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論文

国際核融合エネルギー研究センターの高性能計算機システムHeliosを利用した国内シミュレーション研究プロジェクトの進展

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

幅広いアプローチ協定に基づいて国際核融合エネルギー研究センター(IFERC)の計算機シミュレーションセンター(CSC)に設置された高性能計算機システムHeliosは、2012年1月に運用を開始し、日欧の磁気核融合シミュレーション研究に供用され、高い利用率の実績を示すとともに、炉心プラズマ物理から炉材料・炉工学にわたる広い分野で多くの研究成果に貢献している。本プロジェクトレビューの目的は、国内の大学や研究機関においてHeliosを利用して進められているシミュレーション研究プロジェクトとその成果を一望するとともに、今後予想される研究の進展を紹介することである。はじめにIFERC-CSCの概要を示した後、各研究プロジェクト毎にその目的、用いられる計算手法、これまでの研究成果、そして今後必要とされる計算を紹介する。

論文

ITPA(国際トカマク物理活動)会合報告,52

篠原 孝司; 林 伸彦; 諫山 明彦; 宮戸 直亮; 浦野 創; 相羽 信行

プラズマ・核融合学会誌, 91(12), p.797 - 800, 2015/12

2015年秋季に国際トカマク物理活動(ITPA)に関する5グループの会合が各グループ独立に開催された。「高エネルギー粒子物理」はウィーン(オーストリア)で開催し日本からは4名の参加があった。「統合運転シナリオ」は合肥(中国)で開催し日本からは2名の参加があった。「MHD安定性」はナポリ(イタリア)で開催し日本からは1名の参加があった。「輸送と閉じ込め物理」および「ペデスタル物理」はガルヒング(ドイツ)で開催し日本からは輸送3名(内TV会議参加2名)、ペデスタル3名の参加があった。それぞれ、各極の関係者と国際装置間比較実験やITERの物理に関する今後の課題、及び各グループの活動計画の議論が行われた。これらの会合の概要をまとめて報告する。なお、次回会合は2016年の春季に各グループ独立に開催する予定である。

論文

Integrated tokamak modelling with the fast-ion Fokker-Planck solver adapted for transient analyses

藤間 光徳; 濱松 清隆; 林 伸彦; 本多 充; 井手 俊介

Plasma Physics and Controlled Fusion, 57(9), p.095007_1 - 095007_9, 2015/09

 被引用回数:4 パーセンタイル:18.56(Physics, Fluids & Plasmas)

全放電時間を模擬するトカマク統合モデリングは先進トカマクプラズマ設計において必要不可欠である。我々は統合コードTOPICSの高速イオン解析部分を過渡解析により適したモデルに拡張した。高速イオンとバルクプラズマおよび平衡磁場が互いに整合性を持つ時間発展を実現するために、高速イオンのフォッカープランクソルバをTOPICSのバルク輸送ソルバと同レベルで統合化した。拡張した統合コードによるJT-60SAおよびITERのプラズマ立ち上げシミュレーションにより、過渡解析の可能性および有効性を確認した。その統合シミュレーションにおいて、高速イオン、プラズマ分布、平衡磁場の統合的発展を示した。

論文

Effects of toroidal rotation shear and magnetic shear on thermal and particle transport in plasmas with electron cyclotron heating on JT-60U

吉田 麻衣子; 本多 充; 成田 絵美*; 林 伸彦; 浦野 創; 仲田 資季; 宮戸 直亮; 竹永 秀信; 井手 俊介; 鎌田 裕

Nuclear Fusion, 55(7), p.073014_1 - 073014_9, 2015/07

 被引用回数:14 パーセンタイル:57.79(Physics, Fluids & Plasmas)

多くのトカマク装置では電子サイクロトロン加熱(ECH)時に熱や粒子の輸送が増大することが観測されており、ITERではECHを伴う運転シナリオの開発にとって重要な課題となっている。この課題を解決するために、JT-60Uの正磁気シアHモード放電、内部輸送障壁を伴う弱磁気シア放電と負磁気シア放電において、ECH印加時に熱及び粒子輸送が増加しない条件を調査した。その結果、トロイダル回転シアが負の大きい値をとる条件では、電子サイクロトロン加熱時のイオン熱輸送の上昇が抑えられることが分かった。この条件は、イオン温度対電子温度の比や、電子加熱パワーに寄らないことを明らかにした。磁気シアが負の値をとる条件では、その値の大きさに寄らず、電子熱輸送と粒子輸送が増加しないことが分かった。これらの結果は、ITERでのECH加熱シナリオの開発や電子加熱が主体となるITER及び原型炉でのプラズマ輸送特性の予知に重要な知見を与える。

