Spectral Gap of Shear Alfv\'{e}n Waves in a Periodic Array of Magnetic Mirrors*

A multiple magnetic mirror array is formed at the LArge Plasma Device (LAPD), to study axial periodicity-influenced Alfv\'{e}n spectra. Shear Alfv\'{e}n Waves (SAW) are launched by antennas inserted in the LAPD plasma. From radial wave field scans with B-dot probes at many axial locations, SAW standing-wave formation and wave refraction in mirror cell(s) are observed. Alfv\'{e}n wave spectral gaps and continua are formed similar to wave propagation in other periodic media due to the Bragg effect. The width of the propagation gap scales with the modulation amplitude according to the solutions of Mathieu's equation. A 2-D finite-difference code modeling SAW in a mirror array configuration shows similar spectral features. Machine end-reflection conditions and damping mechanisms including electron-ion Coulomb collision and electron Landau damping are important for simulation.