Benchmarking 2D against 3D FDTD codes for the assessment of the measurement performance of a low field side plasma position reflectometer applicable to IDTT

O-mode reflectometry, a technique to diagnose fusion plasmas, is foreseen as a source of real-time (RT) plasma position and shape measurements for control purposes in the coming generation of machines such as DEMO. It is, thus, of paramount importance to predict the behavior and capabilities of these new reflectometry systems using synthetic diagnostics. Finite-difference time-domain (FDTD) time-dependent codes allow for a comprehensive description of reflectometry but are computationally demanding, especially when it comes to three-dimensional (3D) simulations, which requires access to High Performance Computing (HPC) facilities, making the use of two-dimensional (2D) codes much more common. It is important to understand the compromises made when using a 2D model in order to decide if it is applicable or if a 3D approach is required. This work attempts to answer this question by comparing simulations of a potential plasma position reflectometer (PPR) at the Low Field-Side (LFS) on the Italian Divertor Tokamak Test facility (IDTT) carried out using two full-wave FDTD codes, REFMULF (2D) and REFMUL3 (3D). In particular, the simulations consider one of IDTT’s foreseen plasma scenarios, namely, a Single Null (SN) configuration, at the Start Of Flat-top (SOF) of the plasma current.

Cross-code comparison of the edge codes SOLPS-ITER, SOLEDGE2D and UEDGE in modelling a low-power scenario in the DTT

As reactor-level nuclear fusion experiments are approaching, a solution to the power exhaust issue in future fusion reactors is still missing. The maximum steady-state heat load that can be exhausted by the present technology is around 10 MW/m2. Different promising strategies aiming at successfully managing the power exhaust in reactor-relevant conditions such that the limit is not exceeded are under investigation, and will be tested in the Divertor Tokamak Test (DTT) experiment. Meanwhile, the design of tokamaks beyond the DTT, e.g. EU-DEMO/ARC, is progressing at a high pace. A strategy to work around the present lack of reactor-relevant data consists of exploiting modelling to reduce the uncertainty in the extrapolation in the design phase. Different simulation tools, with their own capabilities and limitations, can be employed for this purpose. In this work, we compare SOLPS-ITER, SOLEDGE2D and UEDGE, three state-of-the-art edge codes heavily used in power exhaust studies, in modelling the same DTT low-power, pure-deuterium, narrow heat-flux-width scenario. This simplified, although still reactor-relevant, testbed eases the cross-comparison and the interpretation of the code predictions, to identify areas where results differ and develop understanding of the underlying causes. Under the conditions investigated, the codes show encouraging agreement in terms of key parameters at both targets, including peak parallel heat flux (1-45%), ion temperature (2-19%), and inner target plasma density (1-23%) when run with similar input. However, strong disagreement is observed for the remaining quantities, from 30% at outer mid-plane up to a factor 4-5 at the targets. The results primarily reflect limitations of the codes: the SOLPS-ITER plasma mesh not reaching the first wall, SOLEDGE2D not including ion-neutral temperature equilibration, and UEDGE enforcing a common ion-neutral temperature. Potential improvements that could help enhance the accuracy of the code models for future applications are also discussed.

Ion–electron energy transfer in kinetic and fluid modelling of the tokamak scrape-off layer

Using the 1D kinetic electron code SOL-KiT, simulations of the divertor tokamak scrape-off layer were carried out to explore the presence of kinetic effects in energy transfer between the ions and electrons. During steady-state conditions, it was found that the ion–electron energy transfer is well described by a fluid model, with only minimal differences seen when electrons are treated kinetically. During transient regimes (featuring a burst of energy into the scrape-off layer), we see evidence of enhanced energy exchange when calculated kinetically as compared to a fluid model. The kinetic correction represents an additional 8–55% ion–electron energy transfer across the domain, depending on the pre-transient plasma collisionality. Compared to the total energy going into the plasma during the transient, the correction is less than 1%, so its impact on plasma profiles may be small. The effect is seen to increase in strength along the domain, peaking in front of the divertor target. The overall discrepancy (integrated along the domain) increases during the transient energy burst and disappears on a similar timescale. However, at the target the effect peaks later and takes several multiples of the transient duration to relax. This effect may be only partially explained by an additional population of cold electrons arising from neutral ionization.

Diffusive time evolution of the Grad–Shafranov equation for a toroidal plasma

We describe the evolution of a plasma equilibrium having a toroidal topology in the presence of constant electric resistivity. After outlining the main analytical properties of the solution, we illustrate its physical implications by reproducing the essential features of a scenario for the upcoming Italian experiment Divertor Tokamak Test Facility, with a good degree of accuracy. Although we find the resistive diffusion time scale to be of the order of $10^4$ s, we observe a macroscopic change in the plasma volume on a time scale of $10^2$ s, comparable to the foreseen duration of the plasma discharge by design. In the final part of the work, we compare our self-consistent solution to the more common Solov'ev one, and to a family of nonlinear configurations.