3.1. Femtosecond Interferometry Results

Interferometric measurements were realized by means of the two-channel polaro-interferometer which provides a possibility to register two interferometric frames with the variable time delay in the range of 0–1000 ps; see Figure 3. To irradiate this system, PALS Ti:Sa femtosecond laser with the wavelength 0.8 μm and the pulse duration ~40 fs was used. Each channel of the polaro-interferometer was equipped with a charge-coupled device camera (RM-4200 GigEV) enabling registration of interferograms with the high spatial resolution (2048 × 2048 pixels with a size of ~6 μm) and the 16-bit dynamics. Cameras are connected to a computer through a Gigabit ethernet interface and controlled by a custom-built application PALS Vision GigEV, which is capable of pre-treatment of the images (modification of the Fourier spectra, correction of histograms, correction of colors, calibration, etc.). In the case of high-quality interferograms, electron density distribution may be obtained after the laser shot with on-the-fly mode. For more detailed analysis of interferograms, a specialized software (created at IPPLM) is used.

Fig. 3. Optical scheme of the polaro-interferometer channel.

The interferometric records were taken in the time periods chosen with respect to the full width at half maximum of the main laser pulse, that is, about 350 ps. Two-frame sequences of interferograms with the time separation between frames about 430 ps were recorded within the range from −100 to 1000 ps related to the maximum intensity of the main laser pulse. The sample sequence of interferograms illustrating the ablative plasma expansion during the laser pulse interaction is presented in Figure 4a.

Fig. 4. Raw interferograms (a), their reconstruction (b), electron density distributions (c), and the axial electron density distributions (d) illustrating the ablative plasma expansion during the laser pulse interaction. The records correspond to the minimum focal spot radius and the pre-plasma absence (only the main beam was used).

The recorded sequence of the interferograms for different time delays enabled us to obtain the detailed information about time evolution of the electron density distribution in the ablative plasma during the laser pulse interaction with the targets. To calculate the electron density distribution, phase distribution was determined on the basis of the reconstructed interferograms (Fig. 4b) using maximum-of-a-fringe method. The reconstruction included also the opacity zone (both in and outside axial region), where phase was extrapolated (Kasperczuk & Pisarczyk, Reference Kasperczuk and Pisarczyk2001). To solve the Abel equation, Fast Fourier Transform was applied (Kalal & Nugent, Reference Kalal and Nugent1988; Burrus, Reference Burrus2008). In the case of the pre-plasma absence, the axial asymmetry does not exceed 10% and the inaccuracy of determination of the shifts of the fringes in the area outside the opacity zone is relatively low (several percent only), therefore this method of the Abel equation solution gives the accuracy of the electron density determination with error about 20%.

To obtain the information about the density gradient scalelength, an exponential fitting of the experimental axial density profiles has been applied: n _e(z) = n ₀e ^−z/L. The parameters of this function determine the maximum electron density gradient in the opacity zone: [dn _e/dz] _z= 0=n ₀/L, where L is the scalelength of the density gradient and n ₀ is the maximum electron density. The electron density distributions calculated on the basis of interferograms from Figure 4a are shown in Figure 4c. The fitting of the axial density profile by the exponential function is shown in Figure 4d.

The sample sequence of interferograms, corresponding electron density distributions and axial profiles of the electron density illustrating the ablative plasma expansion during the laser pulse interaction in the presence of the pre-plasma (both auxiliary and the main beam were applied) are presented in Figure 5. The comparison of the electron density distribution of the ablative plasma obtained under the absence of the pre-plasma at different focal spot radii and for different time of the plasma stream expansion is presented in Figure 6.

Fig. 5. Raw interferograms (a), their reconstruction (b), electron density distributions (c) calculated on the basis of the reconstructions, and the axial electron density distributions (d) illustrating the ablative plasma expansion during the laser pulse interaction at the minimum focal spot radius in the case of the pre-plasma presence.

Fig. 6. Density distributions illustrating the time evolution of the ablative plasma expansion for different focal spot radii in the case of the pre-plasma absence.

