The study of MHD instabilities in elongated tokamaks

Fixed boundary ideal MHD instabilities are studied analytically and computationally for highly elongated axisymmetric toroidal equilibria.

The computational studies of n = 1 large-scale instabilities show that even a slightly diamagnetic plasma with broad current profile and highly elongated cross section is subject to ballooning modes for q values well above unity at the magnetic axis. The maximum stable average betas are achieved with a broad current profile and either a paramagnetic plasma ( (β_ < 1) with a highly elongated cross section (b/a = 3) or a diamagnetic plasma (β > 1) with only a mildly elongated cross section (b/a < 2).

In the analytic study of high n ballooning modes, the marginal pressure gradient is derived as a function of equilibrium parameters such as safety factor, shift, elongation, and inverse aspect ratio. It is found that high elongation reduces the stability by decreasing the stabilizing effects of field line bending and local shear. The stability of a highly elongated plasma depends sensitively on the profile of the safety factor, q(ψ), due to the weakness of the field line bending effect.

The analytic results for high n ballooning modes are compared with computational results obtained by using the ORNL BALOON code. The computational results reveal that high elongation, low aspect ratio, and broad pressure profile enhance the marginal beta for 8, less than unity but severely reduce the marginal beta for β, larger than unity for the equilibrium profiles used in this study.