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Angular distribution and conversion of multi-keV L-shell X-ray sources produced from nanosecond laser irradiated thick-foil targets

Published online by Cambridge University Press:  12 December 2008

G.-Y. Hu ,
J.-Y. Zhang ,
J. Zheng ,
B.-F. Shen ,
S.-Y. Liu ,
J.-M. Yang ,
Y.-K. Ding ,
X. Hu ,
Y.-X. Huang  and
H.-B. Du
...Show all authors
G.-Y. Hu*
Affiliation:
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, CAS, Shanghai, China Research Center of Laser Fusion, CAEP, Mianyang, China CAS Key Laboratory of Basic Plasma Physics, Department of Modern Physics, University of Science and Technology of China, Hefei, China
J.-Y. Zhang
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
J. Zheng
Affiliation:
CAS Key Laboratory of Basic Plasma Physics, Department of Modern Physics, University of Science and Technology of China, Hefei, China
B.-F. Shen
Affiliation:
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, CAS, Shanghai, China
S.-Y. Liu
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
J.-M. Yang
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
Y.-K. Ding
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
X. Hu
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
Y.-X. Huang
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
H.-B. Du
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
R.-Q. Yi
Affiliation:
Research Center of Laser Fusion, CAEP, Mianyang, China
A.-L. Lei
Affiliation:
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, CAS, Shanghai, China
Z.-Z. Xu
Affiliation:
State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, CAS, Shanghai, China
*
Address correspondence and reprint requests to: G.Y. Hu, State Key Laboratory of High Field Laser Physics, Shanghai Institute of Optics and Fine Mechanics, CAS, Shanghai 201800, China. E-mail: gyhu@siom.ac.cn
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Abstract

An experimental study on the angular distribution and conversion of multi-keV X-ray sources produced from 2 ns-duration 527nm laser irradiated thick-foil targets on Shenguang II laser facility (SG-II) is reported. The angular distributions measured in front of the targets can be fitted with the function of f(θ) = α+ (1−α)cosβθ (θ is the viewing angle relative to the target normal), where α = 0.41 ± 0.014, β = 0.77 ± 0.04 for Ti K-shell X-ray sources (~4.75 keV for Ti K-shell), and α = 0.085 ± 0.06, β = 0.59 ± 0.07 for Ag/Pd/Mo L-shell X-ray sources (2–2.8 keV for Mo L-shell, 2.8–3.5 keV for Pd L-shell, and 3–3.8 keV for Ag L-shell). The isotropy of the angular distribution of L-shell emission is worse than that of the K-shell emission at larger viewing angle (>70°), due to its larger optical depth (stronger self-absorption) in the cold plasma side lobe surrounding the central emission region, and in the central hot plasma region (emission region). There is no observable difference in the angular distributions of the L-shell X-ray emission among Ag, Pd, and Mo. The conversion efficiency of Ag/Pd/Mo L-shell X-ray sources is higher than that of the Ti K-shell X-ray sources, but the gain relative to the K-shell emission is not as high as that by using short pulse lasers. The conversion efficiency of the L-shell X-ray sources decreases with increasing atomic numbers (or X-ray photon energy), similar to the behavior of the K-shell X-ray source.

Keywords

Angular distributionLaser plasmaX-ray source
Type
Research Article
Information
Laser and Particle Beams , Volume 26 , Issue 4 , December 2008 , pp. 661 - 670
Copyright
Copyright © Cambridge University Press 2008

