2. EXPERIMENTAL ARRANGEMENT

Both fundamental (λ = 1.315 µm) and the third (0.438 µm) harmonic frequencies of the PALS iodine laser system in Prague (Jungwirth et al., Reference Jungwirth, Cejnarová, Juha, Králiková, Krása, Krouský, Krupičková, Láska, Mašek, Mocek, Pfeifer, Präg, Renner, Rohlena, Rus, Skála, Straka and Ullschmied2001; Jungwirth, Reference Jungwirth2005; Ullschmied, Reference Ullschmied2006), with the laser pulse energies up to 560 J (1ω) and the pulse length lower than 300 ps, were used in our experiments. The Ta target was irradiated either perpendicularly, or at 30°, while the emitted ion stream was investigated at 30° (in the first case) or perpendicularly to the target (second case). The schematic view of the experimental arrangement is shown, e.g., in Wolowski et al. (Reference Wolowski, Badziak, Boody, Gammino, Hora, Jungwirth, Krása, Láska, Parys, Pfeifer, Rohlena, Szydlowski, Torrisi, Ullschmied and Woryna2003). The minimum focus spot position with regard to the Ta target surface was varied in a broad range to make the changes of the interaction conditions of the laser beam with the self-created plasma significant. The convention used is that FP = 0 when minimum focal spot coincides with the target surface, while FP < 0 means that it is located in front of the target surface, and FP > 0 means that it is inside the target. Usually, the target position was fixed, and the focusing lens was movable.

Characteristics of the ions emitted were investigated by the ion collectors (IC, ICR) and by the electrostatic ion energy analyzer (IEA) in the far expansion zone (Woryna et al., Reference Woryna, Parys, Wolowski and Mroz1996; Krása, Reference Krása, Gammino, Mezzasalma, Neri and Torrisi2004). Soft and hard X-ray radiation from the produced plasma was monitored by the diodes with various filters (Ryc et al., Reference Ryc, Badziak, Juha, Krása, Králiková, Láska, Parys, Pfeifer, Rohlena, Skála, Slysz, Ullschmie, Wegrzecki and Wolowski2003). A Kentech low-magnification X-ray streak camera with a sweep range up to 5 ps/mm; placed side-on recorded radiation of energy higher than 0.8 keV, to provide time- and space-resolved information on expanding plasma radiation (Ullschmied, Reference Ullschmied2006). Two different orientations of its entrance slits (parallel and perpendicular to the laser beam axis) provide spatial resolution of 20 µm, either along the target normal or across the laser beam. Three-frame laser interferometric system with an automatic image processing (Pisarczyk et al., Reference Pisarczyk, Badziak, Kasperczuk, Parys, Wolowski, Woryna, Jungwirth, Králiková, Krása, Láska, Mašek, Pfeifer, Rohlena, Skála, Ullschmied, Kálal and Pisarczyk2002) was used to study the plasma expansion and plasma density, both during the laser pulse and in the post interaction phase. The temporal resolution ~0.3 ns was determined and a spatial resolution of ~20 µm was deduced (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006; Nikolaï et al., 2006).

3. LASER PULSE PROPERTIES

Good stability and reproducibility of the PALS laser pulse-length for about 100 shots at 1ω and laser energy of 380 J, of 480 J, and of >500 J is documented in Figure 1. Generally, the pulse length is presented as full width at half maximum (FWHM). However, considering the possible participation of the nonlinear processes, further pulse characteristics are worth mentioning, because of their importance with regard to the possible laser-preformed plasma interactions. Typical shape of the leading edge of the laser pulse (using the logarithmic scale), the reproducibility of which is, however, a little bit worse, is presented in Figure 2a. While the contrast at −2 ns is better than 10⁷, it is about 10⁶ at −1 ns, and only 10² at −0.5 ns. Thus, at laser intensities higher than 10¹⁶ W/cm², the expanding plasma plume appears above the target surface approximately 2 ns before the pulse maximum, moreover, conditions for the appearance of nonlinear processes may be fulfilled approximately 0.5 ns before it. Considering that the measured velocity of various emitted ion-groups range from 5 × 10⁶ to 5 × 10⁸ cm/s (Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Torrisi, Gammino and Boody2006a), the thickness of plasma layer (of varying plasma density) may attain values from tens of µm, at least, up to several mm. For the sake of completeness, small peaks above the background plateau were recorded at 6.6 ns, 1.6 ns, and 800 ps before the pulse maximum. The fall time of the pulse is about twice longer than the rising front. Such laser pulse asymmetry may influence the post-pulse plasma dynamics mainly.

