Diffraction-limited performance and focusing of high harmonics from relativistic plasmas

When a pulse of light reflects from a mirror that is travelling close to the speed of light, Einstein's theory of relativity predicts that it will be up-shifted to a substantially higher frequency and compressed to a much shorter duration. This scenario is realized by the relativistically oscillating plasma surface generated by an ultraintense laser focused onto a solid target. Until now, it has been unclear whether the conditions necessary to exploit such phenomena can survive such an extreme interaction with increasing laser intensity. Here, we provide the first quantitative evidence to suggest that they can. We show that the occurrence of surface smoothing on the scale of the wavelength of the generated harmonics, and plasma denting of the irradiated surface, enables the production of high-quality X-ray beams focused down to the diffraction limit. These results improve the outlook for generating extreme X-ray fields, which could in principle extend to the Schwinger limit.

Dynamics of relativistic transparency and optical shuttering in expanding overdense plasmas

Overdense plasmas are usually opaque to laser light. However, when the light is of sufficient intensity to drive electrons in the plasma to near light speeds, the plasma becomes transparent. This process—known as relativistic transparency—takes just a tenth of a picosecond. Yet all studies of relativistic transparency so far have been restricted to measurements collected over timescales much longer than this, limiting our understanding of the dynamics of this process. Here we present time-resolved electric field measurements (with a temporal resolution of ~ 50 fs) of the light, initially reflected from, and subsequently transmitted through, an expanding overdense plasma. Our result provides insight into the dynamics of the transparent-overdense regime of relativistic plasmas, which should be useful in the development of laser-driven particle accelerators, X-ray sources and techniques for controlling the shape and contrast of intense laser pulses.

Relativistic High Harmonic Generation In Gas Jet Targets

We experimentally demonstrate a new regime of high-order harmonic generation by relativistic-irradiance lasers in gas jet targets. Bright harmonics with both odd and even orders, generated by linearly as well as circularly polarized pulses, are emitted in the forward direction, while the base harmonic frequency is downshifted. A 9 TW laser generates harmonics up to 360 eV, within the 'water window' spectral region. With a 120 TW laser producing 40 uJ/sr per harmonic at 120 eV, we demonstrate the photon number scalability. The observed harmonics cannot be explained by previously suggested scenarios. A novel high-order harmonics generation mechanism [T. Zh. Esirkepov et al., AIP Proceedings, this volume], which explains our experimental findings, is based on the phenomena inherent in the relativistic laser - underdense plasma interactions (self-focusing, cavity evacuation, and bow wave generation), mathematical catastrophe theory which explains formation of electron density singularities (cusps), and collective radiation due to nonlinear oscillations of a compact charge.

High-Order Harmonics from Bow Wave Caustics Driven by a High-Intensity Laser

We propose a new mechanism of high-order harmonic generation during an interaction of a high-intensity laser pulse with underdense plasma. A tightly focused laser pulse creates a cavity in plasma pushing electrons aside and exciting the wake wave and the bow wave. At the joint of the cavity wall and the bow wave boundary, an annular spike of electron density is formed. This spike surrounds the cavity and moves together with the laser pulse. Collective motion of electrons in the spike driven by the laser field generates high-order harmonics. A strong localization of the electron spike, its robustness to oscillations imposed by the laser field and, consequently, its ability to produce high-order harmonics is explained by catastrophe theory. The proposed mechanism explains the experimental observations of high-order harmonics with the 9 TW J-KAREN laser (JAEA, Japan) and the 120 TW Astra Gemini laser (CLF RAL, UK) [A. S. Pirozhkov, et al., arXiv:1004.4514 (2010); A. S. Pirozhkov et al, AIP Proceedings, this volume]. The theory is corroborated by high-resolution two- and three-dimensional particle-in-cell simulations.

Laser driven MeV proton beam focussing by auto-charged electrostatic lens configuration

Significant reduction of inherent large divergence of the laser driven MeV proton beams is achieved by strong (of the order of 10^9 V/m ) electrostatic focussing field generated in the confined region of a suitably shaped structure attached to the proton generating foil. The scheme exploits the positively charging of the target following an intense laser interaction. Reduction in the proton beam divergence, and commensurate increase in proton flux is observed while preserving the beam laminarity. The underlying mechanism has been established by the help of particle tracing simulations. Dynamic focussing power of the lens, mainly due to the target discharging, can also be exploited in order to bring up the desired chromaticity of the lens for the proton beams of broad energy range.

