核融合エネルギー研究開発部門
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Name : Yasuhiro IDOMURA
Title : Principal Researcher
Address : 5-1-5 Kashiwanoha, Kashiwa-shi, Chiba 277-8587, JAPAN

Research Title


  Study of ion turbulent transport and profile formations using global gyrokinetic full-f Vlasov simulation

Abstract

A global gyrokinetic toroidal full-f five dimensional Vlasov simulation GT5D is extended including sources and collisions. Long time tokamak micro-turbulence simulations in open system tokamak plasmas are enabled for the first time based on a full-f gyrokinetic approach with self-consistent evolutions of turbulent transport and equilibrium profiles. The neoclassical physics is implemented using the linear Fokker-Planck collision operator, and the equilibrium radial electric field Er is determined self-consistently by evolving equilibrium profiles. In ion temperature gradient driven turbulence simulations in a normal shear tokamak with on-axis heating, key features of ion turbulent transport are clarified. It is found that stiff ion temperature Ti profiles are sustained with globally constant Lti|Ti/Ti'| near a critical value, and a significant part of the heat flux is carried by avalanches with 1/f type spectra, which suggest a self-organized criticality. The Er shear strongly affects the directions of avalanche propagation and the momentum flux. Nondiffusive momentum transport due to the Er shear stress is observed and a non-zero (intrinsic) toroidal rotation is formed without momentum input near the axis.


Spatio-temporal evolutions of (a) ion heat diffusivity χi,(b) Ti gradient R0/Lti, (c) Er shear, and (d) parallel flows U// observed in source driven ITG turbulence simulations.

Reference

[1] "Study of ion turbulent transport and profile formations using global gyrokinetic full-f Vlasov simulation", Y. Idomura, S. Tokuda, N. Aiba, and H. Urano, Nucl. Fusion 49, 65029 (2009).
[2] "Conservative Global Gyrokinetic Toroidal Full-f 5D Vlasov Simulation", Y. Idomura, S. Tokuda, N. Aiba, and H. Urano, 22nd IAEA Fusion Energy Conference, Geneva, Switzerland, 2008 (International Atomic Energy Agency, Vienna, 2008), IAEA-CN-165/TH/8-2 (oral).

  Conservative Global Gyrokinetic Toroidal Full-f Five Dimensional Vlasov Simulation

Abstract

A new conservative global gyrokinetic toroidal full-f five dimensional Vlasov simulation (GT5D) is developed using a novel non-dissipative conservative finite difference scheme. The scheme guarantees numerical stability by satisfying relevant first principles in the modern gyrokinetic theory, and enables robust and accurate simulations of tokamak micro-turbulence. GT5D is verified through comparisons of zonal flow damping tests, linear analyses of ion temperature gradient driven (ITG) modes, and nonlinear ITG turbulence simulations against a global gyrokinetic toroidal δf particle code. In the comparison, global solutions of the ITG turbulence are identified quantitatively by using two gyrokinetic codes based on particle and mesh approaches.

A typical eigenfunction of the ion temperature gradient driven mode in a ITER like configuration of JT-60SA.


Reference

[1] "Conservative Global Gyrokinetic Toroidal Full-f Five Dimensional Vlasov Simulation", Y. Idomura, M. Ida, T. Kano, N. Aiba, and S. Tokuda, Comput. Phys. Commun. 179, 391-403 (2008)

  Conservative Gyrokinetic Full-f Vlasov Simulation

Abstract

A new conservative gyrokinetic full-f Vlasov code is developed using a finite difference operator which conserves both the L1 and L2 norms. The growth of numerical oscillations is suppressed by conserving the L2 norm, and the code is numerically stable and robust in a long time simulation. In the slab ion temperature gradient driven (ITG) turbulence simulation, the energy conservation and the entropy balance relation are confirmed, and solutions are benchmarked against a conventional δf particle-incell (PIC) code. The results show that the exact particle number conservation and the good energy conservation in the conservative Vlasov simulation are advantageous for a long time micro-turbulence simulation. In the comparison, physical and numerical effects of the v// nonlinearity are clarified for the Vlasov and PIC simulations.



Comparisons of time histories of the total, field, and kinetic energy in long time ITG turbulence simulations using (a) Vlasov and (b) PIC codes. The total energy conservation is dramatically improved in a new conservative Vlasov code.