INTRODUCTION

Multi-keV X-ray sources are widely used in the fields of high energy density physics (HEDP) and inertial confinement fusion (ICF) as backlighting beam (Kalantar et al., Reference Kalantar, Haan, Hammel, Keane, Landen and Munro1997; Pikuz et al., Reference Pikuz, Faenov, Fraenkel, Zigler, Flora, Bollanti, Dilazzaro, Letardi, Grilli, Palladino, Tomassetti, Reale, Reale, Scafati, Limongi, Bonfigli, Alainelli and Sanchez2002; Rafique et al., Reference Rafique, Khaleeq-Ur-Rahman, Riaz, Jalil and Farid2008), probe beam (Glenzer et al., Reference Glenzer, Gregori, Lee, Rogers, Pollaine and Landen2003; Riley et al., Reference Riley, Khattak, Garcia Saiz, Gregori, Bandyopadhyay, Notley, Neely, Chambers, Moore and Comley2007; Schollmeier et al., Reference Schollmeier, Rodriguez Prieto, Rosmej, Schaumann, Blazevic, Rosmej and Roth2006; Abdallah et al., Reference Abdallah, Batani, Desai, Lucchini, Faenov, Pikuz, Magunov and Narayanan2007; Faenov et al., Reference Faenov, Magunov, Pikuz, Skobelev, Gasilov, Stagira, Calegari, Nisoli, De Silvestri, Poletto, Villoresi and Andreev2007; Wong et al., Reference Wong, Woo and Yap2007), or heating beam (Glenzer et al., Reference Glenzer, Gregori, Lee, Rogers, Pollaine and Landen2003; Riley et al., Reference Riley, Weaver, McSherry, Dunne, Neely, Notley and Nardi2002a) for the diagnostics or the production of high density plasmas (Tahir et al., Reference Tahir, Udrea, Deutsch, Fortov, Grandjouan, Gryaznov, Hoffmann, Hulsmann, Kirk, Lomonosov, Piriz, Shutov, Spiller, Temporal and Varentsov2004, Reference Tahir, Spiller, Shutov, Lomonosov, Gryaznov, Piriz, Wouchuk, Deutsch, Fortov, Hoffmann and Schmidt2007; Schollmeier et al., Reference Schollmeier, Becker, Geissel, Flippo, Blazevic, Gaillard, Gautier, Gruner, Harres, Kimmel, Nurnberg, Rambo, Schramm, Schreiber, Schutrumpf, Schwarz, Tahir, Atherton, Habs, Hegelich and Roth2008). The detailed characteristics of multi-keV X-ray emission are important to optimize X-ray sources or design experiments. Most of the articles concerning this issue concentrate on the influence of the laser intensity (Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983; Workman et al., Reference Workman, Lanier and Kyrala2003; Workman & Kyrala, Reference Workman and Kyrala2001a, Reference Workman and Kyrala2001b; Riley et al., Reference Riley, Woolsey, McSherry, Khattak and Weaver2002b; Dunn et al., Reference Dunn, Young, Osterheld, Foord, Walling and Stewart1995; Kodama et al., Reference Kodama, Okada, Ikeda, Mineo, Tanaka, Mochizuki and Yamanaka1986), the atomic number (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983; Workman & Kyrala, Reference Workman and Kyrala2001a, Reference Workman and Kyrala2001b; Dunn et al., Reference Dunn, Young, Osterheld, Foord, Walling and Stewart1995; Ruggles et al., Reference Ruggles, Porter, Rambo, Simpson, Vargas, Bennett and Smith2003; Yaakobi et al., Reference Yaakobi, Bourke, Conturie, Delettrez, Forsyth, Frankel, Goldman, McCrory, Seka and Soures1981; Kodama et al., Reference Kodama, Okada, Ikeda, Mineo, Tanaka, Mochizuki and Yamanaka1986), and the initial density of the target (Back et al., Reference Back, Grun, Decker, Suter, Davis, Landen, Wallace, Hsing, Laming, Feldman, Miller and Wuest2001, Reference Back, Grun, Decker, Suter, Davis, Landen, Wallace, Hsing, Laming, Feldman, Miller and Wuest2003; Fiedorowicz, Reference Fiedorowicz2005; Fournier et al., Reference Fournier, Constantin, Poco, Miller, Back, Suter, Satcher, Davis and Grun2004, Reference Fournier, Constantin, Back, Suter, Chung, Miller, Froula, Gregori, Glenzer, Dewald and Landen2006; Kodama et al., Reference Kodama, Mochizuki, Tanaka and Yamanaka1987; Teubner et al., Reference Teubner, Kuhnle and Schafer1991; Pelletier et al., Reference Pelletier, Chaker and Kieffer1997; Girard et al., Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Miller, Kauffman, Suter, Grun and Davis2005, Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Depierreux, Miller, Kauffman, Suter, Fournier, Glenzer, Back, Grun and Davis2004; Primout, Reference Primout2005). Some papers pay attention to the influence of the laser focus spot size (Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983; Workman et al., Reference Workman, Lanier and Kyrala2003; Workman & Kyrala, Reference Workman and Kyrala2001a, Reference Workman and Kyrala2001b; Riley et al., Reference Riley, Woolsey, McSherry, Khattak and Weaver2002b), the laser wavelength (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Hu et al., Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008; Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983; Yaakobi et al., Reference Yaakobi, Bourke, Conturie, Delettrez, Forsyth, Frankel, Goldman, McCrory, Seka and Soures1981; Kodama et al., Reference Kodama, Okada, Ikeda, Mineo, Tanaka, Mochizuki and Yamanaka1986), the laser incidence angle (Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983), or the laser pulse duration (Mattews et al., Reference Mattews, Campbell, Ceglio, Hermes, Kauffman, Koppel, Lee, Manes, Rupert, Slivinshy, Turner and Ze1983; Workman & Kyrala, Reference Workman and Kyrala2001a, Reference Workman and Kyrala2001b; Riley et al., Reference Riley, Woolsey, McSherry, Khattak and Weaver2002b; Dunn et al., Reference Dunn, Young, Osterheld, Foord, Walling and Stewart1995; Phillion & Hailey, Reference Phillion and Hailey1986; Kodama et al., Reference Kodama, Mochizuki, Tanaka and Yamanaka1987; Teubner et al., Reference Teubner, Kuhnle and Schafer1991; Pelletier et al., Reference Pelletier, Chaker and Kieffer1997; Girard et al., Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Depierreux, Miller, Kauffman, Suter, Fournier, Glenzer, Back, Grun and Davis2004; Eidmann & Schwanda, Reference Eidmann and Schwanda1991; Limpouch et al., Reference Limpouch, Renner, Krousky, Uschmann, Forster, Kalashnikov and Nickles2002; Von Der Linde et al., Reference Von Der Linde, Sokolowski-Tinten, Blome, Dietrich, Zhou, Tarasevitch, Cavalleri, Siders, Barty, Squier, Wilson, Uschmann and Forster2001), etc. We also found that by using a long pulse laser, the laser focus spot size and the thickness of the thin-foil target (the thickness is comparable to the burn through length, which is the initial target thickness that the laser beam can transmit through the entire plasma region with little absorption at the end of the laser pulse) can change the conversion of multi-keV K-shell X-ray emission significantly (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008).