General foundation for the nonlinear ponderomotive four-force in laser-plasma interactions

The interaction of electromagnetic radiation with plasmas is studied in relativistic four-vector formalism. A gauge and Lorentz invariant ponderomotive four-force is derived from the time dependent nonlinear three-force of Hora (1985). This four-force, due to its Lorentz invariance, contains new magnetic field terms. A new gauge and Lorentz invariant model of the response of plasma to electromagnetic radiation is then devised. An expression for the dispersion relation is obtained from this model. It is then proved that the magnetic permeability of plasma is unity for a general reference frame. This is an important result since it has been previously assumed in many plasma models.

Few-cycle relativistic solitons in plasmas

A set of exact one-dimensional solutions to coupled nonlinear equations describing the propagation of a relativistic ultrashort circularly polarized laser pulse in a cold collisionless and bounded plasma where electrons have an initial velocity in the laser propagating direction is presented. The solutions investigated here are in the form of quickly moving envelop solitons at a propagation velocity comparable to the light speed. The features of solitons in both underdense and overdense plasmas with electrons having different given initial velocities in the laser propagating direction are described. It is found that the amplitude of solitons is larger and soliton width shorter in plasmas where electrons have a larger initial velocity. In overdense plasmas, soliton duration is shorter, the amplitude higher than that in underdense plasmas where electrons have the same initial velocity.

Self-focusing, Raman, and modulation instability of shaped relativistic laser pulse in plasmas

The interaction of shaped laser pulses with plasmas is studied in a strict theoretical framework without adopting the slow-varying envelope approximation (SVEA). Any physical quantities involved in the interaction are denoted as a summation of different real quantities of respective phases. The relationships among the phases of those real quantities and their moduli are strictly analyzed. Such strict analyses lead to a more exact equation set for the three-dimensional envelope of the laser pulse, which is not based on SVEA. Based on this equation set, self-focusing, Raman, and modulation instabilities could be discussed in a unified framework. The solutions of this equation set for the laser envelope reveal many possible multicolor laser modes in plasmas. The energy and the shape of a pulse determine its propagation through plasmas in a multicolor mode or in a monochromic mode. A global growth rate is introduced to measure the speed of the transition from the monochromic mode in vacuum to a possible mode in plasmas. (c) 2006 American Institute of Physics.

Standing ultrashort relativistic solitons in overdense plasmas

By using a one-dimensional self-consistent relativistic fluid model, an investigation is made numerically on relativistic electromagnetic solitons with a high intensity in cold overdense plasmas with an electrons' initial velocity opposite to the laser propagating direction. Two types of standing solitons with zero group velocity are found at the given electrons' initial velocities. One is single-humped with a weakly relativistic intensity; the another is multi-humped with a strong relativistic amplitude. The properties of these two types of solitons are presented in detail.

Relativistic laser channeling in plasmas for fast ignition

We report an experimental observation suggesting plasma channel formation by focusing a relativistic laser pulse into a long-scale-length preformed plasma. The channel direction coincides with the laser axis. Laser light transmittance measurement indicates laser channeling into the high-density plasma with relativistic self-focusing. A three-dimensional particle-in-cell simulation reproduces the plasma channel and reveals that the collimated hot-electron beam is generated along the laser axis in the laser channeling. These findings hold the promising possibility of fast heating a dense fuel plasma with a relativistic laser pulse.

Relativistic laser pulse compression in plasmas with a linear axial density gradient

The self-compression of a relativistic Gaussian laser pulse propagating in a non-uniform plasma is investigated. A linear density inhomogeneity (density ramp) is assumed in the axial direction. The nonlinear Schrodinger equation is first solved within a one-dimensional geometry by using the paraxial formalism to demonstrate the occurrence of longitudinal pulse compression and the associated increase in intensity. Both longitudinal and transverse self-compression in plasma is examined for a finite extent Gaussian laser pulse. A pair of appropriate trial functions, for the beam width parameter (in space) and the pulse width parameter (in time) are defined and the corresponding equations of space and time evolution are derived. A numerical investigation shows that inhomogeneity in the plasma can further boost the compression mechanism and localize the pulse intensity, in comparison with a homogeneous plasma. A 100 fs pulse is compressed in an inhomogeneous plasma medium by more than ten times. Our findings indicate the possibility for the generation of particularly intense and short pulses, with relevance to the future development of tabletop high-power ultrashort laser pulse based particle acceleration devices and associated high harmonic generation. An extension of the model is proposed to investigate relativistic laser pulse compression in magnetized plasmas.