Plane wave scattering on hexagonal cylinders

Abstract

Hexagonal cylinders are basic models for ice crystals in cirrus clouds. An understanding of their scattering behaviour in different frequency ranges is important to get an understanding of how they affect radiation transport in clouds. The ray-tracing technique in the geometric optics limit is the method most often used for this purpose, but this method can be applied only for higher size parameters. In this paper we shall demonstrate that the discretized Mie formalism (DMF) can be applied successfully to analyse these structures and to bridge the gap between the resonance region and the geometric optics limit; i.e., it can be used for higher size parameters up to 100. For the first time, the well-known 22 ° halo of hexagonal cylinders can be observed within an exact wave theory. The DMF is a new method to treat non-spherical scattering and has the advantage of conceptual simplicity owing to the fact that it strongly follows what is known from the Mie theory for separable scattering geometries. This makes it an ideal tool for practical applications. Results are presented for different size parameters and obliquely incident plane waves on infinitely extended cylinders with hexagonal cross-sections. Although there is a real practical interest only for finite structures, the infinitely extended cylinder is appropriate as an approximation for sufficiently long particles since it shows characteristic features of the hexagonal crystals. Additionally, the results can serve as benchmarks for other numerical techniques.