Summary form only given. Fundamental processes in atoms, molecules, as well as condensed matter are triggered or mediated by the motion of electrons inside or between atoms. Electronic dynamics on atomic length scales tends to unfold within tens to thousands of attoseconds (1 attosecond [as] = 10-18 s). Recent breakthroughs in laser science are now opening the door to watching and controlling these hitherto inaccessible microscopic dynamics. The key to accessing the attosecond time domain is the control of the electric field of (visible) light, which varies its strength and direction within less than a femtosecond (1 femtosecond = 1000 attoseconds). Atoms exposed to a few oscillations cycles of intense laser light are able to emit a single extreme ultraviolet (XUV) burst lasting less than one femtosecond. Full control of the evolution of the electromagnetic field in laser pulses comprising a few wave cycles have recently allowed the reproducible generation and measurement of isolated sub-femtosecond XUV pulses, demonstrating the control of microscopic processes (electron motion and photon emission) on an attosecond time scale. These tools have enabled us to visualize the oscillating electric field of visible light with an attosecond "oscilloscope", to control single-electron and probe multi-electron dynamics in atoms, molecules and solids. Recent experiments hold promise for the development of an attosecond X-ray source, which may pave the way towards 4D electron imaging with sub-atomic resolution in space and time.

Attosecond Physics

Particle-in-cell (PIC) methods have a long history in the study of laser-plasma interactions. Early electromagnetic codes used the Yee staggered grid for field variables combined with a leapfrog EM-field update and the Boris algorithm for particle pushing. The general properties of such schemes are well documented. Modern PIC codes tend to add to these high-order shape functions for particles, Poisson preserving field updates, collisions, ionisation, a hybrid scheme for solid density and high-field QED effects. In addition to these physics packages, the increase in computing power now allows simulations with real mass ratios, full 3D dynamics and multi-speckle interaction. This paper presents a review of the core algorithms used in current laser-plasma specific PIC codes. Also reported are estimates of self-heating rates, convergence of collisional routines and test of ionisation models which are not readily available elsewhere. Having reviewed the status of PIC algorithms we present a summary of recent applications of such codes in laser-plasma physics, concentrating on SRS, short-pulse laser-solid interactions, fast-electron transport, and QED effects.

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Contemporary particle-in-cell approach to laser-plasma modelling

Strong-field effects in laboratory and astrophysical plasmas and high intensity laser and cavity systems are considered, related to quantum electrodynamical (QED) photon-photon scattering. Current state-of-the-art laser facilities are close to reaching energy scales at which laboratory astrophysics will become possible. In such high energy density laboratory astrophysical systems, quantum electrodynamics will play a crucial role in the dynamics of plasmas and indeed the vacuum itself. Developments such as the free-electron laser may also give a means for exploring remote violent events such as supernovae in a laboratory environment. At the same time, superconducting cavities have steadily increased their quality factors, and quantum nondemolition measurements are capable of retrieving information from systems consisting of a few photons. Thus, not only will QED effects such as elastic photon-photon scattering be important in laboratory experiments, it may also be directly measurable in cavity experiments. Here implications of collective interactions between photons and photon-plasma systems are described. An overview of strong field vacuum effects is given, as formulated through the Heisenberg-Euler Lagrangian. Based on the dispersion relation for a single test photon traveling in a slowly varying background electromagnetic field, a set of equations describing the nonlinear propagation of an electromagnetic pulse on a radiation plasma is derived. The stability of the governing equations is discussed, and it is shown using numerical methods that electromagnetic pulses may collapse and split into pulse trains, as well as be trapped in a relativistic electron hole. Effects, such as the generation of novel electromagnetic modes, introduced by QED in pair plasmas is described. Applications to laser-plasma systems and astrophysical environments are also discussed.

Nonlinear collective effects in photon-photon and photon-plasma interactions

Relativistic interaction of short-pulse lasers with underdense plasmas has recently led to the emergence of a novel generation of femtosecond x-ray sources. Based on radiation from electrons accelerated in plasma, these sources have the common properties to be compact and to deliver collimated, incoherent, and femtosecond radiation. In this article, within a unified formalism, the betatron radiation of trapped and accelerated electrons in the so-called bubble regime, the synchrotron radiation of laser-accelerated electrons in usual meter-scale undulators, the nonlinear Thomson scattering from relativistic electrons oscillating in an intense laser field, and the Thomson backscattered radiation of a laser beam by laser-accelerated electrons are reviewed. The underlying physics is presented using ideal models, the relevant parameters are defined, and analytical expressions providing the features of the sources are given. Numerical simulations and a summary of recent experimental results on the different mechanisms are also presented. Each section ends with the foreseen development of each scheme. Finally, one of the most promising applications of laser-plasma accelerators is discussed: the realization of a compact free-electron laser in the x-ray range of the spectrum. In the conclusion, the relevant parameters characterizing each sources are summarized. Considering typical laser-plasma interaction parameters obtained with currently available lasers, examples of the source features are given. The sources are then compared to each other in order to define their field of applications.

https://hal.archives-ouvertes.fr/hal-01164031/document

Femtosecond x rays from laser-plasma accelerators

Specular reflection is one of the most fundamental processes of optics. At moderate light intensities generated by conventional light sources this process is well understood. But at those capable of being produced by modern ultrahigh-intensity lasers, many new and potentially useful phenomena arise. When a pulse from such a laser hits an optically polished surface, it generates a dense plasma that itself acts as a mirror, known as a plasma mirror (PM). PMs do not just reflect the remainder of the incident beam, but can act as active optical elements. Using a set of three consecutive PMs in different regimes, we significantly improve the temporal contrast of femtosecond pulses, and demonstrate that high-order harmonics of the laser frequency can be generated through two distinct mechanisms. A better understanding of these processes should aid the development of laser-driven attosecond sources for use in fields from materials science to molecular biology.