論文

Integrated modelling of toroidal rotation with the 3D non-local drift-kinetic code and boundary models for JT-60U analyses and predictive simulations

本多 充; 佐竹 真介*; 鈴木 康浩*; 吉田 麻衣子; 林 伸彦; 神谷 健作; 松山 顕之; 篠原 孝司; 松永 剛; 仲田 資季; et al.

Nuclear Fusion, 55(7), p.073033_1 - 073033_11, 2015/07

 被引用回数:7 パーセンタイル:28.43(Physics, Fluids & Plasmas)

The integrated simulation framework for toroidal momentum transport is developed, which self-consistently calculates the neoclassical toroidal viscosity (NTV), the radial electric field $$E_r$$ and the resultant toroidal rotation $$V_phi$$ together with the scrape-off-layer(SOL)-physics based boundary model. The coupling of three codes, the 1.5D transport code, TOPICS, the 3D equilibrium code, VMEC and the 3D $$delta f$$ drift-kinetic equation solver, FORTEC-3D, makes it possible to calculate the NTV due to the non-axisymmetric perturbed magnetic field caused by toroidal field coils. Analyses reveal that the NTV significantly influences $$V_phi$$ in JT-60U and $$E_r$$ holds the key to determine the NTV profile. The sensitivity of the $$V_phi$$ profile to the boundary rotation necessitates a boundary condition modelling for toroidal momentum. Owing to the high-resolution measurement system in JT-60U, the $$E_r$$ gradient is found to be virtually zero at the separatrix regardless of toroidal rotation velocities. Focusing on $$E_r$$, the boundary model of toroidal momentum is developed in conjunction with the SOL/divertor plasma code D5PM. This modelling realizes self-consistent predictive simulations for operation scenario development in ITER.

論文

Analysis of tungsten transport in JT-60U plasmas

清水 友介*; 藤田 隆明*; 有本 英樹*; 仲野 友英; 星野 一生; 林 伸彦

Plasma and Fusion Research (Internet), 10(Sp.2), p.3403062_1 - 3403062_4, 2015/07

In JT-60U, it has been observed that accumulation of tungsten is enhanced with increasing the toroidal rotation in the opposite direction (CTR-rotation) to the plasma current in H-mode plasmas. Two models for convective transport, pinch due to the toroidal rotation (PHZ pinch) and the radial electric field (Er pinch) were proposed. We introduce these two pinch models into integrated transport code TOTAL, and study dependence of the tungsten accumulation on the toroidal rotation. In the high toroidal rotation velocity, we obtained the tungsten accumulation four times as large as in the low one. The model reproduces the trend observed in the experiment.

論文

Advance in integrated modelling towards prediction and control of JT-60SA plasmas

林 伸彦; 本多 充; 白石 淳也; 宮田 良明; 若月 琢馬; 星野 一生; 藤間 光徳; 鈴木 隆博; 浦野 創; 清水 勝宏; et al.

Europhysics Conference Abstracts (Internet), 39E, p.P5.145_1 - P5.145_4, 2015/06

Towards prediction and control of JT-60SA plasmas, we are developing codes/models which can describe physics/engineering factors, and integrating them to one code TOPICS. Physics modelling: Coupling with MINERVA/RWMaC code showed that MHD equilibrium variation by centrifugal force largely affects RWM stability and the toroidal rotation shear stabilizes RWM. Coupling with OFMC code for NB torques, 3D MHD equilibrium code VMEC and drift-kinetic code FORTEC-3D for NTV torque, and toroidal momentum boundary model, predicted the core rotation of $$sim$$2% of Alfv$'e$n speed for a ITER hydrogen L-mode plasma. Coupling with core impurity transport code IMPACT showed the accumulation of Ar seeded to reduce the divertor heat load is so mild that plasma performance can be recovered by additional heating in JT-60SA steady-state (SS) scenario. Simulations coupled with MARG2D code showed that plasma current can be ramped-up to reach $$beta_N ge$$3 with MHD modes stabilized by ideal wall and with no additional flux consumption of central solenoid in JT-60SA. Engineering modelling: Coupling with integrated real-time controller showed that simultaneous control of $$beta_N$$ and $$V_{loop}$$ is possible at $$beta_N ge$$4 in JT-60SA SS scenarios. MHD equilibrium control simulator MECS demonstrated equilibrium control during heating phase and collapse induced events within power supply capability of PF coils in JT-60SA.