Reference

[1] "New conservative gyrokinetic full-f Vlasov code and its comparison to gyrokinetic δf particle-in-cell code", Y. Idomura, M. Ida, S. Tokuda, and L. Villard, J. Comput. Phys. 226, 244-262 (2007).
[2] "Conservative gyrokinetic Vlasov simulation", Y. Idomura, M. Ida, and S. Tokuda, Commun. Nonlinear Sci. Numer. Simul. 13, 227-233 (2007).

  Self-organization in Electron Temperature Gradient Driven Turbulence

Abstract

Based on first principle gyrokinetic calculations, a zonal flow generation mechanism in the slab electron temperature gradient driven (ETG) turbulence with weak magnetic shear is identified as self-organization via the turbulent spectral cascade in the two dimensional rotating fluid turbulence. The inverse energy cascade and the scaling of a zonal flow wavenumber, which is consistent with the Rhines scale length, are confirmed. An impact of the scaling, which depends on the density gradient, on the turbulent structure and transport is demonstrated for the slab ETG turbulence.



Self-organized structures of the ETG turbulence (b) with and (a) without the diamagnetic plasma rotation or the density gradient.

Reference

[1] "Self-organization in electron temperature gradient driven turbulence", Y. Idomura, Phys. Plasmas. 13, 080701 (2006).

  Global Gyrokinetic Simulations of Toroidal Electron Temperature Gradient Driven Turbulence

Abstract

Using a gyrokinetic toroidal particle code with global profile effects, the toroidal electron temperature gradient driven (ETG) turbulence in positive and reversed shear tokamaks is studied. In the simulation, initial saturation levels of the ETG mode are consistent with the mixing length theory, which shows a Bohm (gyro-Bohm) like ρ*-scaling for a ballooning type (slab like) ETG mode in a positive (reversed) shear configuration, where ρ* is the electron Larmor radius ρte divided by the minor radius a. In a realistic small ρ* positive shear configuration, the ETG mode has a higher saturation level than the large ρ* positive shear configuration and the reversed shear configuration. In the nonlinear turbulent state, the ETG turbulence in the positive and reversed shear configurations shows quite different structure formations. In the positive shear configuration, the ETG turbulence is dominated by streamers which have a ballooning type structure, and the electron temperature Te profile is quickly relaxed by enhanced heat transport in a turbulent time scale. In the reversed shear configuration, quasi-steady zonal flows are produced in the negative shear region, while the positive shear region is characterized by streamers. Accordingly, the electron thermal diffusivity χe has a gap structure across the qmin surface, and the Te gradient is sustained above the critical value for a long time. The results suggest a stiffness of the Te profile in positive shear tokamaks and a possibility of the Te transport barrier in reversed shear tokamaks.



Zonal flows and streamers observed in grobal ETG turbulence simulations of reversed shear tokamaks.

Reference

[1] "Global profile effects and structure formations in toroidal electron temperature gradient driven turbulence", Y. Idomura, S. Tokuda, and Y. Kishimoto, Nucl. Fusion 45, 1571-1581 (2005).
[2] "Global Gyrokinetic Simulations of Toroidal Electron Temperature Gradient Driven Mode in Reversed Shear Tokamaks", Y. Idomura, S. Tokuda, and Y. Kishimoto, 20th IAEA Fusion Energy Conference, Vilamoura, Portugal, 2004 (International Atomic Energy Agency, Vienna, 2004), IAEA-CN-116/TH/8-1 (oral).

  Gyrokinetic Simulations of Tokamak Micro-turbulence including Kinetic Electron Effects

Abstract

A gyrokinetic toroidal particle code for a 3-dimensional nonlinear turbulence simulation (GT3D) has been developed to study the ion temperature gradient driven-trapped electron mode (ITG-TEM) turbulence in tokamak plasmas. From linear zonal flow damping tests and nonlinear ITG simulations, it is shown that a new method based on a canonical Maxwellian distribution is essential to simulate correct zonal flow dynamics in tokamaks. Recently, GT3D has been extended including kinetic trapped electrons. A computational cost of ITG-TEM calculations are drastically reduced by using a new bounce-averaged kinetic trapped electron model. A short wavelength unstable region of the ITG-TEM is calculated using a gyrokinetic field solver with a Pade approximation. From preliminary linear ITG-TEM calculations, the validity of these calculation models are confirmed.



Growth rate of ITG-TEM calculated using drift-kinetic, and bounce-averaged electron models.

