Stability analysis of the pickup ion ring-beam distributions in the outer heliosheath

The electromagnetic instabilities driven by the pickup ions in the outer heliosheath play a crucial role in interpreting the energetic neutral atom (ENA) ribbon observed by the Interstellar Boundary EXplorer (IBEX). Previous studies on the stability of the outer heliosheath pickup ions focused on ring-like velocity distributions with pickup angles equal or close to 90°. In this study, we investigate the instabilities driven by a ring-beam velocity distribution of the pickup ions in the outer heliosheath using linear instability analysis. The modes propagating along (both parallel and antiparallel to) the background magnetic field are examined, and the emphasis is on how the instabilities change with the pickup angle, α, varying from zero to 90°. The parallel thermal spread of the pickup ions is chosen to make the plasma parameters lie in the Alfvén cyclotron ‘stability gap’ to exclude the well-studied Alfvén cyclotron instability. Our linear instability analysis reveals that the unstable modes all have left helicity but may propagate parallel or antiparallel to the background magnetic field. At small α, the parallel-propagating modes are unstable in two separate wavenumber (and frequency) ranges. The two unstable ranges merge into one when α increases to 82°. In addition, the antiparallel-propagating modes become unstable when α is above 5°, but the parallel-propagating modes have larger growth rates until α becomes larger than αc = 82.8°. The growth rates of the parallel-propagating modes quickly drop below zero when α goes beyond αc, while the antiparallel-propagating modes remain unstable until α approaches 90°.