Stabilization of the internal kink mode in a tokamak by toroidal plasma rotation

Abstract

The stability of the internal m=n=1 kink mode is analyzed for a tokamak with a toroidally rotating plasma, by a large aspect ratio expansion of the compressible magnetohydrodynamic equations. Assuming that the central poloidal beta is of order unity, it is found that the internal kink mode is stabilized by rotational frequencies of order Ω/ωA∼ε, where ωA is the Alfvén frequency and ε is the inverse aspect ratio. The internal kink then turns into a stable oscillation with a Doppler-shifted frequency ∼ΩM(1−1/Γ)1/2, where Γ is the adiabatic index and ℳ is the sonic Mach number. The stabilization comes from the centrifugal force which gives a stable density (or entropy) distribution within each magnetic surface. The parallel motion associated with the internal kink mode then behaves as the Brunt–Väisälä oscillations of a stably stratified fluid in a gravitational field. At lower rotational frequencies, Ω/ωA∼ε2, the only effect of the rotation is a co-rotation of the usual (nonrotating) m=n=1 instability, whereas the ordering Ω/ωA∼ε3/2 represents a transition regime where the stabilizing effect of the rotation competes with the drive from the internal kink instability. Kinetic behavior along the field lines is expected to influence this stabilization mechanism, as it depends on the adiabatic index Γ.