Simulation of bi-dimensional plasma turbulence and investigation the inverse cascade process -

Abstract

Magnetized plasma turbulence is one of the main phenomena that leads to plasma leaving the confined zone in controlled fusion reactors. In order to understand such a phe-nomenon, we start this thesis by describing some simplified models of turbulence such as the Hasegawa-Mima, the Terry-Horton and the Hasegawa-Wakatani. The model we investigate in details is the Hasegawa-Mima with a diffusive term (HMD). In parallel, we aim at continuing the effort to build in-house a numerical code to simulate the model equation we have. The code, written by F. Hariri to solve the HM equation, is extended by M. Hammoud to solve the same equation with a diffusive term. Various runs are made in this chapter, with the goal of (1) investigating the characteristic scale, say k₀, that the system of the HM model tends to, and (2) knowing whether this tendency is caused by inverse cascade or a non-linear resonance mechanism. It is shown that the HM system tends to form a sine wave structure at k = k₀ in the direction perpendicular to that of the density gradient. It is found that the peak at k₀ does form independently from the posi-tion of filtering of the initial conditions. On the other hand it is found that the higher the diffusion is, the faster the sine wave is reached. In other words, it appears as if the small scales are impeding the formation of the sine wave structure. We have thus found that the formation of the sine wave structure at k = k₀ is NOT caused by an inverse cascade process, but rather by a nonlinear oscillatory behavior occurring at k = k₀.