Fig. 1. Experimental setup. A femtosecond laser pulse with wavelength λ = 800 nm is focused at an angle of 45° onto the surface of a steel foil target in a focal spot with a diameter of 2–4 μm to generate a plasma on the front surface of the target. The X rays from the plasma are measured by the X-ray focusing spectrometer (FSSR) positioned at a distance L = 2045 mm from the plasma source at an angle of 8° to the normal to the target surface.

Fig. 2. X-ray spectra of stainless-steel plasma measured under the experimental conditions described in Table I: (a) case A; (b) case B; (c) case C.

Fig. 3. Sketch of femtosecond ultra-intense laser pulse interaction with foil in the plasma zone concept.

Fig. 4. Time dependences of concentrations of He-like Fe xxv (solid lines) and H-like Fe xxvi (dashed lines) ions calculated for electron temperatures of 1000 eV (a) and 2000 eV (b) and critical plasma densities, correspondent to different laser intensities (in different colors). Black curves correspond to the case of solid density (N_i,solid = 8 × 10²² cm⁻³) and electron temperature T_e = 3000 eV. Gray curves correspond to the case of nonrelativistic critical density (N_e,cr ∼ 1 × 10²¹ cm⁻³) and electron temperature T_e = 3000 eV.

Fig. 5. Dependence of X-ray spectra emitted from plasma zone 1 with critical electron density (N_e1 = N_e,cr = 1 × 10²¹ cm⁻³) on the bulk electron temperature of the plasma T_e1; (a) T_e1 = 5000 eV; (b) T_e1 = 3000 eV; (c) T_e1 = 1000 eV. The modeling results are shown by red lines. The X-ray spectrum measured in experimental case C is shown filled in with gray shading.

Fig. 6. Dependence of X-ray spectra emitted from plasma zone 1 on bulk plasma electron temperature: (a) for electron density N_e = N_rel,cr = 6.5 × 10²² cm⁻³ (the laser intensity of 5 × 10²¹ W/cm²) and plasma thickness l₁ ∼ 2 μm; (b) for solid density N_i,solid = 8 × 10²² cm⁻³ and plasma thickness l₁ = 0.5 μm. The modeling results are shown by red lines. The X-ray spectrum from Fig. 2(c) is shown filled in with gray shading.

Fig. 7. Emission spectra of Fe plasma calculated at solid plasma ion density N_i,solid = 8 × 10²² cm⁻³ for different plasma temperatures T_e. The 0.1% of hot electrons with temperature T_hot = 10 keV are included in the calculations. The X-ray spectrum from Fig. 2(c) is shown filled in with gray shading.

Fig. 8. Emission spectra of Fe plasma calculated as superpositions of emission spectra from zone 1 (T_e1 = 1800 eV) with N_e1 = N_solid and from zone 2 at fixed plasma solid ion density N_i,solid = 8 × 10²² cm⁻³, for different plasma temperatures, with the inclusion of 0.1% of hot electrons with temperature T_hot = 10 keV. The X-ray spectrum from Fig. 2(c) is shown filled in with gray shading.

Fig. 9. Emission spectra of iron plasma calculated as superposition of emission spectra from zones 1 and 2 at fixed plasma solid ion density N_i,solid = 8 × 10²² cm⁻³ and a temperature in zone 1 of T_e1 = 2500 eV for different plasma temperatures T_e2. The X-ray spectrum from Fig. 2(c) is shown filled in with gray shading.

Fig. 10. Comparison of the results of kinetic modeling obtained under the assumption of X-ray emission from three different plasma zones and the experimentally measured spectrum for a laser intensity on target I_lt = 5 × 10²¹ W/cm². (a) Sum of the modeled spectra for the three main plasma zones compared with experimental case C. (b) Contributions of each plasma zone in the sum of the modeled spectra.