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Toroidal drift waves with unconventional mode structures and non-groundeigenstates, which differ from typical ballooning structure mode, are found tobe important recently by large scale global gyrokinetic simulations andespecially become dominant at strong gradient edge plasmas [cf., Xie and Xiao,Phys. Plasmas, 22, 090703 (2015)]. The global stability and mode structures ofdrift wave in this steep edge density and temperature gradients are examined byboth direct numerical solutions of a model two-dimensional eigen equation andanalytical theory employing WKB-ballooning approach. Theory agrees withnumerical solutions quite well. Our results indicate that (i) non-groundeigenstates and unconventional mode structures generally exist and can beroughly described by two parameters `quantum number' $l$ and ballooning angle$\vartheta_k$, (ii) local model can overestimate the growth rate largely, say,$>50\%$, and (iii) the narrow steep equilibrium profile leads to twisting(triangle-like) radial mode structures. With velocity space integral,semi-local theory predicts that the critical jump gradient of the most unstableion temperature gradient mode from ground state $l=0$ to non-ground state $l=1$is $L_T^{-1}R\sim50$. These features can have important consequences toturbulent transport.

Global Theory to Understand Toroidal Drift Waves in Steep Gradient