Scattering of lower-hybrid waves by drift-wave density fluctuations: Solutions of the radiative transfer equation

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Abstract
The investigation of the scattering of lower‐hybrid waves by density fluctuations arising from drift waves in tokamaks is distinguished by the presence in the wave equation of a large, random, derivative‐coupling term. The propagation of the lower‐hybrid waves is well represented by a radiative transfer equation when the scale size of the density fluctuations is small compared to the overall plasma size. The radiative transfer equation is solved in two limits: first, the forward scattering limit, where the scale size of density fluctuations is large compared to the lower‐hybrid perpendicular wavelength, and second, the large‐angle scattering limit, where this inequality is reversed. The most important features of these solutions are well represented by analytical formulas derived by simple arguments. Based on conventional estimates for density fluctuations arising from drift waves and a parabolic density profile, the optical depth τ for scattering through a significant angle, is given by τ≊(2/N2∥) (ωpi0/ω)2 (mec2/2Ti)1/2 [c/α(ΩiΩe)1/2 ], where ωpi0 is the central ion plasma frequency and Ti denotes the ion temperature near the edge of the plasma. Most of the scattering occurs near the surface. The transmission through the scattering region scales as τ−1 and the emerging intensity has an angular spectrum proportional to cos θ, where sin θ=k⊥⋅Bp/(k⊥Bp), and Bp is the poloidal field.