Impurity effects on ion temperature gradient driven multiple modes in transport barriers

The impurity effects on ion temperature gradient (ITG) driven instability in transport barriers (TBs) are numerically investigated with the gyrokinetic integral eigenmode equations in tokamak plasmas. In particular, the effects of temperature and density gradients of the main ions (epsilon(Ti) and epsilon(ni)) are analyzed independently to understand the physical mechanisms better, instead of keeping their ratio eta(i) = epsilon(ni)/epsilon(Ti) = const. as carried out in previous works, when the parameters of impurity ions vary. It is found that the effect of impurity ions with outwardly peaked density profiles on ITG modes depends on the competition between the destabilizing effect of the impurity density gradient (Le)z and the stabilizing effect induced by the dilution of main ions from impurity ions when epsilon(Ti) is fixed, which is in significant contrast with the results for a fixed eta(i). The destabilizing effects include enhancement of ITG modes and coupling to the impurity mode (IM) in weak ITGs (big epsilon(Ti)) and strong impurity density gradient regimes. In addition, the stability boundaries for ITG modes, including high-order modes, are discussed in detail, and compared with previous works (Frojdh et al 1992 Nucl. Fusion 32 419). Furthermore, the impurity ions with either inwardly or slightly outwardly peaked density profiles have weaker and stronger stabilizing effects on small and big poloidal wave vector k(theta)rho(s) modes, respectively. However, the impurity ions with steeper outwardly peaked density profiles have stronger stabilizing effects on big k(theta)rho(s) modes. Moreover, the inwardly peaked impurity ion density profiles are beneficial for main ion confinement and impurity decumulation, due to the main (impurity) ions flowing inwardly (outwardly). Finally, analyses of eigenmode structure and the quasi-linear particle flux are performed in detail. The results show that impurity ions have non-negligible effects, especially on higher-order ITG modes.