石澤 明宏*; 井戸村 泰宏; 今寺 賢志*; 糟谷 直宏*; 菅野 龍太郎*; 佐竹 真介*; 龍野 智哉*; 仲田 資季*; 沼波 政倫*; 前山 伸也*; et al.
プラズマ・核融合学会誌, 92(3), p.157 - 210, 2016/03
Bierwage, A.; Yun, G. S.*; Choe, G. H.*; Nam, Y.*; Lee, W.*; Park, H. K.*; Bae, Y.-S.*
Nuclear Fusion, 55(1), p.013016_1 - 013016_17, 2015/01
The dynamics of multiple flux tubes in the core of a sawtoothing tokamak plasma are studied numerically. This is motivated by observations of long-lived hot spots in the ECE images of KSTAR plasmas with ECH. Using a empirical source term in a reduced set of MHD equations, it is shown that flux tubes with helicity h=1 are easily produced and survive for the observed time intervals only if the safety factor q is close to unity and the magnetic shear is small. It is shown that under these conditions the spatial localization of ECH may allow it to actively induce the formation of the tubes. Using simulations, we examine how the flux tubes merge and annihilate, and how their dynamics depend on the strength of the drive. We conclude that flux tubes play an important role for the dynamic competition between sources and sinks of thermal and magnetic energy during the sawtooth ramp phase. The development of self-consistent simulation models is motivated and directions for experiments are given.
Bierwage, A.; 相羽 信行; 篠原 孝司
Physical Review Letters, 114(1), p.015002_1 - 015002_5, 2015/01
When the plasma beta (ratio of thermal to magnetic pressure) in the core of a tokamak is raised to values of several percent, as required for a thermonuclear fusion reactor, continuous spectra of long-wavelength slow magnetosonic waves enter the frequency band occupied by continuous spectra of shear Alfvn waves. It is found that these two branches can couple strongly, so that Alfvn modes that are resonantly driven by suprathermal ions transfer some of their energy to sound waves. Since sound waves are heavily damped by thermal ion Landau resonances, these results reveal a new energy channel that contributes to the damping of Alfvnic instabilities and the noncollisional heating of bulk ions, with potentially important consequences for confinement and fusion performance.
Bierwage, A.; Lauber, P.*; 相羽 信行; 篠原 孝司; 矢木 雅敏
Proceedings of 14th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems (Internet), 8 Pages, 2015/00
A recently proposed Alfvn acoustic self-heating channel for burning plasmas - where fast-ion-driven shear Alfvn waves transfer energy to sound waves which then heat the bulk ions - is reexamined using a linear gyrokinetic model. A local eigenvalue analysis shows that the ion sound branches required for such a self-heating channel are so strongly damped that they are effectively non-existent when . However, when is increased by a factor 2.8, low-frequency sound continua in the range of beta-induced Alfvn acoustic eigenmodes (BAAE) are recovered and their excitation becomes feasible. This raises the question whether higher-frequency sound branches in the frequency range of beta-induced Alfvn continuum modes (BACM) and the associated self-heating channels may exist under reactor-relevant conditions. Moreover, it is shown that modifications of the continuous spectra by fast ions may need to be taken into account.
Bierwage, A.; 篠原 孝司
Physics of Plasmas, 21(11), p.112116_1 - 112116_21, 2014/11
The resonant interactions between shear Alfvn waves and resonant fast ions are analyzed numerically in realistic geometry and with a realistic particle distribution for a JT-60U plasma driven by two 400 keV N-NBs. In order to deal with the large magnetic drifts of the fast ions, a new orbit-based resonance analysis (ORA) method is developed and applied. The ORA method uses mappings that allows us to unify resonance conditions for trapped and passing particles, determine which harmonics are driven, and which orders of the resonance are involved. After analyzing the resonance conditions, the effects of wave-particle trapping, kinetic compression and linear resonance overlap are examined. Finally, we discuss the implications for frequency chirping, convective amplification, the long-time evolution of the system in the presence of a fast ion source, and for the interpretation of experimental observations.
