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

Abstract

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.

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

“…We have thus obtained a set of mean-field Equations ( 17)-( 20) and ( 28) which can be solved for the mean-field quantities n, ũ|| , Ti , Te and 𝜙. Not surprisingly, the structure of these equations is very similar to that of the original fluid turbulence Equations ( 1)-( 4) and (16). In general, the same terms are present in the mean-field equations, but evaluated with the mean-field (i.e., averaged) values of the parameters.…”

“…so that the closures proposed in Equations ( 30), ( 32) and ( 33) can be used to close the interchange term. This exact relation between the interchange source and the turbulent ion and electron heat fluxes is a key feature of the model, and is to be seen in contrast to the work of References [15,16,19], where a model for the interchange source is proposed based on the linear growth rate of the interchange instability. Note in particular that the term in itself is always present in the equation of 𝜅, and while we call it 'interchange source', its form is not specific to interchange turbulence.…”

“…To obtain the corresponding set of mean-field equations, we split each quantity above in mean and fluctuating components, and time-average the governing Equations ( 1)-( 4) and (16). For a general quantity x we have either a Reynolds decomposition x = x + x ′ , or a Favre decomposition x = x + x ′′ , where x = lim T→∞ 1 T ∫ T xdt and x = nx∕n .…”

“…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.…”

Validation of edge turbulence codes against the TCV-X21 diverted L-mode reference case

“…This reduces the computational cost, which in turn allows transport models to be run for large machines and over long time-scales. However, one limitation of transport modelling is that the diffusive transport coefficients are not self-consistently determined, and instead must be either heuristically fitted to experimental data, computed via reduced models [8] or determined via a coupled turbulence code [9], [10]. This can provide a reasonable match to the mean plasma profiles of existing devices, but cannot describe the timedependent behaviour of the plasma.…”