Transmission and Reflection of a Wave Obliquely Incident on a Nonuniform Magnetized Plasma

Abstract

A theory is given describing the conversion of obliquely incident fast waves to slow waves when propagation is perpendicular to a static magnetic field in a warm inhomogeneous plasma for frequencies near and below the second electron cyclotron harmonic. The half‐space and thin slab are treated with collisional effects included. The results are compared with those of a previously considered normally incident wave case. In particular, the analysis points out that wave conversion is proportional to the scale length of the density gradient at a hybrid resonance point provided the scale length is small compared to a free space wavelength. Both analytical and numerical solutions for the reflection and transmission coefficients and fields within the slab are presented. Between the hybrid resonances the electric field is found to consist of a longitudinal Bernstein mode contribution with rapid spatial variation and a slow variation extraordinary mode contribution. With appreciable losses, a pure standing wave is predicted at the center of the plasma whereas near the hybrid resonance points the longitudinal field is predominantly a traveling wave with an outwardly directed phase velocity. Although the coupling is small, the longitudinal field attains a large amplitude producing strong reflection of the incident wave when resonances occur with even symmetry about the center of the slab. Furthermore, the numerical computations indicate a perturbation in the position of the resonances from those of the normally incident case. This shift is analogous to the azimuthally asymmetric modes of a plasma column. Finally, for a large angle of incidence, the formulation leads to the impedance of a nonuniform plasma capacitor in a magnetic field.