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The acceleration of electrons in laser-plasma channels is one of the contemporary ideas on the energy frontier of accelerators. Demands of low energy spectrum and emittance are especially important for discussed colliders and light sources based on acceleration in plasma channels. The idea to use a laser-plasma accelerator as injector for these installations instead of traditional RF linacs looks like as a very perceptive way to replace the conventional RF linac-injector or linac-driver by a very compact system. Therefore, the new results of beam dynamics simulations in laser-plasma channel having pre-bunching stage are discussed in paper. Main simulations were focused on the study of the longitudinal electron motion stability inside of the plasma channel. It was shown that the form and the value of the plasma potential well are essentially depend on laser pulse amplitude, form and duration. The electron beam dynamics, in turn, is specified by plasma potential well parameters, which define the electrons capturing into acceleration and output parameters of the bunch. Electrons loosed from the synchronous motions in the plasma wave are defocusing soon after falling out from the potential well and are pushed to the plasma channel wall.

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