The influence of the shape of a confining magnetic field in closed toroidal flux surface geometry on drift wave turbulence is reviewed. In particular, the mechanisms of turbulent mode driving, damping and coupling are identified and implications for divertor tokamak and stellarator edge transport are discussed.

Tokamak plasma with negative central current density is known to be unstable for m=1/n=0 resistive kink magnetohydrodynamic instability and the explanation for the absence of negative central current, the so-called current hole phenomena, is made by the destabilization of the mode. However, a strong reversed magnetic shear configuration has two resonant surfaces for low mode numbers and should be unstable for the double tearing mode (DTM). Here, we examine the effects of DTM on the formation of current hole and show that the occurrence of DTM does not change the situation completely. The growth of DTM flattens the current profile near the minimum-q region; here q is the safety factor, and the current gradient to drive n=0 mode usually remains after a reconnection event due to DTM and the stability of m=1/n=0 mode is not affected much by the DTM activity.

The ISLAND module in the National Transport Code Collaboration (NTCC) Module Library computes the saturated widths of multiple magnetic islands due to neoclassical tearing modes by implementing a quasi-linear model that includes the effects of arbitrary aspect ratio, cross-sectional shape, and plasma beta. This paper presents a significantly improved version of the module available at the NTCC Library. The model was updated to include the distortion of islands caused by the radial variation of the perturbed magnetic field near the mode rational surface. The computer algorithm implemented by the module was redesigned to increase its speed, reliability and accuracy. The new module has been successfully interfaced with the BALDUR integrated modeling code, where it is used to compute the saturated widths of multiple islands in tokamak discharges.

The motion of an ablation cloud is investigated in a tokamak by using ideal magnetohydrodynamic equations with ablation processes. The cloud quickly expands along the magnetic field and simultaneously drifts to the lower field side due to a tire tube force and 1/R force. It is found that the acceleration of the cloud increases and subsequently decreases due to the energy deposit from the bulk plasma and, finally, the cloud is stopped due to the poloidal field.

A three-dimensional magnetohydrodynamic (MHD) simulation code has been newly developed. In this code, the physical variables are defined in the staggered mesh system and each of the MHD equations is split into the advection phase and the non-advection phase. The constrained interpolation profile method, which gives a highly accurate solution with less numerical diffusion, is applied to the calculation for the advection phase. In contrast, the non-advection phase is calculated using the finite difference method. The developed code is tested for the relaxation processes of the mass density, plasma pressure and magnetic field in the Large Helical Device (LHD).

We develop a multiple interface variational model, comprising multiple Taylor-relaxed plasma regions separated by ideal magnetohydrodynamic (MHD) barriers. A principal motivation is the development of a mathematically rigorous ideal MHD model to describe intrinsically three-dimensional equilibria, with non-zero internal pressure. A second application is the description of transport barriers as constrained minimum energy states. As a first example, we calculate the plasma solution in a periodic cylinder, generalizing the analysis of the treatment of Kaiser and Uecker (2004 Q. J. Mech. Appl. Math.57, 1–17), who treated the single interface in cylindrical geometry. Expressions for the equilibrium field are generated, and equilibrium states computed. Unlike other Taylor relaxed equilibria, for the equilibria investigated here, only the plasma core necessarily has reverse magnetic shear. We show the existence of tokamak-like equilibria, with increasing safety factor and stepped-pressure profiles.

The dynamics of secondary fluctuations with poloidal long wavelength and low frequency in electron-temperature-gradient (ETG) turbulence saturation is considered in sheared slab geometry. A simplified modeling analysis shows that this kind of large-scale structure including streamers may saturate primary ETG instability through poloidal mode coupling. Spectral analyses in three-dimensional ETG simulations clearly exhibit the secondary excitation and the probable relevancy to ETG saturation. The result may implicate a lower fluctuation level in ETG turbulence.

We have investigated the effect of the background thermal motion on the knock-on ion production and the neutron energy spectrum in deuteron–triton (D–T) fusion plasma. Under the conditions of a typical tokamak D–T plasma, it turned out that the effect is not crucial. Accordingly, it was found that the knock-on ion source strength formulated previously by Ryutov, Helander and Lisak is valid for D–T fusion plasma. The finite temperature effect would become important in knock-on ion production in D–3He fusion plasma.

In order to better understand the feature of turbulent transport in tokamak plasmas dominated by zonal flows and nonlinearly excited tertiary (Kelvin–Helmholtz-like) waves, the radial dependency of the turbulent structure in the back of steady-state zonal flows was analyzed based on gyrofluid simulation of the electron temperature gradient turbulence in a sheared-slab configuration. The zonal flows change the characteristics of plasma turbulence from homogeneous to inhomogeneous. Thus, it is found that turbulent vortices are regulated by a radially alternative potential pattern where the spatiotemporal characteristic scales with respect to local fluctuations change radially. From the cross spectrum analysis between the poloidal electric field and the pressure perturbation, it was found that, in plasmas dominated by zonal flows, the restriction of heat flux is conducted by two mechanisms, i.e. the reduction of coherence and the phase synchronization.

Confinement and loss properties of tangentially co-injected beam ions have been studied for a standard configuration of the Compact Helical System (Rax/Bt=0.921 m/1.9 T) by use of the global particle simulation code DELTA5D. Both ripple transport and collisions with a background plasma are taken into account. It has appeared that partially thermalized, pitch-angle scattered beam ions are dominantly lost at the small major radius side. It has also been shown that the negative potential can enhance beam ions losses.

