The energetic neutral atom ribbon observed by the Interstellar Boundary Explorer spacecraft is believed to originate from the pickup ions in the outer heliosheath. The outer heliosheath pickup ions generally have a ring-beam velocity distribution at a certain pickup angle, α, the angle at which these ions are picked up by the interstellar magnetic field. The pickup ion ring-beam distributions can drive unstable waves of different propagation angles with respect to the background interstellar magnetic field, θ. Previous studies of the outer heliosheath pickup ion dynamics were mainly focused on ring-like pickup ion distributions with α ≈ 90° and/or the parallel- and antiparallel-propagating unstable waves (θ = 0° and 180°). The present study carries out linear kinetic instability analysis to investigate both the parallel and oblique unstable modes (0° ≤ θ ≤ 180°) driven by ring-beam pickup ion distributions of different pickup angles between 0° and 90°. Our linear instability analysis reveals that ring-beam pickup ion distributions can excite oblique mirror waves as well as parallel/quasi-parallel and oblique right- and left-helicity waves. The maximum growth rate among all the instabilities belongs to the parallel-propagating left-helicity waves at most pickup angles. Furthermore, the evolution of the unstable mirror waves by varying pickup angle indicates that as the pickup angle increases, the maximum growth rate of the mirror modes increases, while its propagation angle decreases.
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