Relativistic and ponderomotive self‐focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation

Stabilization and correction of aberrated laser beams via plasma channelling

High-power laser applications, and especially laser wakefield acceleration, continue to draw attention through various research topics, and may bring many industrial applications based on compact accelerators, from ultrafast imaging to cancer therapy. However, one main step towards this is the arch issue of stability. Indeed, the interaction of a complex, aberrated laser beam with plasma involves a lot of physical phenomena and non-linear effects, such as self-focusing and filamentation. Different outcomes can be induced by small laser instabilities (i.e. laser wavefront), therefore harming any practical solution. One promising path to be explored is the use of a plasma channel to possibly guide and correct aberrated beams. Complex and costly experimental facilities are required to investigate such topics. However, one way to quickly and efficiently explore new solutions is numerical simulations, especially Particle-In-Cell (PIC) simulations if, and only if, one is confidently implementing such aberrated beams which, contrary to a Gaussian beam, do not have analytical solutions. In this research, we propose two new advancements: the correct implementation of aberrated laser beams inside a 3D PIC code, showing a great consistency, under vacuum, compared to the calculations with Fresnel theory); and the correction of their quality via the propagation inside a plasma channel. We demonstrate improvements in the beam pattern, becoming closer to a single plasma mode with less distortions, and thus suggesting a better stability for the targeted application. Through this confident calculation technique for distorted laser beams, we are now expecting to proceed with more accurate PIC simulations, closer to experimental conditions, and obtained results with plasma channels indicate promising future research.

Stability of the modulator in a plasma-modulated plasma accelerator

We explore the regime of operation of the modulator stage of a recently proposed laser-plasma accelerator scheme [Phys. Rev. Lett. 127, 184801 (2021)0031-900710.1103/PhysRevLett.127.184801], dubbed the plasma-modulated plasma accelerator (P-MoPA). The P-MoPA scheme offers a potential route to high-repetition-rate, GeV-scale plasma accelerators driven by picosecond-duration laser pulses from, for example, kilohertz thin-disk lasers. The first stage of the P-MoPA scheme is a plasma modulator in which a long, high-energy "drive" pulse is spectrally modulated by copropagating in a plasma channel with the low-amplitude plasma wave driven by a short, low-energy "seed" pulse. The spectrally modulated drive pulse is converted to a train of short pulses, by introducing dispersion, which can resonantly drive a large wakefield in a subsequent accelerator stage with the same on-axis plasma density as the modulator. In this paper we derive the 3D analytic theory for the evolution of the drive pulse in the plasma modulator and show that the spectral modulation is independent of transverse coordinate, which is ideal for compression into a pulse train. We then identify a transverse mode instability (TMI), similar to the TMI observed in optical fiber lasers, which sets limits on the energy of the drive pulse for a given set of laser-plasma parameters. We compare this analytic theory with particle-in-cell (PIC) simulations and find that even higher energy drive pulses can be modulated than those demonstrated in the original proposal.

Existence, multiplicity and non-existence of solutions for modified Schrödinger-Poisson systems

We consider a class of modified Schrödinger-Poisson systems with general nonlinearity by variational methods. The existence and multiplicity of solutions are obtained. Besides, when $ V(x) = 1 $ and $ f(x, u) = |u|^{p-2}u $, we obtain some existence and non-existence results for the modified Schrödinger-Poisson systems.

Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space

We study the following quasilinear Schrödinger equation involving critical exponent - Δ u + V ( x ) u - Δ ( u 2 ) u = A ( x ) | u | p - 1 u + λ B ( x ) u 3 N + 2 N - 2 , u ( x ) > 0 for x ∈ R N and u ( x ) → 0 as | x | → ∞ . By using a monotonicity trick and global compactness lemma, we prove the existence of positive ground state solutions of Pohožaev type. The nonlinear term | u | p - 1 u for the well-studied case p ∈ [ 3 , 3 N + 2 N - 2 ) , and the less-studied case p ∈ [ 2 , 3 ) , and for the latter case few existence results are available in the literature. Our results generalize partial previous works.

