INTRODUCTION
In heavy ion inertial fusion research, energy deposition by incident energetic ion beams is one of the critical issues, and many corresponding studies have been intensively done experimentally and/or theoretically (Hoffmann et al., Reference Hoffmann, Weyrich, Wahl, Gardés, Bimbot and Fleurier1990; Peter et al., Reference Peter and Meyer-Ter-Vehn1991a, Reference Peter and Meyer-Ter-Vehn1991b; Stöckl et al., Reference Stöckl, Boine-Frankenheim, Geißel, Roth, Wetzler, Seelig, Iwase, Spiller, Bock, Süß and Hoffmann1998). In the related experiments, time-of-flight (TOF) is one of the most powerful diagnostics for the purpose in the framework of particle diagnostics (Ogawa et al., Reference Ogawa, Neuner, Kobayashi, Nakajima, Nishigori, Takayama, Iwase, Yoshida, Kojima, Hasegawa, Oguri, Horioka, Nakajima, Miyamoto, Dubenkov and Murakami2000; Oguri et al., Reference Oguri, Tsubuku, Sakumi, Shibata, Sato, Nishigori, Hasegawa and Ogawa2000; Hasegawa et al., Reference Hasegawa, Yokoya, Kobayashi, Yoshida, Kojima, Sasaki, Fukuda, Ogawa, Oguri and Murakami2003). In the category of X-ray diagnostics, which is also one of the promising tools for the above purpose, Goel et al. (Reference Goel, Gupta, Höbel, Marten, MacFarlane and Wang1998) demonstrated some numerical calculations of Kα spectra from low-Z target material heated by a proton beam. In their study, because of cold plasma creation and a small number of M-shell electrons of target material, Kα spectra with M-shell electrons do not seem to have enough spectral-shift to diagnose plasma temperature, and Kα spectra with a partially ionized L-shell are found to be effective. MacFarlane et al. (Reference Macfarlane, Wang, Bailey, Mehlhorn, Dukart and Mancini1993) showed the plasma creation by a proton beam of about 30–45 eV near a target surface with the use of Al5+ Kα radiation. Rosmej et al. (Reference Rosmej, Blazevic, Korostiy, Bock, Hoffmann, Pikuz, Efremov, Fortov, Fertman, Mutin, Pikuz and Faenov2005a, Reference Rosmej, Pikuz, Korostiy, Blazevic, Brambrink, Fertman, Mutin, Efremov, Pikuz, Faenov, Loboda, Golubev and Hoffmann2005b) and Rzadkiewicz et al. (Reference Rzadkiewicz, Gojska, Rosmej, Polasik and Słabkowska2010) experimentally obtained a charge distribution along Ca projectile trajectory in a SiO2 aerogel target, and showed direct observation of Si-Kα lines with L-shell vacancies and chemical bounding with neighbor oxygen. Their studies may lead us to a fruitful understanding of energy deposition by an ion beam, and have a potential to open a new field of cold and/or warm dense matter physics.
In our previous study (Kawamura et al., Reference Kawamura, Horioka and Koike2006), Cl-Kα spectra from polyvinyl-chloride (C2H3Cl), which is often used in laser-produced-plasma (LPP) experiments and chlorine is doped as a tracer, heated by a He2+ beam were examined for dense plasma diagnostic, and a threshold temperature (~85 eV) is found to trace energy deposition by an incident ion beam traveling in a target. In the Kα diagnostics with plasma creation by an ion beam, K-shell ionization and dielectronic capture are competed due to a small density of an ion beam, and the K-shell ionization process governs the kinetics of the Kα emission below the threshold. Due to the threshold, there may be some aspects that the variation of the Kα radiation with high charge states is not enough for the diagnostics. In such a case, the Kα radiation with lower charge states is preferred.
On the other hand, a heating process by laser-produced fast electrons is one of the important issues in an LPP-scheme, and diagnostics using Kα radiation with high charge states works well to observe energy deposition by fast electrons. There is no competition between atomic processes seen in plasma creation by an ion beam since the density of fast electrons is high enough to be near a critical density for an incident laser wavelength (Kawamura et al., Reference Kawamura, Nishimura, Koike, Ochi, Matsui, Miao, Okihara, Sakabe, Uschmann, Förster and Mima2002; Nishimura et al., Reference Nishimura, Kawamura, Matsui, Ochi, Okihara, Sakabe, Koike, Johzaki, Nagatomo, Mima, Uschmann and Förster2003).
In the above studies, Kα radiation with a partially ionized L-shell was intensively focused, resulting in well-separated Kα spectra, which are essentially applicable to moderately hot plasmas, for instance, the electron temperature of near 100 eV is suitable for chlorine.