Bierwage, A.; 藤堂 泰*; 相羽 信行; 篠原 孝司
Nuclear Fusion, 54(10), p.104001_1 - 104001_14, 2014/10
Dynamics of fast ions and shear Alfvn waves are simulated using MEGA, a global nonlinear hybrid code. The scenario 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 = 2, 3, 4 can be destabilized, besides the = 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 possible. When the fast ion drive exceeds a certain threshold, the = 3 mode is enhanced through a convective amplification process while following fast ions that were displaced by the field fluctuations. The fast ion transport in several cases is analyzed and implications of the results for the explanation of ALEs are discussed.
藤堂 泰*; Van Zeeland, M. A.*; Bierwage, A.; Heidbrink, W. W.*
Nuclear Fusion, 54(10), p.104012_1 - 104012_13, 2014/10
The hybrid code MEGA, which simulates the interaction between fast ions and an MHD fluid, is extended with realistic beam deposition profile and collisions. It is used for multi-phase simulations, where classical simulations (fast ion source + collisions) and hybrid simulations (source + collisions + MHD) are run alternatingly. In a multi-phase simulation of DIII-D discharge 142111, it is found that the stored beam ion energy is saturated due to toroidal Alfvn eigenmodes (TAE) at a level lower than in the purely classical simulation. This is consistent with the experimental observation. After the stored fast ion energy is saturated, it is demonstrated by hybrid simulations that the fast ion spatial profile is significantly flattened due to the interaction with the multiple TAEs with amplitude / and / of order 10e-4. The temperature fluctuations caused by TAEs are of the order of 1% of the equilibrium temperature. This is also comparable with ECE measurements in the experiment.
Bierwage, A.; 篠原 孝司; 藤堂 泰*; 矢木 雅敏
Proceedings of 25th IAEA Fusion Energy Conference (FEC 2014) (CD-ROM), 8 Pages, 2014/10
The global nonlinear hybrid code MEGA was extended with a fast ion source and a collision model, so that the formation of the fast ion slowing-down distribution (long time scale, 1ms-1s) and the interaction between the fast ions and MHD waves (short time scale, 0.001-1ms) can be simulated simultaneously. This self-consistent approach, without artificial interfaces, allows to simulate meso-time-scale dynamics (0.1-10ms), such as recurring bursts of MHD activity and the resulting relaxations of the fast ion distribution. When applied to a JT-60U plasma driven by 400 keV negative-ion-based neutral beams (N-NB), the code successfully reproduced experimentally observed bursts of chirping modes. Thus validated, the new multi-time-scale simulations allows for the first time to study the physics of burstiness and frequency chirping in a realistic setting, and first results are presented and discussed. The advances made constitute an important step towards predictive simulations.
相羽 信行; 廣田 真*; 松山 顕之; 白石 淳也; Bierwage, A.
Proceedings of 25th IAEA Fusion Energy Conference (FEC 2014) (CD-ROM), 8 Pages, 2014/10
Bierwage, A.; 篠原 孝司; 相羽 信行; 藤堂 泰*
Nuclear Fusion, 53(7), p.073007_1 - 073007_12, 2013/07
The hybrid code MEGA is used to simulate an Abrupt Large-amplitude Event (ALE) in JT-60U. The goal is to look for a threshold with respect to the fast ion beta beyond which Energetic Particle Modes (EPM) undergo convective amplification and cause 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, bulk pressure and fast ion distribution are used. Consistently with the experiment, the simulation predicts a burst time of about 0.3 ms and peak magnetic fluctuation levels /10 at the plasma boundary. As is increased, a gradual (not sharp) increase in the convective amplification of the EPM and in the convective transport is found. It is concluded that the onset of convective amplification does not suffice as a trigger mechanism for ALE.
