial variation of the local geodesic acoustic mode frequency. The poloidal mode numbers of poloidal velocity fluctuation, plasma density fluctuation, and magnetic fluctuation are m = 0, 1, and 2, respectively. Oscillation frequency, linear growth rate, and spatial width of EGAM are compared for different physics conditions. The EGAM frequency is proportional to the square root of the plasma temperature. The frequency is lower for higher energetic particle β value. The mode spatial width is larger for larger spatial width of the energetic particle distribution and for the reversed shear safety-factor profile than the normal shear profile. It is also found that the EGAM propagates radially outward in the linearly growing phase, and the propagation speed is slower for the spatially broadened modes.

Fast frequency sweeping (fast FS) mode in a JT-60U plasma is investigated with particle-magnetohydrodynamic hybrid simulation. A new kind of energetic particle mode (EPM) is found near the plasma center at a frequency close to the central frequency of the fast FS mode. Frequency sweeping close to that of the fast FS mode takes place. The ratio of the mode damping rate to the linear growth rate is consistent with spontaneous hole-clump pair creation.

This paper examines nonlinear magneto-hydrodynamic effects on the energetic particle driven toroidal Alfvén eigenmode (TAE) for lower dissipation coefficients and with higher numerical resolution than in the previous simulations (Todo et al 2010 Nucl. Fusion 50 084016). The investigation is focused on a TAE mode with toroidal mode number n = 4. It is demonstrated that the mechanism of mode saturation involves generation of zonal (n = 0) and higher-n (n ⩾ 8) sidebands, and that the sidebands effectively increase the mode damping rate via continuum damping. The n = 0 sideband includes the zonal flow peaks at the TAE gap locations. It is also found that the n = 0 poloidal flow represents a balance between the nonlinear driving force from the n = 4 components and the equilibrium plasma response to the n = 0 fluctuations. The spatial profile of the n = 8 sideband peaks at the n = 8 Alfvén continuum, indicating enhanced dissipation due to continuum damping.

A hybrid simulation code for nonlinear magnetohydrodynamics (MHD) and energetic-particle dynamics has been extended to simulate recurrent bursts of Alfvén eigenmodes by implementing the energetic-particle source, collisions and losses. The Alfvén eigenmode bursts with synchronization of multiple modes and beam ion losses at each burst are successfully simulated with nonlinear MHD effects for the physics condition similar to a reduced simulation for a TFTR experiment (Wong et al 1991 Phys. Rev. Lett. 66 1874, Todo et al 2003 Phys. Plasmas 10 2888). It is demonstrated with a comparison between nonlinear MHD and linear MHD simulation results that the nonlinear MHD effects significantly reduce both the saturation amplitude of the Alfvén eigenmodes and the beam ion losses. Two types of time evolution are found depending on the MHD dissipation coefficients, namely viscosity, resistivity and diffusivity. The Alfvén eigenmode bursts take place for higher dissipation coefficients with roughly 10% drop in stored beam energy and the maximum amplitude of the dominant magnetic fluctuation harmonic δB m/n /B ∼ 5 × 10−3 at the mode peak location inside the plasma. Quadratic dependence of beam ion loss rate on magnetic fluctuation amplitude is found for the bursting evolution in the nonlinear MHD simulation. For lower dissipation coefficients, the amplitude of the Alfvén eigenmodes is at steady levels δB m/n /B ∼ 2 × 10−3 and the beam ion losses take place continuously. The beam ion pressure profiles are similar among the different dissipation coefficients, and the stored beam energy is higher for higher dissipation coefficients.

The interaction between energetic particles and Alfven eigenmodes in reversed shear tokamak plasmas were investigated for different minimum safety-factor values using a hybrid simulation code for magnetohydrodynamics (MHD) and energetic particles. When the energetic particle distribution is isotropic in velocity space, the transition from low-frequency reversed shear Alfven eigenmode (RSAE mode) to toroidal Alfven eigenmode (TAE mode) is demonstrated as the minimum safety-factor value decreases. The frequency rises up from a level above the geodesic acoustic mode frequency to the TAE frequency. It is found that the energetic particles both co- and counter-going to the plasma current are transported by the TAE mode, whereas only the co-going particles are transported by the low-frequency RSAE mode. When only the co-passing particles are retained, the low-frequency RSAE modes are destabilized. On the other hand, the high-frequency RSAE modes are destabilized when only the counter-passing particles are retained.

First results from nonlinear simulations of energetic particle modes and the resulting transport of energetic ions using realistic tokamak geometry are presented and compared with results obtained with a shifted-circle model equilibrium and otherwise equivalent parameters. The modes excited in both cases have similar frequen- cies and mode structuresand cause a similar amount of energetic ion transport during the first few hundred Alfven times of the nonlinear evolution. The similarity in transport is interesting since it stands in contrast to the reduced linear growth rate and saturation level in the non-circular case: for the parameters chosen, both are reduced by a factor of 2 compared to the circular case. These results motivate further studies, including a verification of our results with other codes, a clarification of the mechanisms underlying the linear stabilization, and a detailed analysis of the mode activity and particle redistribution during the nonlinear evolution.

