A ray-based algorithm for multi-dimensional linear conversion

A numerical algorithm is proposed for connecting the incoming and outgoing wave fields in studies of linear conversion. This is the first such ray-based algorithm for wave conversion in multiple spatial dimensions. It is demonstrated that, aside from the overall phase of the coupling, one can directly evaluate all quantities needed for the connection coefficients from the ray geometry. The ray dynamics is generated using the determinant of the dispersion matrix as the Hamiltonian. Using information available while following an incoming ray, the algorithm automatically detects that the ray has entered a conversion region, evaluates the transmission and conversion coefficients, and launches the transmitted ray. The algorithm does not require any prior knowledge of the geometry of the conversion region. The algorithm is illustrated using a two-dimensional toroidal model with resonant conversion from a magnetosonic to an ion-hybrid wave.