Isothermal internal kink instability in a toroidally rotating tokamak plasma

Abstract

The properties of the internal kink instability in a tokamak with a toroidally rotating plasma is analysed from the ideal magnetohydrodynamic (MHD) equations, for plasmas satisfying an isothermal equation of state. The plasma equilibrium is assumed to have large aspect ratio, circular cross section, poloidal beta value ( β p) of order unity, and a rotational frequency comparable to the sound frequency. For an isothermal plasma, the rotational effect on the internal kink mode can be expressed in terms of a `rotational beta value' ( β Ω ) of the plasma. This quantity is defined in the same way as β p, with the kinetic energy density of the rotation ( u Ω ) replacing the plasma pressure. The rotation is found to be strongly stabilizing if u Ω is an increasing function of the minor radius ( β Ω<0 ). In the opposite case, the rotation is destabilizing unless the pressure profile is much more peaked than the kinetic energy density profile.