1. INTRODUCTION
The production of small, compact, easily accessible, and short pulse length X-ray sources from laser plasma interactions has significantly facilitated research in advanced science, such as radiobiology, X-ray microscopy, microlithography, astrophysical and fusion applications, measurement of the opacity of materials, X-ray-driven shock studies for equation-of-state (EOS) measurements of materials under extreme conditions, and time-resolved X-ray diffraction of materials (Lewis & Mcglinchey, Reference Lewis and Mcglinchey1984; Chaker et al., Reference Chaker, Pépin, Bareau, Lafontaine, Toubhans, Fabbro and Farsi1988; Förstera et al., Reference Förstera, Gäbel and Uschmanna1989; O'Neill et al., Reference O'neill, Turcu, Tallents, Dickerson, Lindsay, Goodhead, Stretch, Wharton and Meldrum1989; Lindl, Reference Lindl1995; Rischel et al., Reference Rischel, Rousse, Uschmann, Albouy, Geindre, Audebert, Gauthier, Fröster, Martin and Antonetti1997; Daido, Reference Daido2002; Borisenko et al., Reference Borisenko, Bugrov, Burdonskiy, Fasakhov, Gavrilov, Goltsov, Gromov, Khalenkov, Kovalskii, Merkuliev and Petryakov2008; Keiter et al., Reference Keiter, Comely, Morton, Tierney, Workman and Taylor2008; Loupias et al., Reference Loupias, Perez, Benuzzi-Mounaix, Ozaki, Rabec and Gloahec2009; Rossall et al., Reference Rossall, Gartside, Chaurasia, Tripathi, Munda, Gupta, Dhareshwar, Gaffney, Rose and Tallents2010; Grant, Reference Grant2016). The demand for high X-ray fluxes in practical applications has triggered extensive research for the enhancement of the X-ray yield of laser-produced plasmas (LPP) (Rosmej et al., Reference Rosmej, Suslov, Martsovenko, Vergunova, Borisenko, Orlov, Rienecker, Klir, Rezack, Orekhov and Borisenko2015). However, the conversion efficiency of laser energy to X ray from the solid targets is low due to the reflection of most of the laser light near the critical density surface. For a large X-ray yield, absorption of the laser energy inside the target should be high. Therefore, to enhance the X-ray yield, various laser conditions (power density, pulse duration, and wavelength) and target properties have been tested previously. For example, to enhance the X-ray yield, the use of a prepulse (Andreev et al., Reference Andreev, Limpouch, Iskakov and Nakano2002), defocusing the laser to increase the plasma volume (Chaurasia et al., Reference Chaurasia, Tripathi, Leshma, Murali and Pasley2013), structured targets (Nishikawa et al., Reference Nishikawa, Nakano, Oguri, Uesugi, Nakao, Nishio and Masuda2001), gas targets (Fiedorowicz et al., Reference Fiedorowicz, Bartnik, Jarocki, Rakowski and Szczurek2000), and low-density targets (Borisenko et al., Reference Borisenko, Chaurasia, Dhareshwar, Gromov, Gupta, Leshma, Munda, Orekhov, Tripathi and Merkuliev2013) have been used. The use of low-density targets has been proven as a prominent candidate for the enhancement of X-ray emission from LPP. Many targets, such as gold foam (Shang et al., Reference Shang, Yanga and Dong2013), hydrocarbon-based foam (Chaurasia et al., Reference Chaurasia, Leshma, Murali, Borisenko, Munda, Orekhov, Gromov, Merkuliev and Dhareshwar2015), carbon foam (Chaurasia et al., Reference Chaurasia, Leshma, Tripathi, Murali, Munda, Sharma, Kailas, Gupta and Dhareshwar2010a , Reference Chaurasia, Tripathi, Munda, Mishra, Murali, Gupta, Dhareshwar, Rossall, Tallents, Singh and Kohli b ), structured surfaces (Rajeev e t al., Reference Rajeev, Taneja, Ayyub, Sandhu and Kumar2003; Krishnamurthy et al., Reference Krishnamurthy, Kundu, Bane, Lad, Singh, Chatterjee, Kumar and Ray2015), porous Si (Nishikawa et al., Reference Nishikawa, Nakano, Ahn, Uesugi and Serikawa1997), agar–agar foam (Limpouch et al., Reference