Nonlinear magnetohydrodynamic (MHD) effects on Alfvén eigenmode evolution were investigated via hybrid simulations of an MHD fluid interacting with energetic particles. The investigation focused on the evolution of an n = 4 toroidal Alfvén eigenmode (TAE) which is destabilized by energetic particles in a tokamak. In addition to fully nonlinear code, a linear-MHD code was used for comparison. The only nonlinearity in that linear code is from the energetic-particle dynamics. No significant difference was found in the results of the two codes for low saturation levels, δB/B ∼ 10−3. In contrast, when the TAE saturation level predicted by the linear code is δB/B ∼ 10−2, the saturation amplitude in the fully nonlinear simulation was reduced by a factor of 2 due to the generation of zonal (n = 0) and higher-n (n ⩾ 8) modes. This reduction is attributed to the increased dissipation arising from the nonlinearly generated modes. The fully nonlinear simulations also show that geodesic acoustic mode is excited by the MHD nonlinearity after the TAE mode saturation.

The shear Alfven spectrum in three-dimensional configurations, such as stellarators and rippled tokamaks, is more densely populated due to the larger number of mode couplings caused by the variation in the magnetic field in the toroidal dimension. This implies more significant computational requirements that can rapidly become prohibitive as more resolution is requested. Alfven eigenfrequencies and mode structures are a primary point of contact between theory and experiment. A new algorithm based on the Jacobi–Davidson method is developed here and applied for a reduced magnetohydrodynamics model to several stellarator configurations. This technique focuses on finding a subset of eigenmodes clustered about a specified input frequency. This approach can be especially useful in modeling experimental observations, where the mode frequency can generally be measured with good accuracy and several different simultaneous frequency lines may be of interest. For cases considered in this paper, it can be a factor of...

The magnetohydrodynamic (MHD) simulation code MHD Infrastructure for Plasma Simulation (MIPS) was benchmarked on ballooning instability in the Large Helical Device (LHD) plasma. The results were compared to the results of linear analysis by using the CAS3D code. Both the linear growth rates and the spatial profiles were found to be in good agreement. An extended MHD model with finite ion Larmor radius effects was implemented into the MIPS code. Ballooning instabilities were investigated using the extended MHD model, and the results were compared with those using the MHD model. Ion diamagnetic drift was found to reduce the growth rate of the short-wavelength modes; hence, modes with a diamagnetic drift frequency comparable to the ideal MHD growth rate are the most unstable. The most unstable toroidal mode number of ballooning instability in the LHD is reduced to |n| ? 5 for hydrogen plasma with ion number density ni ? 1019 m?3.

Remarkable progress in the physical parameters of net-current free plasmas has been made in the Large Helical Device (LHD) since the last Fusion Energy Conference in Chengdu, 2006 (Motojima et al 2007 Nucl. Fusion 47 S668). The beta value reached 5% and a high-beta state beyond 4.5% from the diamagnetic measurement has been maintained for longer than 100 times the energy confinement time. The density and temperature regimes have also been extended. The central density has exceeded 1 × 1021 m−3 due to the formation of an internal diffusion barrier. The ion temperature has reached 5.2 keV at the density of 1.6 × 1019 m−3, which is associated with the suppression of ion heat conduction loss. Although these parameters have been obtained in separated discharges, each fusion-reactor relevant parameter has elucidated the potential of net-current free heliotron plasmas. Diversified studies in recent LHD experiments are reviewed in this paper.

Bursting energetic particle mode (EPM) and fast ion loss induced by the EPM have been observed and experimentally investigated in the Compact Helical System (CHS). A directional probe method was newly applied to neutral beam heated plasmas for fast ion measurement, and it successfully revealed fast ion behaviour inside the last closed flux surface (LCFS) during bursting EPMs. A convective oscillation was observed only inside the LCFS, and drives little loss of fast ions. An anomalous loss of fast ions produced by the phase difference between the fast ion oscillation and the EPM with m = 3/n = 2 was observed in the outward shifted configurations. Another anomalous loss of fast ions due to EPMs with m = 2/n = 1 was also observed in the inward shifted configuration. The characteristics of the fast-ion-loss flux are different from those observed in the outward shifted configurations, and the loss mechanism seems to be related to a mode mixture between the EPM and a low frequency mode.

"The world fusion effort has embarked into a new age with the construction of ITER in Cadarache, France, which will be the first magnetic confinement fusion plasma experiment dominated by the self-heating of fusion reactions. In order to operate and control burning plasmas and next generation demo fusion reactors, an advanced capability for comprehensive integrated computer simulations that are fully verified and validated against experimental data will be necessary. The ultimate goal is to predict reliably the behaviour of plasmas in toroidal magnetic confinement devices on all relevant scales, both in time and space. In addition to developing a sophisticated integrated simulation codes, directed advanced research in fusion physics, applied mathematics, computer science and software is envisaged. In this paper we review the basic strategy and main research efforts at the Department of Simulation Science of the National Institute for Fusion Science (NIFS)- which is the Inter University Institute and the coordinating Center of Excellence for academic fusion research in Japan. We overview a simulation research at NIFS, in particular relation to experiments in the Large Helical Device (LHD), the world's largest superconducting heliotron device, as a National Users' facility (see Motojima et al. [1]). Our main goal is understanding and systemizing the rich hierarchy of physical mechanisms in fusion plasmas, supported by exploring a basic science of complexity of plasma as a highly nonlinear, non-equilibrium, open system. The aim is to establish a simulation science as a new interdisciplinary field by fostering collaborative research in utilizing the large-scale supercomputer simulators. A concept of the hierarchy-renormalized simulation modelling will be invoked en route toward the LHD numerical test reactor."