Kinetic shear Alfvén modes in tokamak plasmas ͑with or without temperature gradient͒ are numerically investigated in the full gyrokinetic limit. It is shown that, in the presence of ion temperature gradient ͑ITG͒, the threshold value of plasma pressure gradient is well below that for ideal magnetohydrodynamic ballooning instability. It is also demonstrated in a more general sense that, without ITG, the former is identical with the latter. The electromagnetic instability is also found to exist in the second stable region of the ideal modes when a finite ITG is present. The results are compared with previous similar analyses for kinetic collisionless ballooning modes. Possible correlation of the instability with tokamak experiments is discussed.

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The Rayleigh-Taylor (RT) instability in Z pinches with sheared axial flow (SAF) is analyzed using finite Larmor radius (FLR) magnetohydrodynamic theory, in whose momentum equation the FLR effect (also referred to as the effect of gyroviscosity) is introduced through an anisotropic ion (FLR) stress tensor. A dispersion relation is derived for the linear RT instability. Both analytical and numerical solutions of the dispersion equation are given. The results indicate that the short-wavelength modes of the RT instability can be stabilized by a sufficient FLR, whereas the long-wavelength modes can be stabilized by a sufficient SAF. In the small-wavenumber region, for normalized wavenumber K<2.4, the hybrid RT/KH (Kelvin-Helmholtz) instability is shown to be the most difficult to stabilize. However the synergistic effect of the SAF and gyroviscosity can mitigate both the RT instability in the large-wavenumber region (K>2.4) and the hybrid RT/KH instability in the small-wavenumber region. In addition, this synergistic effect can compress the RT instability to a narrow wavenumber region. Even the thorough stabilization of the RT instability in the large-wavenumber region is possible with a sufficient SAF and a sufficient gyroviscosity.

The effects of compressibility on the Rayleigh-Taylor ͑RT͒ instability in a finite Larmor radius ͑FLR͒ plasma of magnetic field acceleration are studied by means of FLR magnetohydrodynamic ͑MHD͒ theory. FLR effects are introduced in the momentum equation of MHD theory through an anisotropic ion stress tensor. The linear mode equation which includes main equilibrium quantities and their high-order differential terms is derived. The dispersion equation is solved numerically. The main results indicate that in the compressible FLR plasma the growth rate of the RT instability displays faster growing and broader wavenumber range; and a new branch of low-frequency and long-wavelength instability, whose real frequency is positive ͑opposite from the negative real frequency of the RT instability͒, is found in the compressible FLR plasma. That is, plasma compressibility is a destabilizing factor for both the FLR stabilized RT instability and the new branch of instability.

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