Fig. 1. (Color online) Statistics of the PALS pulse-length (FWHM) for various laser energy (1ω).

Fig. 2. Front edge (a) and radial homogeneity (b) of the PALS pulse (1ω, 380 J).

The fully flat, homogeneous target irradiation by the PALS laser beam is possible in the case of the first harmonic of the laser radiation, and of the laser energy below 180 J (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006). For higher energies, the intensity distribution becomes concave. This is a special feature of iodine laser amplifiers that produce a stronger amplification in the off-axis region. The depth of the cavity in the center increases with increasing laser energy. For the laser energy of ~600 J, the ratio of the central intensity to that at the edge may reach the value of 0.9. To obtain the same laser energy in the third harmonics, the energy of the first harmonic before the conversion should be 2–3 time higher. Thus, the intensity distribution of the converted laser beam has usually a minimum in the center. After the conversion, this concave character of the intensity distribution is more pronounced due to the nonlinear wavelength transformation by the DKDP crystal. In addition, the intensity distribution may not be fully symmetric across the beam diameter (Fig. 2b). The comparison of laser beam intensity distributions in the target plane for the first harmonic and the laser energies 100 J and 300 J, recorded by the CCD camera, was published in Nicolaï et al. (Reference Nicolaï, Tikhonchuk, Kasperczuk, Pisarczyk, Borodziuk, Rohlena and Ullschmied2006).

4. RESULTS AND DISCUSSION

In contrast to the nominal laser pulse length (~300 ps), the lifetime of the expanding plasma attains values of some tens of ns. The expansion of the produced laser plasma is not isotropic with regard to the target surface—its highest velocity is in the direction of the normal to the target surface, independently of the angle of the target irradiation. Interferometric studies of plasma dynamics led even to a discovery of dense (n_e >10¹⁸ cm⁻³) sharp plasma jets generated at the interaction of defocused laser beam (I_L ~10¹⁴ W/cm²) with planar metallic targets (Al, Cu, Ag, Ta, Pb) (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006; Nicolaï et al., Reference Nicolaï, Tikhonchuk, Kasperczuk, Pisarczyk, Borodziuk, Rohlena and Ullschmied2006). The jets of diameter less than 1 mm are several mm long and last longer than 17 ns. A typical sequence of electron density distributions for Ta at the third harmonics and at laser energy of 100 J is shown in Figure 3, as an example. Based on dimensional analysis and two-dimensional (2D) hydrodynamic simulation, the prevailing mechanism of jet formation was ascribed to the radiative cooling, while magnetic field should play a minor role (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006).

Fig. 3. (Color online) Expanding plasma at 2–17 ns after the target irradiation (3ω, 100 J, FP = +300 µm).

When using the iodine laser, the “optimum” focus position was found to be in front of the target surface (FP < 0) (Láska et al., Reference Láska, Badziak, Boody, Gammino, Hora, Jungwirth, Krása, Parys, Pfeifer, Rohlena, Torrisi, Ullschmid, Wolowski and Woryna2003), in which ions with the highest charge states and kinetic energy can be generated (even higher than those produced in the point of the maximum nominal laser intensity). Also, a significant asymmetry of various dependencies (of maximum ion charge states, ion velocities or ion kinetic energy, current of highly charged ions, crater diameters, X-ray radiation, etc.) on the FP, with regard to the position of the nominal laser intensity maximum at FP = 0, was recorded. This can be understood in terms of various ion-accelerating processes (Láska et al., Reference Láska, Badziak, Boody, Gammino, Jungwirth, Krása, Krouský, Parys, Pfeifer, Rohlena, Ryć, Skála, Torrisi, Ullschmied and Wołowski2007; Margarone et al., Reference Margarone, Torrisi, Gammino, Krasa, Krousky, Laska, Pfeifer, Rohlena, Skala, Ullschmied, Velyhan, Parys, Rosinski, Ryc and Wolowski2006) including nonlinear processes (self-focusing) due to the laser preplasma interactions (Láska et al., Reference Láska, Badziak, Boody, Gammino, Hora, Jungwirth, Krása, Parys, Pfeifer, Rohlena, Torrisi, Ullschmid, Wolowski and Woryna2003, Reference Láska, Jungwirth, Králiková, Krása, Pfeifer, Rohlena, Skála, Ullschmied, Badziak, Parys, Wolowski, Woryna, Torrisi, Gammino and Boody2004aReference Láska, Ryc, Badziak, Boody, Gammino, Jungwirth, Krasa, Krousky, Mezzasalma, Parys, Pfeifer, Rohlena, Torrisi, Ullschmied and Wolowski2005b). It is worth noticing that the new point of symmetry of the dependencies is shifted roughly to a distance of ~200 µm in front of the target surface.