However, relatively little experimental work has been dedicated to the angular distribution of multi-keV X-ray emission, which is necessary in order to explore the physical process of laser target coupling (Max, Reference Max, Balian and Adam1982), test hydrodynamic codes (Girard et al., Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Depierreux, Miller, Kauffman, Suter, Fournier, Glenzer, Back, Grun and Davis2004), and design the experiment (Kalantar et al., Reference Kalantar, Haan, Hammel, Keane, Landen and Munro1997; Pikuz et al., Reference Pikuz, Faenov, Fraenkel, Zigler, Flora, Bollanti, Dilazzaro, Letardi, Grilli, Palladino, Tomassetti, Reale, Reale, Scafati, Limongi, Bonfigli, Alainelli and Sanchez2002; Glenzer et al., Reference Glenzer, Gregori, Lee, Rogers, Pollaine and Landen2003; Riley et al., Reference Riley, Weaver, McSherry, Dunne, Neely, Notley and Nardi2002a, Reference Riley, Khattak, Garcia Saiz, Gregori, Bandyopadhyay, Notley, Neely, Chambers, Moore and Comley2007; Schollmeier et al., Reference Schollmeier, Rodriguez Prieto, Rosmej, Schaumann, Blazevic, Rosmej and Roth2006). Many parameters can effect the angular distribution such as target material, laser wavelength, laser pulse duration, X-ray photon energy, and other factors. X-ray angular distributions have been explored mainly in the region of extreme ultraviolet (EUV) and sub-keV X-ray emission (Higashiguchi et al., Reference Higashiguchi, Kawasaki, Sasaki and Kubodera2006; Kodama et al., Reference Kodama, Okada, Ikeda, Mineo, Tanaka, Mochizuki and Yamanaka1986; Celliers et al., Reference Celliers, Da Silva, Dane, Mrowka, Norton, Harder, Hackel, Matthews, Fiedorowicz, Bartnik, Maldonado and Abate1996; Mead et al., Reference Mead, Campbell, Estabrook, Turner, Kruer, Lee, Pruett, Rupert, Tirsell, Stradling, Ze, Max and Rosen1981, Reference Mead, Campbell, Estabrook, Turner, Kruer, Lee, Pruett, Rupert, Tirsell, Stradling, Ze, Max and Lasinski1983). A few papers paid attention to the angular distribution of multi-keV X-ray emission of Al, Mg K-shell emission (Chase et al., Reference Chase, Jordan, Perez and Pronko1977; Arora et al., Reference Arora, Chakera, Kumbhare, Naik, Gupta and Gupta2001). Additional experiments are needed to study the angular distribution of multi-keV X-ray emission sources produced with the widely used target materials in nowadays experiments of HEDP and ICF. In this article, we measured the angular distribution of multi-keV K- and L-shell X-ray emission (~4.75 keV for Ti K-shell, 3–3.8 keV for Ag, 2.8–3.5 keV for Pd, and 2–2.8 keV for Mo L-shell) produced by 2 ns-duration 527 nm laser irradiated thick-foil target (the thickness is much larger than the burn through length) (Hu et al., Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008).

With long pulse laser beams, the measurements of the conversion efficiency of multi-keV X-ray sources were focused on the K- and M-shell emission in the past (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Babonneau, Reference Babonneau, Bonnet, Jacquemot, Bocher, Boutin, Jadaud and Vilette1999). Multi-keV L-shell X-ray sources produced with long pulse laser irradiated solid targets have been used frequently as heating or backlighting sources (Pikuz et al., Reference Pikuz, Faenov, Fraenkel, Zigler, Flora, Bollanti, Dilazzaro, Letardi, Grilli, Palladino, Tomassetti, Reale, Reale, Scafati, Limongi, Bonfigli, Alainelli and Sanchez2002; Glenzer et al., Reference Glenzer, Gregori, Lee, Rogers, Pollaine and Landen2003; Riley et al., Reference Riley, Khattak, Garcia Saiz, Gregori, Bandyopadhyay, Notley, Neely, Chambers, Moore and Comley2007; Schollmeier et al., Reference Schollmeier, Rodriguez Prieto, Rosmej, Schaumann, Blazevic, Rosmej and Roth2006; Riley et al., Reference Riley, Weaver, McSherry, Dunne, Neely, Notley and Nardi2002a; Glendinning et al., Reference Glendinning, Amendt, Budil, Hammel, Kalantar, Key, Landen, Remington and Desenne1995; Scott et al., Reference Scott, Beck, Batha, Barnes and Tubbs2001). The conversion efficiency of multi-keV L-shell X-ray sources have mainly been explored with short pulse laser beams (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986; Glendinning et al., Reference Glendinning, Amendt, Budil, Hammel, Kalantar, Key, Landen, Remington and Desenne1995; Eidmann & Schwanda, Reference Eidmann and Schwanda1991). A few papers explored the multi-keV L-shell emission with long pulse laser (Eidmann & Schwanda, Reference Eidmann and Schwanda1991; Mochizuki & Yamanaka, Reference Mochizuki and Yamanaka1986; Glibert et al., Reference Glibert, Anthes, Gusinow and Palmer1980). The hydrodynamic behavior of multi-keV L-shell X-ray emission region with long pulse laser beams is different to that with short pulse laser beams, which (the difference of the hydrodynamic behavior) will change the conversion efficiency of X-ray source (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986; Glendinning et al., Reference Glendinning, Amendt, Budil, Hammel, Kalantar, Key, Landen, Remington and Desenne1995). In this article, we explored the conversion of the L-shell multi-keV X-ray emission in the laser parameters range different to that in the previous papers (Eidmann & Schwanda, Reference Eidmann and Schwanda1991; Mochizuki & Yamanaka, Reference Mochizuki and Yamanaka1986; Glibert et al., Reference Glibert, Anthes, Gusinow and Palmer1980). The conversion efficiency of Ag/Pd/Mo L-shell X-ray sources is obviously higher than that of the Ti K-shell X-ray sources, which is benefited from the wider spectral bandwidth of L-shell emission relative to that of the K-shell emission.