Axial density profiles and the scalelength corresponding to these distributions are shown in Figure 7. The time delays of each individual frame relate to the maximal intensity of the main pulse. The electron density distributions presented in Figure 6 demonstrate the quasi-spherical character of the expansion for the small focal spot radius with the characteristic minimum of the density on the axis. When increasing the focal spot radius of the laser beam, the plasma stream expansion becomes more axial. It is seen from both the time sequence of the density distributions, Figure 6, and the axial profiles, Figure 7, related to larger focal spot radii: R _L = 150 and 200 μm. This change in the character of the ablative plasma expansion (from spherical to axial) caused by the increasing focal spot radius and the relevant scalelengths are demonstrated in Figure 7. In the case of the pre-plasma presence, the time sequences of the electron density distribution of the ablative plasma obtained for different irradiation conditions are shown in Figure 8. The electron density distributions indicate that the light plasma with the higher pressure, being generated from the thin plastic layer by auxiliary beam, limits the radial expansion of the central plasma created by the main laser beam. The radial limitation favors the axial character of the plasma expansion particularly in the case of the larger focal spot radii. The radial limitation results in the growth of the electron density on the axis and in the increase of the scalelength. This is clearly demonstrated by the axial density profiles and the scalelength values in Figure 9. In contrast, when the pre-plasma is not created, the scalelength of the ablative plasma is considerably smaller. The detailed comparison of the ablative plasma expansion in the case of absence and presence of the pre-plasma is presented in Figure 10. This figure shows the maximal density gradient, the scalelength and the maximal density for three characteristic times of the expansion: 0, 200, and 600 ps related to the maximum intensity of the main laser beam. Single values corresponding to chosen expansion times have been determined by approximating the experimental data. Figure 10a shows that in the case without the pre-plasma, the density gradient increases with the decreasing R _L for the focal spot radii smaller than 150 μm. The largest growth of the density gradient corresponds to the maximum laser pulse intensity (t = 0). The density gradient achieves value about 1 × 10²² cm⁻⁴ for the minimum focal spot radius (R _L = 50 μm) and this gradient corresponds to the minimal scalelength L = 160 μm. It can be explained that for the time of the ablative plasma expansion t = 0, the favorable conditions for high energy fast electron generation due to resonant absorption occur. This effect is responsible for the energy transfer to the shock wave generated in a solid target. As follows from Figure 10a, the density gradient also increases with increasing the focal spot radii above 150 μm. However, this growth is connected with passage to predominating 1D expansion of the ablative plasma at large focal spot radii (Gus'kov et al., Reference Gus'kov, Demchenko, Kasperczuk, Pisarczyk, Kalinowska, Chodukowski, Renenr, Smid, Krousky, Pfeifer, Skala, Ullschmied and Pisarczyk2014).

Fig. 7. Axial density profiles and the scalelength characterizing the ablative plasma expansion during the laser pulse interaction for different focal spot radii in the case of the pre-plasma absence.

Fig. 8. Electron density distributions illustrating the time evolution of the ablative plasma expansion during the laser pulse interaction with the target at different focal spot radii under the presence of the pre-plasma.

Fig. 9. Axial density profiles and the scalelength characterizing of the ablative plasma expansion during the laser pulse interaction at different focal spot radii in the case of the pre-plasma presence.

Fig. 10. Comparison of the maximal density gradient, the scalelength, and the maximal electron density following from interferometric fitting obtained in the case of (a) absence and (b) presence of the pre-plasma.

In the case of the pre-plasma presence, Figure 10b, the density gradient falls in the whole range of the focal spot radii and the expansion time includes the maximum intensity of the laser pulse and ensuing 600 ps. The scalelength is increased by approximately two times as compared with the case with the pre-plasma absence. At the maximum laser intensity t = 0 and the minimal focal spot radius R _L = 50 μm, the scalelength grows to the level of about L = 330 μm. This proves that under the presence of the pre-plasma, the effect of the energy transfer by fast electrons becomes smaller. The presence of the extended pre-plasma leads to decreasing density gradients of the plasma created by the action of the main beam.

