Stabilization mechanism of ballooning modes by toroidal rotation shear in tokamaks

Furukawa, Masaru; Tokuda, Shinji

A ballooning perturbation in a toroidally rotating tokamak is expanded by square-integrable eigenfunctions of an eigenvalue problem associated with ballooning modes in a static plasma. Especially a weight function is chosen such that the eigenvalue problem has only the discrete spectrum. The eigenvalues evolve in time owing to toroidal rotation shear, resulting in countably infinite number of crossings among them. The crossings cause energy transfer from an unstable mode to the infinite number of stable modes; such transfer works as the stabilization mechanism of the ballooning mode. A simple analytic formula is derived for estimating the toroidal rotation shear required to stabilize the ballooning mode.