Hydromagnetic instability of contra-streaming plasmas

The stability of the system consisting of two contra-streaming plasmas is discussed in the limit of low-frequency perturbations. The existence of an external magnetic field parallel to the velocity of the contra-streaming is admitted. It is shown that the system is unstable whenever the density of kinetic energy belonging to the relative motion of the two plasmas exceeds the magnetic energy density. This is true even when the system is stable in the sense of Penrose's criterion [1].