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Diagnostic of dense plasmas using X-ray spectra
Optics Communications 256 (2005) 470–475 www.elsevier.com/locate/optcom
Diagnostic of dense plasmas using X-ray spectra Q.Z. Yu a, J. Zhang a,*, Y.T. Li a, Z. Zhang a, Z. Jin a, X. Lu a, J. Li b, Y.N. Yu b, X.H. Jiang b, W.H. Li b, S.Y. Liu b a
Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China b Research Center for Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China Received 2 February 2005; received in revised form 15 June 2005; accepted 24 June 2005
Abstract The spectrally and spatially resolved X-ray spectra emitted from a dense aluminum plasma produced by 500 J, 1 ns Nd:glass laser pulses are presented. Six primary hydrogen-like and helium-like lines are identified and simulated with the atomic physics code FLY. We find that the plasma is almost completely ionized under the experimental conditions. The highest electron density we measured reaches up to 1023 cm 3. The spatial variations of the electron temperature and density are compared with the simulations of MEDUSA hydrocode for different geometry targets. The results indicate that lateral expansion of the plasma produced with this laser beam plays an important role. 2005 Elsevier B.V. All rights reserved. PACS: 52.50.Jm; 52.25.Os; 32.30.Rj Keywords: Laser-produced plasma; X-ray spectra; Plasma parameters; Lateral expansion
1. Introduction Detailed measurements of plasma parameters are critical to understand the complicated processes in laser–plasma interactions. In lower density regions, Thomson scattering is efficiently and widely used to probe the hydrodynamic parameters [1–5]. For higher density regions, however, this method is invalid due to the limited propaga*
Corresponding author. Tel./fax: +86 10 82649356. E-mail address: [email protected] (J. Zhang).
tion of the probe beam. The reported studies of Thomson scattering have so far been limited to maximum densities of 1021 cm 3 by using 4x of Nd:glass laser beam (k = 263 nm). Although it has been proposed to probe high density plasmas using X-ray lasers, there are also some problems, such as low energy and short duration of the X-ray probe beam [6,7]. X-ray spectra diagnostic method, however, provides an important tool to infer plasma parameters, particularly ionization degree, electron temperature and density, in the high density regions [8–11]. With these two
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.06.066
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
compensatory methods, one can almost diagnose the whole plasma, from corona up to solid density regions. In this paper, we measure laser-produced aluminum (Al) plasmas with X-ray spectra emitted from the high density regions. The spectrally and spatially resolved K-shell X-ray spectra are obtained experimentally. Six primary hydrogen-like and helium-like X-ray lines are identified and reproduced with the atomic physics code FLY [12]. The hydrodynamic parameters, i.e., the electron temperature and density are deduced as a function of space, and compared with those simulated with the 1-D hydrocode MEDUSA [13] for different geometry targets. We find that lateral expansion of the laser-produced Al plasma should be taken into account for the explanation of the results in our experiments.
2. Experimental setup The experiments were performed using the Shenguang II Nd:glass Laser Facility, at the National Laboratory of High Power Lasers. The experimental setup is shown in Fig. 1. A 1x
471
(k = 1.053 lm) laser beam with an energy 500 J in a 1.1 ns (FWHM) Gaussian pulse shape, smoothed with a random phase plate (RPP), was focused onto a target at an angle of 60 to the target normal. To obtain the focal spot of the laser beam and simultaneously examine the smoothing effect of the RPP, a pinhole camera with 10.7 magnification was used. It was arranged 80 mm away in front of the target surface, with a 22.5 gradient angle from the equatorial surface of the vacuum. To avoid the irradiation of the visible light, a 3 lm thick Al coating was closely put in front of the pinhole. Fig. 2 show the cross-sections of the laser focal spots without (Fig. 2(a)) and with (Fig. 2(b)) RPP, respectively. The elliptic profiles of the focal spots are due to the reason of the 22.5 gradient arrangement of the pinhole camera. We can see that the RPP has strong smoothing effects on the intensity distribution of the laser beam, although the spot size is smaller than that without RPP. The diameter of the smoothed focal beam is about 250 lm at full width at half maximum (FWHM), providing a uniform intensity of 1 · 1015 W/cm2. A 800 lm in diameter, 3.7 lm thick Al coating on a 100 lm thick stainless steel substrate was used as the target.
