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The question of electromagnetic field intensification towards the values typical for strong field Quantum Electrodynamics is of fundamental importance. One of the most promising intensification schemes is based on the relativistic-flying mirror concept, which shows that the electromagnetic radiation reflected by the mirror will be frequency up-shifted by a factor of 4 gamma^2 (gamma: the Lorentz factor of the mirror). In laser-plasma interactions, such a mirror travels with relativistic velocities and typically has a parabolic form, which is advantageous for light intensification. Thus, a relativistic-flying parabolic mirror reflects the counter-propagating radiation in a form of focused and flying electromagnetic wave with a high frequency. The relativistic-flying motion of the laser focus makes the electric and magnetic field distributions of the focus complicated, and the mathematical expressions describing the field distributions of the focus is important. We present analytical expressions describing the field distribution formed by an ideal flying mirror having a perfect reflectance over the entire surface and wavelength range. The peak field strength of an incident laser pulse with a center wavelength of lambda_0 and an effective beam radius of w_e is enhanced by a factor proportional to gamma^3 (w_e/lambda_0) in the relativistic limit. Electron-positron pair production is investigated in the context of invariant fields based on the enhanced electromagnetic field. The pair production rate under the relativistic-flying laser focus is modified by the Lorentz gamma-factor and the beam radius-wavelength ratio (w_e/lambda_0). We show that the electron-positron pairs can be created by colliding two counter-propagating relativistic-flying laser focuses in vacuum, each of which is formed when a 180 TW laser pulse is reflected by a relativistic-flying parabolic mirror with a gamma = 12.2.

Using particle-in-cell simulations of relativistic laser plasma wakes in the presence of an external magnetic field, we demonstrate that there exists a parameter window where the dynamics of the magnetized wake channel are largely independent of the laser wavelength $\lambda_{\rm las}$. One condition for this manifestation of "limited similarity" is that the electron density $n_{\rm e}$ is highly subcritical, so that the plasma does not affect the laser. The freedom to choose a convenient laser wavelength can be useful in experiments and simulations. In simulations, an up-scaled wavelength (and, thus, a coarser mesh and larger time steps) reduces the computational effort, while limited similarity ensures that the overall structure and evolutionary phases of the wake channel are preserved. In our demonstrative example, we begin with a terrawatt$\cdot$picosecond pulse from a ${\rm CO}_2$ laser with $\lambda_{\rm las} = 10\,\mu{\rm m}$, whose field reaches a relativistic amplitude at the center of a sub-millimeter-sized focal spot. The laser is shot into a sparse deuterium gas ($n_{\rm e} \sim 10^{13}\,{\rm cm}^{-3}$) in the presence of a tesla-scale magnetic field. Limited similarity is demonstrated in 2D for $4\,\mu{\rm m} \leq \lambda_{\rm las} \leq 40\,\mu{\rm m}$ and is expected to extend to shorter wavelengths. Assuming that this limited similarity also holds in 3D, increasing the wavelength to $40\,\mu{\rm m}$ enables us to simulate the after-glow dynamics of the wake channel all the way into the nanosecond regime., Comment: 27 pages, 21 figures

We demonstrate coherent hard electromagnetic radiation generation from reflection by the electron density singularity formed at the relativistic bow wave in laser plasma via particle-in-cell simulations. Wake and bow waves driven by an intense laser pulse form an electron density singularity at the laser pulse front where they join. A counter-propagating laser pulse is reflected at the electron density modulations moving with relativistic velocity. The reflected electromagnetic pulse is compressed and its frequency is upshifted. Its frequency spectrum contains relativistic harmonics of the driver pulse frequency generated at the bow wave front, all upshifted with the same factor as the fundamental mode of the incident light., Comment: 3 figures

Singularities in multi-stream flows of relativistic plasmas can efficiently produce coherent high-frequency radiation, as exemplified in the concepts of Relativistic Flying Mirror [S. V. Bulanov, et al., Phys. Rev. Lett. 91, 085001 (2003)] and Burst Intensification by Singularity Emitting Radiation (BISER) [Pirozhkov, et al., Scientific Reports 7, 17968 (2017)]. Direct observation of these singularities is challenging due to their extreme sharpness (tens of nanometers), relativistic velocity, and transient non-local nature. We propose to use ultrafast (a few light cycles) optical probe for identifying relativistic plasma singularities. Our Particle-in-Cell (PIC) simulations show that this diagnostic is feasible., Comment: 11 pages, 6 figures, 32 references

