Electrostatic Electron‐Ion Streaming Instability

When electrons drift relative to ions across a magnetic field, the field‐free instabilities can still persist. However, new possibilities for collective instabilities occur. In particular, an electrostatic instability with growth rate γ ∼ (m e /m i ) 1/4 Ω e can develop when ω pe ≫ Ω e , T e > T i , and the electron drift velocity is less than the electron thermal velocity. This is due to the coupling of a Doppler‐shifted ion mode and the electron cyclotron mode.