SFU MOCAD Seminar: Olivier Lafitte

We consider a magnetized plasma (in the case of a tokamak) where the density of ions $ n_0$ as well as the imposed vertical magnetic field $B_0$ dépend on the horizontal variable $x$. The linearized system of Euler-Maxwell équations (system of 10 PDEs of order 1) around the solution $(E,B, v,n)_0=(0, B_0(x),0, n_0(x))$ is characterized by the two fréquencies denoted by $\omega_p(x)$ and $\omega_c(x)$ (respectively plasma and cyclotron frequencies). Classically, the cyclotron frequency is associated with Landau damping, but this frequency does not appear to be a resonance in the cold plasma model (ax we prove it) but another frequence of interest, called the hybrid frequency $\omega_h(x)=\sqrt{\omega_p^2(x)+\omega_c^2(x)}$ is a resonance for the system: at any point $x_h$ where $\omega$, the imposed oscillation frequency is equal to $\omega_h(x)$ we have energy transfer (from the electrons to the electric field). We prove it using Bessel functions for the study of the corresponding linear system of ODEs near $x_h$. Joint work with Bruno Despres (Sorbonne Université) and Lise-Marie Imbert-Gerard (University of Arizona).