In Figure 4a, four possible combinations of laser wavelength and angle of target irradiation, are compared. More asymmetric dependencies of z_mx on FP were recorded for ions emitted perpendicularly to the target surface at both 1ω and 3ω (irradiation at 30°); while these dependencies for perpendicular target irradiation (ions recorded at 30°) are shifted less. This implicates an anisotropic angular emission of fast ions, which is consistent with the results in Figure 3. The fast ions with the high charge states (around 50+) and of high energy are produced also at the oblique irradiation (lower nominal laser intensity). The group of the fastest ions (with possibly higher charge states) that are emitted into a cone with the angle smaller than 30° (with regard to the target normal), cannot be recorded at the perpendicular irradiation in our experimental arrangement. We can recalculate the dependencies in Figure 4 to those in laser intensity I_L (I_Lλ²). Generally—the higher I_L, the higher charge state and energy of produced ions. Saturation of the values of z_max in a broad region of laser intensities (see Fig. 4b) implicates that the self-focusing of laser beam to the limiting diameter (of about 1λ) determines the maximum attainable laser beam intensity.

Fig. 4. (Color online) Dependence of the maximum charge state z_max on the focus position (a) and on the laser intensity (b) for combinations of 1ω, 3ω, and perpendicular (0^°) and 30^° target angle irradiation (P≡FP>0, N≡FP<0).

Varying the laser FP with regard to the target surface at a fixed laser beam energy E_L, it does not mean changes in the laser intensity only, but also changes in the interaction conditions for the laser beam that interacts with an expanding plasma plume. In Figure 5a (3ω, 150 J), the dependencies of peak kinetic energy of 14 ion subgroups on FP are presented that have been identified in the IC signals at various focus positions and labeled from 2 to 14. They are distributed, in principle, over three generally accepted ion groups (Wolowski et al., Reference Wolowski, Parys, Woryna, Láska, Mašek Rohlena, Mróz and Farny1995; Rohlena et al., Reference Rohlena, Králiková, Krása, Láska, Mašek, Pfeifer, Skála, Parys, Wolowski, Woryna, Farny, Mroz, Roudskoy, Shamaev, Sharkov, Shumshurov, Bryunetkin, Haseroth, Collier, Kuttenberger, Langbein and Kugker1996): slow S (Hora & Kane, Reference Hora and Kane1977; Häuser et al., Reference Häuser, Scheid and Hora1992), thermal T (Hora, Reference Hora1975; Borisov et al., Reference Borisov, Borovskiy, Korobkin, Prokhorov, Shiryaev, Shi, Luk, McPhearson, Solem, Boyer and Rhodes1992), and fast F (Sun et al., Reference Sun, Ott, Lee and Guzdar1987; Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Torrisi, Gammino and Boody2006a) (10, 7). Subgroups (Hora, Reference Hora1969; Torrisi et al., Reference Torrisi, Andò, Gammino, Krása and Láska2001; Margarone et al., Reference Margarone, Torrisi, Gammino, Krasa, Krousky, Laska, Pfeifer, Rohlena, Skala, Ullschmied, Velyhan, Parys, Rosinski, Ryc and Wolowski2006, Láska et al., Reference Láska, Jungwirth, Králiková, Krása, Pfeifer, Rohlena, Skála, Ullschmied, Badziak, Parys, Wolowski, Woryna, Torrisi, Gammino and Boody2004a, Reference Láska, Jungwirth, Krása, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Boody, Gammino and Torrisi2004b, Reference Láska, Jungwirth, Krása, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Gammino, Torrisi and Boody2005a, Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Skála, Ullschmied, Velyhan, Kubeš, Badziak, Parys, Rosinski, Ryc and Wolowski2006b), clearly seen in the region of focus positions −500 µm < FP < 0, represent a super fast (FF) ion group, which is connected with an increased intensity due to self-focusing (Láska et al., Reference Láska, Jungwirth, Krása, Pfeifer, Rohlena and Ullschmied2005c). In the region of the FP printed, the peak ion velocities range from 5 × 10⁶ cm/s to 5 × 10⁸ cm/s, corresponding to the ion energies from ~2 keV to 20 MeV. The limit label 1 may represent impurities (C, O) and missing label 1 fast protons with the energy above 1 MeV. The current density of groups of the fastest ions significantly increases from the threshold value at I_L ~2 × 10¹⁴ W/cm² and attains maximum value up to ~100 mA/cm² (1 m from the target). The duplicity of the main ion groups may be explained by astigmatism of the focusing lens, which produces, in fact, a double focus spot. A similar amount of ion subgroups was recorded at 1ω with the laser pulse energy ~380 J.

