Well-posedness and generalized plane waves simulations of a 2D mode conversion model
For researchers in plasma heating for magnetic confinement fusion, this provides a new numerical tool for simulating mode conversion, but the results are only qualitative and incremental.
This work develops a well-posed mathematical model for wave mode conversion in plasma, introducing generalized plane wave basis functions for numerical simulation. The 2D discontinuous Galerkin simulations produce results consistent with prior qualitative studies.
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.