The paper describes results of the precise kinetic modeling of SIEB (Steadily Injected Electron Beam) problem for very weak beam diffused in velocity space. It is shown that such a run with record low (in sense of uptodate computer simulations possibilities) can be viewed as Crucial Experiment for studying the nature of fine nonlinear mechanisms of beam relaxation, beam instability saturation and the space-time dissipative structures generation for open strongly non-equilibrium systems. Thus, the inconsistancy of quasi-linear theory (QLT) for SIEB problem, even in case of very weak beams, is established. Correlation effects play the principal role in this case. This work is partly supported by RFBR, grant 97-02-17626.

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