Fig. 5. (Color online) Peak ion energy E_i of 14 ion groups, determined from IC signals, in dependence on the focus position FP (a) and four (five) calculated “equivalent” ion temperatures (b).

A linear increase in the ion energy with increasing charge states characterize the ambipolar acceleration mechanism, which acts at different (low or high) plasma temperatures. The shifted Maxwell-Boltzmann-Coulomb function was used (Torrisi et al., Reference Torrisi, Gammino, Andò, Láska, Krása, Rohlena, Ullschmied, Wolowski, Badziak and Parys2006a) to fit the measured charge-energy distribution of Ta ions (1–54+), produced in the presence of nonlinear processes. Four (five) “equivalent temperatures” with the highest one ~80 keV were evaluated (see Fig. 5b) that might be ascribed to four different groups of produced ions. We assume that near LTE conditions, the developed voltage on the distance of the Debye length can be evaluated, knowing the plasma temperature and density. Calculated electric field attains a value of 6.6 MV/cm at the laser intensity of 10¹⁰ W/cm² and 11 GV/cm at the laser intensity of 10¹⁶ W/cm² (Torrisi et al., Reference Torrisi, Gammino, Láska, Krása, Rohlena and Wolowski2006b).

By refining the course of experimental step in FP, we obtained a surprising result. Figure 6 shows a current dependence on the basic ion subgroups (8–14) on the laser focus position. Three maxima are clearly visible within the FP < 0 region in front of the target. Moreover, the maxima and minima of all ion subgroups coincide at the same focus positions FP, approximately, the distance of which is ~200 µm. This is valid also for super fast ion groups (2–7). Similar dependencies were found also for low charged ions (see Fig. 7a); the distance of peaks at FP < 0 is ~150–200 µm again.

Fig. 6. (Color online) Relative amplitude of the current of the super fast (a) and slow, thermal and fast (b) ion groups (from Fig. 5a) in dependence on the focus position FP.

Considering that L_SF ~200 µm is the length necessary for the contraction of the beam, then the position of peak at FP =−500 µm indicates, in fact, the place of plasma density, sufficient for self-focusing of the laser beam at the nominal intensity ~1 × 10¹⁶ W/cm². Independent interferometric measurements (Kasperczuk et al., Reference Kasperczuk, Pisarczyk, Borodziuk, Ullschmied, Krousky, Masek, Rohlena, Skala and Hora2006), performed under similar experimental conditions (Ta, 3ω, 100 J) report the value of n_e = 1 × 10¹⁸ cm³ at the distance of 4 mm (normal to the target) even after 17 ns. It should be remembered that in FP < 0 positions, a front of expanding plume always meets the place of maximum laser intensity, while for FP > 0 plasma expands against the laser beam with a continuously decreasing intensity than the nominal (~5 × 10¹⁴ W/cm² at FP = +500 µm).

