K-epsilon modelling of turbulent transport in the edge-SOL boundary layer

In the K-epsilon framework, a predator-prey like model determines the plasma turbulent transport. It depends on the underlying plasma turbulence via the growth rate chosen for the turbulent energy, the prey K, and its predator epsilon. Compared to our previous work [1], we propose in this paper modifications of the model to be tested in future simulations. A more appropriate expression of the growth rate is proposed by taking into account the fast dynamics of the parallel electron transport. The stabilising terms that are introduced allow for negative values of the growth rate of interchange coupled to drift wave turbulence. Changes to the K-epsilon model are made to adapt it to handle close to marginal states, then allowing one to address a Landau like bifurcation from negative growth rates, without turbulence, to positive growth rates, with turbulence. The closure using the multi-machine SOL width scaling law is revisited to allow the K-epsilon turbulent transport to depend on the growth rate. This is mandatory in the present model to yield increasing turbulent transport towards the edge and enhanced SOL transport governed by the sheath resistivity. Usual predator-prey limit cycles can be achieved whenever the growth rate of the predator is smaller than that of the prey. The growth rates are determined by a simplified 2D turbulence model taking into account magnetic field inhomogeneity and parallel losses, mostly of electrons. These are computed in Fourier space and must be adapted to plasma coarse grained simulations, in particular for edge-SOL-divertor simulations. A growth rate maximisation procedure then determines the wave vector in terms of the plasma parameters. Although the maximisation results are different for drift wave and interchange instabilities, their spectral properties are not discernable and the two instabilities are shown to be difficult to disentangle. Both facets of turbulence are therefore accounted for in the analytical expressions that are obtained for the growth rates, which are to be implemented in K-epsilon simulations of plasma-wall interaction with consistent turbulent transport.