A nonlinear gyrokinetic formalism for low-frequency (legs than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations Is developed.The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due Co finite Lannor radius, plasma inhomogeneities, and magnetic field geometries. The specific case of axigymmetric tokamaVs is then considered, and a model nonlinear equation is derived for electrostatic drift waves.Also, applying the formalism tD the shear Alfven wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear-Alfven waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects.In particular, wave energy is found to cascade in vavenumber instead of frequency.

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The problem of the stability of static, highly conducting, fully ionized plasmas is investigated by means of an energy principle developed from one introduced by Lundquist. The derivation of the principle and the conditions under which it applies are given. The method is applied to find complete stability criteria for two types of equilibrium situations. The first concerns plasmas which are completely separated from the magnetic field by an interface. The second is the general axisymmetric system.

A theory of low-frequency drift (universal) instabilities in a nonuniform collisionless plasma is developed for general magnetic field configurations including trapped particle effects, rather than the plane geometry which has previously received most attention. A type of energy principle shows that the special equilibrium distribution F(∈, μ), of interest in minimum-B mirror configurations, is absolutely stable to these modes provided ∂F/∂∈ < 0 together with a second condition on ∂F/∂μ. For equilibrium distributions not of this special form, in particular for a Maxwell distribution with a density gradient, the case of axisymmetric toroidal configurations with closed poloidal field lines is considered in detail. Three unstable drift modes are found, a flute-like mode, a drift-ballooning mode local to the region of unfavorable curvature, and a drift-universal mode. Stability criteria and growth rates for the modes are given. The equations also describe a recently discussed low-frequency trapped-particle instability.