On the limit of minimum number and depth of periodic modulations for spectral gap formation via Bragg's reflection

Abstract

Although it is well recognized that waves propagating in periodic media have forbidden gaps in their continuous spectra, there is still an unknown about the minimum number and depth of periodic modulations for clear spectral gap formation. This limit is explored by investigating shear Alfvén waves propagating through magnetic mirror arrays in a low-temperature plasma cylinder, referring to an existing experiment (Zhang Y. et al., Phys. Plasmas, 15 (2008) 012103). It is found that the bottom-edge ratio , a defined parameter characterizing how “noisy” the formed spectral gap is, scales with the number (N) and depth (M) of magnetic mirrors in the form of and , respectively, and they need to be bigger than 10 and 0.4, respectively, to form a pronounced spectral gap for the plasma conditions employed. Moreover, it shows that the center of the spectral gap experiences a parabolic shape of descending frequency shift in the form of when the modulation depth increases, which is analyzed theoretically and considered as a new discovery, whereas no frequency shift is observed for varied mirror number. Realistic LAPD (LArge Plasma Device) (Gekelman W. et al., Rev. Sci. Instrum., 62 (1991) 2875) with limited number and depth of periodic modulations and the mixed feature of kinetic and inertial plasma regions is also discussed at the end, and it shows that the computed spectral gap agrees well with the experimental measurement.