## Section: New Results

### Free-streaming ELM formulae vs. Vlasov simulations

Participants : Sever Hirstoaga, Giovanni Manfredi.

One of the main challenges for future tokamak operation, such as ITER, is constituted by the large heat load on the divertor plates. The divertor surfaces are constantly bombarded with high-energy particles and may see their lifetime considerably reduced. The intensity of the particles and energy fluxes is particularly high during transient events known as edge-localised modes (ELMs). Our purpose here is to propose and investigate a kinetic model for ELMs.

The free-streaming model [69] is a simple analytical model for ELM transport in the scrape-off layer (SOL) of a tokamak. It is a force-free Vlasov equation with a source term for the ions distribution function (the Coulomb forces are ignored). Even though this model reproduces with good accuracy some of the main features of an ELM signal, it has two main drawbacks: (i) the self-consistent electric potential is not accounted for and (ii) only solutions for the ion distribution are considered.

In this contribution [24] we propose a set of modified free-streaming equations in order to overcome the above drawbacks. More precisely, some hypotheses on the Maxwellian initial condition lead to a model that includes the self-consistent electric potential. Assuming quasinetrality and using energy conservation we could derive analytical formulae for the electron quantities. This augmented free-streaming model was benchmarked to the Vlasov-Poisson simulations reported in [78] . The match is encouragingly good, thus justifying the applicability of the free-streaming approach.

Finally, from a computational point of view, transport in the SOL was studied by means of three different approaches – fluid, Vlasov and particle-in-cell (PIC). In spite of kinetic effects due to fast electrons which are not captured in the fluid code, the overall agreement between the codes was found to be quite satisfactory [22] .