Ion-temperature-gradient instability in toroidal plasmas

The stability of the ion-temperature gradient mode in a toroidal plasma is investigated. Using the ballooning-mode formalism, an ordinary difference-differential equation is derived which includes full kinetic effects. The equation is then examined in various limits where it reduces to an ordinary differential equation. Analytic and computational studies show that, for η_i ≡ d ln T_i/ d ln n ≫ 1, toroidal effects further destabilize the mode. However, it is also found that toroidal effects give rise to higher η_i threshold compared to the slab case. Extensive numerical calculations over a wide range of parameters are carried out to delineate the regions of instability. It is concluded that the η_i instability is of relevance to present-day beam-heated tokamaks.