EXPERIMENTAL SETUP

The experiment is performed at the Shenguang II (SG-II) laser facility (Lin et al., Reference Lin, Deng, Fan, Wang, Chen, Zhu, Qian, Shen, Xu, Zhu, Ma, Xie, Zheng, Zhang, Chen, Ling, Huang and Zhang1999) located at the Shanghai Institute of Optics and Fine Mechanics (SIOM). The schematic setup of the experiment is shown in Figure 1. The Beam #9 (Peng et al., Reference Peng, Zhang, Zheng, Wei, Huang, Sui, Jing, Zhu, Zhu, Wang, Zhou, Liu, Zeng, Wang, Zhu, Lin and Zhang2006) laser beam (~1.5 kJ, ~2 ns, 527 nm, f/4.5) irradiates solid targets at an incidence angle of either 22.5° or 0°. The solid targets are titanium (22Ti) foil of 6 µm thickness, silver (47Ag), palladium (46Pd), or molybdenum (42Mo) foils of 2 µm thickness. In the shots with Mo target, the incidence angle is 45°. The laser energy changes in the range from 1 kJ to 1.9 kJ in our experiment, as shown in Table 1. The laser beam is focused on the target front with a circular spot of about 350 µm full width at half maximum (FWHM) diameter, or a 400 µm × 400 µm (FWHM) quadrate spot after being smoothed with a lens array (Deng et al., Reference Deng, Liang, Chen, Yu and Ma1986), or defocused to about 230–260 µm diameter (FWHM) circular spot without the lens array (the laser focus spot point at some place behind the target).

Fig. 1. (Color online) Experimental setup and the sketch map of the emission region, the hot laser channel (central hot plasma region), and the cold plasma side lobe surrounding the emission region (left). The schematic view of the laser incidence plane and the detector plane (right). Ψ and θ are respectively the laser incidence angle and the viewing angle of detector relative to the target normal.

Table 1. The 2ns-duration laser parameters (the laser energy, the incidence angle, and the size of the focus spot. ϕ is the diameter (FWHM) of the circular focus spot)

The diagnostic system is similar to that in our previous work (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008). A set of X-ray diodes (XRDs) at different viewing angles are used to give the X-ray flux and the angular distribution with temporal resolution of 250 ps and relative uncertainty of ±30%. The stability of the XRDs is ±10% among different shots. The azimuth angles of XRD are perpendicular to the laser incidence plane, as shown in Figure 1. With appropriate filters, only the K- or L-shell X-rays that we are interested in, as shown in Figure 3b, can be detected by the XRDs (>4 keV for Ti, >2.5 keV for Ag/Pd, and >2 keV for Mo). We also use other assistant detectors, such as an X-ray pinhole camera (XPHC), gives the time-integrated multi-keV X-ray emission region, an X-ray streak pinhole camera (XSC), gives the one-dimensional motions of the multi-keV X-ray emission region around the target axis, a crystal spectrometer (CS), gives the detailed spectrum of K- and L-shell emission recorded on image plate using polyethylene terephthalate (PET) or titanium alkyl phosphates (TIAP) crystal, and a 2000 line/mm transmission grating spectrometer (TGS), gives the whole X-ray spectrum included soft and multi-keV emission recorded on CCD.

Fig. 2. (Color online) (a, b) The laser pulse and X-ray flux given by XRD at 0° viewing angle relative to the target normal, (c, d) the longitudinal temporal profile of the emission region given by XSC, (e, f) the time integrated images of emission region given by XPHC at 76° viewing angle relative to the target normal. The laser parameters for the Ti K-shell emission (>4 keV) in (a, c, e) are 1.6 kJ energy, 2 ns duration, 22.5° incidence angle, and 350 µm diameter (FWHM) focus spot smoothed with a lens arrays, and the laser parameters for the Ag L-shell emission (>2.5 keV) in (b, d, f) are 1.7 kJ energy, 2 ns duration, 22.5° incidence angle, and 350 µm diameter (FWHM) focus spot smoothed with a lens arrays. The horizontal shadows in (c, d) are due to the washer of the targets. The white arrows in (c, d, e, f) show the incidence direction of laser pulse. The white points in (e, f) indicate the target center. The central zones in (e, f) are saturated, so the real longitudinal scale length of the emission region should refer to (c, d).

Fig. 3. (Color online) The detailed X-ray spectra (a) and rough X-ray spectra (b) given by CS and TGS respectively. The relative spectral bandwidth in (b) is useless because the spectral resolution of TGS for Ti K-shell emission is different to that of the Mo/Pd/Ag L-shell emission.