The measurement of properties of exotic nuclei, essential for fundamental nuclear physics, now confronts a formidable challenge for contemporary radiofrequency accelerator technology. A promising option can be found in the combination of state-of-the-art high-intensity short pulse laser system and nuclear measurement techniques. We propose a novel Laser-driven Exotic Nuclei extraction-acceleration method (LENex): a femtosecond petawatt laser, irradiating a target bombarded by an external ion beam, extracts from the target and accelerates to few GeV highly-charged nuclear reaction products. Here a proof-of-principle experiment of LENex is presented: a few hundred-terawatt laser focused onto an aluminum foil, with a small amount of iron simulating nuclear reaction products, extracts almost fully stripped iron nuclei and accelerate them up to 0.9 GeV. Our experiments and numerical simulations show that short-lived, heavy exotic nuclei, with a much larger charge-to-mass ratio than in conventional technology, can be obtained in the form of an energetic, low-emittance, high-current beam., Comment: including supplementary information

A method for the controlled generation of intense high frequency electromagnetic fields by a breaking Langmuir wave (relativistic flying mirrors) in a gradually inhomogeneous plasma is proposed. The wave breaking threshold depends on the local plasma density gradient. Compression, chirping and frequency multiplication of an electromagnetic wave reflected from relativistic mirrors is demonstrated using Particle-In-Cell simulations. Adjusting the shape of the density profile enables control of the reflected light properties., Comment: 5 pages, 4 figures

The structure of the density singularity formed in a relativistically large amplitude plasma wave close to the wavebreaking limit leads to a refraction coefficient which has a coordinate dependence with discontinuous derivatives. This results in a non-exponentially small above-barrier reflection of an electromagnetic wave interacting with the nonlinear plasma wave., Comment: 9 pages, 3 figures

The structure of the singularity that is formed in a relativistically large amplitude plasma wave close to the wavebreaking limit is found by using a simple waterbag electron distribution function. The electron density distribution in the breaking wave has a typical "peakon" form. The maximum value of the electric field in a thermal breaking plasma is obtained and compared to the cold plasma limit. The results of computer simulations for different initial electron distribution functions are in agreement with the theoretical conclusions., Comment: 21 pages, 12 figures

X-ray devices are far superior to optical ones for providing nanometre spatial and attosecond temporal resolutions. Such resolution is indispensable in biology, medicine, physics, material sciences, and their applications. A bright ultrafast coherent X-ray source is highly desirable, for example, for the diffractive imaging of individual large molecules, viruses, or cells. Here we demonstrate experimentally a new compact X-ray source involving high-order harmonics produced by a relativistic-irradiance femtosecond laser in a gas target. In our first implementation using a 9 Terawatt laser, coherent soft X-rays are emitted with a comb-like spectrum reaching the 'water window' range. The generation mechanism is robust being based on phenomena inherent in relativistic laser plasmas: self-focusing, nonlinear wave generation accompanied by electron density singularities, and collective radiation by a compact electric charge. The formation of singularities (electron density spikes) is described by the elegant mathematical catastrophe theory, which explains sudden changes in various complex systems, from physics to social sciences. The new X-ray source has advantageous scalings, as the maximum harmonic order is proportional to the cube of the laser amplitude enhanced by relativistic self-focusing in plasma. This allows straightforward extension of the coherent X-ray generation to the keV and tens of keV spectral regions. The implemented X-ray source is remarkably easily accessible: the requirements for the laser can be met in a university-scale laboratory, the gas jet is a replenishable debris-free target, and the harmonics emanate directly from the gas jet without additional devices. Our results open the way to a compact coherent ultrashort brilliant X-ray source with single shot and high-repetition rate capabilities, suitable for numerous applications and diagnostics in many research fields.

A novel ultra-bright high-intensity source of X-ray and gamma radiation is suggested. It is based on the double Doppler effect, where a relativistic flying mirror reflects a counter-propagating electromagnetic radiation causing its frequency multiplication and intensification, and on the inverse double Doppler effect, where the mirror acquires energy from an ultra-intense co-propagating electromagnetic wave. The role of the flying mirror is played by a high-density thin plasma slab accelerating in the radiation pressure dominant regime. Frequencies of high harmonics generated at the flying mirror by a relativistically strong counter-propagating radiation undergo multiplication with the same factor as the fundamental frequency of the reflected radiation, approximately equal to the quadruple of the square of the mirror Lorentz factor., Comment: 8 pages, 5 figures. Presented at the ELI Workshop and School on "Fundamental Physics with Ultra-High Fields" 29.09.-02.10.2008, in Frauenworth Monastery, Bavaria, Germany