Stable perfectly matched layers for a cold plasma in a strong background magnetic field

This work addresses the question of the construction of stable perfectly matched layers (PMLs) for a cold plasma in the infinitely large background magnetic field. We demonstrate that the traditional, Bérenger's perfectly matched layers are unstable when applied to this model, due to the presence of the backward propagating waves. To overcome this instability, we use a combination of two techniques presented in the article. First of all, we consider a simplified 2D model, which shares with the 3D case one of the difficulties for the PML treatment, namely, the presence of the backward propagating waves. Based on the fact that for a fixed frequency either forward or backward propagating waves are present, we stabilize the PMLs with the help of a frequency-dependent correction. An extra difficulty of the 3D model compared to the 2D case is the presence of both forward and backward waves for a fixed frequency. To overcome this problem we construct a system of equations that consists of two independent systems, which are equivalent to the original model. The first of the systems behaves like the 2D plasma model, and hence the PMLs are stabilized again with the help of the frequency-dependent correction. The second system resembles the Maxwell equations in vacuum, and hence the standard Bérenger's PMLs are stable for it. The systems are solved inside the perfectly matched layer, and coupled to the original Maxwell equations, which are solved in a physical domain, on a discrete level through an artificial layer. The numerical experiments confirm the stability of the new technique.