X-ray spectrometer Spatial resolution
y Spectral resolution
x
X-ray film
z Laser beam slit
TAP crystal
Al target 22.5˚ Pinhole camera Plasma Fig. 1. A schematic diagram of the experiment. A plane Al target is irradiated by a laser beam smoothed with a RPP. The timeintegrated, spatially and spectrally resolved X-ray spectra are recorded by a TAP crystal spectrometer aligned along the target surface. The focal spot of the laser beam is measured with a pinhole camera in front of the target.
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Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
3. Identification and simulation of the X-ray lines
Fig. 2. The cross-sections of the focal beam without (a) and with (b) the RPP, respectively. The focal spot of the laser beam smoothed with RPP is about 250 lm in diameter (FWHM), which is somewhat smaller than that without RPP.
The X-ray spectra emitted from the laserproduced Al plasma, was measured with a flat crystal spectrometer. The dispersion crystal was a ˚, thallium acid phthalate (TAP), 2d = 25.76 A which was cleaved on the (1 0 0) plane. In the spec˚ , the integrated reflection tral range of 4.5–15 A coefficient, peak diffraction efficiency, crystal broadening and homogeneity of the crystal, were similarly determined experimentally as before [14]. Although there existed about 9% of the integrated reflectivity over the whole recorded X-ray spectral range, such a small variation was permitted in our experiments. A 20 lm width entrance silt was incorporated perpendicularly to the direction of the plasma expansion (i.e., along z-axis, as shown in Fig. 1), providing the spatial resolution of the X-ray spectrum. The spectrometer was positioned at 90 to the target normal and 68 mm away from the focus of the laser beam, providing a 4.6 magnified factor. The spectral resolution of the X-ray crystal spectrometer, which was limited by ˚ . A 110 · source broadening, was about 10 mA 20 mm X-ray film was used to record the emitted signal. To ensure the X-ray was recorded by the linear part of the X-ray film, a 60 lm thick Be film placed in front of the TAP crystal, was used as a filter. Film density can be converted to X-ray intensity by use of an unpublished calibration curve, which was performed with the X-ray source on the electron accelerator in the Institute of High Energy Physics, Chinese Academy of Sciences.
Fig. 3 shows the spatial-resolved and timeintegrated X-ray spectra recorded by the TAP ˚. crystal spectrometer, in the range of 5.8–7.8 A Six prominent K-shell X-ray lines identified to be the transitions of hydrogen-like (Ly-a and Ly-b) and helium-like (He-a, He-b, He-c and He-d) Al ions, are listed in Table 1. Here, we use Ly- to denote the hydrogenic Lyman series (1s–np, where n is the upper energy level), and He- to the heliumlike series (1s2–1snp). We can see that the Al plasma is almost fully ionized, with the ionization stage of 11 or 12. Other hydrodynamic parameters of the Al plasma, such as the electron and ion temperatures, electron density, and also plasma velocity, can be deduced from the intensity and width of the measured X-ray lines by using the atomic physics code FLY. The code first calculates the ionization and excitation populations for the given plasma parameters, and then outputs a simulated spectra with these populations, for the interested transition levels. The parameters of the Al plasma, such as the atomic number Z, radiation temperature Tr, electron and ion temperatures Te and Ti, electron density ne, and opacity size L, are required as the inputs of the code to simulate the experimental X-ray spectra. During the simulation process, the Al atomic number Z is assumed as 13, and Ti is set to be half of the Te. Te, Tr, ne and L, which have a great influence on the simulated spectra, are chosen properly to fit the experimental X-ray spectra. We can then obtain a series of plasma parameters corresponding to different regions in the plasma, up to 300 lm from the target surface. Fig. 4 shows the experimental spectrum (solid line) at 90 lm away from the target surface and the simulated spectrum (dash-dot line) from FLY in a steady state. We can see that most of the simulated X-ray lines can well reproduce the experimental spectrum both for the wavelength and the intensity, as well as the width. The broadening effect caused by the resolution of the X-ray spectrometer, has already been taken into account in our calculation. Note that the intensity of the simulated spectra is very sensitive to the radiation temperature Tr,
