1. INTRODUCTION
The production of ions with high intensity, charge state, and kinetic energy, by using power pulsed lasers is assuming more and more importance in many application fields (nuclear fusion, laser ion source, new generation ion accelerators, ion implantation, etc.) (Laska et al., Reference Laska, Badziak, Gammino, Jungwirth, Kasperczuk, Krasa, Krousky, Kubes, Parys, Pfeifer, Pisarczyk, Rohlena, Rosinski, Ryc, Skala, Torrisi, Ullschmied, Velyhan and Wolowsk2007; Malka & Fritzler, Reference Malka and Fritzler2004; Lifschitz et al., Reference Lifschitz, Faure, Glinec, Malka and Mora2006; Mangles et al., Reference Mangles, Walton, Najmudin, Dangor, Krushelnick, Malka, Manclossi, Lopes, Carias, Mendes and Dorchies2006; Batani et al., Reference Batani, Dezulian, Redaelli, Benocci, Stabile, Canova, Desai, Lucchini, Krousky, Masek, Pfeifer, Skala, Dudzak, Rus, Ullschmied, Malka, Faure, Koenig, Limpouch, Nazarov, Pepler, Nagai, Norimatsu and Nishimura2007; Koyama et al., Reference Koyama, Adachi, Miura, Kato, Masuda, Watanabe, Ogata and Tanimoto2006).
Highly charged heavy ions can be obtained by ps and ns high power pulsed laser irradiating heavy elements (Laska et al., Reference Laska, Jungwirth, Kralikova, Krasa, Krousky, Masek, Pfeifer, Rohlena, Skala, Ullschmied, Badziak, Parys, Ryc, Szydlowski, Wolowski, Woryna, Ciavola, Gammino, Torrisi and Boody2004). The electronic temperature of the laser-generated plasma, the average charge state, and the mean ion energy increase with the laser intensity.
Many experiments regarding the generation of highly charged ions are currently accompanied by the laser interaction with preformed plasma. Preformed plasma can be produced by a separate laser pre-pulse preceding the main laser pulse (Laska et al., Reference Laska, Jungwirth, Krasa, Pfeifer, Rohlena and Ullschmied2005a, Reference Laska, Badziak, Gammino, Jungwirth, Kasperczuk, Krasa, Krousky, Kubes, Parys, Pfeifer, Pisarczyk, Rohlena, Rosinski, Ryc, Skala, Torrisi, Ullschmied, Velyhan and Wolowsk2007). However, even the main pulse itself significantly participates in the pre-plasma formation, in fact, self-created pre-plasma is formed from the front part of the long laser pulses or due to the long lasting intensity background of the short pulses (Laska et al., Reference Laska, Jungwirth, Krasa, Krousky, Pfeifer, Rohlena, Skala, Ullschmied, Velyhan, Kubes, Badziak, Parys, Rosinski, Ryc and Wolowski2006a).
The interaction of the laser radiation above some threshold intensity with a plasma of defined properties may significantly increase the charge state and energy of the produced ions, due to a peculiar effect occurring in the plasma, which focalizes further the laser pulse (self-focusing effect) acting so as a small vapor lens placed in front of the target surface. Advances in laser technology have recently enabled the observation of self-focusing in the interaction of intense laser pulses with plasmas. Self-focusing in plasma can occur through thermal, relativistic, and ponderomotive effects (Giulietti & Gizzi, Reference Giulietti and Gizzi1998; Giulietti et al., Reference Giulietti, Galimberti, Gamucci, Giulietti, Gizzi, Koester, Labate, Tomassini, Ceccotti, D'Oliveira, Auguste, Monot and Martin2007; Laska et al., Reference Laska, Jungwirth, Krasa, Krousky, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Gammino, Torrisi and Boody2006b).
Thermal self-focusing is due to collisional heating of plasma exposed to electromagnetic radiation: the rise in temperature induces a hydrodynamic expansion, which leads to an increase of the refraction index and further heating. Relativistic self-focusing is caused by the mass increase of electrons traveling at speed approaching the speed of light, which modifies the plasma refractive index, depending on the electromagnetic and plasma frequencies. Ponderomotive self-focusing is caused by the ponderomotive force, which pushes electrons away from the region where the laser beam is more intense, therefore increasing the refractive index and inducing a focusing effect.
The evaluation of the contribution and interplay of these processes is a complex task, but a reference threshold for plasma self-focusing is the relativistic critical power which must be reached (Sun et al., Reference Sun, Ott, Lee and Guzdar1987):
where m e is the electron mass, c is the speed of light, ω is the radiation angular frequency, e is the electron charge, and ωp is the plasma frequency. This last quantity depends on the relationship (Sun et al., Reference Sun, Ott, Lee and Guzdar1987):
where n is the electron density and ɛo is the permittivity in vacuum.