Limpouch, Borisenko, Demchenko, Gus’kov, Kasperczuk, Khalenkov, Kondrashov, Krousky, Kuba, Masek and Merkul'ev2006), are used for this purpose. A considerable amount of work has been done already for X-ray enhancement using metal-doped (Ti and Ge) low-density silicon oxide foam targets (Fournier et al., Reference Fournier, Constantin, Poco, Miller, Back, Suter, Satcher, Davis and Grun2004, Reference Fournier, Satcher, May, Poco, Sorce, Colvin, Hansen, Maclaren, Moon, Davis and Girard2009). In the previous work (Shang et al., Reference Shang, Yanga and Dong2013), the X-ray conversion efficiency in the case of gold foam was found to increase by 1.34 times as compared with solid gold in the range of multi-eV to multi-keV due to a larger absorption of laser light via inverse bremsstrahlung. Further (Nishikawa et al., Reference Nishikawa, Nakano, Oguri, Uesugi, Nakao, Nishio and Masuda2001) by using ultrashort laser pulse, the penetration depth was found to increase in the case of porous Si targets, which results in a reduction of threshold of prepulse for enhancement of X-ray intensity. Earlier investigation in our laboratory (Chaurasia et al., Reference Chaurasia, Leshma, Tripathi, Murali, Munda, Sharma, Kailas, Gupta and Dhareshwar2010a , Reference Chaurasia, Tripathi, Munda, Mishra, Murali, Gupta, Dhareshwar, Rossall, Tallents, Singh and Kohli b ) indicated an enhancement in the soft X ray by a factor of 1.8 and 2.3 in carbon foam and Pt-doped carbon foam, respectively, when compared with the solid carbon.
The enhancement of soft X rays from the foam target is attributed to the underdense nature of the target, which allows the laser to burn through the target supersonically. In this paper, we have made a contribution in the above area of research by studying X ray and ion emission from SiO2 aerogel foam targets simultaneously with optical shadowgraphy of the plasma. The procedure of preparing of foam targets is also briefly described.
2. EXPERIMENTAL SETUP
The laser system used in these experiments is a 15 J/500 ps Nd:glass laser with intensity 1013–2 × 1014 W/cm2 available at BARC, Mumbai, India. The high-power laser is focused to a focal spot of 100 µm on the target using a f/5 lens and placed in an experimental chamber evacuated to 4 × 10−5 mbar. The schematic of experimental setup is shown in Figure 1. Targets used are solid quartz and 50 mg/cc pure SiO2 aerogel foam and also along with (25% CH3 + 75% SiO2) foam of 60 and 40 mg/cc densities. The continuum X-ray flux (free–free and free–bound) in the soft X-ray (0.8–1.56 keV) and the hard X-ray (3.4–16 keV) spectral range are measured using silicon photodiodes covered with 9 and 20 µm aluminum foils, respectively. The time-integrated X-ray line emission spectra were recorded by dispersing the X rays with a flat TAP (Thallium Acid Phthalate) crystal (2d = 25.75 Å) on to an X-ray CCD camera (M/s Rigaku made, Model-X-vision 4M, Czech Republic) placed at 45° to the target normal. Four identical ion collectors are placed at different angles, that is, 22.5, 30, 45, and 67.5° with respect to the target normal and laser axis to measure the plasma evolution and its size. The details of the crystal spectrometer and ion collectors are described somewhere else (Kaur et al., Reference Kaur, Chaurasia, Poswal, Munda, Rossall, Deo and Sharma2017). To study the dynamic motion of the plasma and its volume, a transverse two-frame optical shadowgraphy system was developed. The magnification at the focal plane of the imaging lens was 3.45 with a spatial resolution of 12 µm and a temporal resolution of 500 ps. The details of the shadowgraphy system are reported elsewhere (Chaurasia et al., Reference Chaurasia, Leshma, Tripathi, Murali, Munda, Sharma, Kailas, Gupta and Dhareshwar2010).
