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The BCS-type second-order phase transition of a classical Langmuir wavesystem is identified theoretically and numerically. The transition takes placebetween two states: Langmuir wave turbulence (LWT) and Langmuir wavesupercontinuum (LWSC), the latter of which exhibits broad power spectra withsignificant spatiotemporal coherence when a certain number of plasmons (plasmawave quanta) are excited in the system. In the LWT-LWSC transition, themodulational instability and resulting creation of plasmon pairs are theclassical counterparts of the Cooper instability and creation of Cooper pairsin superconducting states. The Bose-Einstein condensation of Cooper pairs insuperconducting states is replaced by the Kuramoto oscillator-entrainment ofplasmon pairs in a LWSC. The order parameter of the LWSC state, which isdefined as the mean field of the plasmon pairs, takes on a significant value,which clearly indicates that a macroscopic number of plasmon pairs occupy asingle momentum state with an identical phase in the LWSC. The emergence ofspatiotemporal coherence and the decrease in the phase randomization areconsidered as development of long-range order and spontaneous symmetrybreaking, respectively, indicating that the LWT-LWSC transition is a secondorder phase transition phenomenon. By this transition, U(1) symmetry of LWT isbroken. The LWSC is, in terms of plasma physics, a so-calledBernstein-Greene-Kruskal mode characterized by its undamped nature.

BCS-type second-order phase transition of classical Langmuir wave system