For an electron density of 1019 cm−3 and radiation at the wavelength of 438 nm, the critical power is about 980 GW, lower with respect to the maximum PALS laser power of the order of 1013 W.
Self-focusing in plasma can balance the natural diffraction and channel a laser beam. Such effect is beneficial for many applications, since it helps increasing the length of the interaction between laser and medium. This is crucial, for example, in laser-driven particle acceleration, laser-fusion schemes and high harmonic generation (Malka & Fritzler, Reference Malka and Fritzler2004; Malka et al., Reference Malka, Faure, Glinec and Lifschitz2006; Lifschitz et al., Reference Lifschitz, Faure, Glinec, Malka and Mora2006; Mangles et al., Reference Mangles, Walton, Najmudin, Dangor, Krushelnick, Malka, Manclossi, Lopes, Carias, Mendes and Dorchies2006). Self-focusing effects are obtained overall by using pico-second and femto-second lasers with intensities higher than 2 × 1014 W/cm2, which induce particularly the evidence for the phenomenon because they induce a net increment of the average charge state and ion energy of the plasma (Sun et al., Reference Sun, Ott, Lee and Guzdar1987). In this contribution, the laser generation of Au ions with the highest charge states and the highest energy was studied using long pulse of the PALS iodine laser at the third harmonic frequency, and changing the laser focus positions.
2. MATERIALS AND METHODS
Experiments were performed with the high-power iodine laser system at the PALS Research Center ASCR in Prague, operating at a maximum pulse energy of 1 kJ, a pulse duration of 300 ps, and 1.315 µm fundamental frequency (Jungwirth, Reference Jungwirth2005; Batani et al., Reference Batani, Dezulian, Redaelli, Benocci, Stabile, Canova, Desai, Lucchini, Krousky, Masek, Pfeifer, Skala, Dudzak, Rus, Ullschmied, Malka, Faure, Koenig, Limpouch, Nazarov, Pepler, Nagai, Norimatsu and Nishimura2007). All presented results were obtained irradiating in vacuum (10−6 mbar) Au thin targets (500 µm thick) with the third harmonic (3ω), at 438 nm wavelength, and with laser pulse energy of 150 J.
The ion diagnostics was based mainly in an ion collector ring (ICR) and an electrostatic ion energy analyzer (IEA) useful for online monitor of the ion emission from plasma and to measure the energy-to-charge ratio. Time-of-flight (TOF) technique was employed to measure the arrival time of the ion signal and the corresponding ion velocity and energy. Both ICR and IEA were situated in the far expansion zone of the plasma, orthogonal to the target surface, and at a distance of 190 cm and 262 cm, respectively.
The laser beam was focused on the flat surface of the pure Au target, which was irradiated, with an incidence angle of 30°. The bias of the IEA deflection plates was maintained constant at ±1500 V, i.e., the ratio E/z was maintained constant at 30 keV/charge state (Woryna et al., Reference Woryna, Parys, Wolowski and Mroz1996). The focal position (FP) of the focusing lens has been changed, gradually, in the range −1500 µm ≤ FP ≤ +1500 µm by means of a step motor with a resolution of ±1 µm. The convention used is that FP = 0 when minimum focal spot coincides with the target surface, while FP < 0 means that the minimum focal spot is located in front of the target surface, and FP > 0 means that it is inside the target, as shown in Figure 1.
Fig. 1. Experimental set-up at PALS laboratory.
The laser intensity (IL) is calculable knowing the pulse energy (EL), the spot area on the target surface (S), and the pulse duration (Δt):
The spot size diameter is measurable in-situ, by using a suitable optical microscope, and ex-situ with a surface profiler (Tencor P-10) giving the crater diameter, and the crater depth profile (Torrisi et al., Reference Torrisi, Gammino, Ando, Mezzasalma, Badziak, Parys, Wolowski, Woryna, Jungwirth, Kralikova, Krasa, Laska, Pfeifer, Rohlena, Skala, Ullschmied and Boody2002).
The electronic temperature (Te) of the non-equilibrium plasma was obtained from the theoretical approach (Giulietti & Gizzi, Reference Giulietti and Gizzi1998):
where I L and λ are the laser intensity and laser wavelength, respectively.
The minimum spot size diameter, measured at FP = 0 µm, was 70 µm, at which corresponds to a laser intensity of 1.3 × 1016 W/cm2 and, from Eq. (4), an electronic temperature of 8.14 keV.
