**5. Conclusions**

diffraction patterns to be obtained on time scales shorter than the onset of radiation damage of samples. This approach has been successfully demonstrated in studies of biological samples with the use of X‐ray free electron lasers (XFEL) producing femtosecond pulses of high

There has been remarkable progress in the development of XFELs that hold the great promise for user experiments ranging from atomic physics to biological structure determination. Despite the fact that these lasers are powerful tools in studies of matter structure and physics of light‐matter interaction, they have limited accessibility because of their high cost and large‐ scale. This makes the current search for alternative X‐ray sources of laboratory scale to be of

Presently, there are two main approaches to the development of compact ultrashort‐pulsed sources of coherent soft X‐ray: above considered HHG by gas and solid targets, as well as the generation of coherent X‐ray radiation in the laser plasma. The first one is characterized by low‐intensity soft X‐ray radiation, insufficient for the realization of holographic imaging methods. The laser plasma enables generation of lasing in the soft X‐ray region with beam

Actually, only collisional and recombination schemes of active media excitation to produce soft X‐ray in a laser plasma are of practical interest. The first of them was realized in a laser plasma with high electron temperature, providing a population inversion on transitions between excited states of ions, which typically lie in the range 10–50 nm [72]. The most promising way to extend the spectral range of the X‐ray lasers deeper into the X‐ray region, including the "water window," lies in the further developing recombination scheme of

The first observation of the amplification on the transition to the ground state dates back to 1983 [73] when hydrogen‐like lithium ions were excited in the laser plasma produced due to optical field ionization (OFI) by the UV radiation from a subpicosecond KrF laser. Later that year, this observation was confirmed in different experimental conditions [74–76]. The OFI approach to excitation of recombination soft X‐ray lasers is particularly attractive since it produces fully stripped ions on a time scale of one period of the incident laser electric field and enables formation of cold electrons with low residual energy (for a linearly polarized laser pulse) providing favorable conditions for high‐rate three‐body recombination. Residual energy is proportional to the square of a pump laser wavelength and can be reduced by using

An electron removed from an atom due to OFI interacts with the plane polarized laser field and acquires quiver energy of the coherent electron oscillation in the field and energy of electron drift along the laser field direction [77, 78]. For ultrashort pulses, the quiver energy is returned to the wave, and it does not contribute to residual energy. Most of the electrons are ionized within a narrow interval near the crest of the oscillating electric field because of the exponential dependence of the ionization rate on the electric field amplitude. Classically, the average drift energy, ε, of an electron depends on the phase mismatch, Δϕ, between the phase

at which the electron is freed and the crest of the electromagnetic wave:

excitation of transitions to the ground state of recombining fully stripped ions.

intensity (For example, see [71]).

15020 High Energy and Short Pulse Lasers

performances close to those of XFELs [72].

a short‐wavelength driver pulse.

great importance.

Development of the photochemical method for exciting active media has resulted in the emerging of the new class of gas lasers in the spectral range extending from the NIR to UV regions. The most remarkable achievements of these studies belong to the visible range where no alternatives are available so far for the excitation of broadband gaseous active me‐ dia (XeF(C‐A), Xe2Cl, and Kr2F) that would not be strongly modified by transient absorp‐ tion. This pave the way for the development of hybrid (solid/gas) laser systems towards petawatt peak power in the blue‐green spectral region due to their broad amplification bandwidths, able to support as short as 10 fs pulses, and their relatively high saturation flu‐ ences (0.05–0.2 J cm-2), promising as high as 10 TW peak power to be obtained from square cm of an output aperture.

To demonstrate the high potential of the hybrid approach relying on the optically driven broadband active media in the visible, two femtosecond hybrid systems are now under development with the aim of conducting proof‐of‐principle experiments: THL‐30 at LPI, designed for about 5 TW of output peak power, and THL‐100 at IHCE, designed to be ten times more powerful. Behind these systems is the amplification of the second harmonic of Ti:sap‐ phire front ends in the power‐boosting XeF(C‐A) amplifiers driven by the e‐beam‐to‐VUV flash converters. In the pilot experiments performed in the THL‐100 system, peak power of 14 TW has been attained in the 50 fs pulse at the output energy of 0.7 J. After upgrading pumping source, an energy output has been enhanced up to 2.5 J in the 2.4 ps pulse before its recom‐ pression promising a peak power of 50 TW to be obtained. Besides spectral matching between a solid‐state frond‐end and gas XeF(C‐A) amplifier, the nonlinear frequency upconversion results in efficient temporal cleaning of the ultrashort optical pulse, thereby providing a high contrast ratio for the output blue‐green pulses produced by a hybrid laser chain. This was confirmed by the results of ASE measurements in the XeF(C‐A) amplifier of the THL‐100 system, which argue that a contrast ratio of 1012–1013 is feasible in the blue‐green hybrid femtosecond systems with a peak power of about 100 TW.

By the example of LWFA, HHG, and recombination soft X‐ray lasers, it was shown that, in some cases, application of shorter wavelength lasers (as compared to Ti:sapphire lasers operating in the NIR) for laser‐matter interaction may be advantageous and extends the frontiers of experimental ability to provide deeper insight into the physical mechanisms of the laser‐matter interaction. One of the greatest challenges is the development of recombination‐ pumped soft X‐ray lasers that have potential to extend SXRL spectral range towards "water window" and beyond.

Actually, the above‐discussed blue‐green hybrid concept can be considered as an alternative to the direct nonlinear upconversion of intense NIR laser radiation to the visible with the use of second harmonic generation (SHG) technique. However, to the best of our knowledge, the highest peak power reached so far in the visible with SHG does not exceed 4 TW, producing the peak intensity in a focal spot diameter of about 3 μm as low as 3 × 1018 W/cm<sup>2</sup> because of poor beam quality [83]. Achieving higher parameters in Ti:sapphire laser systems with SHG meets serious technical problems arising from a variety of nonlinear effects in crystals at high intensities leading to a significant spatiotemporal degradation of beam quality [84]. Moreover, a broad spectrum of femtosecond pulses and strong nonlinear wave front distortion require application of very thin (0.5–1 mm) nonlinear crystals of large diameter (>10 cm). The tech‐ nology of such crystals manufacture is not yet available. Nevertheless, a large ongoing effort is presently devoted to overcome these difficulties in SHG and to reach hundreds of TW at wavelength of the second harmonic [85, 86]. The hybrid (solid/gas) laser technology is free of these problems because peak powers of 0.1–1 TW are required for a seed pulse generated by the solid‐state front end in order to extract most of the energy stored in the final gaseous amplifier.

At the same time, it is necessary to say that the hybrid systems relying on the photochemically driven boosting amplifiers are inferior to the all‐solid‐state systems from the view point of a pulse‐repetition rate reaching 1 kHz at moderate output peak powers. The hybrid systems operating in the visible could be of interest for the use in low repetition rate experiments, which require an output peak power of tens and hundreds of TW. In the case of the Xe2Cl active medium, repetition rates up to 10 Hz seems to be attainable with proper engineering.
