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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.

On the basis of theory and computer simulations we show that electrostatic turbulence in a cylindrical plasma with magnetic shear and curvature self-organizes to form a macroscopic potential 0 which depends only on the radial coordinate r and is given by 0(r)-Jo(pr) + C\r 2 + Ci, where C\ and C2 are functions of a constant p. A unique feature of the potential is the existence of a coaxial 0(ro) =0 surface at ro -O.la, where a is the radius of the cylinder. This surface is found to be fairly rigid and is contial enstrophy induces condensation of the turbulence energy into the zero axial and zero azimuthal eigenmode to form an axisymmetric potential surface (/*) in the formwhere p =3.82, r is normalized to unity at the radius of the cylinder, and Jo is the Bessel function. The model equations we use to describe the electrostatic turbulence are the equation of vorticity, (\nn (l) and the equation of continuity,Here the parallel current J\\ is eliminated by the use of a generalized Ohm's law with the assumed isothermal electron pressure gradient. The contribution of the ion parallel current is ignored.

. The perpendicular coordinate is normalized to the cylinder radius a, the parallel coordinate is normalized to the major radius R, and the time is normalized by (co C iP 2 / a 2 ) ~l. The convective derivative is given bysidered to inhibit radial particle transport.PACS numbers: 52.35. Ra, 52.35.Py, 52.55.Pi, 52.65. +z In the presence of appropriate constraints, plasma turbulence is known to self-organize to form semicoherent macroscopic structures 1 " 3 which play crucial roles in the equilibria and transports. In this Letter we present the first evidence of self-organization of electrostatic turbulence in a cylindrical plasma based on threedimensional simulations and a theory. The plasma turbulence is excited by a combination of the resistive drift-wave instability and the resistive interchange instability 4 in the presence of an axisymmetric magnetic field with a curvature and shear. The conservation of potenand the parallel derivative is given byThe curvature term H and the flux function y/ 0 may be represented by the rotational transform i(r) for a heliotron configuration,and n=(a 2 /R 2 )(N/l)[r 2 i(r) + 2 friGOrfr],where / is the pole number and TV is the pitch number. By subtracting Eq. (2) from (1), one can construct the

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 κ̄ (=ρs/Ln, the normalized inverse scale length of the density gradient) and a wavenumber spectrum of the two-dimensional Kolmogorov–Kraichnan type, ∼k−3.

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 quasilinear framework. The complete energy balance equation, which takes account of the anomalous transport and exchange of energy due to the fluctuations, is derived from the ensemble-averaged kinetic equation. The intrinsic ambipolarity of the anomalous particle fluxes is shown to hold for the self-consistent turbulent electromagnetic fields satisfying Poisson's equation and Ampère's law.