Instability of the ion-ion hybrid Alfv\'{e}n resonator in the presence of superthermal alpha-particles

A previous theoretical study has suggested that the ion hybrid wave (or shear Alfv\'{e}n wave) will be unstable in a burning plasma environment due to fusion-born alpha particles [1]. It was concluded that instability occurs for a band of frequencies near the ion-ion hybrid frequency in a homogeneous D-T plasma. In a tokamak, the periodic variation in the strength of the magnetic field along a field--line causes the ion-ion hybrid frequency to vary between the outboard and inboard sides of the device. Because the shear Alfv\'{e}n wave predominantly propagates along a field-line and experiences a parallel cut-off at the ion-ion hybrid frequency, this instability can lead to excitation of the ion-ion hybrid Alfv\'{e}n resonator. Recent experiments [2] in the linear device LAPD at UCLA have demonstrated the existence of such a resonator in a magnetic mirror configuration through excitation by an antenna. In this study, instability of the shear Alfv\'{e}n wave in the magnetic topology of a tokamak due to energetic alpha particles is considered [3]. \\[4pt] [1] C. N. Lashmore-Davies and D. A. Russell. Phys. Plasmas \textbf{4}, 369 (1997).\\[0pt] [2] S. T. Vincena, et al., Phys. Plasmas \textbf{20}, 012111 (2013).\\[0pt] [3] W. A. Farmer and G. J. Morales, Phys. Plasmas \textbf{21}, 062507 (2014).