Nonlinear interactions of kink-unstable flux ropes and shear Alfv\'{e}n waves

Magnetic flux ropes and shear Alfv\'{e}n waves occur simultaneously in plasmas ranging from solar prominences, the solar wind, and the earth's magnetotail. If the flux ropes evolve to become unstable to the kink mode, interactions between the kink oscillations and the shear waves can arise, and may even lead to nonlinear phenomena. Experiments aimed at elucidating such interactions are performed in the upgraded Large Plasma Device at UCLA. Flux ropes are generated using a 20 cm $\times$ 20 cm LaB$_{6}$ cathode discharge (with L=18 m and $\beta\sim 0.1$.) The ropes are embedded in a otherwise current-free, cylindrical ($r=30$cm) ambient plasma produced by a second, BaO cathode. Shear Alfv\'{e}n waves are launched using either internal antennas, or by modulating the BaO cathode-anode discharge current. In the latter case, kink unstable oscillations and driven shear waves nonlinearly generate sidebands about the higher shear wave frequency (evident in power spectra) via three-wave coupling; this is demonstrated though bi-coherence calculations and k-matching. Informational complexity and entropy of the time series are also investigated. Future work will focus on antenna-launched waves to control amplitude and frequency, as well as a possible evolution to a turbulent state.