The channel structure of a continuous long laser park, generated along the axis of the atmospheric propagation path of a "diffraction-free" (Besselian) laser beam, formed by an axicone, is studied. Nanosecond imaging of its initial formation stage demonstrated this channel to consist of a regular sequence of plasma breakdown zones, which then diffuse into a funnel shape. An explanation for such a kind of structure is suggested: it is seen as self-modulation effect in a diffraction- free beam propagating through a non-linear medium.