Spectral broadening of lower-hybrid waves by time-dependent density fluctuations

Lower-hybrid waves injected into tokamaks are scattered by turbulent time-dependent drift-wave density fluctuations. This scattering process gives rise to frequency shifts as well as angular deviations. In tokamaks, most of the frequency spreading occurs in a regime where the angular scattering results from multiple scattering events, each event having a small mean-square scattering angle. A radiative transport equation governing diffusion in both angle and frequency is derived. The solution is obtained in slab geometry via separation of variables and leads to a Mathieu equation. In the limit where the slab thickness l exceeds the typical distance for diffusion through a large angle ls, an explicit generalization of the diffusion solution to the radiative transfer equation is formed. This solution gives the combined angular and frequency spectrum in the scattering layer. In the thick slab limit, the rms frequency width of lower-hybrid waves emerging from the layer is given by Δω=(ωd/ ξ0ρi) N∥ [(Mi/me)βi]1/2 (l/ls), where ωd and ξ−10 are the characteristic angular frequency and correlation length of the drift-wave turbulence.