Observation of an Alfv\'en Wave Parametric Instability in a Laboratory Plasma

A shear Alfv\'en wave parametric instability is observed for the first time in the laboratory. When a single finite $\omega/\Omega_i$ kinetic Alfv\'en wave (KAW) is launched in the Large Plasma Device above a threshold amplitude, three daughter modes are produced. These daughter modes have frequencies and parallel wave numbers that are consistent with copropagating KAW sidebands and a low frequency nonresonant mode. The observed process is parametric in nature, with the frequency of the daughter modes varying as a function of pump wave amplitude. The daughter modes are spatially localized on a gradient of the pump wave magnetic field amplitude in the plane perpendicular to the background field, suggesting that perpendicular nonlinear forces (and therefore $k_{\perp}$ of the pump wave) play an important role in the instability process. Despite this, modulational instability theory with $k_{\perp}=0$ has several features in common with the observed nonresonant mode and Alfv\'en wave sidebands.