## Seminar in Numerical Analysis: Elena Moral Sánchez (Max-Planck Institute for Plasma Physics)

**The cold-plasma model and simulation of wave propagation using B-Spline Finite Elements**

The cold-plasma wave equation describes the propagation of an electromagnetic wave in a magnetized plasma, which is an inhomogeneous, dispersive and anisotropic medium. The thermal effects are assumed to be negligible, which leads to a linear partial differential equation. Besides, we assume that the electromagnetic field of the propagating wave is in the time-harmonic regime.

This model has applications in magnetic confinement fusion devices, like the Tokamak. Namely, electromagnetic waves are used to heat up the plasma (Electron cyclotron resonance heating (ECRH)) or for interferometry and reflectometry diagnostics (to measure plasma density and position, etc.).

In the first part of this talk, we introduce the cold-plasma model, together with a qualitative study of the plasma modes which expose the complexity of the problem.

In the second part, we describe the problem and the simplifications we carry out, which yield the indefinite Helmholtz equation. It is solved with B-Spline Finite Elements provided by the Psydac library and some results are shown. Lastly, we discuss the performance and potential ways of preconditioning.

For further information about the seminar, please visit this webpage.

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