MHD instabilities as an initial boundary-value problem

摘要: The gross MHD instabilities of straight cylindrical plasmas with elongated cross-section are investigated by solving the linearized equations as an initial boundary-value problem on computer. Fourier-analysed along ignorable co-ordinate equilibrium in order to reduce computation two dimensions. method is applied find fixed-boundary rectangular walls. Starting arbitrary perturbation and following it for many Alfven transit times, we that dominant instability overwhelms all stable oscillations after several e-folding times. We determine growth rates fastest growing a function parameters. Then examine spatial structure physical variables (1, 1, p1). velocity field displays distinctive convection pattern. This becomes spatially concentrated around point maximum rotational transform current decreased marginal point, concentrates near wall increased. Given p'(ψ) = Jzc ψ/ψc, ψ (wall) 0, density each mode increases elongated. But higher azimuthal m-modes increase elongation their intervals overlap lower m-modes.