論文

Current ramp-up scenario with reduced central solenoid magnetic flux consumption in JT-60SA

若月 琢馬; 鈴木 隆博; 林 伸彦; 白石 淳也; 井手 俊介; 高瀬 雄一*

Europhysics Conference Abstracts (Internet), 39E, p.P5.144_1 - P5.144_4, 2015/06

We have investigated reduction of the CS flux required in the plasma current ramp-up phase using non-inductive current drive in JT-60SA with an integrated modeling code suite (TOPICS). JT-60SA will be equipped with various types of neutral beams different in the beam trajectories and energies (85 keV and 500 keV). We have made a scenario in which the plasma current is ramped up from 0.6 MA to 2.1 MA in 150 s with no additional CS flux consumption by overdriving the plasma current ($$I_{rm NI} > I_{rm p}$$, $$I_{rm NI}$$ : non-inductively driven current and $$I_{rm p}$$ : plasma current) with neutral-beam-driven and bootstrap current. In order to achieve the current overdrive condition from 0.6 MA, the current drive by the lower energy neutral beam injection (85 keV) is effective. The higher energy neutral beam injection (500 keV) cannot be utilized in this early phase with a low plasma density due to a large shine through loss, while it can effectively be utilized in the later phase. We have also investigated ideal MHD instabilities using a linear ideal MHD stability analysis code (MARG2D). External kink modes can be stabilized in most of the time during the current ramp-up if there is a perfect conducting wall.

論文

Simulation of plasma current ramp-up with reduced magnetic flux consumption in JT-60SA

若月 琢馬; 鈴木 隆博; 林 伸彦; 白石 淳也; 井手 俊介; 高瀬 雄一*

Plasma Physics and Controlled Fusion, 57(6), p.065005_1 - 065005_12, 2015/06

 被引用回数:9 パーセンタイル:41.18(Physics, Fluids & Plasmas)

Current ramp-up with reduced central solenoid (CS) flux consumption in JT-60SA has been investigated using an integrated modeling code suite (TOPICS) with a turbulent model (CDBM). The plasma current can be ramped-up from 0.6 MA to 2.1 MA with no additional CS flux consumption if the plasma current is overdriven by neutral-beam-driven and bootstrap current. The time duration required for the current ramp-up without CS flux consumption becomes as long as 150s. In order to achieve the current overdrive condition from 0.6 MA, the current drive by a lower energy neutral beam (85 keV) is effective. A higher energy neutral beam (500 keV) cannot be utilized in this early phase due to large shine through loss, while it can be effectively utilized in the later phase. Therefore, the main current driver should be switched from the lower energy neutral beam to the higher energy neutral beam during the current ramp-up phase. As a result of an intensive auxiliary heating needed to overdrive the plasma current, plasma beta becomes high. Ideal MHD stabilities of such high beta plasmas have been investigated using a linear ideal MHD stability analysis code (MARG2D). External kink modes can be stabilized in most of the time during the current ramp-up if there is a perfectly conducting wall at the location of the stabilizing plate and the vacuum vessel of JT-60SA and the plasma has a broader pressure profile.

論文

Assessment of operational space for long-pulse scenarios in ITER

Polevoi, A. R.*; Loarte, A.*; 林 伸彦; Kim, H. S.*; Kim, S. H.*; Koechl, F.*; Kukushkin, A. S.*; Leonov, V. M.*; Medvedev, S. Yu.*; 村上 匡且*; et al.