A stainless-steel washer with 50 µm thickness was used to hold the foil (500 µm inner diameter and 1200 µm outer diameter for circular focus spot, and 1200 µm inner diameter and 2000 µm outer diameter for 400 µm ×400 µm quadrate focus spot). In the shots of detecting the angular distribution in Figure 4, one quarter of the target washer was removed and all of the XRDs are at the side of the 90° gap to avoid the shadow of the target washer. But in the shots of Figure 2, there is no gap on the target washer, which induced the horizontal shadows in Figures 2c and 2d.

Fig. 4. (Color online) The angular distribution of multi-keV Ti K-shell and Ag/Pd/Mo L-shell X-ray emission. The black solid line and blue short dash line are the fitting curves for K- and L-shell emission respectively with the function of f(θ) = α + (1 – α) cosβ θ. The red short-dot line (ref) is given by 2D hydrodynamic simulation code FCI2 for Ti K-shell emission (Girard et al., Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Depierreux, Miller, Kauffman, Suter, Fournier, Glenzer, Back, Grun and Davis2004). The relative uncertainty of the X-ray energy is ±30%. The 2ns-duration laser parameters are shown in Table 1.

EMISSION REGION AND X-RAY SPECTRUM

When the laser beam irradiates the thick-foil target, the ablated hot plasma expands along the target normal in one dimension first. Then the central hot plasma will expand laterally and form side lobe plasma surrounding the central hot plasma. At the same time, the X-ray emission comes from the central hot plasma will evaporate the off-spot material and enhance the forming of the side lobe plasma. The effect of the radiation cooling will lower the temperature of the side lobe plasma substantially. Then the plasma region comes to a quasi-steady state (the plasma conditions change very slow) with a central hot plasma region (we call it laser channel in this article) surrounded by a cold plasma side lobe outside the laser-irradiated target region. After several nanoseconds, the pressure balances in the lateral direction, the plasma will form a density depression on axis and a significant cold plasma side lobe. The detailed physical process can be seen elsewhere (Filevich et al., Reference Filevich, Rocca, Jankowska, Hammarsten, Kanizay, Marconi, Moon and Shlyaptsev2003).

In our experiments, the laser pulse duration is not long enough to establish the pressure balance completely; the ablated plasma will just come to a quasi-steady state since the plasma conditions change very slowly, the density depression on axis is not significant. Generally, the quasi-steady state will be obtained when the longitudinal size of the coronal plasma is close to two times the size of the focus spot (Max, Reference Max, Balian and Adam1982; Labate et al., Reference Labate, Cecchetti, Galimberti, Giulietti, Giulietti and Gizzi2005). Then the multi-keV X-ray emission region and the multi-keV X-ray flux will evolve into quasi-steady state because the multi-keV X-rays come from the central hot plasma region (hot underdense coronal plasma zone). In the quasi-steady state, the longitudinal size of the emission region becomes comparable to the size of the focus spot because the multi-keV X-ray flux is proportional to n e2T e (n e and T e are electron density and temperature, respectively) (Labate et al., Reference Labate, Cecchetti, Galimberti, Giulietti, Giulietti and Gizzi2005; Montgomery et al., Reference Montgomery, Landen, Drake, Estabrook, Baldis, Bradley and Procassini1994; Batha et al., Reference Batha, Procassini, Hammel, Shepard, Drake, Bradley, Estabrook, Hsieh, Keane, Montgomery and Phillion1995; Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008). The transverse dimension (FWHM) of the emission region also comes to quasi-steady state with a size slightly larger than that of the focus spot due to the effect of lateral energy transport and radiation cooling (Filevich et al., Reference Filevich, Rocca, Jankowska, Hammarsten, Kanizay, Marconi, Moon and Shlyaptsev2003). This phenomenon is found for various focus spot size (Hu et al., Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008), and for various target materials. As shown in Figure 2, the transverse dimension and the evolvement of the longitudinal size of the emission region (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008) have no difference between the Ti K-shell emission and Ag L-shell emission before and after (>1 ns) the appearance of the quasi-steady state, which indicate that in the case of thick solid target irradiated by long pulse laser, the emission region with the same laser focus spot will remain the same size for various target materials.

The detailed spectra of the Ti K-shell and the Pd, Ag L-shell emission given by CS are shown in Figure 3a. The influences of the diffraction efficiency of crystal and the spectral response efficiency of imaging plate have not been considered. The spectral bandwidth of the L-shell emission spectrum is obviously wider than that of the K-shell emission due to the larger number of charge-state configurations and transition lines, which will increase the conversion efficiency of the L-shell X-ray source (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991), and the phenomenon is shown in Figure 5. The rough emission spectra given by TGS are shown in Figure 3b, which have been modified with the transmission function of the filters used on the XRD (the original spectra given by TGS multiplied with the transmission function of the filters used on the XRD). It indicates that the X-ray photon energy that can enter the XRD are >4 keV for Ti, >2.5 keV for Ag/Pd, and >2 keV for Mo, which mainly come from the corresponding K- or L-shell line emission as shown in Figure 3a.

Fig. 5. (Color online) The X-ray conversion efficiency (CE) of Ti K-shell and Ag/Pd/Mo L-shell emission versus laser energy (a) and X-ray photon energy (b). The laser parameters for Ag, Pd, and Mo are shown in Table 1. The data of Ti K-shell emission of 6 µm thick target with 22.5° incidence angle are taken from the reference of Hu et al. (Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007).