3.2. Crater Volume Measurements

In our previous papers (Kalinowska et al., Reference Kalinowska, Kasperczuk, Pisarczyk, Chodukowski, Gus'kov, Demchenko, Ullschmied, Krousky, Pfeifer, Skala and Pisarczyk2012; Gus'kov et al., Reference Gus'kov, Demchenko, Kasperczuk, Pisarczyk, Kalinowska, Chodukowski, Renenr, Smid, Krousky, Pfeifer, Skala, Ullschmied and Pisarczyk2014; Pisarczyk et al., Reference Pisarczyk, Gus'kov, Kalinowska, Badziak, Batani, Antonelli, Folpini, Maheut, Baffigi, Borodziuk, Chodukowski, Cristoforetti, Demchenko, Gizzi, Kasperczuk, Koester, Krousky, Labate, Parys, Pfeifer, Renner, Smid, Rosinski, Skala, Dudzak, Ullschmied and Pisarczyk2014), it has been shown that the interferometric measurements in combination with the crater volume analysis can provide essential information about mechanisms of the laser radiation absorption. The ratio N/V _cr (where N is the total electron number in the plasma plume and V _cr is the crater volume in cm³) defines a number of thermal electrons participating in the creation of crater volume unit (1 cm³).

To calculate the total electron number (N) in the ablative plasma the following formula was used:

(1)$$N = 2{\rm \pi} \int_0^R {\int_0^Z {n_{\rm e} (r, z)\; r\; dr dz}}$$

where n _e(r, z) is the electron density distribution obtained from the interferometric measurements [after reconstruction of interferograms (Kasperczuk & Pisarczyk, Reference Kasperczuk and Pisarczyk2001)] including electrons inside and outside the opacity zone. The way of the crater volume determination is presented in our previous paper (Pisarczyk et al, Reference Pisarczyk, Gus'kov, Kalinowska, Badziak, Batani, Antonelli, Folpini, Maheut, Baffigi, Borodziuk, Chodukowski, Cristoforetti, Demchenko, Gizzi, Kasperczuk, Koester, Krousky, Labate, Parys, Pfeifer, Renner, Smid, Rosinski, Skala, Dudzak, Ullschmied and Pisarczyk2014). The N/V _cr parameter was evaluated only for expansion time: t = 600 ps, that is, after the end of main laser pulse, when both ablation process and processes related to absorption of laser radiation were completed. Figure 11 presents a comparison of the crater volumes V _cr, total electron number N, and N/V _cr parameter obtained for the target irradiation without and with the pre-plasma.

Fig. 11. Comparison of the crater volumes V _cr, the total electron number N, and the N/V _cr parameter obtained in the case of (a) absence and (b) presence of the pre-plasma.

The rate of increase of the number of plasma electron in the approximation of the axial expansion is determined by the flow of electrons from the surface with the critical plasma density, where the main part of the laser radiation is absorbed:

(2)$$\displaystyle{{dN} \over {dt}} = \; n_{{\rm cr}} C_{\rm s} {\rm \pi} R_{\rm L}^2$$

Here n _cr = 1.12 × 10²¹/λ ² is the critical electron concentration measured in cm⁻³ for the light with the wavelength λ given in μm, C _s is the sound velocity of the plasma near the critical surface:

(3)$$C_{\rm s} = \left[ {\displaystyle{{2({\rm \gamma} - 1)} \over {3{\rm \gamma} - 1}}\displaystyle{{K_{{\rm ab}} I_{\rm L}} \over {{\rm \rho} _{{\rm cr}}}}} \right]^{{1 / 3}}$$

where ρ_cr=Am _pn _cr/Z is the critical plasma density, m _p is the proton mass, A and Z are the ion atomic number and charge, K _ab is the absorption coefficient, I _L and R _L are the laser intensity and beam radius, respectively. Substituting expression (3) into Eq. (2) and assuming the plasma is a perfect totally ionized gas, we have:

(4)$$\displaystyle{{dN} \over {dt}} = 2.1 \times 10^{27} \lambda ^{{4 / 3}} R_{\rm L}^{4/3} \left[ {\displaystyle{{K_{{\rm ab}} E_{\rm L} ({\rm J})} \over {\tau _{\rm L} ({\rm ns})}}} \right]^{{1 / 3}}$$

Here the laser energy E _L(J), pulse duration τ_L(ns), beam radius R _L, and λ are measured in Joule, ns, cm, and μm, respectively.

