Kinetic theory of strongly nonlinear stationary Langmuir waves (T/spl Lt/mc/sup 2/)

Summary form only given. Extremely large-amplitude Langmuir waves are investigated on the basis of relativistic kinetic theory in the low temperature limit (T/spl Lt/mc/sup 2/). Analytic formulae for the electron density and the electric field of the wave differ essentially from the earlier results obtained using the cold-hydrodynamical equations. It's well known that there is a limit on the amplitude of the electric field wave connected with the phenomenon now referred to as "wave breaking". Within the cold-hydrodynamical approximation, "wave breaking" is accompanied by the electron concentration becoming infinity near the minimum modulus of the electric field amplitude. This nonphysical result is due to neglect of the thermal motion of particles; the effect of thermal motion in this case, even at low temperatures, significantly alters the picture and cannot be taken into account simply by thermal corrections. We show that at finite temperatures the electron density in the "wave breaking" region remains finite. Moreover, beginning from a certain value of the wave electric potential amplitude, the build-up of electrons near the minimum electric field modulus results in their spatial division, which is enhanced with increasing potential amplitude. If the wave amplitude reaches its maximum the wave potential exhibits a characteristic plateau near its maxima. In these regions electron bunches of finite width with maximum concentration at their edges are produced.