ANGULAR DISTRIBUTION

The angular distributions of Mo/Pd/Ag L-shell emission and Ti K-shell emission are shown in Figure 4. The laser conditions are shown in Table 1. The viewing angles are relative to the target normal as shown in Figure 1. All of the data were normalized with the maximal value given by the XRD at the viewing angle near the target normal. To keep the visibility of the figure, not all of the error bars of ±30% is added in Figure 4. With the same target material, the differences of the angular distributions between various shots are not significant, which indicates that the effects of laser intensity and focus spot size on the angular distribution are not significant in our experiment. So we add the experimental data of three shots to one profile in the case of Ti, Ag, and Pd targets. The method can increase the density of data points and decrease the influence of the stochastic fluctuation of the data to the fitting. Within the error range, there are no notable differences between the measured angular distribution of Ag, Pd, and Mo L-shell emission in front of the target as shown in Figure 4, so we can fit the angular distribution of Ag/Pd/Mo L-shell emission with the same function. The angular distribution behind the target is beyond the scope of the present paper because it is also influenced by the target thickness. We just consider the angular distribution in front of the target.

Usually the multi-keV X-ray emission is reduced away from the target normal but not zero at the 90° viewing angle, which is perpendicular to the target normal, so we can fit the data in front of the target roughly with the function of f(θ) = α +(1−α) cosβ θ, where f(θ) is the X-ray energy detected by the XRD at some viewing angle normalized with the maximal X-ray energy value given by the XRD at the viewing angle near the target normal, θ is the viewing angle relative to the target normal. We found that the fitting index of K-shell emission are α = 0.41 ± 0.014, β = 0.77 ± 0.04, and the fitting index of L-shell emission are α = 0.085 ± 0.06, β = 0.59 ± 0.074. The fitting index of L-shell emission is similar to that of Au soft X-ray emission calculated with LASNEX (150 µm diameter focus spot and 600-ps laser pulse) (Mead et al., Reference Mead, Campbell, Estabrook, Turner, Kruer, Lee, Pruett, Rupert, Tirsell, Stradling, Ze, Max and Rosen1981). In Figure 4, the two-dimensional hydrodynamic code FCI2 simulation result for the angular distribution of Ti K-shell emission (Girard et al., Reference Girard, Jadaud, Naudy, Villette, Babonneau, Primout, Depierreux, Miller, Kauffman, Suter, Fournier, Glenzer, Back, Grun and Davis2004) was also shown. The simulation result is in good agreement with our experimental data, which indicates that the reliable angular distribution can be obtained with the two-dimensional hydrodynamic simulation code FCI2. The slight difference may be induced by the different laser incidence angle between the simulation setting and our experiment.

It is evident from the experimental data and the fitting function in Figure 4 that the X-ray energy decreases away from the target normal, and the isotropy of the L-shell emission is slightly worse than that of the K-shell emission at large viewing angle (>70°). The multi-keV X-ray emission region locates in the central hot plasma region (laser channel), and it is always surrounded by the cold plasma side lobe outside the laser channel that does not emit multi-keV X-rays before and after the coming of the quasi-steady state (Filevich et al., Reference Filevich, Rocca, Jankowska, Hammarsten, Kanizay, Marconi, Moon and Shlyaptsev2003). When the X-rays emitted by the central hot emission traverse through the cold surrounding plasma side lobe, it will be absorbed partially. Because the density of the surrounding cold plasma side lobe descends exponentially away from the target, the area density (plasma density multiplied by length) of the cold plasma side lobe where the multi-keV X-rays traverse increases with the increasing of the viewing angle relative to the target normal, which will increase the absorption and reduce the X-ray energy that enters the detector. So the X-ray energy will decrease with the increasing of the viewing angle relative to the target normal. In the cold plasma side lobe surrounding the emission region, the optical depth of the L-shell emission is larger than that of the K-shell emission, which will increase the absorption, so the isotropy of the L-shell emission is slightly worse than that of the K-shell emission at larger viewing angle. The optical depth of the Ag, Pd, and Mo L-shell emission in the cold plasma is approximately the same for the corresponding target materials of Ag, Pd, and Mo, so there are no obvious differences between the angular distributions of L-shell emission. Besides the self-absorption in the surrounding cold plasma side lobe, the self-absorption in the central hot plasma region can also effect the angular distribution of multi-keV X-rays. But the self-absorption in the central hot plasma region is not as strong as that in the cold plasma side lobe because the temperature of the central hot plasma is very high.

With the fitted angular distribution, the relative total X-ray energies are 0.74 and 0.66 of that obtained with the assumption of isotropy emission for K- and L-shell emission, respectively (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007). The decrease of the X-ray energy at large viewing angle is serious compared to that at the 0° viewing angle, the effect of the angular distribution should be considered carefully in experiments using the X-ray source at large viewing angle (Kalantar et al., Reference Kalantar, Haan, Hammel, Keane, Landen and Munro1997; Pikuz et al., Reference Pikuz, Faenov, Fraenkel, Zigler, Flora, Bollanti, Dilazzaro, Letardi, Grilli, Palladino, Tomassetti, Reale, Reale, Scafati, Limongi, Bonfigli, Alainelli and Sanchez2002; Glenzer et al., Reference Glenzer, Gregori, Lee, Rogers, Pollaine and Landen2003; Riley et al., Reference Riley, Woolsey, McSherry, Khattak and Weaver2002b, Reference Riley, Khattak, Garcia Saiz, Gregori, Bandyopadhyay, Notley, Neely, Chambers, Moore and Comley2007; Schollmeier et al., Reference Schollmeier, Rodriguez Prieto, Rosmej, Schaumann, Blazevic, Rosmej and Roth2006).

