# Victor DUBOIS

**PhD Student**

**Resarch activities at CPHT:** Theory of Plasmas

Address |
CPHT, Ecole Polytechnique, 91128 Palaiseau cedex, France |

Phone number |
+33 (0) 11 69 33 42 94 |

Email |
firstname.lastname@polytechnique.edu |

Office |
Building 6, Office 06.1021 |

**Thesis:** Fluid and Kinetic macroscopic instabilities in a tokamak plasma

Advisors: Hinrich Lutjens

**Research interests: ** plasma physics, MHD, gyrokinetic theory, numerical methods, simulations and modelling

**Abstract:**

The dynamics governing the macroscopic instabilities in a tokamak plasma depend on a wide range of space-time scales. A detailed description of the underlying physics requires an appropriate physical model. It must be more advanced than an extended fluid model, the latter being restricted to the study of MHD or bi/multi-fluid effects. Its generalization towards a totally kinetic description makes it possible to study new phenomena, such as wave-particle resonances or finite Larmor radius effects. These effects give access to new families of instabilities, prohibited in the more restricted model, or in a model with a simplified geometry.

The shape of the small section of the torus has indeed a significant influence on the resonant modes in the system. The presence of a singular magnetic surface at equilibrium, the consideration of resistive effects inside the tokamak wall or the presence of external poloidal coils that define the magnetic field at equilibrium directly influence the families of resonant modes that are allowed in the system.

The development of ever more complex models is also motivated by experimental observations, which demonstrate that a simple fluid model such as MHD does not make it possible to accurately describe the physics involved, and that it is necessary to tend towards a kinetic model. This evolution of the physical model is conditioned by the numerical method used and the HPC resources available. The purpose of it is to evolve in a state-of-the-art model from a physical and numerical point of view.

This thesis work is based on the 2-fluid/kinetic hybrid code XTOR-K developed at CPhT. In XTOR-K, the fluid dynamics of the electrons and of a given fraction of the ions of the thermalized background plasma are coupled in a self-consistent way with the dynamics of selected populations of kinetic ions, which makes it possible to address all nonlinearities of the problem. The kinetic ions are handled by a PIC 6D method, integrating exactly the trajectories along the cyclotron gyrations. Unfortunately, the latter method is very costly in computational resources. Thus, one of the goals of this thesis is to try and implement a gyrokinetic solver that would compete with the current kinetic one. Since a gyrokinetic model neglects any finite Larmor radius effect, such a solver would make it possible to significantly reduce the computational time needed for each simulation.

The current version of our XTOR-K code assumes that the boundary of the simulation domain is a perfectly conducting toroidal shell. However, a large number of instabilities are located close to this shell, and their dynamics is significantly impacted by this proximity. In order to free ourselves from this constraint, we have to continue our development effort allowing us to adopt more realistic boundary conditions, with ultimately a resistive shell and a set of poloidal magnetic coils allowing the control in time of the shape of the small plasma section as well as its vertical stability.