Shinji Tokuda

Generation and termination of runaway electrons at major disruptions in JT-60U

The operation conditions to avoid runaway electron generation at the major disruption have been investigated in JT-60U tokamak plasmas. It has been found that runaway electrons are not observed for low Bt of ? 2.2?T or low plasma current quench rates (I? ? -(dIp/dt)/Ip) of <50?s-1. Furthermore, they are not observed for low effective safety factors defined at the plasma edge (qeff) of ? 2.5 even for high I? of 300-400?s-1, which is the case for uncontrolled disruptions accompanied by large plasma displacements (e.g., vertical displacement events (VDEs)). On the other hand, in controlled disruptions with small plasma shifts, qeff easily increases above 8, and runaway electrons are observed even for low current quench rates of 50-100?s-1. Furthermore, it has been found that in these position controlled disruptions the runaway current tail can rapidly decay even for zero or weakly positive plasma surface voltages. These observations of the avoidance and termination of runaway electrons suggest an anomalous loss mechanism for runaway electrons.

Global gyrokinetic simulation of ion temperature gradient driven turbulence in plasmas using a canonical Maxwellian distribution

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(P,e,μ), which is defined by three constants of motion in the axisymmetric toroidal system—the canonical angular momentum P, the energy e, 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 q min 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,e,μ), do not appear in the nonlinear regime.

Runaway electrons in magnetic turbulence and runaway current termination in tokamak discharges

The behaviour of runaway electrons in three types of magnetic turbulence in tokamak discharges is reviewed: (a) micromagnetic turbulence, (b) low-m/n magnetic islands in a sea of stochasticity, (c) macroscale magnetic turbulence. The confinement of runaway electrons is much better than that of bulk thermal electrons in (a) and (b), but is greatly degraded in (c). Spontaneous and intrinsic termination of runaway current, which will be favourable for tokamak fusion reactors in order to reduce the heat flux on the first wall, was first found in JT-60U by decreasing the safety factor at the plasma surface qs to around 2 or 3 by three different methods: (i) controlled inward plasma shift, (ii) a vertical displacement event, (iii) plasma current rampup.

Computation of MHD equilibrium of Tokamak Plasma

Abstract Computation of the MHD equilibrium of a tokamak plasma is reviewed as comprehensively as possible. The basic equation of this problem is the Grad-Shafranov equation. General remarks on this equation and related issues are, first, summarized with historical survey of the MHD equilibrium solution, where some mathematical discussions on the numerical analysis of the problem are also presented. Distinguishing features of this problem are seen in treatment of the boundary condition and constraining conditions and we describe them in a rather detailed manner. In the main part of this review paper we present a concrete description on the numerical procedures of the MHD equilibrium solvers which are classified into two groups, that is, the real space solvers and the inverse equilibrium solvers. We also describe topics on more general equilibrium models, that is, the equilibrium with steady flow, anisotropic equilibria, equilibria with specified current sources, and equilibrium evolution. Brief comments on three-dimensional equilibrium solvers are also presented. As for application of the MHD equilibrium solvers we present only a small part, that is, beta limit optimization, design of external coils, analysis of positional instability, and analysis of experimentally obtained data from electromagnetic measurement. It is concluded that among various kinds of numerical solution methods we can usually find most adequate ones for the present problem.

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.

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

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 qmin-surface region. Stability analyses of the electrostatic Kelvin–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.

A new eigenvalue problem associated with the two-dimensional Newcomb equation without continuous spectra

A new eigenvalue problem associated with the two-dimensional Newcomb equation in an axisymmetric toroidal plasma, such as a tokamak, has been posed and solved numerically by using a finite element method. In the formulation of the eigenvalue problem, the weight functions (the kinetic energy integral) and the boundary conditions at rational surfaces are chosen such that the spectra of the eigenvalue problem are comprised of only the real and denumerable eigenvalues (point spectra) without continuous spectra. Applications to the ideal m=1 mode have verified that this formulation is able to identify stable states as well as unstable states, and that the numerically obtained eigenfunctions show the singular behavior predicted by the theory at rational surfaces.

Global profile effects and structure formations in toroidal electron temperature gradient driven turbulence

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.

New conservative gyrokinetic full-f Vlasov code and its comparison to gyrokinetic δf particle-in-cell code

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 delta f particle-in-cell (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 nu(parallel to) nonlinearity are clarified for the Vlasov and PIC simulations

Effects of a hollow current profile on the ideal MHD stability of high beta p plasmas in a tokamak

The effects of current profiles on the n = 1 internal kink mode, the infinite n ballooning mode and the infernal mode in a tokamak are analysed numerically. The stabilities of plasmas with a circular cross-section and a peaked pressure profile are investigated for three types of current profile, that is parabolic, flat and hollow with an inverted q profile. In a low beta state (βp 0.5), the growth rate of the n = 1 internal kink mode for the plasma with the hollow current profile becomes larger, and the unstable region spreads to the region of higher qmin (qmin > 2). When the plasma has a more peaked pressure profile in the hollow part of the current profile, the unstable regions of the n = 1 internal kink mode and ballooning mode shrink, and the infernal mode disappears