waves are also concentrated into clumps in the regions where the plasma gradient is negative. To explain why the structure leaves the plasma waves we note the negative shift in phase velocity of Langmuir waves in the regions with a decreasing density. Due to this shift we have more waves with low phase velocity than the electrons are able to absorb at the back. As a result the low velocity waves form a “trace” of the structure ([@Kontar01]).

As was discussed previously, the quasilinear time is small but finite value. Therefore, the BPS experiences spatial expansion ([@Kontar98]). The initial width-at-half-height of the structure is less than $2d$ whereas the spatial width of the structure at $t=5.0$s is about $5d$. Most of the energy and the majority of particles are concentrated within the width of the structure. Since the quasilinear time depends on the beam density, the quasilinear time for the particles far from the center of the structure is much larger than for the structure electrons. In these regions we can observe the situation where the influence of the plasma inhomogeneity is comparable with the quasilinear time. Indeed, in the tail of the structure we have regions with zero level 