Plasma Physics

This application is devoted to the numerical simulation of problems in Plasma Physics and particle beams propagation. The leading candidate for magnetic confinement of a fusion plasma is the tokamak. A tokamak is a toroidal (doughnut shape) magnetic bottle that contains the fusion plasma. The magnetic fields that confine the plasma are provided primarily by cylinderical magnetics (toroidal magnetic field) and an internal plasma current (poloidal magnetic field). Combining the toroidal and poloidal magnetic fields creates a helical field that contains the plasma. The figure aside shows an artists drawing of a tokamak. On the outside are the red toroidal field coils that produce a magnetic field in the toroidal direction. The blue coils are used for special shaping of the plasma. Underneath these coils is the grey vacuum vessel that contains the fusion plasma. The plasma itself is very hot (white) at the center cooling off (red) towards the outside. A current is driven through the plasma in the toroidal direction which produces a magnetic field in the poloidal direction.

In absence of collisions the ensemble of particles can be described by a particle density $ f(t,x,v)$ in six dimensional phase space. The mathematical model corresponding to the evolution of the particle density is given by the Vlasov equation. The aim of this project is to approximate the evolution of the distribution function $ f(t,x,v)$

  • using a grid in the 6 dimensional phaser space with $ 64^6$ points.
  • in 4D transverse space using $ 128^4$ points.
Finally, we want to describe the plasma evolution for long time (more than one thousand time iterations).

A set of slides presents the parallelization of the application [PostScript]

Figure : A Tokamak