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
473
Fig. 3. Typical spatially and spectrally resolved and time-integrated X-ray spectra recorded by the TAP crystal spectrometer. Six primary X-ray lines form hydrogen-like (Ly-a and Ly-b) and helium-like (He-a, He-b, He-c and He-d) ions are identified, respectively. ˚. The wavelength of the X-ray lines is mainly ranged from 5.8 to 7.8 A
Table 1 The wavelength and transition level of the K-shell Al emission lines ˚) Label Transition level Line Ion Wavelength (A 1s–3p 1s2–1s5p 1s2–1s4p 1s2–1s3p 1s–2p 1s2–1s2p
Intensity (arb.units)
A B C D E F
250
Ly-b He-d He-c He-b Ly-a He-a
Al12+ Al11+ Al11+ Al11+ Al12+ Al11+
Ly- α He- α
Experi Synthe Ly- β He- β He- δ He- γ
200 150 100
6.021 6.142 6.298 6.616 7.170 7.760
50 0
6.0
6.5
7.0
7.5
8.0
Wavelength (Å) Fig. 4. Comparison between the experimental X-ray spectra at 90 lm from the target surface (solid line) and the simulated spectra generated from the code FLY (dash-dot line). The parameters used to calculate the X-ray spectra are: Z = 13, Tr = 500 eV, Te = 650 eV, Ti = 325 eV, ne = 7 · 1022 cm 3, and L = 500 lm, respectively.
which varies in the range of 450–550 eV during the calculation. Furthermore, none of the X-ray lines of interest are optically thin. The plasma opacity scale L in FLY is vital to reproduce the simulated X-ray spectra, both for the intensity and width of the lines. In our simulation, the opacity size is
carefully chosen together with other plasma parameters. It changes from several tens micron to several hundreds micron, according with the spatial expansion of the plasma. Although inevitable errors of the plasma parameters can be introduced for the imprecise values of the opacity size in the FLY code, it does not much influence the whole analysis of the expansion process of the laser-produced plasma.
4. Results and discussion Fig. 5(a) shows the spatial variation of the electron temperature of the Al plasma, derived from the experimental X-ray spectra. The theoretical electron temperature using the hydrocode MEDUSA, for a 1-D planar geometry (solid line) at the end of the laser pulse, is also presented. Note here that the flux limit, which corresponds to the fraction of the laser energy dumped at the critical density, is assumed 0.1 in the simulations. Significant differences can be seen between the experimental data and the 1-D planer simulation result. This implies that the Al plasma, produced in our experimental conditions, cannot be described properly by the 1-D expansion model. Lateral expansion should be considered carefully. In order to estimate the cooling effect caused by lateral expansion, the MEDUSA code was run in a hemispherical geometry, with different radiuses of 2500 lm (large dashes), 500 lm (dash-dots), 250 lm (small dashes), and 200 lm (dots), respectively. Although this simulation still provides a 1-D result, the effects of lateral expansion can be taken into account using hemispherical geometry target.
Experi-data Planer simu r=2500 µm r=500 µm r=250 µm r=200 µm
2000 1500
a
1000 500 0
0
100
200
300
400
-3
2500
Electron density (cm )
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
Electron temperature (eV)
474
1E23
b
1E22 Experi Planer simu r=2500 µ m r=500 µ m r=205 µ m r=200 µ m
1E21
0
100
200
300
400
500
z ( µm)
z ( µm)
Fig. 5. The spatial variations of the electron temperature (a) and the electron density (b) of the Al plasma. The experimental data are compared with the simulation lines from that simulated using MEDUSA hydrocode, at the end of the laser pulse, for a 1-D planer geometry and four hemispherical geometries, with radius of 2500 lm (large dashes), 500 lm (dash-dots), 250 lm (small dashes), and 200 lm (dots), respectively.