3. RESULTS
Figure 2 shows three typical ion collector spectra acquired using 150 J laser pulse energy for FP = −1500 µm (a), FP = −700 µm (b), and FP = −200 µm (c), which corresponds to spot sizes 46.6 × 10−4, 12.6 × 10−4, and 1.8 × 10−4 cm2, respectively. The spectra indicate that two ion groups are evident at high and low spot size, i.e., at low and high laser intensity, respectively. The first group contains fast ions (TOF < 2 µs) and the second group contains slow ions (TOF > 2 µs), respectively. The first group is generated by high charge states while the second one by low charge states, as demonstrated by contemporary IEA measurements of ion charge states reported below. The mean amplitude, yield, width and time of the TOF peak, for the two ion groups, depend on the used value of the focal position FP.
Fig. 2. ICR spectra comparison at three different focal positions: FP = −1500 µm (a), FP = −700 µm (b), and FP = −200 µm (c).
The ion collector measurements of the emitted slow group versus the nominal spot size, performed with the ICR placed along the normal to the target surface, indicate that the ion emission increases linearly with the spot size, except for spots lower than 2 × 10−4 cm2, i.e., −200 µm < FP < 0, as reported in Figure 3a. Improving the laser beam focalization, i.e., reducing the spot size, the signal amplitude of the peak due to low charge states contribution decreases, while the laser intensity and the plasma electron temperature increase.
Fig. 3. Ion yield vs. nominal spot area for low and high charge states in linear (a) and semi-logarithmic (b) plots.
A different effect characterizes the fast ion group. The ion collector amplitude signal of the emitted fast group versus the spot size, performed with the ICR placed along the normal to the target surface, indicates that the ion emission is independent of the spot size. At the nominal spot size of 1.8 × 10−4 cm2 the fast component shows a peak, as evident from the semi-logarithmic plot reported in Figure 3b.
Thus, at large spot sizes, the ion current is due mainly to the slow and low charge ion group while at little spot sizes, lower than that 3 × 10−4 cm2, the ion current is due mainly to the fast and high charge ion group.
The two detected ion groups are evident also from the IEA spectra. Figure 4 shows a typical IEA-TOF spectrum comparison registered at different focus positions during the Au target irradiation. The faster peak is due to hydrogen ions as contaminant of the Au target. The spectrum obtained at FP = +500 µm (a) shows only low charge states group for Au ions, from 1+ up to 6+, due to the large distance from the best nominal focus position (FP = 0). Because at this distance the laser spot is large, the corresponding laser intensity and the electronic plasma temperature are low and the ionization is minimal.
Fig. 4. IEA spectra comparison at four different focal positions: FP = +500 µm (a), FP = 0 µm (b), FP = −200 µm (c) and FP = −400 µm (d).
The IEA signal at FP = 0 (b) shows two different ion groups, probably attributable to two main ionization mechanisms occurring in the plasma, i.e., the inverse bremsstrahlung and the resonant absorption (Bell, Reference Bell and Dendy1996). The first group includes slower Au ions with charge states between 16+ and 35+, while the second one includes faster Au ions with charge states between 36+ and 51+. Moreover, this spectrum indicates that the yield of the fast ion group, at higher charge states, is about a factor of three higher with respect to that of the slow ion group, at lower charge states. This result indicates that at this focal position, the laser intensity is high, and that the resonant absorption mechanism, responsible for the higher charge state formation, is predominant. In these conditions of best nominal focus position, it is not possible to distinguish the lowest charge states, from 1+ to 15+, due to the high laser intensity that permits to strip about 16 electrons from the plasma atoms, indicating that the laser spot is small and the corresponding laser intensity and electronic temperature high.
The TOF spectrum obtained at FP = −200 µm (c) is again constituted of two ion groups, where the slow one includes charge states between 10+ and 35+, while the fast one includes charge states between 36+ and 56+. Two important results have been obtained for this negative focus position: the highest charge state for Au ions (56+) and the highest amount of the fast ion group (about a factor of six higher than the slow ion group). Both results are correlated to the overcoming of the minimal threshold of self-focusing process appearance (typically about 2 × 1014 W/cm2 (Sun et al., Reference Sun, Ott, Lee and Guzdar1987)) produced by the very intense laser beam with the preformed plasma, which find a maximum effect when it is focused before the target surface (FP < 0) and at 200 µm distance.
