Resonant parametric excitations driven by lower-hybrid fields

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Abstract
Three‐wave parametric excitation in inhomogeneous plasmas is examined in a two‐dimensional geometry relevant to supplementary rf heating of tokamaks. The stabilization of resonant parametric excitation due to a linear mismatch in wavenumbers and to the Landau‐damping rates of the decay waves is analyzed, assuming that the magnitude of the pump field is constant in time and in the spatial region where the resonant interaction takes place. Both types of temporally growing modes and spatially amplified instabilities are studied, using a WKB analysis. It is shown that either by increasing the strength of the mismatch K′ or the width of the pump L, the growth rate of the fastest growing normal mode will decrease. When the excited waves are slightly damped, it is shown that there exists a finite value of the product K′L, such that, above it, no temporal normal modes are excited. The amount of spatial amplification is also reduced by the mismatch in wavenumbers and by the damping rates of the excited waves. Because of the finite spatial extent of the pump electric field, the amplification length is found to be smaller than or equal to L, depending on the strength of the mismatch and damping rates.

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