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The asymptotic solutions to the second‐order differential equations governing the wave propagation in inhomogeneous plasma are given where the external magnetic field is assumed to be in the longitudinal direction. The zero‐, first‐, second‐, third‐, fourth,‐ and fifth‐order approximations are explicitly given. It is further shown that the third‐order asymptotic approximation agrees with the WKBJ approximation. Numerical results for a linear profile of electron concentration are given, and they are found to improve the WKBJ approximation.

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The three-dimensional electric field wave equation for propagation in homogeneous, gyrotropic, compressible, drifting plasma is derived. The static magnetic field and the drift velocity are both arbitrarily directed. The refractive index equation for oblique plane waves and other particular cases are obtained and shown to agree with previous results.