As one expected, the simulated electron temperature in the large spherical geometry plasma (for example, r = 2500 lm), approaches to that in the planar geometry plasma. For the smaller radius of the hemispherical target, the laterally cooling effect becomes important. The simulated electron temperature, for the spherical radius of 250 lm, approaches to the experimental values for the regions less than 200 lm from the target surface. For the regions z > 200 lm, smaller hemispherical radius target (for example, r = 200 lm) is more reasonable. Our simulation results show that the cooling effect caused by the lateral expansion of the plasma should be taken into account in laser–plasma interactions. Fig. 5(b) shows the experimental electron density as a function of space from the target surface. We can see that with the X-ray diagnostic method, the high density regions, from 5 · 1021 cm 2 up to 1023 cm 3, can be measured. This greatly extends the diagnostic range of the plasma. Simulation results, for a 1-D planer geometry and four hemispherical geometries (also r = 2500, 500, 250, and 200 lm, respectively), and also at the end of the laser pulse, are shown and compared with the measured electron density inferred from the X-ray spectra. One can see that the electron density simulated for the hemispherical geometry with smaller radius is also more reasonable, similar to the electron temperature situation. This again supports
the case of lateral expansion of the laser-produced Al plasma in our experiment.
5. Conclusions In summary, we have experimentally obtained the K-shell X-ray spectra emitted from high density regions of Al plasma produced by a 500 J, 1 ns Nd:glass laser pulse. Six primary hydrogenlike and helium-like lines, i.e., Ly-a, Ly-b, He-a, He-b, He-c and He-d, are identified, respectively. We find that the plasma is almost completely ionized under the experimental conditions. The highest electron density measured with this method, reaches up to 1023 cm 3. The electron temperature and density, as a function of distance up to 300 lm from the target surface, are obtained by reproducing the X-ray spectra using the atomic physics code FLY. Simulation results using MEDUSA hydrocode, at the end of the laser pulse, for a 1-D planer geometry and four hemispherical geometries (r = 2500, 500, 250, and 200 lm), are compared with the experimental electron temperature and density, respectively. The results show that lateral expansion should be taken into account in the understanding of the laser–plasma interactions. To obtain a 1-D expansion plasma in some experiments, not only a RPP but also a larger focal spot of the laser beam is needed.
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
Acknowledgements The authors like to thank the staff of the Shenguang II Laser Facility at the National Laboratory of High Power Laser. This work was supported by the National Natural Science Foundation of China under Grant Nos. 10176034, 60321003, 10374115, and 10390160, and National Hi-tech ICF Program of China.
References [1] S.H. Glenzer, W. Rozmus, V.Yu. Bychenkov, J.D. Moody, J. Albritton, R.L. Berger, A. Brabtov, M.E. Foord, B.J. MacGowan, R.K. Kirkwood, H.A. Baldis, E.A. Williams, Phys. Rev. Lett. 88 (2002) 235002. [2] V. Malka, E. De Wispelaere, Ph. Mounaix, S. Hu¨ller, F. Amiranoff, F. Dorchies, A. Modena, Phys. Plasmas 10 (2003) 495. [3] J. Hawreliak, D. Chambers, S.H. Glenzer, et al., J. Quan. Spec. Rad. Trans. 71 (2001) 383.
