A Boundary Layer Theory for the Scrape Off Layer

The handling of power entering the scrape-off-layer (SOL) and reaching the plasma facing components is one of the major challenges to achieve long pulse operation in future fusion machines. Goldston’s Heuristic Drift Model [1] yields a thin SOL for laminar flow, but more recently, Chu et. al. [2] showed through scaling arguments that the SOL could be broadened beyond the HD limit via turbulence spreading from the pedestal.

The purpose of this work is to expand upon Chu et al’s scaling arguments via a full model of a “straight” turbulent SOL. This is accomplished through a boundary layer approximation of the Braginskii equations coupled to a nonlinear Fisher equation model of drift wave turbulence [3]. Magnetic shear is accounted for by varying streamwise extent as a function of penetration into the SOL. Instability is introduced to the system via a stochastic flux of turbulent kinetic energy through the LCFS and interchange instability within the SOL. Through scaling arguments, numerical simulations, and analysis of a reduced model we find a parallel-direction SOL-width profile independent of flux expansion, and that interchange effects add a small additional broadening. Even intermittent “puffs” of turbulence are capable of broadening SOL widths an interesting amount.

[1] R.J. Goldston. In: Nuclear Fusion 52.1 (Dec. 2011), p. 013009.

[2] Xu Chu et al. In: 62.6 (Apr. 2022).

[3] Ö. D. Gürcan et al., Phys. Plasmas 1 May 2006; 13 (5): 052306