There have been many attempts to include kinetic effects into the MHD equations to describe macroscopic instabilities. We are developing a numerical code to solve Maxwell's equations using kinetic dielectric tensor to include the kinetic effects systematically. In this presentation, however, we present the results using a dielectric tensor derived from multi-fluid equations, taking the effect of electron inertia, pressure gradient, and parallel current into account.

The code we use solves Maxwell's equations for scalar potential and vector potential using magnetic flux coordinate system (α, β, φ), where α is the toroidal flux, β is the poloidal angle, φ is the toroidal angle. Finite difference method is used in α direction, and Fourier decomposition in β and φ directions. We obtain eigen functions, eigen frequencies, and decay or growth rate by searching for the complex frequencies which make the wave electric field maximum for given external current.

We study the kink mode and the toroidicity induced Alfvén eigenmode, and the results are compared with these of conventional MHD analysis.