The nonlinear electronic susceptibility induced by an electrostatic wave slowly varying in space and time, which is the key parameter for the kinetic modeling of stimulated Raman scattering (SRS), is derived analytically. When calculating the real part of the susceptibility, by making the adiabatic approximation, account is taken of the amplitude dependence of the wave frequency. Then, the “loss of resonance” of a plasma wave is found to occur at much larger amplitudes than has been predicted by Rose and Russel [H. A. Rose and D. A. Russell, Phys. Plasmas 11, 4784 (2001)] using the constant-frequency approximation. The imaginary part of the susceptibility, from which is deduced the Landau damping rate of the plasma wave, is derived using two different approaches (perturbative or not) depending on the wave amplitude. It is shown to be a nonlocal function of the wave amplitude, which underlines the importance of interspeckle interactions in SRS.

The stability analysis of an electron-beam-plasma system is of critical relevance in many areas of physics. Surprisingly, decades of extensive investigation have not yet resulted in a realistic unified picture of the multidimensional unstable spectrum within a fully relativistic and kinetic framework. All attempts made so far in this direction were indeed restricted to simplistic distribution functions and/or did not aim at a complete mapping of the beam-plasma parameter space. The present Letter comprehensively tackles this problem by implementing an exact linear model. Three kinds of modes compete in the linear phase, which can be classified according to the direction of their wave number with respect to the beam. We determine their respective domain of preponderance in a three-dimensional parameter space and support our results with multidimensional particle-in-cell simulations.

Following a recent Letter by Bret [Phys. Rev. Lett. 100, 205008 (2008)], we present a detailed report of the entire unstable k spectrum of a relativistic collisionless beam-plasma system within a fully kinetic framework. In contrast to a number of previously published studies, our linear analysis makes use of smooth momentum distribution functions of the Maxwell-Jüttner form. The three competing classes of instabilities, namely, two-stream, filamentation, and oblique modes, are dealt with in a unified manner, no approximation being made regarding the beam-plasma densities, temperatures, and drift energies. We investigate the hierarchy between the competing modes, paying particular attention to the relatively poorly known quasielectrostatic oblique modes in the regime where they govern the system. The properties of the fastest growing oblique modes are examined in terms of the system parameters and compared to those of the dominant two-stream and filamentation modes.