It should be noticed that the measured angular distribution of X-ray emission is influenced not only by the viewing angle of the detector relative to the target normal, but also possibly by the laser incidence angle. But in our experiments, the influence of laser incidence angle can not be distinguished due to the small variation range of the incidence angle (0° and 22.5°). Although in the shots of Mo target, the incidence angle is 45°, but unfortunately there is just one kind of incidence angle with Mo target and we can not compare it with that of other incidence angle. We will explore this problem in the future.

CONVERSION EFFICIENCY

In this article, the X-ray energy CE is defined as the total multi-keV X-ray energy in 2π space in front of the target (>4 keV for Ti K-shell emission, >2.5 keV for Ag/Pd, and >2 keV for Mo L-shell emission, as shown in Fig. 3b) divided by the laser energy, which is different from that of our previous article (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007). We use the data given by the XRD nearest to the target normal and the fitting function of the angular distribution of K- and L-shell emission to calculate the total X-ray energy and the conversion efficiency.

Figure 5 shows the CE of K- and L-shell X-ray emission measured with XRD. The CEs are 0.6%–0.7% for Ti K-shell emission with 350 µm diameter (FWHM) smoothed circular focus spot, which is smaller than that obtained with the assumption of isotropy emission in 4π space significantly (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007), 1.2%–1.4% for Ag L-shell emission with 230–260 µm diameter (FWHM) defocused circular focus spot, 1.7%–2.7% for Pd L-shell emission with 230 µm diameter (FWHM) defocused or 350 µm diameter (FWHM) smoothed circular focus spot, and 3.7% for Mo L-shell emission with 350 µm diameter (FWHM) smoothed circular focus spot. The CE of the Pd L-shell emission increases with the laser energy. It’s very strange respect with that of the Ti K-shell and Ag L-shell emission. The reason is not clear. Maybe the laser intensity for Pd is near to the optimized laser intensity, similar to that in the work of Workman et al. (Reference Workman, Lanier and Kyrala2003).

The CE of Ag/Pd/Mo L-shell emission is significantly higher than that of the Ti K-shell emission. As shown in Figure 2, it is not induced by the change of the size of the emission region, so it should be because of the atomic transition process. First, the L-shell emission with larger number of charge-state configurations has more transition channels relative to that of the K-shell emission, represented by the more transition lines and wider spectral bandwidth as shown in Figure 3a, which can increase the transition probability and the emission energy (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991). Second, with the same temperature, the transition with lower X-ray photon energy of 2–4 keV Ag/Pd/Mo L-shell emission has more population in the higher level relative to that of the >4 keV Ti K-shell emission, which can increase the photon number and the emission power (Griem, Reference Griem1997). Those two factors enhance the CE of the Ag/Pd/Mo L-shell emission relative to that of the Ti K-shell emission.

The gain of the CE of the L-shell emission relative to that of the K-shell emission using long pulse laser beam in our experiment is not as high as that of using short pulse laser (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986). The CE of the Pd L-shell emission is about 29–31 times that of the Ti K-shell emission with 120 ps or 60 ps short pulse laser (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986), but in our experiment with the 2 ns-duration long pulse laser, the gain is just 2.8–4.5. This phenomenon was also found in other experiments (Mochizuki & Yamanaka, Reference Mochizuki and Yamanaka1986; Glibert et al., Reference Glibert, Anthes, Gusinow and Palmer1980). In the case of short pulse laser (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986), not only the difference of the charge-state configurations, but also the difference of the hydrodynamic behavior, which determine the volume of the emission region, will influence the conversion of the L-shell emission relative to that of the K-shell emission. But with the long pulse laser in our experiment, the coronal plasma that emits multi-keV X-rays and the volume of the emission region remains the same for various target material as shown in Figure 2 (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008), only the difference of the charge-state configurations will benefit the conversion of the L-shell emission. So, with a long pulse laser beam, the gain of the CE of the Ag/Pd/Mo L-shell emission relative to that of the Ti K-shell emission is not as high as that with a short pulse laser.

For the L-shell emission, the CE increases steadily with the decrease of the X-ray photon energy and target atomic number, which is similar to the behavior of K-shell emission (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Ruggles et al., Reference Ruggles, Porter, Rambo, Simpson, Vargas, Bennett and Smith2003; Workman & Kyrala, Reference Workman and Kyrala2001a, Reference Workman and Kyrala2001b). In the same row in the periodic table of the elements and with the same temperature, the lower X-ray photon energy (smaller atomic number) with the lower transition energy has more population in the higher level, which can increase the photon number and the emission energy. In accordance with bound-bound and bound-free emissivity behavior, the CE can be scaled as T e1/2 exp(–hv/T e) approximately (hv is the X-ray photon energy) (Griem, Reference Griem1997), where T e can be estimated with the analytic theory (Fabbro et al., Reference Fabbro, Max and Fabre1985). But in our experiment, the data have not the same laser parameters, such as the laser focus spot and beam smoothing etc, which will change the CE markedly (Hu et al., Reference Hu, Liu, Zheng, Wu, Li, Wu, Zhang, Yang, Yang, Yi, Du, Huang, Hu and Ding2007, Reference Hu, Zheng, Shen, Lei, Liu, Zhang, Yang, Yang, Ding, Hu, Huang, Du, Yi and Xu2008). So, we can not give a reliable scaling rule of CE as a function of X-ray photon energy that is suitable for the whole L-shell emission range in our experiment.

