Poincare analysis of wave motion in ultrarelativistic electron-ion plasmas

Based on a relativistic Maxwell-fluid description, the existence of ultrarelativistic laser-induced periodic waves in an electron-ion plasma is investigated. Within a one-dimensional propagation geometry nonlinear coupling of the electromagnetic and electrostatic components occurs that makes the fourth-order problem nonintegrable. A Hamiltonian description is derived, and the manifolds of periodic solutions are studied by Poincare section plots. The influence of ion motion is investigated in different intensity regimes. For ultrarelativistic laser intensities the phase-space structures change significantly compared to the weakly relativistic case. Ion motion becomes very important such that finally electron-ion plasmas in the far-ultrarelativistic regime behave similarly to electron-positron plasmas. The characteristic new types of periodic solutions of the system are identified and discussed.