The development of small-scale self-focusing in a nonlinear Kerr medium after preliminary self-filtering of a laser beam propagating in free space is studied numerically. It is shown that, under definite conditions, due to self-filtering, filamentation instability (beam splitting into filaments) either occurs at significantly larger values of the B-integral, or does not occur at all. In the latter case, there develops the honeycomb instability revealed in this work. This instability is the formation of a random honeycomb structure in the beam cross-section. It is shown that self-filtering can significantly increase the permissible values of the B-integral, at which the beam quality remains acceptable.

It was shown experimentally that for a 65-fs 17-J pulse, the effect of filamentation instability, also known as small-scale self-focusing, is much weaker than that predicted by stationary and nonstationary theoretical models for high B-integral values. Although this discrepancy has been left unexplained at the moment, in practice no signs of filamentation may allow a breakthrough in nonlinear pulse post-compression at high laser energy.

We examine the electron acceleration induced by an ultra-relativistic intensity laser–plasma interaction in a two-dimensional plasma channel in the presence of a self-generated transverse magnetic field. We find that the electron dynamics is strongly affected by the laser pulse polarization angle, plasma density, and magnetic field strength. We investigate in detail, the dependencies of the electron acceleration in terms of different parameters and find excellent agreement with non-magnetized plasma in the absence of the magnetic field. The numerical results show that the self-generated magnetic field plays a constructive role in the electron acceleration process. It is shown that electron acceleration is more affected by self-generated magnetic field for the laser radiations with large polarization angles. The numerical results show the maximum enhancement for electron acceleration for a laser radiation with polarization angle θ = π/2.

The paper presents a review of dynamic stabilization mechanisms for plasma instabilities. One of the dynamic stabilization mechanisms for plasma instability was proposed in the paper [Kawata, Phys. Plasmas 19, 024503 (2012)], based on a perturbation phase control. In general, instabilities emerge from the perturbations. Normally the perturbation phase is unknown, and so the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superimposition of perturbations imposed actively. Based on this mechanism we present the application results of the dynamic stabilization mechanism to the Rayleigh–Taylor instability (RTI) and to the filamentation instability as typical examples in this paper. On the other hand, in the paper [Boris, Comments Plasma Phys. Control. Fusion 3, 1 (1977)] another mechanism was proposed to stabilize RTI, and was realized by the pulse train or the laser intensity modulation in laser inertial fusion [Betti et al., Phys. Rev. Lett. 71, 3131 (1993)]. In this latter mechanism, an oscillating strong force is applied to modify the basic equation, and consequently the new stabilization window is created. Originally the latter was proposed by Kapitza. We review the two stabilization mechanisms, and present the application results of the former dynamic stabilization mechanism.

Filamentation is one of the most common nonlinear phenomena taking place in the laser–plasma interaction that splits the laser beam into high-intensity spikes. The present study deals with the nonlinear evolution of filamentation instability in laser–plasma interaction and the development of chaos in contrast to linear growth as reported by Kaw et al. in 1973. We have considered a non-uniform perturbation superimposed on plane-wave pump such that due to non-uniformity of the perturbation a finite intensity gradient arises and gives rise to ponderomotive force. This causes filamentation of wave, which has been studied presently using numerical methods as well as analytical tools. The results reveal that the intensity of perturbation gets localized and delocalized with the distance of propagation. The numerical simulation results also reveal that the intensity of perturbation route from ordered to chaotic behavior depending upon the pump laser and perturbation parameters. To study the chaotic behavior, Lyapunov exponents has also been calculated. The semi-analytical method is also developed to have an insight into some of the features of simulation like the formation of localized structures.

