Wave-Trapping in an Inhomogeneous Magnetoplasma

The multi-dimensional wave equations for the waves propagating along a magnetic field in an inhomogeneous plasma are derived and the wave-trapping is discussed. It is shown that the wave equations are reduced to the Schrödinger-type ones in which the sign of the coefficient of the second derivative depends on (ψ/θ) θ=0 where ψ is the angle between the field line and the ray, and θ is the angle between the field line and the wave normal. The physical reason of the wave trapping is explained by comparing the sign of (ψ/θ) θ=0 with that of the effective potential in the wave equation. As an example, the wave trapping of the whistler wave in geo-magnetosphere is considered.