Studies of the linear and nonlinear properties of Alfv\'{e}n waves in LAPD*

An overview will be given of recent experimental research into linear and nonlinear properties of Alfv\'{e}n waves in the Large Plasma Device (LAPD). The nonlinear three-wave interaction process at the heart of the parametric decay instability is studied by launching counter-propagating Alfv{\'e}n waves from antennas placed at either end of LAPD, producing a damped ion acoustic mode.\footnote{S. Dorfman and T.A. Carter, Phys. Rev. Lett. 110, 195001 (2013)} The decay of a lone, large amplitude Alfv\'{e}n wave has been observed, producing co-propagating daughter waves with characteristics consistent with kinetic Alfv\'{e}n waves. The process has an amplitude threshold and the frequency of the daughter modes varies with the amplitude of the pump. A new plasma source based on LaB$_6$ cathode has been added to LAPD, enabling much higher density (x50), electron temperature (x2) and ion temperature (x6). This provides the opportunity to study the physics of waves and instabilities with space and astrophysically relevant $\beta$. Topics under investigation include the physics of Alfv\'{e}n waves in increased $\beta$ plasmas, electromagnetic effects in drift-Alfv\'en wave turbulence and the excitation of ion-temperature-anisotropy driven modes such as the mirror and firehose.