Zonal Flow and Zonal Magnetic Field Generation by FiniteβDrift Waves: A Theory for Low to High Transitions in Tokamaks

The understanding of low to high (L-H) transition in tokamaks has been an important area of investigation for more than a decade. Recent 3D finite $\beta$ simulations of drift-resistive ballooning modes in a flux tube geometry by Rogers et al. [Phys. Rev. Lett. 81, 4396 (1998)] have provided a unique parametrization of the transition in a two-dimensional phase space. Comparison of the threshold curve in this phase space with data from ASDEX and C-MOD has shown very good agreement. In this Letter we provide a simple theory, based on the generation of zonal flow and zonal magnetic field in a finite-beta plasma, which explains this threshold curve for L-H transition in tokamaks.