**Topic/Type**:
1. Plasma Simulation, Oral

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Non-linear MHD simulations of Edge Localised Modes in Tokamaks

**
G. Huysmans
**

*
IRFM, CEA, Cadarache, 13108, France*

The edge of a tokamak plasma in the so-called high confinement regime (H-mode) is characterized by a large pressure gradient which forms due to the local stabilization of turbulent transport. Above a critical value, the pressure gradient drives an MHD instability, an Edge Localised Mode or ELM. The ELMs occur on a time scale of a few hundred micro-seconds. During this time a significant part of the plasma thermal energy is lost towards the plasma facing components leading to very large heat fluxes. Extrapolations to ITER indicate that the energy losses due to ELMs may become unacceptably large and lead to an increased erosion of the first wall. In ITER, the amplitude of the ELMs will have to be controlled by external means.

Numerical simulations of the ELM phenomena can contribute to improve the physics understanding of the ELM energy losses, the saturation mechanism etc. This includes the methods to control/stabilize ELMs, such as the injection of pellets or the application of resonant magnetic field perturbation.

A non-linear MHD code, named JOREK, has been developed to simulate the non-linear evolution of the ELMs. The codes uses cubic Hermite finite elements reformulated as Bezier patches in order to allow local refinement of the elements. The finite elements are aligned to the magnetic field (poloidal flux) to improve the numerical representation of the anisotropy in, for example, the heat conduction. The time evolution scheme is completely implicit. The resulting large sparse matrices are solved using an iterative method with the preconditioning matrices being solved using the parallel sparse matrix solver PastiX.

Numerical simulations of an unstable plasma shows the formation of filamentary structures in the density. The perturbations in the temperature profile are predominantly due to the perturbation to the magnetic field which becomes ergodic in the plasma edge. The simulation results agree well qualitatively with experimentally measured perturbations to the density and temperature. Also the patterns in the heat flux at the divertor are in reasonable agreement. Non-linear MHD simulations of pellets injection, modeled as a large local density perturbation, indicate that the resulting large pressure perturbation may lead to an ELM like phenomena.