Constraints for the aperiodic O-mode streaming instability

In plasmas where the thermal energy density exceeds the magnetic energy density (${\beta }_{\parallel }>1$), the aperiodic ordinary mode (O-mode) instability is driven by an excess of parallel temperature $A = T_\perp /T_\parallel < 1$(where$\parallel$and$\perp$ denote directions relative to the uniform magnetic field). When stimulated by parallel plasma streams the instability conditions extend to low beta states, i.e., ${\beta }_{\parallel }<1$, and recent studies have proven the existence of a new regime, where the anisotropy threshold decreases steeply with lowering ${\beta }_{\parallel }\to 0$ if the streaming velocity is sufficiently high. However, the occurrence of this instability is questionable especially in the low-beta plasmas, where the electrostatic two-stream instabilities are expected to develop much faster in the process of relaxation of the counterstreams. It is therefore proposed here to identify the instability conditions for the O-mode below those required for the onset of the electrostatic instability. An hierarchy of these two instabilities is established for both the low ${\beta }_{\parallel }<1$ and large ${\beta }_{\parallel }>1$ plasmas. The conditions where the O-mode instability can operate efficiently are markedly constrained by the electrostatic instabilities especially in the low-beta plasmas.