Abstract

Velocity and magnetic shears are ubiquitous in tokamaks. Both of them play critical roles in plasma dynamics and confinement performance by affecting the coherence of fluctuations in space and time. In the past few decades, especially with the recent development of large-scale gyrokinetic numerical simulations, there has been a growing understanding of the shears in tokamaks.  However, theoretical discussions, which treat magnetic shear and E×B shear in tokamaks on an equal footing, have rarely been done. In this talk, I will start from the idea of resonance and demonstrate the analogies between velocity and magnetic shear. Shearing coordinates, introduced to eliminate the parallel gradient operator, serve as a useful tool to describe fluctuations in shear. With the adoption of shearing coordinates, we lose the normal mode description and instead gain a ‘quasi-mode’—an effective wave packet of spatially localized resistive interchange modes. Compared with resistive interchange mode, quasi-mode exhibits a broader mode structure, thus enhancing mixing. In addition, quasi-mode has many resemblances to the ballooning mode, which is a typical plasma instability arising from the toroidal geometry of tokamaks. Therefore, quasi-mode could be a bridge between cylindrical and toroidal geometries, and studying it helps us better understand the toroidicity effects in tokamaks. The talk ends with two traditional theoretical methods for ballooning mode studies: the Bloch eigenmode equation and the ballooning mode representation. This talk is an instructive resource for understanding the basics of shearing dynamics and toroidicity effects in tokamaks.