Master thesis project for students at KTH
http://www.nada.kth.se/~jaun/Projects.html
NADA, Royal Institute of Technology, Stockholm, Sweden

Ray-tracing with mode-conversion in a tokamak

In a plasma where two types of waves propagate with the same phase velocity, a linear coupling occurs through which energy can be transfered from one wave branch to another. This so-called mode-conversion phenomenon has been known for decades in basic plasma science and plays a major role in the heating and current generation with waves. The shear complexity of the problem, however, made it impossible to solve in anything but the simplest 1D configurations. Only recently, with the advent of powerful computers and sophisticated mathematical methods, has it become possible to tackle the 2D geometry of a tokamak using either a global or a ray-tracing approach [1].

This work follows the latter and builds on a powerfull formalism assimilating waves with rays, which evolve according to Hamilton's equations and can be described with symplectic methods in phase space [2]. The implementation of the algorithm in Matlab is pursued in a collaboration with two leading theoreticians --Profs. A.N.Kaufman (UC Berkeley, USA) and E.R.Tracy (William & Mary, USA)-- so that the exact outline of your project depends on the status when it starts. Possible topics for a M.Sc. project deal with the treatment of caustics, matching the amplitude and phase accross the conversion layers and the inclusion of relativistic effects.

This is a wonderfull project for a skilled theoretician who is willing to apply advanced mathematical methods to solve a computational problem at the forefront of scientific research.

  1. Amplitude Transport Along Electromagnetic Rays in a Tokamak, Olga Mishchenko, MSc thesis (2004)
  2. Eikonal Waves, Caustics and Mode Conversion Modelling in Toroidal Fusion Plasmas, A. Jaun, A.N. Kaufman, E.R. Tracy, MMWP, Vaxjo (2005)
  3. Poloidal Field Effects in Multidimensional Mode Conversion in Tokamaks, A. Kaufman, E.R. Tracy, A. Jaun, A. Brizard, DPP-APS, Savannah (2004)
  4. A Ray-Based Algorithm for Numerical Computation of Multi-Dimensional Linear Conversion, E.R. Tracy, A. Kaufman, A. Jaun, Phys. Lett. A 290 (2001) 309
  5. Geometrical Methods of Mathematical Physics, Bernard Schutz, Cambridge University Press (1980)

For further information, contact André JAUN and consult http://www.nada.kth.se/~jaun.