This paper studies the turbulent kinetic energy (k ⊥ ) in 2D isothermal electrostatic interchange-dominated ExB drift turbulence in the scrape-off layer, and its relation to particle transport. An evolution equation for the former is analytically derived from the underlying turbulence equations. Evaluating this equation shows that the dominant source for the turbulent kinetic energy is due to interchange drive, while the parallel current loss to the sheath constitutes the main sink. Perpendicular transport of the turbulent kinetic energy seems to play a minor role in the balance equation. Reynolds stress energy transfer also seems to be negligible, presumably because no significant shear flow develops under the given assumptions of isothermal sheath-limited conditions in the open field line region. The interchange source of the turbulence is analytically related to the average turbulent ExB energy flux, while a regression analysis of TOKAM2D data suggests a model that is linear in the turbulent kinetic energy for the sheath loss. A similar regression analysis yields a diffusive model for the average radial particle flux, in which the anomalous diffusion coefficient scales with the square root of the turbulent kinetic energy. Combining these three components, a closed set of equations for the mean-field particle transport is obtained, in which the source of the turbulence depends on mean flow gradients and k ⊥ through the particle flux, while the turbulence is saturated by parallel losses to the sheath. Implementation of this new model in a 1D mean-field code shows good agreement with the original TOKAM2D data over a range of model parameters.Recently, Bufferand et al. 19 proposed a mean-field model for the turbulent particle transport in the plasma edge that draws inspiration from these RANS models. More specifically, the model bears similarity to k(−ε) models, where equations for the turbulent kinetic energy k (and dissipation ε) are solved to provide time-and length scales to model the closure terms 18 . Bufferand et al. proposed a diffusive model for the radial particle transport where the anomalous trans-

This is the peer reviewed version of the following article: R. Coosemans, W. Dekeyser, M. Baelmans. A new mean-field plasma edge transport model based on turbulent kinetic energy and enstrophy.

While turbulent transport is known to dominate the radial particle and energy transport in the plasma edge, a self-consistent description of turbulent transport in mean-field transport codes remains lacking. Mean-field closure models based on the turbulent kinetic energy (k ⊥) and turbulent enstrophy (ζ⊥) have recently been proposed to self-consistently model this transport. This contribution analyses the diffusive particle transport relations of these models by means of the Bayesian framework for parameter estimation and model comparison. The reference data includes a set of isothermal simulations that not only include the scrape-off layer (SOL) but also the outer core region (in which a drift wave-like model is activated) and a set of anisothermal SOL simulations, both obtained with the TOKAM2D turbulence code. This analysis shows that the k ⊥(–ζ⊥) model does not appropriately capture the diffusion coefficients for these new data sets, presumably due to the strong flows in the diamagnetic direction that appear in these new cases. While flow shear is expected to quench the turbulence and the turbulent transport, its effect was not explicitly taken into account in the earlier k ⊥(–ζ⊥) transport models. As flow shear provides a new mechanism for the decorrelation of the turbulence, we propose to introduce an additional time scale in the diffusive transport relation as D ∼ k ⊥ / ( ζ ⊥ + Ω S ) . Inspiration is drawn from shear decorrelation times reported in literature to propose several new candidate models, which are then analysed in a Bayesian setting. This allowed identifying irrelevant terms for certain models and to rank all models according to the Bayesian evidence. While the new models accounting for shear do improve the match to the data, significant errors still remain. Also, no single model could be identified that performs best for all data sets.

In this paper, a self‐consistent model for the average radial turbulent transport of heat and particles in 2D anisothermal interchange‐dominated electrostatic ExB drift turbulence in sheath‐limited scrape‐off layers is presented. Diffusion models are used for the turbulent particle and heat fluxes, in which the transport coefficients scale with the square root of the turbulent kinetic energy (k⊥). The interchange drive proves to be the main source of turbulent kinetic energy, while the sheath term provides the main sink. These observations are qualitatively the same as for the isothermal case studied earlier. An analytical relation for the interchange term is derived, showing that the turbulent ExB thermal energy flux is the direct driver for k⊥ through the interchange source. A series decomposition of the sheath term in the k⊥ equation shows it includes a sink contribution that was also present in the isothermal case, but also a new source due to the sheath‐driven conducting‐wall (SCW) instability caused by electron temperature fluctuations. Using a simple regression model to close the total sheath term, a closed model for the turbulent transport is obtained. The interchange drive due to the ExB energy flux leads to a self‐saturation mechanism in the model, where the gradients and turbulence intensity increase until a sufficient transport level is reached to carry the power and particles across the field lines to find a balance with the sheath sink. An implementation of this model in a 1D mean‐field code approximates the profiles of the turbulence simulations with remarkable accuracy in part of the parameter space, while the error increases in parameter regimes where the relative importance of the SCW term is varied.

Mean-field plasma edge transport codes such as SOLPS-ITER heavily rely on adhoc radial diffusion coefficients to approximately model anomalous transport. Such coefficients are experimentally determined and vary between different machines, and also depend on the operational regime and plasma location within the same device. Therefore, to match experimental data the modeler is required to manually tune several free parameters in expensive simulations, and the code's predictive capabilities are significantly downgraded. As a solution, a new model has been developed for SOLPS-ITER, solving an additional transport equation for the turbulent kinetic energy , derived by consistently time-averaging the Braginskii equations, and including a diffusive closure for the anomalous particle flux. This closure model relates the anomalous diffusion coefficient to the local value. The resulting equation structure and its closure are inspired by TOKAM2D isothermal interchange turbulence simulation results. Within this model, fewer and hopefully more universal free parameters are retained, thus improving the code's predictive capabilities. The new model has been tested on a COMPASS case for which upstream plasma profiles were available. Experimental data and a reference solution, obtained by matching the profiles through manual tuning of radial diffusivities, have been used to estimate the parameters of our new transport model. A ballooned particle diffusivity profile is retrieved by the new radial transport model, thanks to the proposed interchange drive. The obtained upstream profiles qualitatively agree with the experiment and prove the new model is a promising first attempt to be further refined.