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[4] F. Amiranoff, S.D. Baton, S. Hu¨ller, V. Malka, A. Modena, Ph. Mounaix, N. Renard-Le Galloudec, C. Rousseaux, M. Salvati, Phys. Rev. E 61 (2000) 1949. [5] W.L. Kruer, Phys. Plasmas 10 (2003) 2087. [6] F.Y. Khattak, D. Riley, S. Topping, A.M. McEvoy, J. Angulo, C.L.S. Lewis, M. Notley, D. Neely, Central Laser Facility Annual Report, 2001/2002. [7] H.A. Baldis, J. Dunn, M.E. Foord, W. Rozmus, Rev. Sci. Instrum. 73 (2002) 4223. [8] J.S. Wark, S.J. Rose, P.K. Patel, A. Djaoui, O. Renner, A. Hauer, Phys. Plasmas 4 (1996) 2004. [9] D.M. Chambers, S.H. Glenzer, J. Hawreliak, E. Wolfrum, A. Gouveia, R.W. Lee, R.S. Marjoribanks, O. Renner, P. Sondhauss, S. Topping, P.A. Pinto, J.S. Wark, JQSRT 71 (2001) 237. [10] D.M. Chambers, P.A. Pinto, J. Hawreliak, I.R. AlMiev, A. Gouveia, P. Sondhauss, E. Woffrum, J.S. Wark, S.H. Glenzer, R.W. Lee, P.E. Young, O. Renner, R.S. Marjoribanks, S. Topping, Phys. Rev. E 66 (2002) 026410. [11] O. Renner, J. Limpouch, E. Krousky, I. Uschmann, E. Fo¨rster, JQSRT 81 (2003) 385. [12] R.W. Lee, J.T. Larsen, JQSRT 56 (1996) 535. [13] J.P. Christiansen, D.E.T.F. Ashby, K.V. Roberts, Comp. Phys. Commun. 7 (1974) 271. [14] R.X. Lu, C.S. Mao, G.Y. Yin, H.C. Shen, Acta Optic. Sinica 2 (1982) 568 (in Chinese).
Diagnostic of dense plasmas using X-ray spectra Q.Z. Yu a, J. Zhang a,*, Y.T. Li a, Z. Zhang a, Z. Jin a, X. Lu a, J. Li b, Y.N. Yu b, X.H. Jiang b, W.H. Li b, S.Y. Liu b a
Laboratory of Optical Physics, Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, China b Research Center for Laser Fusion, China Academy of Engineering Physics, Mianyang 621900, China Received 2 February 2005; received in revised form 15 June 2005; accepted 24 June 2005
Abstract The spectrally and spatially resolved X-ray spectra emitted from a dense aluminum plasma produced by 500 J, 1 ns Nd:glass laser pulses are presented. Six primary hydrogen-like and helium-like lines are identified and simulated with the atomic physics code FLY. We find that the plasma is almost completely ionized under the experimental conditions. The highest electron density we measured reaches up to 1023 cm 3. The spatial variations of the electron temperature and density are compared with the simulations of MEDUSA hydrocode for different geometry targets. The results indicate that lateral expansion of the plasma produced with this laser beam plays an important role. 2005 Elsevier B.V. All rights reserved. PACS: 52.50.Jm; 52.25.Os; 32.30.Rj Keywords: Laser-produced plasma; X-ray spectra; Plasma parameters; Lateral expansion
1. Introduction Detailed measurements of plasma parameters are critical to understand the complicated processes in laser–plasma interactions. In lower density regions, Thomson scattering is efficiently and widely used to probe the hydrodynamic parameters [1–5]. For higher density regions, however, this method is invalid due to the limited propaga*
Corresponding author. Tel./fax: +86 10 82649356. E-mail address: [email protected] (J. Zhang).
tion of the probe beam. The reported studies of Thomson scattering have so far been limited to maximum densities of 1021 cm 3 by using 4x of Nd:glass laser beam (k = 263 nm). Although it has been proposed to probe high density plasmas using X-ray lasers, there are also some problems, such as low energy and short duration of the X-ray probe beam [6,7]. X-ray spectra diagnostic method, however, provides an important tool to infer plasma parameters, particularly ionization degree, electron temperature and density, in the high density regions [8–11]. With these two
0030-4018/$ - see front matter 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2005.06.066
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
compensatory methods, one can almost diagnose the whole plasma, from corona up to solid density regions. In this paper, we measure laser-produced aluminum (Al) plasmas with X-ray spectra emitted from the high density regions. The spectrally and spatially resolved K-shell X-ray spectra are obtained experimentally. Six primary hydrogen-like and helium-like X-ray lines are identified and reproduced with the atomic physics code FLY [12]. The hydrodynamic parameters, i.e., the electron temperature and density are deduced as a function of space, and compared with those simulated with the 1-D hydrocode MEDUSA [13] for different geometry targets. We find that lateral expansion of the laser-produced Al plasma should be taken into account for the explanation of the results in our experiments.
