Propagation of shear Alvén waves in two-ion species plasmas confined by a nonuniform magnetic field

Ray tracing calculations are performed for shear Alfvén waves in two-ion species plasmas in which the magnetic field varies with position. Three different magnetic topologies of contemporary interest are explored: a linear magnetic mirror, a pure toroidal field, and a tokamak field. The wave frequency is chosen to lie in the upper propagation band, so that reflection at the ion-ion hybrid frequency can occur for waves originally propagating along the magnetic field direction. Calculations are performed for a magnetic well configuration used in recent experiments [S. T. Vincena et al., Geophys. Res. Lett. 38, L11101 (2011) and S. T. Vincena et al., Phys. Plasmas 20, 012111 (2013)] in the Large Plasma Device (LAPD) related to the ion-ion hybrid resonator. It is found that radial spreading cannot explain the relatively low values of the resonator quality factor (Q) measured in those experiments, even when finite ion temperature is considered. This identifies that a damping mechanism is present that is at least an order of magnitude larger than dissipation due to radial energy loss. Calculations are also performed for a magnetic field with pure toroidal geometry, without a poloidal field, as in experiments being planned for the Enormous Toroidal Plasma Device. In this case, the effects of field-line curvature cause radial reflections. A poloidal field is included to explore a tokamak geometry with plasma parameters expected in ITER. When ion temperature is ignored, it is found that the ion-ion hybrid resonator can exist and trap waves for multiples bounces. The effects of finite ion temperature combine with field line curvature to cause the reflection point to move towards the tritium cyclotron frequency when electron temperature is negligible. However, for ITER parameters, it is shown that the electrons must be treated in the adiabatic limit to properly describe resonator phenomena