This simple evaluation gives an explanation of the measurements of the thermal electron number of the plasma torch. For E _L = 250 J, τ_L = 0.3 ns, λ = 1.351 μm, R _L = 100 μm, and absorption coefficient K _ab ≈ 0.3, the rate dN/dt is approximately 4.5 × 10²⁵ electrons per second. The rate dN/dt which can be concluded from the data of Figure 11a is approximately 5 × 10²⁵ that is very close to the theoretical evaluation. For the time t = 0, that is, for the maximum of laser pulse, the rate of 4.5 × 10²⁵ provides the number of electrons close to 7 × 10¹⁵ and three times larger number for the time t = 300 ps. It is to be noted that at approximately the same experimental and calculated rates of the electron number growth, the measured number of electrons is larger by a factor of 1.4 than the theoretical estimates. It can be explained by the fact that in the experiment, the plasma creation occurs during the time period including the pre-pulse.

In the case of the pre-plasma absence, Figure 11a, the crater volumes and the N/V _cr parameter demonstrate the increased efficiency of the crater creation with the decreasing focal spot radius in the range of R _L < 150 μm. According to our previous papers (Gus'kov et al., Reference Gus'kov, Demchenko, Kasperczuk, Pisarczyk, Kalinowska, Chodukowski, Renenr, Smid, Krousky, Pfeifer, Skala, Ullschmied and Pisarczyk2014; Pisarczyk et al., Reference Pisarczyk, Gus'kov, Kalinowska, Badziak, Batani, Antonelli, Folpini, Maheut, Baffigi, Borodziuk, Chodukowski, Cristoforetti, Demchenko, Gizzi, Kasperczuk, Koester, Krousky, Labate, Parys, Pfeifer, Renner, Smid, Rosinski, Skala, Dudzak, Ullschmied and Pisarczyk2014), this corresponds directly to the energy transfer into the target by fast electrons generated due to resonant absorption. However, the crater creation efficiency also grows in the range of the focal spot radii larger than R _L = 150 μm. When the beam radius exceeds this value, the fast electron temperature decreases (with decreasing the laser intensity) and the role of the fast electron energy transfer in the ablation process becomes smaller than the role of thermal conductivity. In this case, the crater volume growth is due to decreasing the transverse expansion of the laser-produced plasma. It is confirmed by interferometric results, which show the increasing density gradient (see Figure 10a) that is connected with the axial (1D) expansion of the ablative plasma, which predominates in the case of the 1ω radiation and R _L > 150 μm. The transverse plasma expansion decreases, the pressure increases and, hence, the efficiency of the energy transformation to the shock wave also increases. According to Borodziuk et al. (Reference Borodziuk, Kasperczuk, Pisarczyk, Gus'kov, Ullschmied, Kralikova, Rohlena, Skala, Kalal and Pisarczyk2004), the largest crater in the massive Cu target is created by means of the 1ω laser beam focused to the focal spot radius about 300 μm.

At the pre-plasma presence, Figure 11b, the crater volume decreases to the level about 3 × 10⁻⁵ cm⁻³, and this value does not depend on the focal spot radius of the main laser beam. Comparison with Figure 11a indicates that in the presence of pre-plasma, the effect of the fast electron energy transfer to the solid target is suppressed.

