A new mean‐field plasma edge transport model based on turbulent kinetic energy and enstrophy

Coosemans, Reinart; Dekeyser, Wouter; Baelmans, Martine

doi:10.1002/ctpp.201900156

Cited by 9 publications

(39 citation statements)

References 18 publications

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“…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.…”

Section: Interchange Source Of 𝜿mentioning

confidence: 72%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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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

Dekeyser

Coosemans

Carli

et al. 2022

Contributions to Plasma Physics

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The ad‐hoc description of anomalous transport through diffusive relations with manually tuned coefficients is currently one of the main limitations in mean‐field plasma edge codes, seriously restricting their interpretive and predictive capabilities. In this paper, we attempt to improve that description by relating the anomalous transport coefficients to the turbulent kinetic energy κ as a measure for the local intensity of the turbulence. Using RANS techniques from hydrodynamic turbulence and insights from their recent successful application to 2D electrostatic E×B drift turbulence modelling for the scrape‐off layer, we propose a transport equation for κ and discuss its coupling with the mean‐field transport equations. The main features of the model include (a) an analytically exact interchange source of κ which introduces the ballooning character of the transport; (b) fast parallel transport of κ through the connection with parallel current fluctuations; and (c) consistent transport reduction due to the impact of mean E×B flow shear. The resulting model has been implemented in the new extended grids version of SOLPS‐ITER, enabling for the first time mean‐field simulations self‐consistently combining classical parallel transport with mean‐field drifts and anomalous transport with the code. A first assessment of the model has been made for a representative C‐Mod case study, highlighting the promising features of the model. Further analysis is needed to investigate in detail the impact of the different new terms in the model across operational regimes, and determine the new closures constants based on larger sets of turbulence simulations and experimental data.

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Section: Interchange Source Of 𝜿mentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

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

Dekeyser

Coosemans

Carli

et al. 2022

Contributions to Plasma Physics

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“…The particle transport model might also still be improved; taking into account the underlying convective nature of transport might be especially interesting. The viscous dissipation term in the turbulent kinetic energy equation scales with the product of the viscosity and the enstrophy, while the scaling for the turbulent particle diffusion coefficient could also be improved by including the enstrophy 36 .…”

Section: Discussionmentioning

confidence: 99%

“…This is explored in Ref. 36, where an additional equation for the turbulent enstrophy is derived to provide a measure for viscous dissipation of k ⊥ . It is interesting to see that a purely linear sink follows from the regression analysis.…”

Section: Sinks Of K ⊥ and Turbulence Saturationmentioning

confidence: 99%

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

2021

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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-

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“…We proposes here to follow a similar procedure, thus introducing evolution equations for κ and ε and from these deriving the dependence on space and time of the plasma transport coefficients mentioned above. A similar approach was recently proposed by [33], but in a simpler configuration for isothermal plasma and 2D closed field lines domain. In this work, the perpendicular transport coefficients are determined from the turbulent kinetic energy κ and the enstrophy which is an invariant in 2D turbulence.…”

Section: Introductionmentioning

confidence: 99%

Self-consistent cross-field transport model for core and edge plasma transport

Baschetti

Bufferand²,

Ciraolo³

et al. 2021

Nucl. Fusion

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The 2D mean-field plasma edge transport description of plasma wall interaction is completed by a κ-ε model as in Reynolds Average Navier Stokes simulations for neutral fluids. The local evolution of the turbulent kinetic energy κ and its dissipation rate ε are revisited and slightly modified. It is shown that the κ-ε extends the quasilinear approach by self-consistently determining κ and the relevant time κ/ε leading to the diffusion coefficient κ 2 /ε. The κ-ε evolution is also shown to be equivalent to both coupled Ginzburg-Landau amplitude equations and predator-prey systems where κ is the prey and ε the predator. The dissipation process ε we enforce describes the small scale dissipation of Kolmogorov cascades. It depends on a free parameter akin to a velocity V . The chosen closure relates V to the the parallel connection time and the normalized Scrape-Off layer width qρ * , q is the safety factor and ρ * the ratio of the characteristic Larmor radius and plasma minor radius. A 1D model with κ-ε self-organized transport is used for comparison to empirical scaling laws of SOL width and energy confinement time in L-mode plasmas. Shortfalls of the scaling laws are analyzed. Possible changes of the closure for V are discussed. The 1D model is also used to test the transport response to a dependence of V to large scale velocity shear. Spontaneous confinement improvement when increasing the heating power 1 is observed with the development of an interface barrier at the separatrix. Plasma-wall interaction simulations for TCV and WEST are analyzed. A single scalar free parameter tunes the cross field transport. Experimental midplane and divertor profiles are compared to the simulations. Remarkable agreement is observed. The SOL width determined by the simulation for WEST is close to the experimental value with less than 20 % difference, while the scaling law for L-mode is off my more than a factor 3. The turbulent transport described by the κ-ε is not homogeneous, but ballooned as experimentally observed together with cross-field transport in the divertor SOL on the low field side, and nearly none in the private flux region.

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A new mean‐field plasma edge transport model based on turbulent kinetic energy and enstrophy

Abstract: 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.

Cited by 9 publications

References 18 publications

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

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

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

Self-consistent cross-field transport model for core and edge plasma transport

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