Mirror-induced Alfv\'{e}n Eigenmodes (MAE) in Periodic Magnetic Mirror Geometry

Waves in a periodic medium (optical Floquet-Bloch waves in dielectric gratings, electron wavefunctions in a 1D solid-state lattice, etc.) have propagation gaps in frequency. The famous Toroidicity-induced Alfv\'{e}n Eigenmodes (TAE) are also caused by toroidal and poloidal periodicities. As part of the fast-ion campaign in the LArge Plasma Device (LAPD), the magnetic field profile was modulated spatially into a mirror array (4 to 5 mirror throats separated by $\sim$ 4 m) to study Mirror-induced Alfv\'{e}n Eigenmodes (MAE) and the associated frequency gap. In a typical Helium plasma in LAPD, modulated sine waves and impulsive bursts drive Shear Alfv\'{e}n Waves (SAW) ($\lambda$ $_{//}$ $\sim$ 1 m, f $\sim$ 300 kHz, $\delta$ B/B $\sim$ 0.1\%) through antennae including a field-aligned copper cylinder (disk) and a picture-frame loop. The observed frequency spectra for a variety of mirror configurations and boundary conditions are compared with the predictions of the MHD model.