The experimental data stating the rate of the electron number growth in the presence of the pre-plasma (Figure 11b) are approximately by a factor of 1.5 larger in comparison with the case of the pre-plasma absence. It can be explained by the fact that in this case the absorption coefficient [see Eq. (3)] according to the results of numerical simulation presented below is twice higher than in the case of the pre-plasma absence. The rate of 8 × 10²⁵ electrons per second can provide the number of electrons equal to approximately 1.2 × 10¹⁶ and 3.6 × 10¹⁶. These values are about twice smaller than the data of Figure 11b which is ascribed to the contribution of the electrons from the pre-plasma.

To conclude, according to the temporary changes of the gradient determined from interferometric measurements the temporal changes of the N/V _cr parameter confirm that electrons produced in time t = 0 provide the largest contribution to the creation of the craters, corresponding to the maximum of the main laser pulse intensity.

4.1. X-ray Spectroscopy Measurements

To obtain information about the electron temperature in the ablative plasma, a spectrometer with the spherically bent crystal of mica was applied. As mentioned above, the Cu massive targets were coated with 25 μm-thick layer of plastic containing chlorine (parylene-C and C₈H₇Cl). The Cl He_α and Ly_α emission were measured in the 4th spectroscopic order, whereas the He_δ and Ly_β emission in the 5th order. The spectra were observed at an angle of 11.5° from the target surface and they were recorded on X-ray film Kodak Industrex AA400. The spatial resolution of the spectroscopic geometry used was 10 μm. Typically, the recorded spectra were intentionally saturated in the He_α region to increase the signal intensity for diagnostically important He_δ and Ly_β lines which were used for evaluation of the effective plasma parameters. The exposed films were digitized using a scanner with spatial resolution of 5.3 μm and the recorded signal was recalculated to incident photon fluxes via known characteristics of the scanner and X-ray film. The spectra were further corrected with respect to the wavelength-dependent crystal reflectivity and filter transmission. The wavelength calibration was done by using the ray-traced dispersion relation and tabulated wavelengths of the dominant X-ray lines. The evaluated spectra correspond to the emission from plasma regions close to the center of the focal spot on the laser-irradiated target surface.

To determine the effective plasma parameters, the measured spectra were fitted with synthetic spectra calculated by the PrismSpect code (MacFarlane et al., Reference Macfarlane, Golovkin, Wang, Woodruff and Pereyra2007) using the steady-state approximation. This model is dependent on three parameters: Effective plasma temperature T, density ρ, and size L. The plasma size L has been estimated by using the Cl He_α line which undergoes strong opacity broadening thus being very sensitive to L. The remaining two plasma parameters, T and ρ, were evaluated for each shot using a previously described fitting procedure (Smid et al., Reference Smid, Antonelli and Renner2013). The spectra fitting converged relatively fast, especially because the thickness of He_δ is highly sensitive to the plasma density and the ratio of He_δ and Ly_β varies with its temperature. The uncertainty estimates following from the procedure used amount to 5 eV for the plasma temperature and 10% for its density. The typical experimental spectra and their numerical fitting by the above-mentioned procedure are presented in Figure 12. They show dependences of the intensity of the He_δ and Ly_β lines on various conditions of the target irradiation. These three experimental spectra (colored lines, each tenth measured point depicted by a symbol) along with their best fits (black lines), all normalized with respect to the He_δ intensity, demonstrate the contingency between spectroscopic data and the plasma parameters. When going from the green via red to blue line, the characteristic gradual broadening (FWHM) of the He_δ profile is related to the increasing plasma density.

Fig. 12. The line profiles of the Cl He_δ and Ly_β lines measured for the different focal spot radius of the laser beam and their numerical fitting by the PrismSpect code (MacFarlane et al., Reference Macfarlane, Golovkin, Wang, Woodruff and Pereyra2007).

Similarly, the increase of the plasma temperature is connected with the increased intensity of the Ly_β line with respect to the He_δ emission. Figure 13 shows the dependence of the effective plasma density and temperature, as determined from the time-integrated X-ray emission, on the intensity of the main laser beam. These values characterize the density and temperature of plasma torch in the 100 μm-thick plasma region near the ablation surface. The real incident intensity was calculated from the measured beam energy and the focal spot radius estimated from the streak camera records.