The main purpose of this theory is to present a simple picture of magnetic field generation by a relativistic equilibrium counterstreaming electron–negative hydrogen ion (e–H−) plasmas propagating parallel to an ambient external magnetic field. The existence of such kind of plasma flows can be imagined during the negative hydrogen ion propagation through neutralizing plasma, in order to generate an energetic neutral hydrogen beam. The produced magnetic field deflects the electron and negative hydrogen ion flows and reduces the efficiency of hydrogen neutral beam generation. We focused our analysis on the influences of the negative hydrogen ion contribution, the particles thermal velocity and the external magnetic field on the growth rate of generated sheared magnetic field. The dispersion relation is obtained using a relativistic two-fluid model and Maxwell equations. The analytical and numerical solutions admit generation of a purely growing transverse electromagnetic field across the ambient external magnetic field. It is shown that H− current filaments are responsible for deep penetration of the sheared magnetic fields into plasma, however, applying a weak magnetic field ${\rm \omega} _{{\rm ce}}^2 {\rm \ll} {\rm \omega} _{{\rm pe}}^2 $ suppresses magnetic field generation for a counterstreaming e–H− plasma in the absence of H− ions dynamics. On the other hand, a magnetic field exists with a small growth rate for strongly magnetized (${\rm \omega} _{{\rm ce}}^2 \;{\rm \gg}\; {\rm \omega} _{{\rm pe}}^2 $) e–H− plasma when the influence of H− ions is included. Although the growth rate is small, we expect that magnetic field generation is further amplified and the penetration depth is increased owing to H− ions stream, on a time scale much longer than the plasma period $t\;{\rm \gg}\; {\rm \omega} _{{\rm pe}}^{ - 1} $.

Collisional effects on the current-filamentation instability (CFI), accounting for the space charge effect (SCE), are investigated kinetically for a relativistic beam propagating in dense plasmas. It is shown that collisions can completely suppress the SCE in low temperature dense plasma, leading to enhancement of the CFI. This kind of decoupling mechanism is quite different from the well-known resistive mechanism [Molvig (1975). Phys. Rev. Lett. 35, 1504]. In particular, we find the present decoupling mechanism can well explain the recent numerical simulation results [Karmakar et al. (2008). Phys. Rev. Lett. doi: 101, 255001]. In the parameter regime related to the laser-solid interaction and fast ignition scenario (FIS), the CFI growth rate with SCE included is enhanced in the low plasma density region through the decoupling mechanism. In the high plasma density region, it is enhanced mainly through the resistive mechanism.

A thorough analysis of the electromagnetic instabilities encountered in the beam plasma interaction physics shows that the most unstable modes are not the ones which are usually studies. We characterize these most unstable modes and determine the patterns they create.

In the fast ignition scenario for inertial fusion, a relativistic electron beam is supposed to travel from the side of the fusion pellet to its core. One one hand, a relativistic electron beam passing through a plasma is a highly unstable system. On the other hand, the pellet core is denser than its side by four orders of magnitude so that the beam makes its way through a important density gradient. We here investigate the effect of this gradient on the instabilities. It is found that they should develop so early that gradient effects are negligible in the linear phase.

We will consider relativistic electron beam interacting with plasma and study the electromagnetic instabilities obtained for arbitrarily oriented wave vectors ranging from two-stream to filamentation instabilities. For these unstable modes, we will study every temperature effects, namely beam and plasma normal, and parallel temperatures. Temperatures are supposed to be non-relativistic and modeled through water bag distributions. It is found that only normal beam temperature and parallel plasma temperature have a significative influence over the growth rates for wave vector making an angle with the beam larger than a critical angle θc which is determined exactly. The largest growth rate being reached for a wave vector making an angle with the beam smaller than θc, it is not damped by any kind of temperatures. We finally explore collisions effects and show they can reduce the largest growth rate.

We investigate intermediate unstable modes between two stream and filamentation instabilities. We detail the problem of the angle between the wave vector and its electric field and use an electromagnetic formalism allowing for any value for this angle. We display analytical results for 3 different models: cold beam-cold plasma, cold beam-hot plasma and cold relativistic beam-hot plasma. We demonstrate that plasma temperature prompts a critical angle for which waves are unstable at any k and show that for a relativistic beam, the most unstable waves are obtained for wave vectors which are neither normal nor perpendicular to the beam.