On the existence of weak stationary electron-acoustic double layers

The recent interest in the electron-acoustic wave as a source of broad-band electrostatic noise in the terrestrial magnetosphere makes it interesting to ask whether it can support stationary electrostatic double layers. We investigate this problem in a fluid plasma composed of cool ions, cool electrons and a hot Boltzmann electron component – which is known to support electron-acoustic waves. Although a formal application of the reductive perturbation technique to our dynamical equations leads to an mKdV equation for electron-acoustic waves, it is found that within the present physical model the consistency conditions and required ordering of the coefficients cannot be satisfied simultaneously for reasonable parameter values. As a consequence, it is shown that the neglect of the φ(2) term in deriving the mKdV equation is unjustified under general circumstances, and furthermore that the cubic nonlinearity introduced by the mKdV equation is negligible when compared with this term. Finally, we are led to conclude that stationary, weak electron-acoustic double layers cannot exist in such a plasma.