Fig. 13. Dependences of (a) the electron density and (b) the temperature on the laser intensity at the absence and presence of the pre-plasma. The parameters correspond to the 100 μm-thick plasma region at the focal spot center on irradiated targets.

The data are plotted using the logarithmic scale for laser intensity axis, four vertical lines correspond to the nominal interaction parameters, that is, to the energy of 240 J focused to focal spot radii R _L = 200, 150, 100, and 50 μm. The shown points and lines correspond to the shots performed without (blue) and with (orange) the pre-pulse. The density fit is approximated by a linear regression, while the temperature fit is a logarithmic curve (we emphasize that the laser intensity is depicted in the logarithmic scale). Figure 14 shows analogous plasma parameters plotted with respect to the nominal R _L. The plotted points correspond to the intersection of the fitted curves shown in Figure 13 with vertical lines marking nominal intensities. In addition, results for shots with R _L and the laser energy closest to the nominal values are also introduced. Figures 13 and 14 demonstrate that despite obvious shot-to-shot fluctuation, several distinct trends are clearly seen. The temperature decreases with the increasing focal spot radius (i.e., it grows with the laser intensity), both under the absence and, slightly less, under the presence of the pre-pulse. On the other hand, the observed dependences of the plasma density are significantly influenced by the presence of the pre-pulse.

Fig. 14. Near-surface electron density (a) and temperature (b) as a function of the focal spot radius at the absence and presence of the pre-plasma.

It should be underlined, that the spectroscopically determined trends observed in the electron density deduced from spectroscopic measurements (cf. Figs 13 and 14) are very similar to those obtained from interferometry, despite some quantitative differences. For cases without the pre-pulse and the focal spot radii ranging from R _L = 50 μm to 150 μm, the electron densities determined by both methods decrease almost identically (about two times). The differences between spectroscopic and interferometric measurements relate to the R _L range larger than 150 μm and the expansion time close to t = 0. Here the electron density obtained from interferometry increases because of the predominating axial plasma expansion. This incompatibility is due to the fact that spectroscopy gives information about the effective value of the electron density averaged over time.

The presence of the pre-plasma clearly reduces the electron density which decreases to the same level for all focal spot radii. Namely, the value of ablation density determines the efficiency of the energy transfer from high-temperature plasma to non-evaporated part of the target by means of the shock wave. The ratio η of the energies of the shock wave E _s and the plasma plume E _P is determined by the ratio of the energy fluxes in the shock wave q _s and the plasma plume q _p at the ablation surface. In the plane approximation, the fluxes q _s and q _p are P _sw _s and P _aw _a, respectively. Here the pressure behind the shock wave P _s is close to the ablation pressure P _a (the pressure at the ablation front, that is, at the border between the plasma plume and the target), and the ablation and shock wave velocities are w _a ≈ (P _a/ρ_a)^1/2 and w _s ≈ (P _s/ρ_s)^1/2, respectively (ρ_a is the ablation density). Consequently the efficiency of the energy transformation to the shock wave increases with the increasing ablation density as η≈(ρ_a/ρ_s)^1/2 (Gus'kov et al., Reference Gus'kov, Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Pfeifer, Skala and Pisarczyk2007).

Summarizing the results of the spectroscopic measurements, we can formulate two important conclusions:

• • Without the pre-plasma, a sharp increase in ablation density with the focal spot radius decreasing from 100 to 50 μm indicates the effect of the fast electron energy transfer into the deeper region of the plasma larger than that provided by thermal conductivity. This conjecture is supported by interferometric measurements. Both X-ray spectroscopy and interferometric results confirm the conclusion that increasing efficiency of the energy transfer with the decreasing beam radius (which follows from measurements of the crater volume) results from increasing the ablation density due to the effect of fast electron energy transfer.

• • The presence of the pre-plasma leads to suppression of the effect of fast electron energy transfer.

