The kinetic theory of low-frequency Alfvén modes in tokamaks is presented. The inclusion of both diamagnetic effects and finite core-plasma ion compressibility generalizes previous theoretical analyses (Tsai S T and Chen L 1993 Phys. Fluids B 5 3284) of kinetic ballooning modes and clarifies their strong connection to beta-induced Alfvén eigenmodes. The derivation of an analytic mode dispersion relation allows us to study the linear stability of both types of modes as a function of the parameters characterizing the local plasma equilibrium and to demonstrate that the most unstable regime corresponds to a strong coupling between the two branches due to the finite thermal ion temperature gradient. In addition, we also show that, under certain circumstances, non-collective modes may be present in the plasma, formed as a superposition of local oscillations which are quasi-exponentially growing in time. * pi 7 4 + τ q, corresponds to the most unstable regime, as anticipated in the previous section.

The existence of unstable ion temperature gradient driven Alfvén eigenmodes (AITG) is demonstrated in tokamak plasmas, which are ideally stable with respect to magnetohydrodynamics (MHD). Conditions for the destabilization of such modes are quantitatively discussed on the basis of numerical solutions of a set of one-dimensional integral equations along the ballooning coordinate (quasi-neutrality and parallel Ampère’s law). Furthermore, theoretical analyses of the eigenmode dispersion relation, which is given in a compact analytical form in the small ion orbit width limit (compared to the radial wavelength), provide a basis for explaining the general properties of the modes. It is emphasized that instability requires both sufficiently strong thermal ion temperature gradients and that the plasma be not too far away from ideal MHD marginal stability.

A coronal mass ejection (CME) observed by LASCO exhibits evidence that its magnetic field geometry is that of a flux rope. The dynamical properties throughout the fields of view of C2 and C3 telescopes are examined. The results are compared with theoretical predictions based on a model of solar flux ropes. It is shown that the LASCO observations are consistent with a two-dimensional projection of a three-dimensional magnetic flux rope with legs that remain connected to the Sun.

In this letter, we demonstrate the existence of unstable ion temperature gradient driven Alfvén eigenmodes in tokamak plasmas, which are ideally stable with respect to magnetohydrodynamics (MHD). Conditions for the destabilization of such modes are quantitatively discussed on the basis of theoretical analyses of the mode dispersion relation, which is given in a compact analytical form. It is emphasized that instability requires both sufficiently strong thermal ion temperature gradients and that the plasma be sufficiently close to ideal MHD marginal stability.

Results from a fully nonlinear three-dimensional toroidal electrostatic gyrokinetic simulation of the ion temperature gradient instability are presented. The model has adiabatic electrons and the complete gyrophase-averaged ion dynamics, including trapped particles. Results include the confirmation of the radially elongated ballooning mode structure predicted by linear theory, and the nonlinear saturation of these toroidal modes. The ensuing turbulent spectrum retains remnants of the linear mode structure, and has very similar features as recent experimental fluctuation measurements.PACS numbers: 52.35. Ra, 52.25.Gj, 52.35.Qz Recent advances in both nonlinear df methods for gyrokinetic simulation [1,2] and massively parallel supercomputing now make it possible to simulate a sizable fraction of a tokamak plasma using realistic physical parameters. Here, we report results from the first whole cross section three-dimensional (3D) electrostatic toroidal gyrokinetic simulation. We investigate the nonlinear evolution of the ion temperature gradient (ITG) driven instability and the associated turbulence and transport in realistic geometry and dimensionality. The ITG mode has long been considered a plausible candidate to explain the observed anomalous ion heat transport in tokamak plasmas, which is substantially above the predicted neoclassical values [3,4]. The simulation results presented below show very similar features in terms of the fluctuation spectrum as the recent beam emission spectroscopy (BES) diagnostic on TFTR [5].In these simulations, the ions are fully gyrokinetic, including trapped particles. The electrons are treated as adiabatic which permits a moderate size time step (simulations with kinetic electrons are feasible, but the time step would need to be smaller by the factor ivAv/). The simulation is running efficiently on massively parallel supercomputers (currently the CM-200 and CM-5) which allow simulations of relatively large systems (e.g., a ^ lOOp/ minor radius. Ax ^=^ pi). Typical runs up to this point have used 10^ to 10^ particles with 1 to 2 particles per grid cell, and a timing of 2-3 jUS per particle per time step on a fully configured CM-200. Fine grid resolution is needed in the toroidal direction because the mode structure is helical (elongated along the magnetic field lines, i.e., k\\<^k±), resulting in a smaller number of particles per grid cell relative to conventional slab simulations.Starting with the electrostatic gyrokinetic equations with a nonuniform equilibrium B field [6], we write /(z,r) ==/o(z) + ^/(z,/), where z = (R,rii,/x), and expand z into its equilibrium and perturbed parts: z=z^-f-z^ /o(z) is a Maxwellian and satisfies z^S^o(z)=0. The equation for the perturbed ion distribution function 5f is then [1] S,5/+z9z^/=--z^9j^o,where the magnetic moment fi is time independent and the other equilibrium and perturbed phase space variables are evolved using (R",r,r)=(-riib*-h^bxV5,b*-A/V5), tLu^ ii /,i^ = (R\n|)

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Nonlinear saturation of toroidal Alfvén eigenmodes (TAE) via mode-mode couplings is investigated both analytically and numerically. It is demonstrated that, as the TAE mode amplitude increases, the corresponding nonlinear ponderomotive force produces a fine-structure density modulation, which then causes enhanced energy dissipation in the short scales and leads eventually to the nonlinear saturation of TAE.