Nuclear Fusion, 55(6), p.063019_1 - 063019_8, 2015/05

 被引用回数:33 パーセンタイル:84.89(Physics, Fluids & Plasmas)

The operational space ($$I_p$$-$$n$$) for long pulse scenarios of ITER was assessed by 1.5D core transport modelling with pedestal parameters predicted by the EPED1 code. The analyses include the majority of transport models presently used for interpretation of experiments and ITER predictions. The EPED1 code was modified to take into account boundary conditions predicted by SOLPS for ITER. In contrast with standard EPED1 assumptions, EPED1 with the SOLPS boundary conditions predicts no degradation of the pedestal pressure as density is reduced. Lowering the plasma density to $$n_e sim$$ 5-6 $$times$$ 10$$^{19}$$ m$$^{-3}$$ leads to an increased plasma temperature (similar pedestal pressure), which reduces the loop voltage and increases the duration of the burn phase to $$Delta t_{rm burn} sim$$ 1000 s with Q $$ge$$ 5 for $$I_p ge$$ 13 MA at moderate normalised pressure ($$beta_N sim$$ 2). These ITER plasmas require the same level of additional heating power as the reference Q = 10 inductive scenario at 15 MA. However, unlike the "hybrid" scenarios considered previously, these H-mode plasmas do not require specially shaped q profiles nor improved confinement in the core for the transport models considered in this study. Thus, these medium density H-mode plasma scenarios with $$I_p ge$$ 13 MA present an attractive alternative to hybrid scenarios to achieve ITER's long pulse Q $$ge$$ 5 and deserve further analysis and experimental demonstration in present tokamaks.

論文

Roles of argon seeding in energy confinement and pedestal structure in JT-60U

浦野 創; 仲田 資季; 相羽 信行; 久保 博孝; 本多 充; 林 伸彦; 吉田 麻衣子; 鎌田 裕; JT-60チーム

Nuclear Fusion, 55(3), p.033010_1 - 033010_9, 2015/03

 被引用回数:40 パーセンタイル:89.45(Physics, Fluids & Plasmas)

JT-60UにおけるHモードプラズマへのアルゴン入射効果を調べた。従来のHモードでは密度の増加とともに閉じ込め性能は低下するが、アルゴン入射によって閉じ込め劣化を回避することができる。特に高密度領域ではアルゴン入射によって電子密度分布は中心ピーク型となり、周辺及びコア部の温度が上昇する。アルゴン入射時にはELM周波数が大きく低減するが、これは主プラズマ領域での放射損失の増大によりセパラトリクスを通過するパワーが減少するためである。アルゴン入射による周辺プラズマ圧力自体の増加は小さいことが分かった。

論文

Gyrokinetic analyses of core heat transport in JT-60U plasmas with different toroidal rotation direction

成田 絵美*; 本多 充; 林 伸彦; 浦野 創; 井手 俊介; 福田 武司*

Plasma and Fusion Research (Internet), 10, p.1403019_1 - 1403019_11, 2015/03

The internal transport barriers (ITBs) formed in the tokamak plasmas with the weak magnetic shear and the weak radial electric field shear are often observed and the pressure gradient at the ITB is not very steep. In such plasmas the electron temperature ITB is steeper for co toroidal rotation cases than that for counter rotation cases. Clarifying the relationship between the rotation direction and heat transport in the ITB region, dominant instabilities are examined by the flux-tube gyrokinetic code GS2 to show that the linear growth rates $$gamma$$ for the co and counter rotation cases are comparable in magnitude, but the counter case shows the more trapped electron mode like frequency. The ratio of the electron heat diffusivity to the ion's is higher for the counter-rotation case. The difference in the ratio between the two cases agrees with the experiment. Investigating the flow shear effect on $$gamma$$ reveals that its effect is not so large as to change the aforementioned tendency.

論文

Integrated modeling of toroidal rotation with the 3D non-local drift-kinetic code and boundary models for JT-60U analyses and predictive simulations

本多 充; 佐竹 真介*; 鈴木 康浩*; 吉田 麻衣子; 林 伸彦; 神谷 健作; 松山 顕之; 篠原 孝司; 松永 剛; 仲田 資季; et al.

