When are driven Langmuir waves resonant?

We are taught that small amplitude plasma waves are associated with zeroes of the linear dielectric function, $\varepsilon _0 \left( {k,\omega } \right)$, in the complex \textit{$\omega $} plane and that, for Langmuir waves (LW) in particular, Landau damping diminishes their response to an external potential as $k\lambda _D $ increases. But finite amplitude LWs trap electrons, thus reducing Landau damping (O'Neil, Phys. Fluids \textbf{8} (1965)). Do trapping effects strengthen the response indefinitely with increase of LW amplitude or is there a $k\lambda _D $ dependent limit? One-dimensional (1D), small amplitude theory (Holloway and Dorning, Phys. Rev. \textbf{A44} (1991)) showed that thermal plasma supports traveling LWs if $k\lambda _D \mathbin{\lower.3ex\hbox{$\buildrel<\over {\smash{\scriptstyle\sim}\vphantom{_x}}$}} $ 0.53, consistent with LW resonance, $Re\left[ {\varepsilon _0 \left( {k,\omega } \right)} \right]=0$ for real \textit{$\omega $}. Resonance is not possible for larger $k\lambda _D $. A model of 1D finite amplitude traveling LWs (Rose and Russell, Phys. Plasmas \textbf{8} (2001)) showed that increase of wave amplitude leads to a decrease of the resonant $k\lambda _D $ range, and diminished SRS gain rate (Rose and Yin, Phys Plasmas \textbf{15} (2008)). Results of 2D Vlasov simulations will be presented that manifest similar behavior: there is an amplitude limit to driven LWs, beyond which the LW response to an external potential is nonresonant. This limit decreases as $k\lambda _D $ approaches $\approx $ 0.5.