On the stability of self-consistent large-amplitude waves in a cold plasma. Part 2. Longitudinal waves in the absence of large-scale magnetic field

We demonstrate that self-consistent large-amplitude longitudinal waves in a cold plasma are unstable to at least transverse perturbations, with an instability growth rate which is roughly of the order of the plasma frequency of the system. The instability statements derived here are conservative, since modes not discussed may be more unstable.