Masahiro Wakatani

A collisional drift wave description of plasma edge turbulence

Model mode‐coupling equations for the resistive drift wave instability are numerically solved for realistic parameters found in tokamak edge plasmas. The Bohm diffusion is found to result if the parallel wavenumber is chosen to maximize the growth rate for a given value of the perpendicular wavenumber. The saturated turbulence energy has a broad frequency spectrum with a large fluctuation level proportional to κ (=ρs/Ln, the normalized inverse scale length of the density gradient) and a wavenumber spectrum of the two‐dimensional Kolmogorov–Kraichnan type, ∼k−3.

A review of internal transport barrier physics for steady-state operation of tokamaks

Tokamak discharges with improved energy confinement properties arising from internal transport barriers (ITBs) have certain attractive features, such as a large bootstrap current fraction, which suggest a potential route to the steady-state mode of operation desirable for fusion power plants. This paper first reviews the present state of theoretical and experimental knowledge regarding the formation and characteristics of ITBs in tokamaks. Specifically, the current status of theoretical modelling of ITBs is presented; then, an international ITB database based on experimental information extracted from some nine tokamaks is described and used to draw some general conclusions concerning the necessary conditions for ITBs to appear, comparing these with the theoretical models. The experimental situation regarding the steady-state, or at least quasi-steady-state, operation of tokamaks is reviewed and finally the issues and prospects for achieving such operational modes in ITER are discussed. More detailed information on the characteristics of ITBs in some 13 tokamaks (as well as helical devices) appears in the appendix.

Transport processes and entropy production in toroidal plasmas with gyrokinetic electromagnetic turbulence

Transport processes and resultant entropy production in magnetically confined plasmas are studied in detail for toroidal systems with gyrokinetic electromagnetic turbulence. The kinetic equation including the turbulent fluctuations are double averaged over the ensemble and the gyrophase. The entropy balance equation is derived from the double‐averaged kinetic equation with the nonlinear gyrokinetic equation for the fluctuating distribution function. The result clarifies the spatial transport and local production of the entropy due to the classical, neoclassical and anomalous transport processes, respectively. For the anomalous transport process due to the electromagnetic turbulence as well as the classical and neoclassical processes, the kinetic form of the entropy production is rewritten as the thermodynamic form, from which the conjugate pairs of the thermodynamic forces and the transport fluxes are identified. The Onsager symmetry for the anomalous transport equations is shown to be valid within the qu...

First plasmas in Heliotron J

Results obtained in the initial experimental phase of Heliotron J are reported. Electron beam mapping of the magnetic surfaces at a reduced DC magnetic field has revealed that the observed surfaces are in basic agreement with the ones calculated on the basis of the measured ambient field around the device. For 53.2 GHz second harmonic ECH hydrogen plasmas, a fairly wide resonance range for breakdown and heating by the TE02 mode has been observed in Heliotron J as compared with that in Heliotron E. With ECH injection powers up to ≈ 400 kW, diamagnetic stored energies up to ≈ 0.7 kJ were obtained without optimized density control.

Progress in stellarator/heliotron research: 1981?1986

Substantial progress was made during the period 1981-1986 in plasma parameters, physics understanding, and improvement of the stellarator/heliotron concept. Recent advances include (1) substantial achievements in higher plasma parameters and currentless plasma operation, (2) new theoretical results with respect to higher beta limits, second stability region, effect of a helical axis, effect of electric fields on transport, and reduction of secondary currents; and (3) improvements to the reactor concept. The key issues have been further refined, and the short-term direction of the program is clear; a number of new facilities that were designed to resolve these issues are about to come into operation or are in the final design stages. This report summarizes these advances.

Finite‐Larmor‐radius magnetohydrodynamic equations for microturbulence

A set of nonlinear fluid equations which includes the effect of finite ion Larmor radius is derived to describe microturbulence [k⊥ ρs ≂O(1), k∥R≂O(1), n1/n0≂ ρs/Ln, and B1/B0≂ρs/R ] in an inhomogeneous plasma with a strong magnetic field of general geometry. Here ρs is the ion Larmor radius at the electron temperature, Ln is the density gradient scale length, R is the radius of curvature of the magnetic line of force, k is the wave vector, and n1/n0 and B1/B0 are relative levels of density and magnetic field perturbations.

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.

EFFECTS OF NET TOROIDAL CURRENT ON THE MERCIER CRITERION IN THE LARGE HELICAL DEVICE

The effects of the net toroidal current on the local ideal MHD stability or the Mercier criterion are investigated for a plasma in the heliotron/torsatron configuration by taking the Large Helical Device as an example. The three dimensional equilibrium code VMEC is used to study the local stability of equilibria with given net toroidal currents. It is found that a subtractive current that decreases the rotational transform improves the stability, while an additive current that increases the rotational transform reduces the stability. The change of the rotational transform at the magnetic axis due to the net toroidal current is the essential mechanism for the change of stability. Mercier stability diagrams are given for the configurations of the Large Helical Device in which the plasma position is shifted inward or outward

Nonlinear Evolution of q = 1 Triple Tearing Modes in a Tokamak Plasma

In magnetic configurations with two or three q=1 (with q being the safety factor) resonant surfaces in a tokamak plasma, resistive magnetohydrodynamic modes with poloidal mode numbers m much larger than 1 are found to be linearly unstable. It is found that these high-m double or triple tearing modes significantly enhance through nonlinear interactions the growth of the m=1 mode. This may account for the sudden onset of the internal resistive kink, i.e., the fast sawtooth trigger. Based on the subsequent reconnection dynamics that can proceed without formation of the m=1 islands, it is proposed that high-m triple tearing modes are a possible mechanism for precursor-free partial collapses during sawtooth oscillations.

Effect of collisionality and radial electric field on bootstrap current in the large helical device

The bootstrap current decreases in a more highly collisional regime, and in stellarator/heliotron it is predicted that a neoclassical current component proportional to the radial electric field exists when electrons and ions belong to different regimes of collisionality. To evaluate the bootstrap current in stellarator/heliotron in the whole range of collisionality from the collisionless 1/ν to the Pfirsch-Schluter regime, a new connection formula has been proposed. This connection formula has been applied to Large Helical Device (LHD) plasmas in which ions and electrons belong to different collisionality regimes, and finite beta MHD equilibria including the bootstrap current have been obtained. For LHD plasmas such as ECRH (T1 << Te) in electron root, the bootstrap current with an electric potential twice as high as the electron temperature reduces to about 1/5 to 2/3 of that with zero electric potential. Then, the MHD equilibrium configuration changes significantly, depending on collisionality and radial electric field, even for the same beta value of the LHD plasmas