Wave-Breaking Limits of Arbitrary-Amplitude Nonlinear Periodic Electrostatic Waves in a Relativistically Degenerate Electronegative Plasma

Arbitrary-amplitude nonlinear periodic electrostatic waves and the wave-breaking limit are considered in a one-dimensional relativistic electronegative plasma consisting of positive ions, negative ions, and a relativistically degenerate electron-fluid background. A cold, inertial fluid description is adopted for the ions, while the electrons are described by a relativistic Fermi–Dirac equation of state, which provides the required restoring physics through degeneracy rather than ordinary thermal pressure. After transforming to a travelling coordinate system, we reduce the general multicomponent plasma dynamical system to a pseudopotential energy form with a constant of motion. We then determine the allowed potential range, the associated asymmetric pseudopotentials, and the wave-breaking electric field for both linear and nonlinear waves on each of the two admissible branches. We find that arbitrary-amplitude nonlinear periodic waves are intrinsically asymmetric and that the maximum field strength is set by the effective charge-density boundary of each plasma species along the field direction. Parametric analysis suggests that the critical minimum field strength required for nonlinear wave formation may be controlled by increasing either the negative-ion mass ratio, the wave propagation speed, or the negative-ion concentration; however, each of these changes produces a distinct modification of the pseudopotential geometry. This illustrates that relativistic and interspecies effects are not merely responsible for quantitative deviations from the non-relativistic and single-species cases, but instead completely reshape the nonlinear phase space governing the persistence, deformation, and breaking of periodic electrostatic waves.