  Evolution of a network of vortex loops in HeII due to the fusion and
breakdown of vortex loops is studied. We perform investigation on the base of
the ''rate equation'' for the distribution function $n(l)$ of number of loops
of length $l$ proposed by Copeland with coauthors. By using the special ansatz
in the ''collision'' integral we have found the exact power-like solution of
''kinetic equation'' in stationary case. That solution is the famous
equilibrium distribution $n(l)\varpropto l^{-5/2}$ obtained earlier in
numerical calculations. Our result, however, is not equilibrium, but on the
contrary, it describes the state with two mutual fluxes of the length (or
energy) in space of the vortex loop sizes. Analyzing this solution we drew
several results on the structure and dynamics of the vortex tangle in the
superfluid turbulent helium. In particular, we obtained that the mean radius of
the curvature is of order of interline space. We also obtain that the decay of
the vortex tangle obeys the Vinen equation, obtained earlier
phenomenologically. We evaluate also the full rate of reconnection events.
PACS-number 67.40
