On the stability of self-consistent large amplitude waves in a cold plasma. I - Transverse circularly polarized waves in the absence of a large scale magnetic field

It is demonstrated that a self-consistent circularly polarized wave in an otherwise field-free homogeneous cold plasma is unstable to small amplitude perturbations. For either an electron-positron plasma or an electron-proton plasma the instability rate is at least about the order of the effective plasma frequency when the bulk flow speed is zero. For finite bulk flow speeds of the plasma, it is shown that the electron-positron plasma is unstable, again with a growth rate of the order of the effective plasma frequency; it is also shown that the electron-proton plasma is unstable (at least at small wave numbers, k) with a growth rate proportional to k. The calculated instability rates are conservative, for other modes not investigated here may be more unstable. The results of these calculations bear directly on the understanding of plasma systems thought to be driven by large amplitude waves.