Electron self-injection during interaction of tightly focused few-cycle laser pulses with underdense plasma

We study the interaction of short laser pulses tightly focused in a tiny volume proportional to the cube of the pulse wavelength (lambda3) with underdense plasma by means of real-geometry particle-in-cell simulations. Underdense plasma irradiated by relatively low-energy lambda3 (and lambda2) laser pulses is shown to be an efficient source of multi-MeV electrons, approximately 50 nC/J , and coherent hard x rays, despite a strong pulse diffraction. Transverse wave breaking in the vicinity of the laser focus is found to give rise to an immense electron charge loading to the acceleration phase of a laser wake field. A strong blowout regime provoked by the injected electrons resulting in the distribution of accelerated electrons is found for lambda3 pulses (further electron acceleration driving by lambda2 pulses runs in the usual way). With an increase of pulse energy, wiggling and electron-hose instabilities in the lambda3 pulse wake are recognized in the blowout regime. For higher-energy lambda3 pulses, the injected beams are well modulated and may serve as a good source of coherent x rays.

Observation of strong correlation between quasimonoenergetic electron beam generation by laser wakefield and laser guiding inside a preplasma cavity

We use a one-shot measurement technique to study effects of laser prepulses on the electron laser wakefield acceleration driven by relativistically intense laser pulses (lambda=790 nm, 11 TW, 37 fs) in dense helium gas jets. A quasimonoenergetic electron bunch with an energy peak approximately 11.5 MeV[DeltaE/E approximately 10% (FWHM)] and with a narrow-cone angle (0.04pi mm mrad) of ejection is detected at a plasma density of 8 x 10(19) cm(-3). A strong correlation between the generation of monoenergetic electrons and optical guiding of the pulse in a thin channel produced by picosecond laser prepulses is observed. This generation mechanism is well corroborated by two-dimensional particle-in-cell simulations.

Self-magnetized effects in relativistic cold plasmas due to ponderomotive forces: application to relativistic magnetic guiding of light

Nonlinear equations are derived relevant to describe the propagation of powerful electromagnetic fields launched within a plasma. The nonlinear generation of self-induced collective electromagnetic perturbations are obtained with matter lying in the relativistic regime. Our main result is the self-consistent treatment of the coupled equations between the pump and its self-induced fields. In particular, a mechanism is pointed out for self-generation of quasistatic magnetic field that is due to the relativistic ponderomotive force. This process is found to be more efficient to produce quasistatic magnetic fields, as confirmed by recent experiments, as compared to known effects such as the inverse Faraday effect. As an application, we investigate conditions for relativistic magnetic guiding of light to occur under the combined action of the self-induced density and magnetic field.

Anisotropic filamentation instability of intense laser beams in plasmas near the critical density

The relativistic filamentation instability (RFI) of linearly polarized intense laser beams in plasmas near the critical density is investigated. It is found that the RFI is anisotropic to transverse perturbations in this case; a homogeneous laser beam evolves to a stratified structure parallel to the laser polarization direction, as demonstrated recently with three-dimensional particle-in-cell simulations by Nishihara et al. [Proc. SPIE 3886, 90 (2000)]. A weakly relativistic theory is developed for plasmas near the critical density. It shows that the anisotropy of the RFI results from a suppression of the instability in the laser polarization direction due to the electrostatic response. The anisotropic RFI is also analyzed based on an envelope equation for the laser beam. Finally, the envelope equation is solved numerically, and anisotropic filamentation and self-focusing are illustrated.

Stabilization of the kerr effect by self-induced ionization: formation of optical light spatially localized structures

The nonlinear propagation of ultrashort laser pulses launched into the air is investigated. The formation of optical light "bullets," or spatially localized structures, has been experimentally observed recently. Their stability is shown as due to the occurrence of a dynamical balance between two opposite nonlinear effects: an optical focusing Kerr effect balanced by a defocusing self-induced multiphoton partial ionization of the neutral gas. Characteristics of the "bullets" are predicted analytically and confirmed numerically. They are found to be in agreement with observations.