Bierwage, A.; 相羽 信行; 篠原 孝司; 藤堂 泰*; Deng, W.*; 石川 正男; 松永 剛; 矢木 雅敏
Proceedings of 24th IAEA Fusion Energy Conference (FEC 2012) (CD-ROM), 8 Pages, 2012/10
Energetic particle mode (EPM) dynamics are simulated using a global nonlinear hybrid code (MEGA). The scenario considered is based on JT-60U shot E039672, just before the onset of a so-called Abrupt Large Event (ALE). The simulation model is gradually extended towards a more realistic representation of the JT-60U plasma, including realistic geometry, realistic pressure, and realistic fast ion distributions. It is found that the mode structure and frequency of the EPM is very robust and can be reproduced by simple models. In contrast, accurate prediction of the growth rate, fluctuation amplitude and fast ion transport may require realistic models. The progress made - in particular, the use of realistic geometry and a realistic fast ion distribution computed by an orbit-following Monte-Carlo code - constitutes an important step forward towards predictive simulations and integrated modelling of energetic particle dynamics in burning plasmas, such as in ITER and DEMO.
Bierwage, A.; 相羽 信行; 藤堂 泰*; Deng, W.*; 石川 正男; 松永 剛; 篠原 孝司; 矢木 雅敏
Plasma and Fusion Research (Internet), 7(Sp.1), p.2403081_1 - 2403081_4, 2012/07
The global hybrid code MEGA is used to study the dynamics of energetic particle modes (EPM) in parameter regimes close to the onset of ideal magnetohydrodynamic (MHD) ballooning instability. This work is motivated by observations of energetic-particle-driven modes in the wall-stabilized regime (so called EWM) in JT-60U, the physics of which have not been fully understood yet. In this study, nonlinear simulations of energetic particle modes (EPM, high frequency, 40-60 kHz) are carried out under conditions, where EWM (low frequency, 1-3 kHz) are observed. Although, EPM are unlikely to interact with EWM directly, the energetic particle transport caused by EPM may affect the total pressure profile and, hence, the stability of kink-ballooning modes, which are thought to be the fundamental modes underlying EWM. The dynamics of EPM near ideal MHD ballooning stability boundary is examined for the first time.
Bierwage, A.; Di Troia, C.*; Briguglio, S.*; Vlad, G.*
Computer Physics Communications, 183(5), p.1107 - 1123, 2012/05
This work deals with the initial loading of phase space markers for global gyrokinetic particle-in-cell (PIC) simulations of plasmas that are magnetically confined in a toroidally axisymmetric configuration. A method is presented, which allows to prepare a marker distribution that is independent of time. This is achieved by loading markers on the toroidal surfaces of unperturbed guiding center orbits, where they are distributed uniformly in time. This allows to initialize global PIC codes with an accurate equilibrium distribution function and facilitates simulations with minimal noise-signal correlation. The concrete problem considered is the representation of energetic ions in tokamaks, which are characterized by large drifts across magnetic surfaces.
松永 剛; 神谷 健作; 篠原 孝司; 宮戸 直亮; 小島 有志; Bierwage, A.; JT-60チーム
Europhysics Conference Abstracts (Internet), 36F, p.P2.062_1 - P2.062_4, 2012/00
In the JT-60U experimental operations with high normalized beta or high bootstrap fraction , magnetic fluctuations with multiple peaks in the geodesic acoustic mode (GAM) frequency range are observed. These peaks appear just after tangential NB injection with 90 keV beam energy in L-mode phase to form weak/strong reversed magnetic shear plasmas. Observed magnetic fluctuations have = 0 axisymmetric toroidal mode structures and = 2 poloidal ones, where and are the toroidal and poloidal mode number, respectively. Interestingly, the poloidal mode structure sometimes behaves like standing wave. Usually, the standing wave nodes are located around the inboard and outboard midplanes, and the top and bottom of plasmas. Namely, these modes have = 2 components in both ion and electron diamagnetic directions. We will report the detail of the observed = 0 axisymmetric modes in the JT-60U tokamak.
