Classification and stability of plasma motion in periodic linearly polarized relativistic waves

Based on a relativistic fluid-Maxwell model, laser-induced plasma dynamics is investigated for relativistic periodic waves. Within a one-dimensional (1D) description, the Akhiezer–Polovin model is applied to the existence of periodic, nonlinearly coupled electromagnetic and electrostatic waves, and the corresponding particle motion. Known existence criteria for periodic solutions are generalized. The corresponding stability behaviors are investigated by 1D integrators of the relativistic fluid-Maxwell model. It is shown that in contrast to the vacuum solution, linearly polarized coupled electromagnetic-electrostatic waves are unstable in plasmas. The magnitudes of the growth rates are investigated in terms of the maximum amplitudes and normalized phase velocities.