Ultrafast optical probing is a widely used method of underdense plasma diagnostic. In relativistic plasma, the motion blur limits spatial resolution in the direction of motion. For many high-power lasers the initial pulse duration of 30–50 fs results in a 10–15 μm motion blur, which can be reduced by probe pulse post-compression. Here we used the compression after compressor approach [Phys.-Usp. 62, 1096 (2019); JINST 17 P07035 (2022)], where spectral broadening is performed in thin optical plates and is followed by reflections from negative-dispersion mirrors. Our initially low-intensity probe beam was down-collimated for a more efficient spectral broadening and higher probe-to-self-emission intensity ratio. The setup is compact, fits in a vacuum chamber and can be implemented within a short experimental time slot. We proved that the compressed pulse retained the high quality necessary for plasma probing.

Tight focusing with very small f-numbers is necessary to achieve the highest at-focus irradiances. However, tight focusing imposes strong demands on precise target positioning in-focus to achieve the highest on-target irradiance. We describe several near-infrared, visible, ultraviolet and soft and hard X-ray diagnostics employed in a ∼1022 W/cm2 laser–plasma experiment. We used nearly 10 J total energy femtosecond laser pulses focused into an approximately 1.3-μm focal spot on 5–20 μm thick stainless-steel targets. We discuss the applicability of these diagnostics to determine the best in-focus target position with approximately 5 μm accuracy (i.e., around half of the short Rayleigh length) and show that several diagnostics (in particular, 3$\omega$ reflection and on-axis hard X-rays) can ensure this accuracy. We demonstrated target positioning within several micrometers from the focus, ensuring over 80% of the ideal peak laser intensity on-target. Our approach is relatively fast (it requires 10–20 laser shots) and does not rely on the coincidence of low-power and high-power focal planes.

Enhancement of the quality of laser wake-field accelerated (LWFA) electron beams implies the improvement and controllability of the properties of the wake waves generated by ultra-short pulse lasers in underdense plasmas. In this work we present a compendium of useful formulas giving relations between the laser and plasma target parameters allowing one to obtain basic dependences, e.g. the energy scaling of the electrons accelerated by the wake field excited in inhomogeneous media including multi-stage LWFA accelerators. Consideration of the effects of using the chirped laser pulse driver allows us to find the regimes where the chirp enhances the wake field amplitude. We present an analysis of the three-dimensional effects on the electron beam loading and on the unlimited LWFA acceleration in inhomogeneous plasmas. Using the conditions of electron trapping to the wake-field acceleration phase we analyse the multi-equal stage and multiuneven stage LWFA configurations. In the first configuration the energy of fast electrons is a linear function of the number of stages, and in the second case, the accelerated electron energy grows exponentially with the number of stages. The results of the two-dimensional particle-in-cell simulations presented here show the high quality electron acceleration in the triple stage injection–acceleration configuration.

To increase X-ray photon number generated by laser-cluster interaction, it is important to understand the dependence of X-ray generation on cluster size. We carried out Xe K-shell X-ray generation using a conical nozzle with Xe clusters, the radius of which was controllable by adjusting the backing pressure. The experiment clarifies the result that the Xe K-shell X-ray photon number increases with increasing cluster radius from 8 to 12 nm, and saturates at the radius between 12 and 17 nm. We also investigated the Xe K-shell X-ray photon number dependence on laser intensity, and found that the threshold laser intensity of the Xe K-shell X-ray generation exists between 2 × 1017 and 5 × 1018 W/cm2.

It is shown that various spectroscopic methods based on measurements of X-ray spectra radiated from cluster targets can be used for estimation of the destruction degree of clusters by laser prepulses. These methods allow insight to be gained regarding the important issue of preservation of the dense cluster core at the moment of the arrival of the main laser pulse. In addition, they can be used for quantitative estimation of the size of the undestroyed parts of the clusters and also for measuring the temperature and density of the preplasmas produced by the laser prepulses.