  Certain types of electro-magnetic waves propagating in a plasma can undergo a
mode conversion process. In magnetic confinement fusion, this phenomenon is
very useful to heat the plasma, since it permits to transfer the heat at or
near the plasma center. This work focuses on a mathematical model of wave
propagation around the mode conversion region, from both theoretical and
numerical points of view. It aims at developing, for a well-posed equation,
specific basis functions to study a wave mode conversion process. These basis
functions, called generalized plane waves, are intrinsically based on variable
coefficients. As such, they are particularly adapted to the mode conversion
problem. The design of generalized plane waves for the proposed model is
described in detail. Their implementation within a discontinuous Galerkin
method then provides numerical simulations of the process. These first 2D
simulations for this model agree with qualitative aspects studied in previous
works.
