## Section: New Results

### The two temperature MHD model

Participants : HervĂ© Guillard, Afeintou Sangam, Elise Estibals.

The dynamics of plasma charged particles can be described by a two-fluid MHD model. This description considers a plasma as a mixture of ions fluid and electrons flow that are coupled by exchanged terms such as momentum transfer terms, ion and electron heating terms due to collisions, supplemented by the Maxwell's equations. This system is quite intricate so that it is usually reduced to more tractable models. We first derive the two-temperature model, the ideal and resistive MHD equations from the two-fluid MHD system, and show that they correspond to asymptotic regimes for weakly and strongly magnetized plasmas. We then propose a finite volume approximation to compute the solutions of these models in unstructured tessellations used to appropriate mesh the toroidal geometry of the tokamak, where flows the plasma. The formulation of the magnetic field as Euler potential ensures the divergence free constraint in cheap manner, while a relaxation scheme for the two temperature allows an accurate computation of the electron and ion temperatures.