2. Experimental setup The experiments were performed using the Shenguang II Nd:glass Laser Facility, at the National Laboratory of High Power Lasers. The experimental setup is shown in Fig. 1. A 1x
471
(k = 1.053 lm) laser beam with an energy 500 J in a 1.1 ns (FWHM) Gaussian pulse shape, smoothed with a random phase plate (RPP), was focused onto a target at an angle of 60 to the target normal. To obtain the focal spot of the laser beam and simultaneously examine the smoothing effect of the RPP, a pinhole camera with 10.7 magnification was used. It was arranged 80 mm away in front of the target surface, with a 22.5 gradient angle from the equatorial surface of the vacuum. To avoid the irradiation of the visible light, a 3 lm thick Al coating was closely put in front of the pinhole. Fig. 2 show the cross-sections of the laser focal spots without (Fig. 2(a)) and with (Fig. 2(b)) RPP, respectively. The elliptic profiles of the focal spots are due to the reason of the 22.5 gradient arrangement of the pinhole camera. We can see that the RPP has strong smoothing effects on the intensity distribution of the laser beam, although the spot size is smaller than that without RPP. The diameter of the smoothed focal beam is about 250 lm at full width at half maximum (FWHM), providing a uniform intensity of 1 · 1015 W/cm2. A 800 lm in diameter, 3.7 lm thick Al coating on a 100 lm thick stainless steel substrate was used as the target.
X-ray spectrometer Spatial resolution
y Spectral resolution
x
X-ray film
z Laser beam slit
TAP crystal
Al target 22.5˚ Pinhole camera Plasma Fig. 1. A schematic diagram of the experiment. A plane Al target is irradiated by a laser beam smoothed with a RPP. The timeintegrated, spatially and spectrally resolved X-ray spectra are recorded by a TAP crystal spectrometer aligned along the target surface. The focal spot of the laser beam is measured with a pinhole camera in front of the target.
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Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
3. Identification and simulation of the X-ray lines
Fig. 2. The cross-sections of the focal beam without (a) and with (b) the RPP, respectively. The focal spot of the laser beam smoothed with RPP is about 250 lm in diameter (FWHM), which is somewhat smaller than that without RPP.
The X-ray spectra emitted from the laserproduced Al plasma, was measured with a flat crystal spectrometer. The dispersion crystal was a ˚, thallium acid phthalate (TAP), 2d = 25.76 A which was cleaved on the (1 0 0) plane. In the spec˚ , the integrated reflection tral range of 4.5–15 A coefficient, peak diffraction efficiency, crystal broadening and homogeneity of the crystal, were similarly determined experimentally as before [14]. Although there existed about 9% of the integrated reflectivity over the whole recorded X-ray spectral range, such a small variation was permitted in our experiments. A 20 lm width entrance silt was incorporated perpendicularly to the direction of the plasma expansion (i.e., along z-axis, as shown in Fig. 1), providing the spatial resolution of the X-ray spectrum. The spectrometer was positioned at 90 to the target normal and 68 mm away from the focus of the laser beam, providing a 4.6 magnified factor. The spectral resolution of the X-ray crystal spectrometer, which was limited by ˚ . A 110 · source broadening, was about 10 mA 20 mm X-ray film was used to record the emitted signal. To ensure the X-ray was recorded by the linear part of the X-ray film, a 60 lm thick Be film placed in front of the TAP crystal, was used as a filter. Film density can be converted to X-ray intensity by use of an unpublished calibration curve, which was performed with the X-ray source on the electron accelerator in the Institute of High Energy Physics, Chinese Academy of Sciences.