Schematic of various X-ray and ions diagnostics used in experiment.
3. METHOD OF PREPARATION OF SIO2 FOAM TARGETS
The preparation of silica aerogel mainly includes three steps: gel preparation, aging of the gel, and drying of the gel. The aerogel (i.e., silica foam targets) is prepared by the sol–gel process followed by supercritical drying in which tetramethoxysilane (TMOS) is the source of silica. In the first step, the hydrolysis of TMOS is done by adding 0.001 M oxalic acid to initiate polymerization. As the TMOS is only partially miscible with water, alcohol (methanol) is added as a solvent to this solution to ensure the same phase for the reaction to occur. Ammonium hydroxide is used as a catalyst to increase the condensation reaction speed. To obtain the low-density silica aerogels, the molar ratio of TMOS:MeOH:H2O was kept constant at 1:12:4. All the solutions (silicon alkoxide, solvent, water, and catalyst) were mixed in a 100 ml Pyrex beaker, and the resulting sols were immediately transferred to Pyrex test tubes and closed air tight. After gelation, the resulting alcogels were covered with methanol to prevent the shrinkage and cracking of the wetgels. All of the alcogels were supercritically dried in an autoclave to obtain the low-density silica aerogels. The 25% CH3 and 75% silica aerogels (foam targets) were produced by using the methyltrimethoxy precursor in the place of TMOS precursor, and followed the same procedures in making the aerogels. The MTMS precursor was diluted with methanol and hydrolyzed using the 0.001 M oxalic acid. After 12 hours of hydrolysis, the condensation of the resulting methyl modified silica sol (25% CH3 and 75% silica) was carried out using 13 M ammonium hydroxide. The 60 mg/cc and 40 mg/cc MTMS based aerogel were obtained by keeping the molar ratios of MTMS: Methanol: water at 1:20:4 and 1:34:4, respectively. The acidic and basic catalysts were added in the form of water. More details are given on the preparation of the silica aerogels elsewhere (Pajonk et al., Reference Pajonk, Rao, Sawant, Parvathy and Sawant1997; Rao et al., Reference Rao, Pajonk, Haranath and Wagh1998, Reference Rao, Kulkarni, Amalnerkar and Seth2003, Reference Rao, Bhagat, Hirashima and Pajonk2006). The scanning electron microscope (SEM) image of 50 mg/cc silica aerogel foam is shown in Figure 2.
SEM image of 50 mg/cc pure silica aerogel foam with 25 kV electron beam and ×700 magnification.
4. RESULTS AND DISCUSSION
4.1. Effect of target densities on soft and hard X-ray yields
When an intense laser focuses on a target, a highly dense and hot plasma is produced. The emitted radiations are in the X-ray spectral region. There are three mechanisms of production of X rays in plasma, that is, free–free, free–bound, and bound–bound (Eliezer, Reference Eliezer2002). The laser wavelength, pulse duration, and choice of target material strongly affect the X-ray yield (conversion factor of laser pulse to X rays). In our case, we measured the X-ray radiation due to free–free and free–bound transitions using X-ray photodiodes covered with different filters to measure the soft and hard X rays. The output of the photodiode signals for the soft and hard X rays are plotted with respect to the laser intensity in Figure 3a, 3b, respectively. From the figures, it can be seen that the X-ray flux (I x) scales with the laser intensity (I L) at a constant pulse duration and wavelength as I x = (I L)α, where α is constant. However, the value of α is calculated by slope of the graph plotted between ln(I x) versus ln(I L) and found to be 1 and 0.5 for quartz and SiO2 aerogel foam targets, respectively, in case of soft X rays. However, in the case of hard X rays, these values are 0.9 and 0.6 for quartz and SiO2 aerogel foam targets, respectively. It is observed that the soft X-ray emission (0.9–1.56 keV) from the low-density (50 mg/cc) SiO2 aerogel foam is almost 2–2.5 times higher than in solid quartz for almost all of the investigated laser intensities and decreases with increase of the foam density. The X-ray yield from 70 mg/cc pure SiO2 is lying in between solid quartz and 50 mg/cc pure SiO2 aerogel foam target. However, in the case of hard X-ray emission (3.4–16 keV), the flux from low-density SiO2 aerogel foam is ~1.8 times lower than the yields from the solid quartz. The X-ray flux from the silica foam with composition (25% CH3 + 75% SiO2) of densities 60 and 40 mg/cc are also measured. It is observed that the soft X-ray yield from these targets are slightly lower than the pure SiO2 aerogel foam target of density 50 mg/cc and at the same time higher than the X-ray yield from the quartz target.
