Studies of nonlinear interactions between counter-propagating Alfv\'{e}n waves in the LAPD

From a weak turbulence point of view, nonlinear interactions between shear Alfv\'{e}n waves are fundamental to the energy cascade in low-frequency magnetic turbulence. We report here on an experimental study of counter-propagating Alfv\'{e}n wave interactions in the Large Plasma Device (LAPD) at UCLA. Colliding, orthogonally polarized kinetic Alfv\'{e}n waves are generated by two antennae, separated by ~5m along the guide magnetic field. Magnetic field and langmuir probes record plasma behavior between the antennae. When each antenna is operated separately, linearly polarized Alfv\'{e}n waves propagate in opposite directions along the guide field. When two antennae simultaneously excite counter propagating waves, we observe multiple side bands in the frequency domain, whose amplitude scales quadratically with wave amplitude. In the spatial domain we observe non-linear superposition in the 2D structure of the waves and spectral broadening in the perpendicular wave-number spectrum. This indicates the presence of nonlinear interaction of the counter propagating Alfv\'{e}n waves, and opens the possiblity to investigate Alfv\'{e}nic plasma turbulence in controlled and reproducible laboratory experiments.