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.

In contrast to hydrodynamic vortices, vortices in a plasma contain an electric current circulating around the centre of the vortex, which generates a magnetic field localized inside. Using computer simulations, we demonstrate that the magnetic field associated with the vortex gives rise to a mechanism of dissipation of the vortex pair in a collisionless plasma, leading to fast annihilation of the magnetic field with its energy transforming into the energy of fast electrons, secondary vortices and plasma waves. Two major contributors to the energy damping of a double vortex system, namely, magnetic field annihilation and secondary vortex formation, are regulated by the size of the vortex with respect to the electron skin depth, which scales with the electron $\unicode[STIX]{x1D6FE}$ factor, $\unicode[STIX]{x1D6FE}_{e}$, as $R/d_{e}\propto \unicode[STIX]{x1D6FE}_{e}^{1/2}$. Magnetic field annihilation appears to be dominant in mildly relativistic vortices, while for the ultrarelativistic case, secondary vortex formation is the main channel for damping of the initial double vortex system.

The multiple colliding laser pulse concept formulated by Bulanov et al. (Phys. Rev. Lett., vol. 104, 2010b, 220404) is beneficial for achieving an extremely high amplitude of coherent electromagnetic field. Since the topology of electric and magnetic fields of multiple colliding laser pulses oscillating in time is far from trivial and the radiation friction effects are significant in the high field limit, the dynamics of charged particles interacting with the multiple colliding laser pulses demonstrates remarkable features corresponding to random walk trajectories, limit circles, attractors, regular patterns and Lévy flights. Under extremely high intensity conditions the nonlinear dissipation mechanism stabilizes the particle motion resulting in the charged particle trajectory being located within narrow regions and in the occurrence of a new class of regular patterns made by the particle ensembles.

Fast magnetic field annihilation in a collisionless plasma is induced by using TEM(1,0) laser pulse. The magnetic quadrupole structure formation, expansion and annihilation stages are demonstrated with 2.5-dimensional particle-in-cell simulations. The magnetic field energy is converted to the electric field and accelerate the particles inside the annihilation plane. A bunch of high energy electrons moving backwards is detected in the current sheet. The strong displacement current is the dominant contribution which induces the longitudinal inductive electric field.

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.