Comparison of (a) soft X-ray flux and (b) hard X-ray flux from solid quartz with SiO2 aerogel foam of various densities, such as 50 mg/cc, 25% CH3 + 75% SiO2 aerogel foam of 60 and 40 mg/cc densities.
The enhancement of soft X-ray emission in the low-density foam target is mainly due to two reasons. Firstly, it is due to lower losses to hydrodynamic phenomenon (shock formation), and secondly and more prominently it is due to volumetric heating. Xu et al. (Reference Xu, Zhu, LI and Yang2011) have done simulation studies using a one-dimensional (1D) multigroup radiation hydrodynamic code and have shown that in the case of a subcritically dense plasma, it is heated supersonically and no shock wave formation takes place, while in an overdense plasma, the percentage loss of energy increases with the target density and is at maximum for the solid targets. Secondly, the enhancement of the volume of the X-ray emission is due to the initial penetration of the laser due to the transparency. The dynamics of laser light absorption in low-density porous material is explained by a long inhomogeneous period during which there exists a stochastic distribution in the low-density region in the plasma. As a result, the radiation is absorbed in a volume at the so-called geometrical transparency length, which is determined by the classical collision mechanism (Bugrov et al., Reference Bugrov, Gus'kov, Rozanov, Burdonskii, Gavrilov, Gol'tsov, Zhuzhukalo, Koval'skii, Pergament and Petryakov1997), as given in following equation:
$$L_{\rm T} = \displaystyle{{9.2 \times {10}^{ - 8}} \over Z}\left( {\displaystyle{A \over Z}} \right)^2\displaystyle{{T^{3/2}} \over {{\rm \lambda }^2 \cdot {\rm \rho }^2}}.$$
Here A and Z are the atomic number and charge of the plasma ions, respectively, λ is the wavelength of the laser light (μm), T is the electron temperature (keV), and ρ is the plasma density (g/cm3). From the above equation, it can be seen that the penetration depth and hence the volume of plasma is inversely proportional to the square of the density. The same can be seen from the shadowgraphs for the quartz (Fig. 4a–4c) and for 50 mg/cc SiO2 aerogel foam targets (Fig. 4d–4f) at a delay times of 2 and 8 ns after the arrival of the main laser pulse on targets. From Figure 4c, 4f, it can be seen that after 8 ns of the arrival of incident laser, the lateral plasma size in the SiO2 aerogel foam case is 1.35 times larger than the solid quartz. It can also be seen from Figure 4d (without laser), 4e (2 ns delay), and 4f (8 ns delay) that the heated volume is larger inside the targets (shown with dotted circles). However, in the case of quartz, the interaction is only at the solid surface.
Shadowgraph of solid quartz (a) at t = 0 ns, (b) at t = 2 ns, and (c) at t = 8 ns after laser pulse on the targets, and for foam targets at (d) t = 0 ns, (e) at t = 2 ns, and (f) at t = 8 ns after laser pulse on the targets. The dotted circle in each image is showing the region of plasma.
