Turbulent kinetic energy in 2D isothermal interchange-dominated scrape-off layer E × B drift turbulence: Governing equation and relation to particle transport

Abstract

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-

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

“…In this paper, we adopt recent insights from the development of 𝜅 models based on 2D electrostatic interchange E × B drift turbulence simulations for the scrape-off layer (SOL) [17,24,25] using the TOKAM2D code. [9,27] In Reference [17] it is shown that the anomalous transport due to isothermal electrostatic E × B fluctuations can be described rather accurately through a diffusive model…”

“…We also left out the smaller contributions from the viscosity to the perpendicular currents. † The contribution of the diamagnetic current to the right-hand side of this equation can be elaborated as [17,36]…”

“…Moreover, knowledge and insights obtained with these codes is not fully integrated in the edge codes at present. This paper focuses on further development of simplified yet self-consistent transport models based on the so-called Reynolds-Averaged Navier Stokes (RANS) approach from hydrodynamic turbulence, [14] recently introduced for plasma edge modelling in References [15][16][17]. These models do not resolve the turbulent length and time scales, and can be solved at a strongly reduced computational cost comparable to that of regular transport simulations, while providing a significant step forward compared to ad-hoc transport descriptions.…”

“…These models do not resolve the turbulent length and time scales, and can be solved at a strongly reduced computational cost comparable to that of regular transport simulations, while providing a significant step forward compared to ad-hoc transport descriptions. They have proven their ability to recover turbulent characteristics and global scaling laws in 1D mean-field setting, [17][18][19][20] and features such as the ballooning of anomalous transport in 2D mean-field simulations. [15,21] In this work, we apply the RANS approach to the Braginskii-like plasma equations implemented in SOLPS-ITER.…”

Bayesian maximum a posteriori‐estimation of κ turbulence model parameters using algorithmic differentiation in SOLPS‐ITER

“…We adopt the tangent mode of AD for an accurate gradient computation. To keep the parameter set limited, we do not estimate such coefficients directly, but we employ the recently developed 𝜅-model for interchange turbulence, [21] which allows retrieving spatially dependent transport coefficients using fewer modelling parameters. [22] In Section 2, we describe the parameter estimation framework developed, while in Section 3, we give a brief overview of the 𝜅-model equations.…”