Reversible energy conversion between magnetic and kinetic energies has been recently demonstrated in a system of counterstreaming electron beams [see A. Ghizzo et al., Phys. Rev. Lett. 131, 035101 (2023)]. During the first step of the instability, the growth of a current-driven filamentation magnetic field is observed when propagative oblique solutions are considered, followed by the reversal of energy transfer from magnetic to kinetic energy in a second step. This highlights a new physical mechanism of the Vlasov equation: the enhancement of filamentation of the distribution function in the presence of the phase synchronization of the Van Kampen eigenmodes. This gives rise to a bifurcation toward self-organization and to a strong plasma heating. This new plasma heating mechanism possibly provides a new perspective on the role played by the filamentation in phase space in the relativistic regime of Weibel-type instabilities.