Fig. 3 shows the spatial-resolved and timeintegrated X-ray spectra recorded by the TAP ˚. crystal spectrometer, in the range of 5.8–7.8 A Six prominent K-shell X-ray lines identified to be the transitions of hydrogen-like (Ly-a and Ly-b) and helium-like (He-a, He-b, He-c and He-d) Al ions, are listed in Table 1. Here, we use Ly- to denote the hydrogenic Lyman series (1s–np, where n is the upper energy level), and He- to the heliumlike series (1s2–1snp). We can see that the Al plasma is almost fully ionized, with the ionization stage of 11 or 12. Other hydrodynamic parameters of the Al plasma, such as the electron and ion temperatures, electron density, and also plasma velocity, can be deduced from the intensity and width of the measured X-ray lines by using the atomic physics code FLY. The code first calculates the ionization and excitation populations for the given plasma parameters, and then outputs a simulated spectra with these populations, for the interested transition levels. The parameters of the Al plasma, such as the atomic number Z, radiation temperature Tr, electron and ion temperatures Te and Ti, electron density ne, and opacity size L, are required as the inputs of the code to simulate the experimental X-ray spectra. During the simulation process, the Al atomic number Z is assumed as 13, and Ti is set to be half of the Te. Te, Tr, ne and L, which have a great influence on the simulated spectra, are chosen properly to fit the experimental X-ray spectra. We can then obtain a series of plasma parameters corresponding to different regions in the plasma, up to 300 lm from the target surface. Fig. 4 shows the experimental spectrum (solid line) at 90 lm away from the target surface and the simulated spectrum (dash-dot line) from FLY in a steady state. We can see that most of the simulated X-ray lines can well reproduce the experimental spectrum both for the wavelength and the intensity, as well as the width. The broadening effect caused by the resolution of the X-ray spectrometer, has already been taken into account in our calculation. Note that the intensity of the simulated spectra is very sensitive to the radiation temperature Tr,
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
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Fig. 3. Typical spatially and spectrally resolved and time-integrated X-ray spectra recorded by the TAP crystal spectrometer. Six primary X-ray lines form hydrogen-like (Ly-a and Ly-b) and helium-like (He-a, He-b, He-c and He-d) ions are identified, respectively. ˚. The wavelength of the X-ray lines is mainly ranged from 5.8 to 7.8 A
Table 1 The wavelength and transition level of the K-shell Al emission lines ˚) Label Transition level Line Ion Wavelength (A 1s–3p 1s2–1s5p 1s2–1s4p 1s2–1s3p 1s–2p 1s2–1s2p
Intensity (arb.units)
A B C D E F
250
Ly-b He-d He-c He-b Ly-a He-a
Al12+ Al11+ Al11+ Al11+ Al12+ Al11+
Ly- α He- α
Experi Synthe Ly- β He- β He- δ He- γ
200 150 100
6.021 6.142 6.298 6.616 7.170 7.760
50 0
6.0
6.5
7.0
7.5
8.0
Wavelength (Å) Fig. 4. Comparison between the experimental X-ray spectra at 90 lm from the target surface (solid line) and the simulated spectra generated from the code FLY (dash-dot line). The parameters used to calculate the X-ray spectra are: Z = 13, Tr = 500 eV, Te = 650 eV, Ti = 325 eV, ne = 7 · 1022 cm 3, and L = 500 lm, respectively.
which varies in the range of 450–550 eV during the calculation. Furthermore, none of the X-ray lines of interest are optically thin. The plasma opacity scale L in FLY is vital to reproduce the simulated X-ray spectra, both for the intensity and width of the lines. In our simulation, the opacity size is
carefully chosen together with other plasma parameters. It changes from several tens micron to several hundreds micron, according with the spatial expansion of the plasma. Although inevitable errors of the plasma parameters can be introduced for the imprecise values of the opacity size in the FLY code, it does not much influence the whole analysis of the expansion process of the laser-produced plasma.