Increasing further the focal position distance from the target surface (defocusing in front of the target), the charge state distribution shows a decrement. The spectrum reported in (d) was obtained for FP = −400 µm at which it is possible to distinguish two different ion groups and, as expected, the slower one (Au8+ ÷ Au29+) becomes higher with respect to the faster one (Au30+ ÷ Au44+), due to the spot increase, i.e., to the corresponding decrease in laser intensity and temperature.
Measurements demonstrated that although the minimum spot size diameter (70 µm) corresponds to a laser intensity of 1.3 × 1016 W/cm2 and an electronic temperature of 8.14 keV, when FP = −200 µm is chosen, due to the self-focusing effect, a sort of further laser beam focalization reduces subsequently the laser spot diameter on the target surface, increasing the laser intensity, and the electronic plasma temperature and producing an ionization of high charge states.
In order to show the self-focusing effect, some IEA measurements of ion yield for specific ion charge states were plot reported as a function of the focus position. Figure 5 shows typical results of amplitude of Au ion signals versus focal position obtained using the IEA analyzer.
Fig. 5. Ion yield versus focal position for different charge states from Au7+ to Au56+.
It is evident that the shape of the plots changes with the considered charge states. The amplitude of Au7+ and Au8+ signals, for example, presents a broad minimum for −500 µm < FP < +100 µm (centered at FP = −200 µm) and two pronounced lateral maxima for FP > +100 µm and FP < −500 µm. Thus the lower charge state group is negligible around the minimum focal spot position of FP = −200 µm. A similar behavior is shown for Au15+ and Au20+ but in this case, the minimum is narrower (−300 µm < FP < −50 µm) and it is not possible to distinguish ion signals for FP < −500 µm and FP > +100 µm.
The higher charge state signals have a complementary behavior. From Au44+ to Au56+ yields, in fact, the ion yields have a maximum peak at FP = −200 µm instead of the minimum obtained for lower charge states, moreover no ion signals are detected for FP < −400 µm and FP > +50 µm. The maximum detected charge state was Au56+, surprisingly reached at FP = −200 µm (experimental best focus position) instead that FP = 0 (nominal best focus position).
The presented dependencies demonstrate an asymmetry with respect to the FP = 0 position (nominal maximum of laser intensity), in agreement with literature concerning the laser-plasma generation of highly charged ions (Laska et al., Reference Laska, Jungwirth, Krasa, Krousky, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Gammino, Torrisi and Boody2006b). This effect is due to the nonlinear phenomena (both relativistic and charge displacement) related to the interaction of the intense laser beam with the preformed plasma, leading to a spatial confined (channeled) propagation of the electromagnetic wave. The self-focusing of the laser beam is considered to shrink the laser beam diameter down to the laser wavelength and increase the local laser intensity up to 1019 W/cm2 (Laska et al., Reference Laska, Jungwirth, Kralikova, Krasa, Krousky, Masek, Pfeifer, Rohlena, Skala, Ullschmied, Badziak, Parys, Ryc, Szydlowski, Wolowski, Woryna, Ciavola, Gammino, Torrisi and Boody2004, Reference Laska, Jungwirth, Krasa, Krousky, Pfeifer, Rohlena, Ullschmied, Badziak, Parys, Wolowski, Gammino, Torrisi and Boody2006b). The duration of the laser-beam interaction with the expanding plasma plume influences the highest charge state and the kinetic energy of emitted ions, as well as the composition of the expanding plasma. For this reason, the highest charge state, that in principle should be detected at FP = 0, is reached at FP = −200 µm (best focus position due to self-focusing effect), i.e. there is a shift towards the lower FP < 0 positions.
Fig. 6 shows the calculated laser pulse intensity on the target surface (a) and the electronic plasma temperature (b) vs. the focus position for not-self-focusing and self-focusing conditions. The calculation of the nominal laser intensity has been performed by using Eq. (3). The spot diameter obtained at low laser energy, in not-self-focusing conditions, was measured through optical microscopy of the target surface craters for different focal positions. The used approximation to calculate the spot diameter at high laser energy, in self-focusing conditions, will be discussed in the next section. Self-focusing effect increments the maximum intensity of about 100% with respect to not self-focusing. Moreover self-focusing increments the maximum electronic temperature of about 25% with respect to the not-self-focusing conditions, justifying the higher charge states and kinetic energies of detected ions along the normal to the target surface.
Fig. 6. Calculated laser intensity (a) and plasma electron temperature (b) versus focal position for self-focusing and not self-focusing conditions.
