Numerical simulation of Alfven waves in non uniform plasmas

Abstract

Nuclear fusion can provide a sustainable and nearly unlimited source of energy, but for it to become a viable alternative, the fuel must reach very high temperatures, which inevitably leads to the creation of a plasma medium inside a fusion reactor. Thus, a thorough understanding of this state of matter is essential for this goal. One of the best known models of the plasma is the magneto-hydrodinamic model, or MHD, which describes it as particular fluid, subjected to equations analogous to Naver-Stokes’ equations, where the Maxwell equations also play an important role in defining the behaviour of the plasma. Using this model, it is possible to predict certain instabilities that hinder the containment of the plasma in a nuclear fusion reactor. One of the most relevant instabilities of this kind is the Shear Alfven Wave, or SAW, the object of study of this thesis. ´ For this project a simple plasma system is assumed, from which a compact equation for the Shear Alfven Wave is deduced. However, the equation features a singular point, which is treated ´ performing a Fourier Transform and solving it through numerical methods, returning a profile for the SAW in real space.