Bierwage, A.; 藤堂 泰*; 相羽 信行; 篠原 孝司; 石川 正男; 矢木 雅敏
Plasma and Fusion Research (Internet), 6, p.2403109_1 - 2403109_5, 2011/08
The nonlinear dynamics of energetic particles in tokamak plasmas and their interaction with MHD modes have previously been studied using models which include only the most essential ingredients in order to understand the fundamental processes. Work is now underway to carry out simulations with more detailed models in order to enhance our predictive capabilities with respect to the excitation of MHD modes and energetic particle transport, which is expected to play an important role in burning plasmas. The present work focuses on the role of the equilibrium geometry, comparing results obtained for circular and for realistic flux surface geometry. For this purpose, earlier studies of so-called Abrupt Large-amplitude Events (ALE) in JT-60U are revisited. The simulations are carried out with the hybrid code MEGA. For the simple geometry, results obtained with another hybrid code, HMGC, serve as a benchmark, which may show how the choice of the numerical implementation affects the results.
Bierwage, A.; Di Troia, C.*; Zonca, F.*
no journal, ,
A new software tool is presented which allows to initialize particle simulations of magnetically confined plasmas with an arbitrary particle distribution function. Besides facilitating simulations with (in principle) arbitrary spatial localization and velocity-space anisotropicity, the distinguishing feature of this tool is that it allows to construct an exact kinetic equilibrium for cases where magnetic drift orbits play an important role. One timely example is the interaction between energetic ions and magnetohydrodynamic modes in tokamaks used to study burning plasma conditions. In such cases, input data that consists of measurable (and physically meaningful) quantities is not sufficient to uniquely describe the equilibrium distribution function. The additional information required to design an exact equilibrium from incomplete input data is obtained by pre-computing the unperturbed drift orbits of all phase-space samples. Marker particles are distributed along these trajectories (excluding loss orbits) and appropriate weight factors are assigned. First simulation results with the new marker loading module will be presented as they become available.
相羽 信行; 石井 康友; Bierwage, A.; 廣田 真; 白石 淳也; 矢木 雅敏
no journal, ,
no journal, ,
VisualStart is a unified initialization tool for hybrid (MHD+particle) codes. Its input consists of model parameters, numerical parameters, data computed by equilibrium solvers and orbit-following Monte-Carlo codes, and experimentally measured plasma profiles. It produces a complete snapshot of the plasma to be used by high-performance initial-value solvers as an initial condition. Presently, it is used to initialize two global nonlinear hybrid codes, HMGC and MEGA. VisualStart is implemented in an interpreted language (Matlab) and equipped with an interactive graphical user interface (GUI), which provides the control and visual information needed to complete the design of a kinetic equilibrium. Being an easy-to-use, unified tool that initializes different codes with the same initial condition using state-of-the-art computational techniques, VisualStart has the potential to enhance the accuracy and versatility of plasma simulation codes, and aid verification and validation efforts.
Bierwage, A.; 相羽 信行; Deng, W.*; 石川 正男; 松永 剛; 篠原 孝司; 藤堂 泰*; 矢木 雅敏
no journal, ,
Energetic Particle Modes observed in JT-60U are studied using the global nonlinear code MEGA. For the first time, these modes are simulated in realistic geometry and with realistic bulk plasma pressure. The effect of plasma shaping, bulk pressure and compressibility is examined, looking at the linear growth, initial nonlinear saturation, nonlinear evolution and energetic particle transport. It is found that growth, saturation and evolution of the MHD modes vary significantly depending on the simulation setup. However, the resulting particle transport caused by these strongly driven modes is not correlated to the growth rates and saturation levels. The reduction of the energetic ion density in the central region of the plasma is comparable in all cases studied: circular and shaped plasma, zero and finite bulk beta, weak and strong compressibility effect.
Bierwage, A.; 篠原 孝司
no journal, ,
The distribution function of fast ions is determined by plasma geometry, sources, collisions and waves-particle interactions. A general framework for simulating the evolution of fast ions and bulk plasma subject to the above processes is presented. Exploiting the separation of time scales, the problem is tackled using specialized simulation codes and interfaces. An equilibrium solver reconstructs a JT-60U plasma equilibrium. An orbit-following Monte Carlo code computes a distribution function for the fast ions. Using an orbit-based marker loading technique, the distribution function is mapped into the constant-of-motion space. This gives a realistic distribution function that contains information about the fast ion sources and experimental setup. It is also an exact equilibrium, as required for the initialization of instability codes. The method will be used to simulate fast ion driven modes and to construct self-consistent equilibria that take into account the presence of fast ions.