Adaptive finite elements method for the solution of the Maxwell equations in inhomogeneous magnetized plasma

The wave propagation in magnetized cold plasma inhomogeneous in one direction (the slab plasma model) involves solution of the set of the second order ODE’s. Several problems have to be treated in the numerical solution. An initial value approach cannot be used for the boundary problem where exponentially growing solution exists. The equations are stiff (the O and X modes have different wavelengths) and there is also, in the cold plasma model, a singularity of the solution in the upper hybrid resonance. For the boundary problem of this type, the finite elements method fits well. To remove the singularity at UHR, we introduce small ad hoc collisions. In warm plasma, the O and X waves are converted in the UHR region to the electron Bernstein waves. It is well known that the power of the O and X waves absorbed in UHR region in a weakly collisional cold plasma represents the power converted to EBW. To minimize the computational requirements of the algorithm, an adaptive mesh, based on the local error estimation, is constructed. The code is used to analyze electron cyclotron emission (ECE) from the spherical tokamak MAST.