FENICIA: a generic plasma simulation code using a Flux-indepENdent fIeld-aligned CoordInate Approach

Farah Hariri carried her research work in the area of Computational Plasma Physics at the French Alternative Energies and Atomic Energy Commission (CEA, France) as a member of the Institute for Magnetic Fusion Research (IRFM) within the Physical sciences Division (DSM). She successfully defended her PhD thesis in November 2013 in front of an international panel of senior experts. Her thesis is entitled: “*FENICIA: **a generic plasma simulation code using a Flux-indepENdent fIeld-aligned CoordInate Approach*”.

“The presence of a magnetic field in plasmas is known to introduce a strong anisotropy in the system. This is commonly met in fusion and most astrophysical plasmas. The anisotropy of the perturbations can become extreme, and this poses great challenges to the numerical resolution methods. This is in particular the case for the turbulence associated with anomalous transport in magnetically confined plasmas of interest for nuclear fusion research. It is worth reminding that countries representing more than half the world’s population have teamed up to build the ITER project (International Thermonuclear Experimental Reactor), currently under construction in Cadarache, south of France. ITER is the largest international scientific project on Earth, aiming at demonstrating the feasibility of nuclear fusion as a new, abundant, and safe source of energy. It is based on the '*tokamak*' concept of magnetic confinement, in which the plasma is contained in a doughnut-shaped vacuum vessel. The fuel (a mixture of deuterium and tritium, two isotopes of hydrogen) is heated to temperatures in excess of 150 million degrees Celsius, forming a hot plasma. The ITER tokamak is a one-of-a-kind device and one of the most complicated machines ever engineered with a very complex geometry. It will be a huge machine, thirty meters in diameter and nearly as many in height. Numerical studies of plasma confinement is playing a profoundly important role in designing these machines. It is an essential tool in analyzing the equilibrium, stability, and transport of all current major fusion experiments. Nowadays, the simulation of turbulence in a full device like ITER that takes into account its complex geometry, is very challenging since one must simultaneously resolve the machine size and the scales of turbulence. Therefore, developing efficient computer codes that would take into account the strong plasma anisotropy with minimal loss of computational resources is crucial.” says Dr. Hariri.

3D nonlinear numerical simulation of plasma turbulence performed by the FENICIA code developed by Farah Hariri. “This simulation is a demonstration of the robustness of the FCI approach and its validity. It shows elongated structures along the magnetic field lines. Few tens of toroidal points are used to describe the target physics problem, regardless of the toroidal mode number, provided that adequate resolution is available in the poloidal plane,” says Dr. Hariri

In her work published in the Computer Physics Communications journal (F. Hariri, M. Ottaviani, *A flux-coordinate independent field-aligned approach to plasma turbulence simulations*, Computer Physics Communications, 2013, ISSN 0010-4655, http://dx.doi.org/10.1016/j.cpc.2013.06.005.), Farah Hariri developed and validated a new set of coordinates for any strongly anisotropic system. In this article, the validity of the approach is demonstrated on the geometry of a nuclear fusion device. Dr. Hariri refers to it as the FCI system of coordinates, standing for *F**lux Coordinate Independent*. The particularity of this system, as shown in this article, is that it is constructed in such a way to exploit the anisotropic nature of the plasma while at the same time avoiding the pitfalls of previously derived methods. The computer code that Farah Hariri developed from scratch, and called FENICIA, embeds this field-aligned coordinate system and tackles for the first time a crucial geometry for simulating the plasma edge of a nuclear fusion device like ITER where an axisymmetric magnetic separatrix is present.

The flexible nature of FENICIA allowed for the first time to demonstrate the application of the field-aligned coordinate system FCI, to an X-point magnetic geometry.

“It is estimated that the turbulence anisotropy in ITER will be of the order of 10^{3}. The FCI method that I propose takes advantage of this anisotropy by exploiting the elongated nature of turbulence. Mathematically speaking, the FCI approach relies on local transformations that align a suitable coordinate to the magnetic field to allow efficient computation of the parallel derivative. The idea is to make use of the magnetic field background structure to discretize the parallel operators while allowing for arbitrary choices of discretization across the magnetic field. In particular, it allows for the use of non-magnetic coordinates in the perpendicular plane, which can avoid the singularity of previously developed field-aligned coordinate systems. Through systematic testing of the plasma turbulence model, I have demonstrated that grid coarsening can be taken very far in both the cylindrical and the X-point magnetic configuration cases. I showed a gain of a factor of 100 in the number of meshgrid points needed for typical turbulence simulations. When applied to turbulence simulations in ITER, this could lead to again of one or two orders of magnitude in computational efficiency. The FCI approach also permits flexibility in implementing different complex geometries. FENICIA is the first numerical code that tackles X-point magnetic geometries using field-aligned coordinates.” says Dr. Hariri.

Last update : 09/06 2018 (364)