Fig. 1. (a) Nanosecond and sub-picosecond PHELIX laser pulses (red) focused by means of 150 cm off-axis parabola on the foam target and diagnostic setup for characterization of electron and proton beams. (b) Optically transparent highly uniform 3D network structure of polymer aerogel and a picture of foam enclosed in a Cu disk.

Fig. 2. (a) Nanosecond pulse of 10¹³ W/cm² intensity and 3 ns duration used to ionize a 450 ± 50 μm thick polymer foam layer of 2 mg/cm³ density. (b) Energy distribution of electrons and (c) protons accelerated by the PHELIX sub-ps pulse. (d) Angular distribution of electrons with E_e > 7.5 MeV detected using the cylinder stack. In this shot, the delay between the ns pulse and sub-ps relativistic laser pulse was 3 ± 0.5 ns. The positions of the magnetic spectrometers are marked with red stars.

Fig. 3. (a) Nanosecond pulse of 3×10¹⁴ W/cm² intensity and 1.5 ns duration used to ionize a 450 ± 50 μm thick polymer foam layer of 2 mg/cm³ density. (b) Energy distribution of electrons and (c) protons accelerated by the PHELIX sub-ps pulse. (d) Angular distribution of electrons with E > 7.5 MeV detected using the cylinder stack; here the positions of the magnetic spectrometers are marked with red stars. (e) RCF stack, half covered with a Cu foil, hit by the laser pulse and DLA electrons. In this shot, the delay between the ns pulse and the relativistic sub-ps laser pulse was 4.5 ± 0.5 ns.

Fig. 4. (a), (c) 2D map of the mass density (g/cm³) at 1 and 3 ns after the interaction of the laser pulse of 10¹³ W/cm² with the structured foam, where z is the cylindrical axis of symmetry and r is the radial axis, both given in μm. The initial foam size is 450 μm in the z-direction and 180 μm in the r-direction. The initial foam density of 2 mg/cm³ is shown with a black arrow on the colour bar. (b), (d) Plasma density and temperature profiles at the time of the relativistic pulse arrival: mass density (black line), electron density in cm^–3 (blue line), and electron temperature in eV (red line), along the laser propagation direction z. The grey shadow shows the initial position and density of the foam.

Fig. 5. (a) Two-dimensional mass density profile at 0.5, 3 and 4.5 ns during and after interaction of the 3 × 10¹⁴ W/cm² ns pulse of 1.5 ns duration with the structured foam. Here, z is a cylindrical symmetry axis and the direction of laser pulse propagation, while the r-axis corresponds to the radius of the foam disc considered in the simulations (x, r in μm). (b)–(d) Plasma density and temperature profiles along the z-axis at 0.5, 3 and 4.5 ns: mass density in g/cm³ (black solid line), electron density in cm^–3 (blue solid line) and electron temperature in eV (red solid line).

Fig. 6. (a) Electron density profile 3.1 ns after action of the ns pulse and ps pre-pulse. (b) Electron density distribution in the OXY (laser polarization) plane at ct = 240 μm and ct = 440 μm.  Normalized laser field E_y on the OX axis and in the OXY plane, as well as the snapshots of the electron distribution in the phase plane (x, p_x) at (c) ct = 240 μm and (d) ct = 440 μm. (e) Energy distribution of electrons inside the simulation box at ct = 40, 140, 240 and 440 μm.

Fig. 7. (a) Simulated electron energy distribution per MeV per sr at ±10° to the laser axis (). (b) Angular distribution of the electrons with E > 7.5 MeV in spherical coordinates with a polar axis OX along the laser propagation direction: , .

Fig. 8. Measured (green line) and simulated (blue line) angle-dependent fluence dN/dΩ of electrons with energy of more than 7.5 MeV. Green dots denote corresponding positions of MSs in the experiment. The blue curve shows a simulated angle-dependent electron fluence for E > 7.5 MeV.

Fig. 9. Electron energy spectra simulated for different density profiles: step-like electron density profile with 0.65n_cr, a₀ = 4.28 (red); plasma profiles from Figure 4(b), a₀ = 3.15 (green), Figure 4(d), a₀ = 3.55 (black) and Figure 5(d), a₀ = 3.55 (blue).

Fig. 10. Electron spectra measured at 0° to the laser axis. The grey spectrum belongs to the PHELIX shot with high ns-ASE of approximately 10¹¹ at intensity of 10¹⁹ W/cm² on Al foil, while in the case of the light blue spectrum the foil was pre-ionized with a ns pulse. The other colours represent electron spectra measured after irradiation of foams with densities of 2 and 8 mg/cm³ and thickness between 250 and 1000 μm. All shots were performed with ns pulses in the range of 10¹³–3 × 10¹⁴ W/cm² and delay of 3–5 ns between ns and sub-ps pulses.

Table 1. Number of DLA electrons and their effective temperature for different plasma density profiles.