Reference

[1] "Gyrokinetic simulations of tokamak micro-turbulence including kinetic electron effects", Y. Idomura, S. Tokuda, and Y. Kishimoto, J. Fusion Plasma Res. SERIES Vol.6, 17-22 (2004).

  Global Gyrokinetic Simulation of Ion Temperature Gradient Driven Turbulence with Canonical Maxwellian Distribution

Abstract

A new gyrokinetic toroidal particle code has been developed to study the ion temperature gradient (ITG) driven turbulence in reactor relevant tokamak parameters. We use a new method based on a canonical Maxwellian distribution FCM(Pφ, ε, μ), which is defined by three constants of motion in the axisymmetric toroidal system-the canonical angular momentum Pφ, the energy ε, and the magnetic moment μ. A quasi-ballooning representation enables linear and nonlinear high-m,n global calculations to be carried out, with a good numerical convergence. Conservation properties are improved by using optimized particle loading. From comprehensive linear global analyses over a wide range of unstable toroidal mode numbers (n=0~100) in large tokamak parameters (a/ρti=320~460), it is found that the reversed shear configuration produces an effective stabilizing effect on the ITG mode in the qmin region through global effects. In the nonlinear simulation, it is found that the new method based on FCM can simulate a zonal flow damping correctly; and spurious zonal flow oscillations, which are observed in a conventional method based on a local Maxwellian distribution FLM(Ψ, ε, μ), do not appear in the nonlinear regime.



(a) ITG turbulence simulations and (b) Zonal flow damping tests using local and Canonical Maxwellian distributions.

Reference

[1] "Global gyrokinetic simulation of ion temperature gradient driven turbulence in plasmas with canonical Maxwellian distribution", Y. Idomura, S. Tokuda, and Y. Kishimoto, Nucl. Fusion 43, 234-243 (2003).
[2] "Gyrokinetic global analysis of ion temperature gradient driven mode in reversed shear tokamaks", Y. Idomura, S. Tokuda and Y. Kishimoto, 19th IAEA Fusion Energy Conference, Lyon, France, 2002 (International Atomic Energy Agency, Vienna, 2002), p. IAEA-CN-94/TH/P1-08 (poster).

  Development of Large Scale Fusion Plasma Simulation and Storage Grid on JAERI Origin3800 System

Abstract

Under the Numerical EXperiment of Tokamak (NEXT) research project, various fluid, particle, and hybrid codes have been developed. These codes require a computational environment which consists of high performance processors, high speed storage system, and high speed parallelized visualization system. In this paper, the performance of the JAERI Origin3800 system is examined from a point of view of these requests. In the performance tests, it is shown that the representative particle and fluid codes operate with 15~40% of processing efficiency up to 512 processors. A storage area network (SAN) provides high speed parallel data transfer. A parallel visualization system enables order of magnitude faster visualization of a large scale simulation data compared with the previous graphic workstations. Accordingly, an extremely advanced simulation environment is realized on the JAERI Origin3800 system. Recently, development of a storage grid is underway in order to improve a computational environment of remote users. The storage grid is constructed by a combination of SAN and a wavelength division multiplexer (WDM). The preliminary tests show that compared with the existing data transfer methods, it enables dramatically high speed data transfer ~100 Gbps over a wide area network.



Reference

[1] "Development of large scale fusion plasma simulation and Storage Grid on JAERI Origin3800 system", Y. Idomura, M. Adachi, K. Gorai, Y. Suzuki, and X. Wang, J. Plasma Fusion Res. 79, 172-187 (2003).

  Slablike ion temperature gradient driven mode in reversed shear tokamaks

Abstract

The ion temperature gradient driven (ITG) mode in reversed shear tokamaks is analysed using a gyrokinetic toroidal particle code. It is found that the ITG mode in the reversed shear configuration shows a coupled mode structure between the slab and toroidal ITG modes. Especially in the qmin-region, a slablike feature due to the reversed shear slab ITG mode becomes strong. This coupled eigenmode structure is changed from a slab mode to a toroidal mode depending on ηi =Ln/Lti and Lti. Results show that in reversed shear tokamaks the ITG mode is determined from a competition between the slab and toroidal ITG modes.



Poloidal harmonics structures of toroidal ITG modes in (a) normal and (b) reversed shear tokamaks.

Reference

[1] "Slablike ion temperature gradient driven mode in reversed shear tokamaks", Y. Idomura, S. Tokuda, and Y. Kishimoto, New J. Phys. 4, 101.1-101.13 (2002).

