Early out-of-equilibrium beam-plasma evolution

We solve analytically the out-of-equilibrium initial stage that follows the injection of a radially finite electron beam into a plasma at rest and test it against particle-in-cell simulations. For initial large beam edge gradients and not too large beam radius, compared to the electron skin depth, the electron beam is shown to evolve into a ring structure. For low enough transverse temperatures, the filamentation instability eventually proceeds and saturates when transverse isotropy is reached. The analysis accounts for the variety of very recent experimental beam transverse observations.Comment: to appear in Phys. Rev. Letter

Instabilities for a relativistic electron beam interacting with a laser irradiated plasma

The effects of a radiation field (RF) on the unstable modes developed in relativistic electron beam--plasma interaction are investigated assuming that $\omega_{0} >\omega_{p}$, where $\omega_{0}$ is the frequency of the RF and $\omega_{p}$ is the plasma frequency. These unstable modes are parametrically coupled to each other due to the RF and are a mix between two--stream and parametric instabilities. The dispersion equations are derived by the linearization of the kinetic equations for a beam--plasma system as well as the Maxwell equations. In order to highlight the effect of the radiation field we present a comparison of our analytical and numerical results obtained for nonzero RF with those for vanishing RF. Assuming that the drift velocity $\mathbf{u}_{b}$ of the beam is parallel to the wave vector $\mathbf{k}$ of the excitations two particular transversal and parallel configurations of the polarization vector $\mathbf{E}_{0}$ of the RF with respect to $\mathbf{k}$ are considered in detail. It is shown that in both geometries resonant and nonresonant couplings between different modes are possible. The largest growth rates are expected at the transversal configuration when $\mathbf{E}_{0}$ is perpendicular to $\mathbf{k}$. In this case it is demonstrated that in general the spectrum of the unstable modes in $\omega$--$k$ plane is split into two distinct domains with long and short wavelengths, where the unstable modes are mainly sensitive to the beam or the RF parameters, respectively. In parallel configuration, $\mathbf{E}_{0} \parallel \mathbf{k}$, and at short wavelengths the growth rates of the unstable modes are sensitive to both beam and RF parameters remaining insensitive to the RF at long wavelengths.Comment: 23 pages, 5 figure

Characterization of the initial filamentation of a relativistic electron beam passing through a plasma

The linear instability that induces a relativistic electron beam passing through a return plasma current to filament transversely is often related to some filamentation mode with wave vector normal to the beam or confused with Weibel modes. We show that these modes may not be relevant in this matter and identify the most unstable mode on the two-stream/filamentation branch as the main trigger for filamentation. This sets both the characteristic transverse and longitudinal filamentation scales in the non-resistive initial stage.Comment: 4 page, 3 figures, to appear in PR