Effects of nuclear elastic scattering (NES) on the neutral beam injection (NBI) and α-particle plasma heating operations are examined by solving the Boltzmann–Fokker–Planck (BFP) equations for beam ions and α-particles in deuteron–triton thermonuclear plasmas. The BFP calculations show that the enhancement in the fraction of the NBI and α-particle heating powers deposited to ions due to NES can be appreciable in reactor-grade plasmas.

Two-fluid flowing equilibrium configurations of a helicity-driven spherical torus (HD-ST) in the realistic region including the spherical flux conserver and the coaxial helicity source are numerically determined by using the combination of the finite difference and the boundary element methods. It is found from the numerical results that the ultra low-$q$ HD-ST with diamagnetic toroidal field and high-$\beta$ (volume average $\beta$ value, $\langle\beta\rangle\cong 18\%$) can be obtained by reversing the toroidal field over the whole region and by increasing the toroidal ion flow up to the Alfv${\rm \acute e}$n Mach number $M_{\rm A}\cong 0.7$. The ion diamagnetic drift velocity is larger than the ${\bf E}\times {\bf B}$ drift velocity and has the same direction.

An analytical formula of the thermal conductivity due to given coexisting electrostatic and magnetic fluctuations is derived in a large aspect straight tokamak with a small gyro-radius. The dependence of the thermal conductivity on particle species and the types of the fluctuations is clearly shown. When the ratio of the electrostatic energy to the magnetic energy is the order of the mass ratio of electrons to ions, χe is governed by the magnetic fluctuations and χi is governed by the electrostatic fluctuations, where χe and χi are thermal conductivities of electrons and ions, respectively.

To improve the understanding of reflectometry diagnostics, simulations of full reflectometer systems are needed and should include: (i) wave propagation; (ii) proper antenna setup and signal injection technique; (iii) signal detection and signal processing techniques; and (iv) real size of the system. Simulation of wide band frequency modulated reflectometry where the frequency is continuously swept adds further requirements. A good plasma description is also vital. In this work we apply this concept of full reflectometer simulation to the ITER position reflectometer taking into account the technological constraints.

A numerical scheme is presented which is able to solve the Grad–Shafranov (GS) equation in tokamak plasmas with toroidal current reversal for input profiles that are not restricted to any particularly chosen models. Its flexibility is subsequently tested, computing a GS equilibrium with off-axis negative toroidal current density strong enough to generate two nested current-reversal surfaces.

The magnetohydrodynamic equilibrium of a helical-axis heliotron with large-vacuum magnetic islands is investigated. Since the helical-axis heliotron is an $L\,{=}\,1/M\,{=}\,4$ low-magnetic-shear configuration, there is the sensitivity to the perturbed field. By assuming the external trim coil, low-order magnetic islands with $n/m\,{=}\,$1/2 can be generated. The effect and change of low-order ($n/m\,{=}\,1/2$) vacuum islands to the finite $\beta$ equilibrium are investigated. For a finite β equilibrium, $n/m\,{=}\,$1/2 islands disappear but $n/m\,{=}\, 4/8$ islands appear by the pressure-induced field. For another case, $n/m\,{=}\,$1/2 islands disappear and other resonances are suppressed. This property depends on the phase of islands.

We have numerically solved the coupled ordinary differential equations (ODEs) representing the ballooning modes in toroidally rotating tokamaks. The ODEs were derived by the eigenfunction expansion of the ballooning mode, of which the governing equation was originally derived as a partial differential equation (PDE). Generally, the truncation of the coupled ODEs to a finite number can generate essential differences between the solutions to the ODEs and to the corresponding PDE, because the truncation reduces the degree of freedom of the motion of the oscillators, or the expansion coefficients. The comparison between the solutions shows that the regularized eigenfunctions used for the expansion, developed by Furukawa and Tokuda (2005 Phys. Rev. Lett.94, 175001), efficiently confine the motion of the oscillators in the phase space with a small number of dimensions; the solution to the truncated ODEs can approximate well the ballooning mode obtained as a solution to the corresponding PDE within a finite time.

Nonlinear behavior of the resistive wall modes (RWMs) has been studied using nonlinear three-dimensional simulation code based on the reduced magnetohydrodynamic equations in a cylindrical tokamak. The vacuum is replaced by a highly resistive plasma using the pseudo-vacuum model. For the case that the RWM with $(m,n)\,{=}\,(3,1)$ mode and the internal $(m,n)\,{=}\,(5,2)$ mode are unstable, the RWM with $(m,n) \,{=}\, (3,1)$ mode enhances the growth rate of the internal $(m,n)\,{=}\,(5,2)$ mode in the nonlinear phase. The magnetic field line stochastization is obtained around the plasma edge due to the overlapping of the magnetic islands of the $(m,n)\,{=}\,(3,1)$ mode and the $(m,n)\,{=}\,(5,2)$ mode.

A new and simple approach for stellarator edge modeling is presented. This is based on averaging of edge plasma parameters and introducing effective two-dimensional flux surfaces which allow us to use the UEDGE transport code, widely used for tokamak edge plasma modeling. This approach is applied to edge modeling of the Large Helical Device (LHD). It should be noted that our model is based on a two-dimensional configuration which is called the stellarator-equivalent tokamak (SET), while a stellarator system is inherently three-dimensional. Numerical simulations show that a bump of ion density in the private flux region just inside the separatrix appears, and flow reversal or a vortex structure of the ion flow is observed. Detailed analyses are necessary for validating this approach.

Three-dimensional particle-in-cell simulation code for the investigation of physics in scrape-off-layer plasmas is developed. The code is parallelized by using High Performance Fortran (HPF) and good performance is attained in the computation at the Plasma Simulator at the National Institute for Fusion Science (NIFS) (NEC SX-7/160M5). The code represents resonable physics related to sheath and presheath formation as well as the formation of the self-consistent potential structure related to blob transport across a magnetic field.