Proceedings of 25th IAEA Fusion Energy Conference (FEC 2014) (CD-ROM), 8 Pages, 2014/10

The integrated framework for toroidal momentum transport is developed, which self-consistently calculates the neoclassical toroidal viscosity (NTV), the radial electric field $$E_r$$ and resultant toroidal rotation together with the scrape-off-layer (SOL) physics-based boundary model. The coupling of three codes, TOPICS, VMEC and FORTEC-3D, can calculate rotation caused by the NTV due to the non-axisymmetric perturbed magnetic field caused by toroidal field coils. It is found that the NTV influences toroidal rotation in JT-60U and $$E_r$$ holds the key to determine the NTV profile. The sensitivity of the toroidal rotation profile to the boundary rotation necessitates the boundary condition modeling. From the measurement in JT-60U, the $$E_r$$ gradient is found to be insensitive at the separatrix. Focusing on $$E_r$$, the boundary model of toroidal momentum is developed in conjunction with the SOL/divertor plasma code. This modeling realizes self-consistent predictive simulations for operation scenario development in ITER.

論文

Extension of kinetic-magnetohydrodynamic model to include toroidal rotation shear effect and its application to stability analysis of resistive wall modes

白石 淳也; 宮戸 直亮; 松永 剛; 本多 充; 林 伸彦; 井手 俊介

Proceedings of 25th IAEA Fusion Energy Conference (FEC 2014) (CD-ROM), 8 Pages, 2014/10

トカマクプラズマにおいて発生する電磁流体力学(MHD: Magnetohydrodynamics)モードに対する、トロイダル回転シア効果及び運動論的効果を解明するため、運動論的MHDモデルの拡張を行った。回転の効果を含む案内中心ラグランジアンを用いて、運動論的MHDモデルの再定式化を行った。その結果、案内中心の運動がコリオリ力と遠心力の効果を受けて、MHDモードと粒子運動の共鳴によるエネルギー項が拡張されることを示した。また、平衡の分布関数に回転の効果を入れることでも拡張を行った。これらの効果は、従来の運動論的MHDモデルでは見落とされてきた。この拡張された運動論的MHDモデルをトカマク配位における抵抗性壁モード(RWM: Resistive Wall Mode)解析コードMINERVA/RWMaCに実装し、ベンチマークに成功した。また、当コードをJT-60Uを模擬した平衡に応用し、回転シア効果によって、RWMが粒子運動と共鳴してエネルギーが減衰することが明らかになった。

論文

Physics comparison and modelling of the JET and JT-60U core and edge; Towards JT-60SA predictions

Garcia, J.*; 林 伸彦; Baiocchi, B.*; Giruzzi, G.*; 本多 充; 井手 俊介; Maget, P.*; 成田 絵美*; Schneider, M.*; 浦野 創; et al.

Nuclear Fusion, 54(9), p.093010_1 - 093010_13, 2014/09

 被引用回数:38 パーセンタイル:86.74(Physics, Fluids & Plasmas)

Extensive physics analysis and modelling has been undertaken for the typical operational regimes of the tokamak devices JET and JT-60U with the aim of extrapolating present day experiments to JT-60SA, which shares important characteristics with both tokamaks. A series of representative discharges of two operational scenarios, H-mode and hybrid, have been used for this purpose. Predictive simulations of core turbulence, particle transport, current diffusion and pedestal pressure have been carried out with different combinations of models. The ability of the models for reproducing the experimental data is analysed and scenario calculations for JT-60SA are performed following an optimum set of models.

論文

Integrated simulation study of ELM pacing by pellet injection in ITER

林 伸彦; 相羽 信行; 滝塚 知典*; 大山 直幸

Contributions to Plasma Physics, 54(4-6), p.599 - 604, 2014/06

 被引用回数:0 パーセンタイル:0.01(Physics, Fluids & Plasmas)

Simulations with an integrated code TOPICS-IB showed that a small pellet can significantly reduce the ELM energy loss by penetrating deeply into the pedestal and triggering high-n ballooning modes localized near the pedestal top, with conditions; the injection from the low-field-side with a speed fast enough to approach the pedestal top when the pedestal pressure is about 95 % of natural ELM onset. The effectiveness of the above suitable conditions of pellet injection for ELM pacing has been confirmed by JT-60U and then ITER simulations. The pellet particle content required for ELM pacing is larger for the pedestal plasma with higher density and farther from the stability boundary of ideal ballooning mode near the pedestal top. For an ITER standard scenario, the required pellet particle content is about a few % of pedestal particle content, which gives the physics background to the present design value. Simulations also shows that fueling pellets can be injected from the high-field-side just after ELM pacing pellets without disturbing the pacing.