CONCLUSION

The angular distributions of multi-keV X-ray sources produced by long pulse laser irradiated thick-foil target are measured and can be fitted with the function of f(θ) = α + (1 – α)cosβ θ, where α = 0.41 ± 0.014, β = 0.77 ± 0.04 for Ti K-shell emission, and α = 0.085 ± 0.06, β = 0.059 ± 0.74, for Mo/Pd/Ag L-shell emission, respectively. The K-shell emission, with smaller optical depth in the cold plasma side lobe surrounding the emission region and in the central hot plasma region, is closer to isotropy distribution than L-shell emission. There are no significant differences between the angular distributions of Ag, Pd, and Mo L-shell emission. With long pulse laser, the X-ray conversion efficiency of the Ag/Pd/Mo L-shell emission is significantly higher than that of the Ti K-shell emission, but the gain relative to the K-shell X-ray emission is not as high as that with short pulse laser (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Phillion & Hailey, Reference Phillion and Hailey1986). The X-ray conversion efficiency of the L-shell emission increases with the decreasing of the X-ray photon energy and atomic number, which is similar to the behavior of the K-shell emission (Kauffman, Reference Kauffman, Rubenchik and Witkowski1991; Ruggles et al., Reference Ruggles, Porter, Rambo, Simpson, Vargas, Bennett and Smith2003; Workman, & Kyrala, Reference Workman and Kyrala2001a, 2001b).

ACKNOWLEDGEMENTS

The authors are grateful to the SG-II laser operation group and the target fabrication group for their laborious work and close collaboration. This work was supported by the National High Technology Programs on Inertial Confinement Fusion, Science and Technology Development Fund of CAEP under Grant No. 2007B08003, National Natural Science Foundation of China under Grant Nos. 10375064, 10625523, and 10775165, and National Basic Research Program of China (973 Program) under Grant No. 2006CB806000.

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Figure 0

Fig. 1. (Color online) Experimental setup and the sketch map of the emission region, the hot laser channel (central hot plasma region), and the cold plasma side lobe surrounding the emission region (left). The schematic view of the laser incidence plane and the detector plane (right). Ψ and θ are respectively the laser incidence angle and the viewing angle of detector relative to the target normal.

Figure 1

Table 1. The 2ns-duration laser parameters (the laser energy, the incidence angle, and the size of the focus spot. ϕ is the diameter (FWHM) of the circular focus spot)

Figure 2

Fig. 2. (Color online) (a, b) The laser pulse and X-ray flux given by XRD at 0° viewing angle relative to the target normal, (c, d) the longitudinal temporal profile of the emission region given by XSC, (e, f) the time integrated images of emission region given by XPHC at 76° viewing angle relative to the target normal. The laser parameters for the Ti K-shell emission (>4 keV) in (a, c, e) are 1.6 kJ energy, 2 ns duration, 22.5° incidence angle, and 350 µm diameter (FWHM) focus spot smoothed with a lens arrays, and the laser parameters for the Ag L-shell emission (>2.5 keV) in (b, d, f) are 1.7 kJ energy, 2 ns duration, 22.5° incidence angle, and 350 µm diameter (FWHM) focus spot smoothed with a lens arrays. The horizontal shadows in (c, d) are due to the washer of the targets. The white arrows in (c, d, e, f) show the incidence direction of laser pulse. The white points in (e, f) indicate the target center. The central zones in (e, f) are saturated, so the real longitudinal scale length of the emission region should refer to (c, d).

Figure 3

Fig. 3. (Color online) The detailed X-ray spectra (a) and rough X-ray spectra (b) given by CS and TGS respectively. The relative spectral bandwidth in (b) is useless because the spectral resolution of TGS for Ti K-shell emission is different to that of the Mo/Pd/Ag L-shell emission.

Figure 4

Fig. 4. (Color online) The angular distribution of multi-keV Ti K-shell and Ag/Pd/Mo L-shell X-ray emission. The black solid line and blue short dash line are the fitting curves for K- and L-shell emission respectively with the function of f(θ) = α + (1 – α) cosβ θ. The red short-dot line (ref) is given by 2D hydrodynamic simulation code FCI2 for Ti K-shell emission (Girard et al., 2004). The relative uncertainty of the X-ray energy is ±30%. The 2ns-duration laser parameters are shown in Table 1.

Figure 5

Fig. 5. (Color online) The X-ray conversion efficiency (CE) of Ti K-shell and Ag/Pd/Mo L-shell emission versus laser energy (a) and X-ray photon energy (b). The laser parameters for Ag, Pd, and Mo are shown in Table 1. The data of Ti K-shell emission of 6 µm thick target with 22.5° incidence angle are taken from the reference of Hu et al. (2007).