# Edge Localised Modes (ELMs) in Tokamaks

The operational limits with respect to the maximum pressure and current in tokamak fusion plasmas are determined by large-scale instabilities of the plasma. These instabilities are well described by the magneto-hydro-dynamic (MHD) model: the instabilities are commonly called MHD instabilities. Even away from the operational limits in the standard operating scenarios, as in the case of the plasma scenarios foreseen in ITER, MHD instabilities are commonly observed. Examples include the so-called sawtooth instability, which causes a periodic relaxation of the pressure in the very center of the plasma. At medium to high plasma pressures, magnetic island-like structures can form in the bulk of the plasma leading to a local loss of the energy confinement properties of the magnetic field.

One MHD instability, the so-called Edge Localized Mode (ELM), is of particular concern for the operation of ITER. As its name implies, this instability is located at the edge of the plasma. Its driving force comes from a locally very large pressure gradient which forms due to a small region of several centimeters of improved energy confinement (the H-mode operating regime). The ELM instability limits the maximum pressure gradient at the edge by periodic (typically 1-100Hz) expulsions of plasma energy in very short bursts (~200 μs). Extrapolation to ITER of the energy lost during an ELM suggests that these energy losses, (10-30MJ on a contact surface of 3 m2 in 300 μs) could be causing important damage to the tokamak walls in ITER. However, this extrapolation is based on experimental measurements combined with simple model assumptions. At present no theory exists on which to base such an extrapolation. The underlying MHD instabilities have been identified but at present no numerical MHD simulations exist of a full cycle of the ELM instability. A recent overview of the theory and modeling of ELMs can be found in [Huysmans]. The details of the mechanisms through which the energy is lost and what determines the amplitude of the energy losses are not known in enough detail to make predictions nor to compare with existing experiments.

The MHD simulation of a full ELM cycle is one of the important challenges to the modeling of fusion plasmas. ELM simulations are required not only to improve our understanding but also to be able to confidently predict the ELM energy losses in ITER. In addition, ELM simulations are essential to device and verify proposed methods for the control of the ELM losses by external means (such as external magnetic field perturbations [Bécoulet]). At present no non-linear MHD code exists that can simulate the complete ELM instability.

The objective of this project is the high resolution MHD simulation of a complete cycle of the ELM instability, from its onset, the highly non-linear phase and its decay. The nonlinear MHD code JOREK, under development at CEA/DRFC, will be used as the simulation code. Very recently, first simulations of the ELM have been obtained with the JOREK code (but at reduced toroidal resolution). The code uses a fully implicit time evolution scheme leading to large sparse matrices which are solved using the PastiX library developed by INRIA ScAlApplix team. The same ScAlApplix team also develops a compressible fluid solver, FluidBox that has been closely coupled with the PaStiX library. FluidBox is a 2D and 3D solver which is able to run on a wide variety of flow configurations, in particular when large gradient develops with the flow or with complex EOS. It included a fully implicit version similar to the JOREK numerical scheme. Further developments are needed to run MHD configurations.

### References

G.T.A. Huysmans, ELMs: MHD instabilities at the transport barrier, Plasma Phys. Control. Fusion 47 (2005) B165-B178.G.T.A. Huysmans and O. Czarny, MHD stability in X-point geometry: simulation of ELMs, Nucl. Fusion 47 No 7 (July 2007) 659-666