| Abstract: |
| We study wave propagation in a waveguide with local geometric perturbations filled with a cold, strongly magnetized plasma, modeled by the 2D Maxwell equations with a current term. The corresponding frequency-domain model reduces to a Helmholtz equation with frequency-dependent coefficients, namely
\begin{align*}
\partial_y^2 u+(1-\frac{\omega_p^2}{\omega^2})^{-1}\partial_x^2 u+\omega^2 u =0,
\end{align*}
where $\omega>0$ is a given frequency and $\omega_p>0$ is the plasma frequency. The main difficulty stems from the fact that the principal symbol of the underlying operator becomes hyperbolic for frequencies not exceeding the plasma frequency.
Our goal is to understand the behavior of the viscosity limits of this problem.
We prove a limiting absorption principle for a class of geometric perturbations, based on the behavior of the Dirichlet-to-Neumann operators and on techniques used in the analysis of time-dependent problems.
Next, we give a meaning to a time-harmonic problem that is reminiscent of the wave equation with boundary conditions at the initial and final times.
If time permits, we discuss the construction of the numerical methods used to simulate this type of problem, in particular perfectly matched layers. |
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