The amount of various kinds of ions depends on the volume of the produced plasma and its temperature. The composition of emitted plasma plume is reflected by the height of the separate ion current peaks in Figure 7a. Two principal side-maxima (modulated) are dominant for ions with the charge states lower than ~25+ (similarly as for soft X-ray radiation (Tallents et al., Reference Tallents, Luther-Davies and Horsburgh1986)) can be with certainty ascribed to the thermal electrons. For the higher charge states (~30+), an independent maximum around FP = 0 appears, which is shifted for the charge states higher than 30+ to a FP < 0 position. This maximum (as well as that similar for hard X-rays) is connected with the presence of fast electrons. Substantial amount of ions with the highest charge states (above 40+) were recorded only at FP < 0, when conditions for the self-focusing of laser beam were met. Self-focusing lengths ~100–400 µm can be estimated from the distances of the superimposed maxima; this spread might be explained by a gradually change of the laser beam intensity and of the electron density during the laser interaction within the expanding plasma plume due to the onset of self-forming.

Fig. 7. (Color online) Relative amplitude of the low-charged single ions (a) and hard X-ray radiation (b) dependence on the focus position FP.

In addition, the same maxima were found on the intensity curves of the emitted hard X-ray radiation (<20 keV)—see Figure 7b (1ω, 380 J, 0°). The emission of the both soft (0.9–7.1 keV) and hard (5.1–20 keV) X-rays increases with the laser intensity. The position of the hard X-ray maximum and the maximum of the highest charged ions correlate. Both the maxima of soft X-rays are almost symmetrically positioned with regard to the hard X-ray maximum and correspond to the optimum relation of volume and temperature of produced plasma, in agreement with earlier published results (Láska et al., Reference Láska, Ryc, Badziak, Boody, Gammino, Jungwirth, Krasa, Krousky, Mezzasalma, Parys, Pfeifer, Rohlena, Torrisi, Ullschmied and Wolowski2005b).

The formation of a longitudinal structure of the self-focused laser beam was theoretically analyzed (Sun et al., Reference Sun, Ott, Lee and Guzdar1987; Sharma et al., Reference Sharma, Verma, Sodha and Kumar2004); the constriction of laser beam may not be equidistant and differs from tens to hundreds of μm. Borisov et al. (Reference Borisov, Borovskiy, Korobkin, Prokhorov, Shiryaev, Shi, Luk, McPhearson, Solem, Boyer and Rhodes1992) gave the first experimental evidence for the formation of a stable mode of spatially confined (channeled) propagation of the beam with a longitudinal structure. They observed the distribution of intensity along the filament: moon-like spots of decreasing intensity with a spatial distance ~200 µm.

Using the X-ray streak camera we recorded similar moon-like spots with the time distance of ~100 ps and with the changing intensity in the expanding plasma plume (even splitting into two plasma plumes). Examples are presented in Figure 8, in which the size of the black area is about 2 ns (time-axis x) times 0.6 mm (space-axis y). The plasma produced survives several times the laser pulse length, the total length of which is, in fact, much higher than that presented as FWHM. The measured velocity of majority of emitted fast ions is ~2 × 10⁸ cm/s (Láska et al., Reference Láska, Jungwirth, Krása, Krouský, Pfeifer, Rohlena, Skála, Ullschmied, Velyhan, Kubeš, Badziak, Parys, Rosinski, Ryc and Wolowski2006b); it means that time distance of the bright spots ~100 ps could correspond to a space distance of ~200 µm.

Fig. 8. (Color online) The X-ray streak camera image of an expanding plasma with a longitudinal structure (1ω, 380 J, FP = +200 µm) (a) and even split (1ω, 486 J, FP = −400 µm) (b).

Various bright spots (moon-like, half- moon-like) can be distinguished on the trace in Figure 8. The structure of the trace for the time above ~800 ps is not possible to ascribe to the effect of self-focused laser beam, but likely to a transformation and dissipation of the internal magnetic field. The pinching of very intense ion current beam due to very high (~MG) self-created magnetic field (Pukhov & Meyer-ter-Vehn, Reference Pukhov and Meyer-ter-Vehn1996; Borghesi et al., Reference Borghesi, Mackinnon, Gaillard, Willi, Pukhov and Meyer-ter-Vehn1998) may increase the plasma temperature and consequently contribute again to the production of ions with the highest charge states and energy. Since all these phenomena proceed within ~2 ns, the detailed processes cannot be distinguished from each other (are integrated) in the far expansion zone (~2 m), of course.