Electron parametric instabilities of ultraintense laser pulses propagating in plasmas of arbitrary density

The dispersion relation for electron parametric instabilities of a circularly polarized laser wave of arbitrary intensity is established without restrictions on the plasma density. It is obtained in an implicit analytical form and solved numerically. The well-known stimulated Raman scattering, relativistic modulational instability, relativistic filamentation instability, and two-plasmon decay are recovered at low intensity. Their behavior in the ultrarelativistic regime is characterized by a wide extent of the unstable region in the wave vector space, with growth rates equal to a fraction of the laser frequency, and a strong harmonic generation. Particle-in-cell simulations confirm these results and show that the instability leads to a very strong heating of the plasma.