Non-linear Coupling and Decay Instability of Plasma Waves

We measure the non-linear coupling of plasma waves, for both the ``standard'' Langmuir waves with $\mbox{v}_{phase} \gg \mbox{v}_{bar} $, and for the unusual ``EAW'' (KEEN) waves with $\mbox{v}_{phase} \sim \mbox{v}_{bar} $. These are $\theta $-symmetric standing modes on pure ion and (separately) pure electron plasma columns, with discrete wavenumbers $k_{z} =m_{z} (\pi /L_{p} )$. The non-linear coupling rates are measured between large amplitude $m_{z} =2$ waves and small amplitude $m_{z} =1$ waves, which have a small detuning $\Delta \omega =2\omega_{1} -\omega_{2} $. For Langmuir waves at small excitation amplitudes, this detuning causes the $m_{z} =1$ mode amplitude to ``bounce'' at rate $\Delta \omega $, with amplitude excursions $\Delta A_{1} \propto \delta n_{2} /n_{0} $ consistent with cold fluid theory and Vlasov simulations. At larger excitation amplitudes, theory and simulations predict phase-locked exponential growth of the $m_{z} =1$ mode. Experimentally we find the effects of detuning to be more pervasive than simple theory would suggest. Typically at these large amplitudes we observe strong amplitude bouncing, with a yet unexplained slower average growth. In contrast, EAW waves exhibit phased-locked exponential growth or no growth at all, apparently due to ``frequency fungibility'' of the EAW waves. Measurements on higher temperature Langmuir waves with $\mbox{v}_{phase} \sim 4\mbox{v}_{bar} $ are being conducted to investigate the effects of wave-particle kinetics on the non-linear coupling rates.