The BCS-type second-order phase transition of a classical Langmuir wave system is identified theoretically and numerically. The transition takes place between two states: Langmuir wave turbulence (LWT) and Langmuir wave supercontinuum (LWSC), the latter of which exhibits broad power spectra with significant spatiotemporal coherence when a certain number of plasmons (plasma wave quanta) are excited in the system. In the LWT-LWSC transition, the modulational instability and resulting creation of plasmon pairs are the classical counterparts of the Cooper instability and creation of Cooper pairs in superconducting states. The Bose–Einstein condensation of Cooper pairs in superconducting states is replaced by the Kuramoto oscillator-entrainment of plasmon pairs in a LWSC. The order parameter of the LWSC state, which is defined as the mean field of the plasmon pairs, takes on a significant value, which clearly indicates that a macroscopic number of plasmon pairs occupy a single momentum state with an identical phase in the LWSC. The emergence of spatiotemporal coherence and the decrease in the phase randomization are considered as development of long-range order and spontaneous symmetry breaking, respectively, indicating that the LWT-LWSC transition is a second order phase transition phenomenon. By this transition, U(1) symmetry of LWT is broken. The LWSC is, in terms of plasma physics, a so-called Bernstein–Greene–Kruskal mode characterized by its undamped nature. |

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