Nonlinear steady-state coupling of LH waves

The coupling of lower hybrd waves at the plasma edge by a two waveguide array with self-consistent densitv modulation is sol\\Cd numerically. For a linear density profile. the governing nonlinear Klein-Gordon equation ' for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k-space. Numerical solutions to the nonlinear system satisfying radiation condition are ob-tained. Spectral broadening and modifications to resonance cone trajectories are observed with increase of incident power. The electromagnetic coupling problem of lower hybrid waves with self- consist cnt density modulation is Jescribed by the nonlinear Klein- Gordon equation. In dimensionless space variables (normalized by c/w), the (qiation is [1] 2 + 2 + I [Kg + (K1- 1)--E2 =0 (1)X2.J2no where Kq = 1-, = exp(-p E1 2)-1, # = 1/(4mp 2 (T, + Ti)) Eq.(1) is derived from the steady-statc Maxwell's equations in a cold plasma under the assumptions Ev ~ I, K = 1, and K. = 0 which are valid near the plasma edge. A slab model is applicable since the coupling is localized in a small region in front of the external source. The distance into the plasma is measured by x,