4. DISCUSSION AND CONCLUSIONS
The ion yield versus focus position plot of Figure 5 indicates that for low charge states, two main maxima occurs for FP < −500 µm and FP > 200 µm, and a minimum occurs for −500 µm < FP < 200 µm. These low charge state ions are due to ionization by thermal electrons generated by inverse bremsstrahlung mechanism. Such a result was ascribed to the volume effect of produced plasma due to the interaction of continuously decreasing diameter of the laser beam with respect to the target surface that, in the case of self-focusing mechanisms, is found to a forward negative focus positions, FP = −200 µm, instead that at FP = 0.
In contrast, ions with higher charge states, connected with the presence of fast electrons, and generated by resonant absorption mechanism, create a maximum yield of FP = −200 µm. The inverse bremsstrahlung prevails for both the lateral maxima, which Iλ2 < 1015 Wµm2/cm2, while the maximum yield of FP = −200 µm is related to the resonant absorption process, which Iλ2 > 1015 Wµm2/cm2 (Margarone et al., Reference Margarone, Laska, Torrisi, Gammino, Krasa, Krousky, Parys, Pfeifer, Rohlena, Rosinski, Ryc, Skala, Ullschmied and Velyhan2007).
The initial laser beam diameter of 29 cm, focused by an aspheric lens (f = 600 mm for 3ω), reaches a minimum diameter value of 70 µm at FP = 0. When the focal position is FP = −200 µm and the laser energy is very low, the self-focusing cannot happen because the conditions are below the threshold value of Eq. (1) being the measured nominal spot diameter on the target surface about 160 µm, due to the laser beam divergence in the region −200 µm < FP < 0 µm, as reported in the scheme of Figure 7a. When the focal position is FP = −200 µm and the laser intensity is above the self-focusing threshold, the high light refraction effect produces a further laser beam focalization, due to the dense plasma volume in front of the target, which converges the beam so as a focusing lens. This focusing produces a laser spot diameter on the target lower than 70 µm, as depicted in the sketch of the plasma lens in Figure 7b. Such convergent plasma lens permits to reach a smaller diameter on the target surface and, as a consequence, the maximum laser intensity is not reached at FP = 0 (minimum nominal diameter) but at FP = −200 µm (best self-focusing position). Thus, the first part of the relative long pulse width (300 ps) is responsible of the formation of a pre-plasma with an electron density sufficient to allow the self-focusing process to happen and shrink the laser beam.
Fig. 7. Schemes of the plasma dimension developed in front of the target in condition of not self-focusing (a) and self-focusing (b).
An estimation of the spot diameter on the target surface due to self-focusing process occurring at FP = −200 µm was given taking into account Eq. (3) indicating that the spot area is inversely proportional to the laser intensity. Assuming, as a first approximation, that the maximum charge state increases linearly with the laser intensity, in agreement with literature data (Laska et al., Reference Laska, Ryc, Badziak, Boody, Gammino, Jungwirth, Krasa, Krousky, Mezzasalma, Parys, Pfeifer, Rohlena, Torrisi, Ullschmied and Wolowski2005b, Reference Laska, Badziak, Gammino, Jungwirth, Kasperczuk, Krasa, Krousky, Kubes, Parys, Pfeifer, Pisarczyk, Rohlena, Rosinski, Ryc, Skala, Torrisi, Ullschmied, Velyhan and Wolowsk2007), the maximum charge increment from Au44+ up to Au56+, can be correlated to an increment of the laser intensity. Because the ionization potential of Au44+ and Au56+ are I 1 = 1.834 keV and I 2 = 3.395 keV, respectively, the spot diameters D2 and D1, in the presence of self-focusing and not-self-focusing effects, respectively, can be correlated to the ionization potentials through the expression:
indicating that a 72% reduction of the laser spot diameter occurs during the self-focusing effect.
The insets in Figure 7 report the typical IEA spectra obtained in the two cases of non-self-focusing (a) and self-focusing occurrence (b).
The self-focusing electron density threshold (n e) may be calculated by Eqs (1) and (2). In our experimental conditions, the laser frequency ωL is 4.3 × 1015 rad/s, which corresponds to a laser power and a critical density of 5 × 1011 W and 5.8 × 1022 electrons/cm3, respectively. Thus the corresponding electron density threshold is 1.88 × 1021 electrons/cm3.
Assuming, during self-focusing effect, to have a mean charge state of 28+ , this means that the maximum atom density should be 6.7 × 1019 atoms/cm3. These atoms can be represented inside a plasma lens having an approximated volume of the order of 6.5 × 10−7 cm3 (230 µm length and 60 µm diameter).
Experimental results demonstrated that this volume represents only a small part (less than 10%) of the final crater volume created by the laser pulse on the Au target.
ACKNOWLEDGEMENT
This work was partly supported by the Grant Agency of the ASCR (Grant IAA100100715).
