  The classical wave-particle Hamiltonian is considered in its generalized
version, where two modes are assumed to interact with the co-evolving charged
particles. The equilibrium statistical mechanics solution of the model is
worked out analytically, both in the canonical and the microcanonical
ensembles. The competition between the two modes is shown to yield ensemble
inequivalence, at variance with the standard scenario where just one wave is
allowed to develop. As a consequence, both temperature jumps and negative
specific heat can show up in the microcanonical ensemble. The relevance of
these findings for both plasma physics and Free Electron Laser applications is
discussed.