  Gyrokinetic theory of drift waves in negative shear tokamaks

Abstract

Linear and non-linear properties of slab drift waves in the negative sheared slab configuration modelling of the qmin surface region in negative shear tokamaks are studied, where qmin is the minimum value of the safety factor q. Linear calculations show that both the slab ion temperature gradient (ITG) driven mode and the slab electron temperature gradient (ETG) driven mode become strongly unstable around the qmin surface. Non-linear simulations are performed for ETG turbulence, which evolves on a much faster timescale than ITG turbulence. It is found that quasi-steady Er×B zonal fows are generated by an inverse wave energy cascade process. Linear stability analyses of the electrostatic Kelvin-Helmholtz (KH) mode show that the quasisteady Er×B zonal flow profile is closely related to the q profile or to the magnetic shear, which has a stabilizing effect on the KH mode. It is shown that the microscopic quasi-steady Er×B zonal fows arising from ETG turbulence have a strong stabilizing effect on the slab ITG mode.



(a) real frequency and (b) growth rate of slab ITG modes suppressed by microscopic ETG zonal flows with a flow amplitude v0.

Reference

[1] "Gyrokinetic theory of drift waves in negative shear tokamaks", Y. Idomura, S. Tokuda, Y. Kishimoto, and M. Wakatani, Nuclear Fusion 41, 437-445 (2001).
[2] "Gyrokinetic theory of drift waves in negative shear tokamaks", Y. Idomura, S. Tokuda, Y. Kishimoto, and M. Wakatani, 18th IAEA Fusion Energy Conference, Sorrento, Italy, 2000 (International Atomic Energy Agency, Vienna, 2000), IAEA-CN-77/TH2/6 (oral).

  Stability of E×B zonal flow in electron temperature gradient driven turbulence

Abstract

The electron temperature gradient driven turbulence in a slab configuration modeling the negative shear tokamak is studied using a gyrokinetic finite element particle-in-cell code. It is found that quasisteady Er×B zonal flows are generated in finite magnetic shear regions in both sides of the qmin-surface, where the electron thermal transport is reduced substantially compared with the qminsurface region. Stability analyses of the electrostatic Kelvin。V Helmholtz (KH) mode show that the quasisteady Er×B zonal flow pattern is closely related to the q profile or the magnetic shear, which has a stabilizing effect on the KH mode. By changing the q profile to reduce the magnetic shear, the KH mode becomes unstable for the quasisteady Er×B zonal flow, and the Er×B zonal flows disappear in the weak magnetic shear region. Numerical results show a possibility of controlling Er×B zonal flows with the magnetic shear, which depends on the stability of the KH mode.



Time histories of ETG turbulence showing self-organization of zonal flows.

Reference

[1] "Stability of E×B zonal flow in electron temperature gradient driven turbulence", Y. Idomura, S. Tokuda, and M. Wakatani, Phys. Plasmas 7, 3551-3566 (2000).

  Gyrokinetic eigenmode analysis of slab ITG and ETG modes in negative shear tokamaks

Abstract

With a gyrokinetic integral eigenvalue code, it is shown that both the slab ion temperature gradient (ITG) mode and the slab electron temperature gradient (ETG) mode have three types of branches in the negative shear configuration: a single moderational surface mode, a double mode-rational surface mode, and a nonresonant mode. For typical fusion plasma parameters satisfying λDe2 >> ρte2, a Weber-type differential eigenmode equation of the ETG mode becomes essentially different from that of the ITG mode, because of the Debye shielding effect, where λDe is the Debye length and ρte is the electron Larmor radius. A scale length of the ETG modes is characterized by λDe, and different types of analytic solutions are obtained for the ETG modes. From a comparison of the transport coefficient based on the mixing length theory, it is shown that in the negative shear configuration, the slab ETG mode gives an order of magnitude larger transport coefficient compared with an estimate for the conventional normal-sheared slab ETG mode.



Multi-scale spectra of ITG and ETG modes in normal shear and reversed shear configurations.

Reference

[1] "Gyrokinetic theory of slab electron temperature gradient mode in negative shear tokamaks", Y. Idomura, S. Tokuda, and M. Wakatani, Phys. Plasmas 7, 2456-2468 (2000).
[2] "Gyrokinetic theory of slab ion temperature gradient mode in negative shear tokamaks", Y. Idomura, S. Tokuda, and M. Wakatani, Phys. Plasmas 6, 4658-4671 (1999).