Instabilities of a circularly polarized wave with trapped particles in an isotropic plasma

The structure and stability of a transverse electromagnetic wave propagating with a velocity lower than the speed of light in an unmagnetized plasma are considered. The stationary finite-amplitude wave is described by exact solutions to the Vlasov-Maxwell equations. However, unlike the well-known electrostatic analog, the Bernstein-Greene-Kruskal wave, the wave structure is determined to a large extent by the presence of trapped particles with a shear of transverse velocities, without which the existence of waves with a refraction index larger than unity is impossible. It is shown that the main origin of the wave instability is the longitudinal motion of trapped particles relative to the background plasma. Expressions for the growth rates in the main instability regimes are found under definite restrictions on the wave parameters.