Global Theory to Understand Toroidal Drift Waves in Steep Gradient

TL;DR

This paper combines numerical and analytical methods to study unconventional toroidal drift wave modes in steep gradient plasmas, revealing new mode structures and stability features relevant to plasma turbulence.

Contribution

It introduces a semi-local analytical theory that accurately describes non-ground eigenstates and mode structures in steep gradient plasmas, improving understanding over local models.

Findings

Non-ground eigenstates and unconventional mode structures exist.

Local models can significantly overestimate growth rates.

Steep profiles cause twisting radial mode structures.

Abstract

Toroidal drift waves with unconventional mode structures and non-ground eigenstates, which differ from typical ballooning structure mode, are found to be important recently by large scale global gyrokinetic simulations and especially become dominant at strong gradient edge plasmas [cf., Xie and Xiao, Phys. Plasmas, 22, 090703 (2015)]. The global stability and mode structures of drift wave in this steep edge density and temperature gradients are examined by both direct numerical solutions of a model two-dimensional eigen equation and analytical theory employing WKB-ballooning approach. Theory agrees with numerical solutions quite well. Our results indicate that (i) non-ground eigenstates and unconventional mode structures generally exist and can be roughly 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 unstable ion 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 to turbulent transport.