Bayesian analysis of turbulent transport coefficients in 2D interchange dominated ExB turbulence involving flow shear

Abstract

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.

A self‐consistent κ‐model for anomalous transport due to electrostatic, interchange‐dominated E × B drift turbulence in the scrape‐off layer and implementation in SOLPS‐ITER

“…The last term on the right-hand side of Equation ( 41), −p ′ V ′ E ⋅ ∇ ln B 2 , is the source of 𝜅 due to the interchange mechanism. This was found to be the dominant source of 𝜅 in recent studies of interchange E × B drift turbulence for the SOL using TOKAM2D simulations, [17,20,24,25] which form the basis for the present work. Interestingly, no additional closure is needed † The full form of the polarization current and additional currents could easily be included, but we will neglect them in a later stage, so we chose to leave them out from the start for clarity of the derivation.…”

“…The model further assumes that 𝜌 L is the relevant length scale, implying eventually the time scale T ∼ 𝜌 L ∕ √ 𝜅∕m. The possibility for a diffusive closure is further confirmed in the context of isothermal drift-wave turbulence and anisothermal 2D electrostatic interchange simulations in Reference [24], but the proportionality constant may differ depending on the regime. Furthermore, in Reference [25] it is additionally shown that the electron and ion heat fluxes due to E × B fluctuations can be approximated with a diffusive relation, where the diffusivities follow the same characteristic scaling as D E×B up to a constant of order unity:…”

“…In regions without flow shear, this expression falls back to the "standard" model D E×B ∼ √ 𝜅, while in the case of strong flow shear it becomes D E×B ∼ 𝜅∕ |S mean | as suggested in Reference [24]. C D is a model constant that relates the strength of 𝜅 to the strength of the transport in the absence of flow shear.…”

“…where, as in the particle flux, there is an additional current due to the Reynolds stress 𝚷 RS , see Equations ( 23) and (24).…”

“…with 𝜈 E×B ∼ D E×B . Finally, Reference [24] analysed modifications of the relation between the transport coefficients and 𝜅 to account for the effect of flow shear. Based on the observation that E × B flow shear tends to tear turbulent eddies apart and reduce transport, [28][29][30] a Bayesian inference on various possible tranport models was performed, revealing that one of the best performing models out the ones analysed has a form…”