We also recorded the time-integrated spectrum of ions from LPP with the help of ions collectors placed at four different angles from target normal (i.e., at 22.5, 30, 45, and 67.5°) to verify the volumetric heating concept. The angular distribution of the amplitude of the thermal ions (plasma) are plotted in Figure 5, for two different laser shots of same energies on the targets of 50 mg/cc SiO2 aerogel foam and quartz target. The angular distribution of the thermal ions are scaled as P(θ) = P(0) cos n θ, where n = 3.8 and 4.8 for the foam and quartz targets, respectively. It can be seen from Figure 5, that the thermal ion flux from the foam target is larger and closer to isotropic (hence the larger volume) compared with the thermal ion flux from the quartz. A similar behavior has been observed via theoretical simulation done by our group using 2D Eulerian radiative–hydrodynamic code POLLUX, which is briefly described in the next section.
Angular distribution of the thermal ion flux from the 50 mg/cc SiO2 aerogel foam and quartz targets for two laser shots of approximately same energy.
4.2. Simulation results to verify the volume effect
The 2D Eulerian radiative–hydrodynamic code POLLUX was originally developed to model moderate irradiance (1010 W/cm2) optical and infrared laser irradiation of a solid target and the subsequently produced strongly ionized plasma, which further interacts with the incident laser beam. The code solves the three first-order quasi-linear partial differential equations of hydrodynamic flow using the flux-corrected transport model of Boris & Book (Reference Boris and Book1976), with an upwind algorithm (Courant et al., Reference Courant, Isaacson and Rees1952) for the first term. The energy is absorbed by the plasma electrons through inverse bremsstrahlung and distributed through electron–ion collisions, the equilibration of which is determined by the Spitzer plasma collision rate (Spitzer & Härm, Reference Spitzer and Härm1953). For calculation of the EOS variables, POLLUX utilizes in-line hydrodynamic EOS subroutines from the Chart-D (Thompson, Reference Thompson1970) EOS package developed at Sandia National Laboratories, Livermore, CA, USA. This code uses an explicit solver; therefore, a Courant number of ~1 has been used to increase stability where the Courant number (C) is given by
$$C = \displaystyle{{u_x{\rm \Delta} t} \over {{\rm \Delta} x}} + \displaystyle{{u_y{\rm \Delta} t} \over {{\rm \Delta} y}} \sim 1,$$
where u x and u y are magnitudes of the particle velocities in the respective directions, Δt is the time step, and Δx and Δy are the cell spatial dimensions. The ionization and level populations are calculated assuming local thermodynamic equilibrium, an assumption which is justified for hydrodynamic time scales (>1 ps).
To enable the ray tracing of the incident laser pulse within the code, the Eulerian mesh is subdivided into triangular cells with the Eulerian mesh center points at the triangle corners allowing for the refractive index and associated gradient within each cell to be calculated via direct differencing. The refractive index is continuous across cell boundaries and assumes a linear electron density variation within each cell. The (x, y) trajectory of each ray in the cell is then assumed to be parabolic dependent upon the refractive index (n 0) and its derivative (n 1), given by,
$$y^2 = 4\left( {\displaystyle{{n_0} \over {n_1}}} \right)x.$$
The parameters used in the code were a p-polarized laser intensity of 1 × 1014 W/cm2 incident onto solid quartz with a density of 2.65 g/cm3 and silica foam with a density of 50 mg/cm3.
The contour plot for the electron density and electron temperature at t = 1 ns after the start of the laser pulse are shown in Figure 6. It can be seen from Figure 6 that the plasma expansion differs greatly between the two targets with the foam targets creating much larger lower density plasma. It proves that the enhancement is due to a volume effect where the foam target has a much greater volume of emitting plasma, which is in consistent with the results obtained by shadowgraphy and the ion collector.
(a, b) Contour plots for solid quartz and SiO2 aerogel foam for electron density and (c, d) for electron temperature after a delay of t = 1 ns with respect to the start of the laser pulse on the target.