4. Results and discussion Fig. 5(a) shows the spatial variation of the electron temperature of the Al plasma, derived from the experimental X-ray spectra. The theoretical electron temperature using the hydrocode MEDUSA, for a 1-D planar geometry (solid line) at the end of the laser pulse, is also presented. Note here that the flux limit, which corresponds to the fraction of the laser energy dumped at the critical density, is assumed 0.1 in the simulations. Significant differences can be seen between the experimental data and the 1-D planer simulation result. This implies that the Al plasma, produced in our experimental conditions, cannot be described properly by the 1-D expansion model. Lateral expansion should be considered carefully. In order to estimate the cooling effect caused by lateral expansion, the MEDUSA code was run in a hemispherical geometry, with different radiuses of 2500 lm (large dashes), 500 lm (dash-dots), 250 lm (small dashes), and 200 lm (dots), respectively. Although this simulation still provides a 1-D result, the effects of lateral expansion can be taken into account using hemispherical geometry target.
Experi-data Planer simu r=2500 µm r=500 µm r=250 µm r=200 µm
2000 1500
a
1000 500 0
0
100
200
300
400
-3
2500
Electron density (cm )
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
Electron temperature (eV)
474
1E23
b
1E22 Experi Planer simu r=2500 µ m r=500 µ m r=205 µ m r=200 µ m
1E21
0
100
200
300
400
500
z ( µm)
z ( µm)
Fig. 5. The spatial variations of the electron temperature (a) and the electron density (b) of the Al plasma. The experimental data are compared with the simulation lines from that simulated using MEDUSA hydrocode, at the end of the laser pulse, for a 1-D planer geometry and four hemispherical geometries, with radius of 2500 lm (large dashes), 500 lm (dash-dots), 250 lm (small dashes), and 200 lm (dots), respectively.
As one expected, the simulated electron temperature in the large spherical geometry plasma (for example, r = 2500 lm), approaches to that in the planar geometry plasma. For the smaller radius of the hemispherical target, the laterally cooling effect becomes important. The simulated electron temperature, for the spherical radius of 250 lm, approaches to the experimental values for the regions less than 200 lm from the target surface. For the regions z > 200 lm, smaller hemispherical radius target (for example, r = 200 lm) is more reasonable. Our simulation results show that the cooling effect caused by the lateral expansion of the plasma should be taken into account in laser–plasma interactions. Fig. 5(b) shows the experimental electron density as a function of space from the target surface. We can see that with the X-ray diagnostic method, the high density regions, from 5 · 1021 cm 2 up to 1023 cm 3, can be measured. This greatly extends the diagnostic range of the plasma. Simulation results, for a 1-D planer geometry and four hemispherical geometries (also r = 2500, 500, 250, and 200 lm, respectively), and also at the end of the laser pulse, are shown and compared with the measured electron density inferred from the X-ray spectra. One can see that the electron density simulated for the hemispherical geometry with smaller radius is also more reasonable, similar to the electron temperature situation. This again supports
the case of lateral expansion of the laser-produced Al plasma in our experiment.
5. Conclusions In summary, we have experimentally obtained the K-shell X-ray spectra emitted from high density regions of Al plasma produced by a 500 J, 1 ns Nd:glass laser pulse. Six primary hydrogenlike and helium-like lines, i.e., Ly-a, Ly-b, He-a, He-b, He-c and He-d, are identified, respectively. We find that the plasma is almost completely ionized under the experimental conditions. The highest electron density measured with this method, reaches up to 1023 cm 3. The electron temperature and density, as a function of distance up to 300 lm from the target surface, are obtained by reproducing the X-ray spectra using the atomic physics code FLY. Simulation results using MEDUSA hydrocode, at the end of the laser pulse, for a 1-D planer geometry and four hemispherical geometries (r = 2500, 500, 250, and 200 lm), are compared with the experimental electron temperature and density, respectively. The results show that lateral expansion should be taken into account in the understanding of the laser–plasma interactions. To obtain a 1-D expansion plasma in some experiments, not only a RPP but also a larger focal spot of the laser beam is needed.
Q.Z. Yu et al. / Optics Communications 256 (2005) 470–475
Acknowledgements The authors like to thank the staff of the Shenguang II Laser Facility at the National Laboratory of High Power Laser. This work was supported by the National Natural Science Foundation of China under Grant Nos. 10176034, 60321003, 10374115, and 10390160, and National Hi-tech ICF Program of China.
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