論文

Role of seed impurity for H-mode plasmas in JT-60U

浦野 創; 仲田 資季; 相羽 信行; 久保 博孝; 本多 充; 吉田 麻衣子; 林 伸彦; 鎌田 裕; JT-60チーム

Europhysics Conference Abstracts (Internet), 38F, p.P4.018_1 - P4.018_4, 2014/06

JT-60UにおけるHモードプラズマへのアルゴン入射効果を調べた。従来のHモードでは密度の増加とともに閉じ込め性能は低下するが、アルゴン入射によって閉じ込め劣化を回避することができる。特に高密度領域ではアルゴン入射によって周辺及びコア部の温度が上昇し、電子密度分布は中心ピーク型となる。アルゴン入射時にはELM周波数が大きく低減するが、これは主プラズマ領域での放射損失の増大によりセパラトリクスを通過するパワーが減少するためである。アルゴン入射による周辺プラズマ圧力自体の増加は小さいことが分かった。

論文

Analysis of JT-60SA scenarios on the basis of JET and JT-60U discharges

Garcia, J.*; 林 伸彦; Giruzzi, G.*; Schneider, M.*; Joffrin, E.*; 井手 俊介; 坂本 宜照; 鈴木 隆博; 浦野 創; JT-60チーム; et al.

Europhysics Conference Abstracts (Internet), 38F, p.P1.029_1 - P1.029_4, 2014/06

Creation of JT-60SA scenarios is necessary in order to make deeper analyses: Fast ions, heating schemes, MHD. Validation exercise: a series of representative discharges of the three main operational scenarios, H-mode, hybrid and steady-state have been selected for each device in order to extrapolate to JT-60SA. An extensive analysis of the main physics similarities and differences among the discharges has been carried out in order to explain results. Using integrated modelling codes CRONOS and TOPICS, benchmark of the codes is done. Predictive core turbulence simulations have been carried out with three transport models: Bohm-GyroBohm, CDBM and GLF23. Particle transport is analyzed with GLF23. Pressure pedestal predictions are simulated with Cordey MHD scaling. Fully predictive simulations of temperatures, density and pedestal have been performed with GLF23 and CDBM models for the temperatures and GLF23 for the density. Calculations for JT-60SA are performed following the best combination of models found.

論文

Kinetic modelling of divertor fluxes during ELMs in ITER

細川 哲成*; Loarte, A.*; Huijsmans, G.*; 滝塚 知典*; 林 伸彦

Europhysics Conference Abstracts (Internet), 38F, p.P5.003_1 - P5.003_4, 2014/06

The Type I ELMy H-mode is the reference inductive operation for ITER, but the periodic ELM power loads on plasma facing components need to be understood and controlled. Understanding of the mechanisms of ELM particle and heat loads is required: electron/ion contributions, in/out asymmetry and timescale of ELM heat fluxes. Modelling of typical edge plasma conditions during ITER ELMs has been carried out with PARASOL (PARticle Advanced code for SOL and divertor plasmas) code, which has been developed in JAEA. Simulations show that ions carry larger heat flux than electrons for large ELM particle loss, whereas ions and electrons deposit comparable heat flux for small ELM particle loss. The total energy loss to the two divertors is similar for the two divertors for ELM energy loss larger than 10 MJ independent inter-ELM divertor conditions. Even though inner peak heat flux is larger than outer one in some cases, inner time-integrated heat load is smaller than outer one. This is due to strong current flow in SOL during ELM.

論文

ITPA(国際トカマク物理活動)会合報告,45

林 伸彦; 相羽 信行; 諫山 明彦; 篠原 孝司; 本多 充

プラズマ・核融合学会誌, 90(6), p.352 - 355, 2014/06

2014年の春季に国際トカマク物理活動(ITPA)に関する5つの会合(「MHD安定性」、「高エネルギー粒子物理」、「統合運転シナリオ」、「輸送と閉じ込め物理」、「ペデスタル物理」)が開催された。各会合の概要をまとめて報告する。なお、次回会合は、2014年の秋季のIAEA国際会議直後に開催する予定である。

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