4.3. Estimation of plasma parameters with K-shell spectra
The K-shell spectra of silicon in quartz and SiO2 aerogel foam targets are recorded with the help of TAP crystal spectrometer as shown in Figure 7a, 7b. The crystal spectrometer is optimized to measure the He-α line (1s 2–1s2p), the intercombination line (1s 2 1 S 0–1s2p 3 P 1), and the Li-like satellite of He-α line (1s 22p–1s2p 2). These lines are important for determination of the plasma temperature and density. The plasma temperature and density are estimated by taking into account the ratio of the dielectronic satellite of He-α line (i.e., 1s 22p–1s2p 2) to its parent resonance line, that is, He-α line(1s 2–1s2p) and intercombination line (1s 2 1 S 0–1s2p 3 P 1) to He-α (1s 21 S 0–1s2p 1 P 1), respectively. For determination of temperature and density, simulation is carried out using the FLYCHK software (Chung et al., Reference Chung, Chen, Morgan, Ralchenko and Lee2005), which generates a synthetic spectrum that is matched with the experimental data after several iterations for a range of temperatures and densities. The experimental spectra matched with FLYCHK for He-like lines of the silicon in the quartz target at T c = 180 eV, T h = 1000 eV, f = 0.009, n e = 7 × 1020 cm−3, and for SiO2 aerogel foam at T c = 190 eV, T h = 800 eV, f = 0.01, and n e = 4 × 1020 cm−3 as shown in Figure 7a, 7b, where T c and T h are the cold and hot electron temperatures, respectively, f is the hot to cold component fraction and n e is the electron density. The amplitude of the line emission is lower in the case of the foam target, which is due to a lower plasma density as can be seen from simulation results where the density of the foam plasma is 4 × 1020 cm−3. The hot electron temperature is lower and the value of f is higher in the case of foam targets, which indicates lower hard X-ray emission than the solid quartz as shown in Figure 3b.
Experimental spectrum matched with FLYCHK for He-like lines of the silicon in the (a) quartz at T c = 180 eV, T h = 1000 eV, f = 0.009, and n e = 7 × 1020 cm−3 and (b) SiO2 aerogel foam at T c = 190 eV, T h = 800 eV, f = 0.01, and n e = 4 × 1020 cm−3.
4.4. Conclusions
A comparison of soft and hard X rays flux from quartz and low-density SiO2 aerogel foam targets is done. Pure SiO2 aerogel foam with density 50 and 70 mg/cc, and (25% CH3 + 75% SiO2) of densities 60 and 40 mg/cc are used. Two X-ray diodes with different filters are used to examine X-ray emission in soft (0.9–1.56 keV) and hard X-ray (3.4–16 keV) regions. An enhancement of 2.5 times in soft X-ray emission and a decrease of 1.8 times in hard X-ray emission for 50 mg/cc SiO2 aerogel foam is observed compared with the solid quartz. The ion collector's data show that, the ion flux from the solid quartz is found to be more directional, whereas from SiO2 aerogel foam, it is nearly isotropic. This behavior was attributed to the volume effect, which has been further verified by shadowgraph profiles of the plasma plume at two different time scales during the plasma evolution (2 and 8 ns) and simulation. Simulations with a 2D hydrodynamic code POLLUX supported the indication of volume heating of plasma being the cause for the change in X-ray emission. For determination of the plasma temperature and density, the spectra including He-like resonance line along with satellites and intercombination of Si plasma were matched with synthetic spectrum generated by using FLYCHK for both quartz and 50 mg/cc SiO2 aerogel foam targets. The calculated plasma parameters are T c = 180 eV, T h = 1000 eV, f = 0.009, and n e = 7 × 1020 cm−3 and T c = 190, T h = 800 eV, f = 0.01, and n e = 4 × 1020 cm−3 for quartz and SiO2 aerogel foam, respectively.
ACKNOWLEDGMENTS
The authors from BARC wish to acknowledge the support and continuous encouragement received from Dr. S. M. Sharma, former Director, Physics group and Dr. N. K. Sahoo, Director, Physics Group, BARC. Also, we acknowledge the excellent support given by Mr. C. G. Murali, Mrs P. Leshma and Mr Ritesh Sable in design and implementation of laser electronics and smooth operation of laser system. Dr. Venkateswara Rao is highly thankful to the University Grants Commission (UGC), New Delhi, Government of India, for the UGC-Basic Science Research (BSR) Faculty Fellowship. Dr. A. A. Pisal acknowledges the stipendiary grant received from the UGC.
