The ion temperature gradient (ITG) modes in transport barriers (TBs) of tokamak plasmas are numerically studied with a code solving gyrokinetic integral eigenvalue equations in toroidal configurations. It is found that multiple ITG modes with conventional and unconventional ballooning mode structures can be excited simultaneously in TBs with steep gradients of ion temperature and density. The characteristics of the modes, including the dependence of the mode frequencies, growth rate and structure on plasma parameters, are systematically investigated. Unconventional modes with large mode-number (where denotes a certain parity and peak number in ballooning space) dominate in the large region (), while the conventional mode with dominates in the medium region (), and unconventional modes with small mode-number dominate in the small region (). Thus, the spectra of these conventional and unconventional modes at steep gradients are qualitatively different from those of the conventional ITG modes at small or medium gradients, in which the growth rate of the only ITG mode with reaches maximum at the medium value . Through scanning ion temperature gradient and density gradient separately, it is proven that the synergetic effect of and , rather than alone, drives the unconventional ITG modes in TBs. Moreover, it is found that the critical value of for driving the unconventional ITG modes with large l number increases with increasing . In addition, the effects of magnetic shear on conventional and unconventional ITG modes in the high confinement regime (H-mode) are analyzed in detail, and compared with equivalent effects on conventional modes in the low and intermediate gradient regimes (L- and I- modes). Finally, the effects of the poloidal wave number and gradients of ion temperature and density on radial transport are analyzed based on quasi-linear mixing length estimations.
Fully toroidal ion temperature gradient driven drift modes