Plasma mirrors for ultrahigh-intensity optics

We report on a numerical observation of the train of zeptosecond pulses produced by the reflection of a relativistically intense femtosecond laser pulse from the oscillating boundary of an overdense plasma because of the Doppler effect. These pulses promise to become unique experimental and technological tools since their length is of the order of the Bohr radius and the intensity is extremely high $\ensuremath{\propto}{10}^{19}\text{ }\text{ }\mathrm{W}/{\mathrm{c}\mathrm{m}}^{2}$. We present the physical mechanism, analytical theory, and direct particle-in-cell simulations. We show that the harmonic spectrum is universal: the intensity of $n$th harmonic scales as $1/{n}^{p}$ for $nl4{\ensuremath{\gamma}}^{2}$, where $\ensuremath{\gamma}$ is the largest $\ensuremath{\gamma}$ factor of the electron fluid boundary, and $p=3$ and $p=5/2$ for the broadband and quasimonochromatic laser pulses, respectively.

https://arxiv.org/pdf/physics/0405042.pdf

Relativistic Doppler effect: universal spectra and zeptosecond pulses.

We demonstrate analytically and numerically that focusing of high harmonics produced by the reflection of a few-femtosecond laser pulse from a concave plasma surface opens a new way to unprecedentally high intensities. The key features allowing the boosting of the focal intensity are the harmonics coherency and the small exponent of the power-law decay of the harmonics spectrum. Using similarity theory and direct particle-in-cell simulations, we find that the intensity at the focus scales as ${I}_{\mathrm{C}\mathrm{H}\mathrm{F}}\ensuremath{\propto}{a}_{0}^{3}{I}_{0}$, where ${a}_{0}$ and ${I}_{0}\ensuremath{\propto}{a}_{0}^{2}$ are the dimensionless relativistic amplitude and the intensity of the incident laser pulse. The scaling suggests that due to the coherent harmonic focusing (CHF), the Schwinger intensity limit can be reached using lasers with ${I}_{0}\ensuremath{\approx}{10}^{22}\text{ }\text{ }\mathrm{W}/{\mathrm{c}\mathrm{m}}^{2}$. The pulse duration at the focus scales as ${\ensuremath{\tau}}_{\mathrm{C}\mathrm{H}\mathrm{F}}\ensuremath{\propto}1/{a}_{0}^{2}$ and reaches the subattosecond range.

Coherent focusing of high harmonics: a new way towards the extreme intensities.

We study self-compression of weakly relativistically intense laser pulses in subcritical plasmas using one- (1D) and three-dimensional (3D) direct particle-in-cell (PIC) simulations. The self-compression works in the density window from $1/4$ critical to slightly below critical density, where the Raman instability is prohibited. An analytical model is developed to describe the self-compression. The model admits pulsing Gaussian solutions and a long-lived running soliton solution. The 1D PIC results agree well with the analytical model, and compressions by an order of magnitude are observed. In the 3D geometry, the longitudinal self-compression competes with the transverse self-focusing/filamentation. To damp the filamentation we use a periodic plasma-vacuum structure. The 3D PIC simulations suggest that a 30 fs long laser pulse is efficiently compressed to 5 fs.

Self-compression of laser pulses in plasma.

We consider ion acceleration at the front surface of overdense plasma by a short laser pulse. In this configuration, the laser ponderomotive pressure pushes the background electrons, and a double layer is produced at the boundary of the overdense region. The ions are accelerated by the electrostatic field of the double layer. If the laser intensity is so large that the plasma becomes relativistically transparent, then ion trapping in the running double layer and acceleration to relativistic energies is possible. We study this physics using one-dimensional particle-in-cell simulations. Ion acceleration in one- and two-component plasmas is considered. It is shown that the proton acceleration is more effective when they represent only a small dope to the heavy background ions.

Ion acceleration in overdense plasma by short laser pulse

Using direct three-dimensional particle-in-cell (PIC) simulations we study the acceleration of electrons and ions in laser–plasma. The PIC simulations allow us to understand the results of actual experiments better, and to look beyond the presently available technology and model for laser parameters that will be obtained in the nearest future. The code VLPL (Virtual Laser-Plasma Laboratory) has been further developed and now it can model the x-ray emission by relativistic electrons in the synchrotron regime. It appears that the strongly non-linear plasma wave excited by a short laser pulse works as a compact high-brightness source of x-ray radiation. We have also checked the possibility of proton trapping in the non-linear plasma wave and find that this is already possible at intensities around 1022 W cm−2.

O. Shorokhov

Papers

Relativistic Doppler effect: universal spectra and zeptosecond pulses.

Coherent focusing of high harmonics: a new way towards the extreme intensities.

Self-compression of laser pulses in plasma.

Ion acceleration in overdense plasma by short laser pulse

Relativistic laser–plasma bubbles: new sources of energetic particles and x-rays