4.2. 2D Imaging of the Cu K_α Line Emission

The Cu K_α images were taken using a spherically bent crystal of quartz (422) which was set up as an imaging mode monochromator (with the Bragg angle θ = 88.2°) to provide a quasi-monochromatic distribution of the K_α emission, 2D-spatially resolved along the target surface. The time-integrated K_α signals were again registered on the Kodak AA400 film. The recorded images were digitized using a calibrated table-top scanner, recalculated to optical densities and, by using the characteristic curve of the film, to intensities of the impinging radiation. The 2D-spatially resolved records contain information on emitting area and intensity of the K_α emission.

The images of the Cu K_α emission under conditions of the two-layer target irradiation (see Fig. 1) were recorded in laser shots with the absence of pre-pulses only. Typical images obtained when focusing the laser beam to focal spots with radii R_L = 50 μm and R_L = 100 μm are presented in Figure 15. The intensity of the K_α signal obviously grows with the decreasing focal spot size and with the increasing energy of the laser beam. The K_α images provide direct information on the lateral range of the hot electron propagation. After subtracting the background from the detected signal, the number of photons registered over the active detector area was recalculated to the Cu K_α emission from the target benefitting from the results of ray-tracing code (Podorov et al., Reference Podorov, Renner, Wehrhan and Furster2001; NIST ESTAR database; Morace & Batani, Reference Morace and Batani2010). With respect to relevant geometric factors (source-to-crystal-to-detector distance, crystal and detector dimension), crystal reflectivity, and transmission of the radiation through protective foils, the number of K_α photons N _Kα emitted by the source into the full solid angle is related to the number of photons striking the detector by a factor of 1/3.74 × 10⁻⁷. The results of the measurements of number of K_α photons for different focal spot radii and various laser energies are presented in Table 1. The growth of the emitted K_α photons with the increasing laser intensity demonstrates the growth of fast electron population. Taking into account our recent papers (Gus'kov et al., Reference Gus'kov, Demchenko, Kasperczuk, Pisarczyk, Kalinowska, Chodukowski, Renenr, Smid, Krousky, Pfeifer, Skala, Ullschmied and Pisarczyk2014; Pisarczyk et al., Reference Pisarczyk, Gus'kov, Kalinowska, Badziak, Batani, Antonelli, Folpini, Maheut, Baffigi, Borodziuk, Chodukowski, Cristoforetti, Demchenko, Gizzi, Kasperczuk, Koester, Krousky, Labate, Parys, Pfeifer, Renner, Smid, Rosinski, Skala, Dudzak, Ullschmied and Pisarczyk2014), this supports conjecture of the dominant role of fast electrons in the energy transfer to the shock wave generated in a solid target under the absence of the pre-plasma. It is very important, that the K_α emission was not observed for the focal spot radii larger than R _L = 100 μm and in the case of the pre-plasma presence. This indicates that the effect of the fast electron energy transfer occurs only when irradiating the targets by higher laser intensities and under the absence of the pre-plasma. On the other hand, this effect is suppressed at the pre-plasma presence.

Fig. 15. Images of the Cu K_α emission registered without the presence of the pre-plasma using the minimal focal spot radii and the laser energy: (a) 290 J and (b) 590 J.

Table 1. The comparison of the number of K_α photons for different focus spot radii and various laser energies.

However, the influence of the pre-plasma on K_α emission is not unequivocal when taking into account the results of 2D simulations presented later in Section 6 and conclusions formulated on their basis (Section 7). They suggest that the pre-plasma presence might lead to enhanced resonant absorption due to the increase of scalelength and better adjusting of the laser rays to the optimal angle (Gus'kov et al., Reference Gus'kov, Demchenko, Kasperczuk, Pisarczyk, Kalinowska, Chodukowski, Renenr, Smid, Krousky, Pfeifer, Skala, Ullschmied and Pisarczyk2014).

According to these conclusions, observation and discussion of Cu K_α images presented in this section should be treated as preliminary results that also require to take into consideration X-ray spectroscopic and fast electron energy measurements for various conditions of irradiation of the two-layer targets. Such experiments are planned for a further stage of SI-related research carried out at PALS.