Waves in Inhomogeneous Magnetoplasmas

The linearized Vlasov equation for a hot inhomogeneous magnetoplasma is solved through the particle-orbit theory using the techniques of Fourier transforms. An analytical integral expression in $\overrightarrow{\mathrm{k}}$ space is obtained for the current density for waves propagating across the static magnetic field. When inverse Fourier transformed, it gives rise to a differential expression which is accurate up to order ${\left(\frac{{\mathcal{r}}_c}{\lambda }\right)}^2$, ($\frac{{\mathcal{r}}_c^2}{\lambda L}$), and ${\left(\frac{{\mathcal{r}}_c}{L}\right)}^2$. The integral equation is solved numerically for the problems of Buchsbaum-Hasegawa resonances and the Bernstein modes propagating in an inhomogeneous magnetoplasma.