Wave excitation in inhomogeneous dielectric media

The equation describing the propagation of a mode driven by external currents in an inhomogeneous dielectric is derived from the principle of the conservation of wave energy density and wave momentum density. The wave amplitude in steady state is obtained in terms of a simple spatial integration of the driving current. The contribution from the spatial derivative of the dielectric response is found to be important. The analytical predictions are verified through comparison with $\delta f$ particle-in-cell computations of electron Bernstein wave propagation, thus showing applicability to kinetic systems.

Figure 1

(Color online) Comparison of the simulation and theoretical prediction for a resonant driving with $J_0=200\mathrm{A}$. (a) Normalized density (dotted line) and driving current. (b) $k{\rho }_e$ versus $\mathbf{x}$ from linear EBW dispersion relation (solid line) and from the simulation (circles). (c) Spatial distribution of $E_x$ at $t=574∕\omega$: the solid line is from the $\delta f$ simulation, the red dotted line is from Eq. (14), and the blue dashed line is what would be obtained by neglecting the factors of $\partial D_0∕\partial k_x$ in Eq. (14).

Figure 2

(Color online) Normalized density and driving current, $k_0=$ (a) $0.3∕{\rho }_e$ and (c) $0.72∕{\rho }_e$, for two different cases of nonresonant current excitation. (b) and (d) show the corresponding results for the electric field response, with the solid line the results from the $\delta f$ simulation at $t=574∕\omega$, the red dashed line showing the results from Eq. (14), and the blue dotted line showing the results obtained upon neglecting the factors of $\partial D_0∕\partial k_x$.