Section: New Results

Eulerian simulations of parallel transport in the SOL

Participants : S. Hirstoaga, G. Manfredi.

During the year 2013, we have progressed in the implementation of an asymptotic preserving (AP) Eulerian Vlasov code (VESPA: Vlasov Eulerian Simulator of PArallel transport ) for the study of parallel transport in the scrape-off layer of tokamaks. An AP Vlasov-Poisson code had already been partially developed for the quasi-neutral regime. In this case the small parameter is the Debye length $\lambda$ (normalized to the parallel connection length). The Poisson equation becomes singular when $\lambda \to 0$: the AP solution consists in reformulating Poisson's equation in a way that is no longer singular in this limit. In theory, any value of $\lambda$ can be used, including $\lambda =0$, without numerical instability and without any constraint on the grid spacing and time-step. In practice, we have observed a CFL stability condition (although not very restrictive) and a limit on the smallness of $\lambda$. During the past year, we have performed systematic tests on the code, which is now capable of attaining very small values of $\lambda$, down to ${10}^{-4}$ or even lower. Meaningful results can be obtained with just 1-2 hours of computation on a standard desktop computer (see for example [29] ).

The next upgrade of the VESPA code concerns the modelling of collisions, which have been implemented through a relaxation (BGK) term that also retains the possibility to include ionization and recombination in the model. The BGK term has been tested and validated against analytical results. In particular, the AP scheme had to be modified in order to correctly treat the BGK term. These upgrades are now fully integrated into the VESPA code.

Using the VESPA code, we have studied the dynamical response of a stationary sheath-presheath system to an external perturbation, which takes the form of a small density disturbance in the central region of the plasma, far from the sheaths. The numerical results suggest that, for most regimes of physical interest, the perturbation is damped away before it reaches the wall and does not have a significant impact on the structure of the sheath. This scenario has been studied for different temperatures and density profiles of the disturbance.

We have started to look at the impact of secondary electrons (SE) on the structure and the formation of the sheath. SEs were neglected in previous versions of the code but can play a significant role on the wall potential. In the VESPA code, they are now modelled as a Maxwellian electron source located near the wall. First results indicate that a large yield rate of SEs reduces the potential drop between the plasma bulk and the wall.