In this paper, the demonstration of Kα lines from low charge chlorine with M-shell electrons (including a closed L-shell without M-shell electrons), which are associated with Cl+–Cl7+ (including Cl8+) and called “cold-Kα” hereafter, is examined for cold dense plasma diagnostics. Ionization between lower charge states results in small spectral shift of line radiation. Kα radiation is an atomic transition between L and K-shells. The resultant spectral shift by M-shell ionization of chlorine is much smaller than that by L-shell ionization, and cold-Kα is generally emitted at low plasma temperature.
In the calculation, a C2H3Cl target is used and the spectral shift from Cl+ Kα in accordance with M-shell ionization is clearly shown. Neutral chlorine has the electronic configuration of 3s 23p 5 in the M-shell, and total blue-shift due to the ionization from Cl+ up to Cl8+ is expected to be enough for distinct spectral diagnostics. Resultant spectral calculation shows the clear deformation of a line-shape at the electron temperatures of ≤30 eV. Hansen et al. (Reference Hansen, Faenov, Pikuz, Fournier, Shepherd, Chen, Widmann, Wilks, Ping, Chung, Niles, Hunter, Dyer and Ditmire2005) derived such an electron temperature from a laser-irradiated Al-coated Ti foil plasma using low charge Ti-Kα radiation. Neutral Ti has the electronic configuration of 3s 23p 63d 24s 2 in the outer-shell, and the clear spectral shift may be seen from the charge state of more than ~5, of which outermost 3p-orbital is open. Since the blue-shift of Ti-Kα with the ionization state of less than five may be small, the electron temperature must be higher than ~40 eV for distinct spectral diagnostics. Chlorine has an open 3p-orbital at neutral, and is expected to be a good candidate for cold dense plasma diagnostics. In addition, recent studies on the topic were done by Sengebusch et al. (Reference Sengebusch, Glenzer, Kritcher, Reinholz and Röpke2007) and Neumayer et al. (Reference Neumayer, Lee, Offerman, Shipton, Kemp, Kritcher, Döppner, Back and Glenzer2009). They observed small spectral shift of Cl-Kα radiation. Kα radiation with a lower charge state also gives low emission density, which is the same as that with a higher charge state (Kawamura et al., Reference Kawamura, Horioka and Koike2006). However, in the study, a resultant volume of plasma creation with an ion-beam-produced-plasma (IPP) scheme is much greater than that by an LPP-scheme, and the above problem may be solved.
DESCRIPTIONS ON MODELING OF ATOMIC PROCESSES
Emission energies and oscillator strengths of Cl-Kα lines are calculated with the use of GRASP92 and RATIP codes, which are based on a multi-configuration Dirac-Fock (MCDF) method (Parpia et al., Reference Parpia, Froese Fischer and Grant1996; Fritzsche, Reference Fritzsche2001, Reference Fritzsche2002). Figure 1 shows the radiative decay rates of Cl-Kα lines from the charge states of Cl+–Cl8+, and they come from the ground-states with a vacant K-shell, namely, Cl+: 1s2s 22p 63s 23p 5 → 1s 22s 22p 53s 23p 5 + hν, Cl2+: 1s2s 22p 63s 23p 4 → 1s 22s 22p 53s 23p 4 + hν, ···, Cl8+: 1s2s 22p 6 → 1s 22s 22p 5 + hν. The resultant Kα1 and Kα2 are found to be calculated within the accuracy of ~0.5 eV compared with one of available data (National Astronomical Observatory, 2006). The Kα lines overlap with those of the next charge state, and cold-Kα is mainly composed of the lines from Cl+–Cl6+, which are distributed in 2.62 keV–2.63 keV, and the spectral blue-shift due to M-shell ionization of ~10 eV is found. The cold-Kα lines can be expected to be good candidates for cold dense plasma diagnostics with the spectral resolution on the order of 1 eV. As is discussed in our previous study, it should be noted again that the non-radiative channels due to Auger transitions must be considered for the estimation of net Kα emission as the fluorescence yields of Cl-Kα lines with low charge states are ~0.05.
Radiative decay rates and transition energies of Cl cold-Kα lines calculated by GRASP92 and RATIP codes. From the chronological scientific tables of National Astronomical Observatory (2006), Kα1, Kα2 are, respectively, 2622.3 eV and 2620.7 eV.
The model of population kinetics considered here is presented in Figure 2. Since the population of 1s-vacant ions is very small, the average charge state of total Cl-ions Z total ≈ Z bulk ≈ Z 1s−vacant − 1, where Z bulk and Z 1s−vacant stand for the average charge state of bulk-ions and 1s-vacant ions, respectively (Kawamura et al., Reference Kawamura, Nishimura, Koike, Ochi, Matsui, Miao, Okihara, Sakabe, Uschmann, Förster and Mima2002). According to Figure 6 given in Kawamura et al. (Reference Kawamura, Horioka and Koike2006), an intensity ratio between cold-Kα radiation and high charge one is an effective index to deduce an electron temperature T e in the range of 50 eV ≤ T e ≤ 100 eV, in which the ratios give almost 0.1–10. For T e ≤ 50 eV, it is suggested that only Kα lines with M-shell electrons can be applicable.
Population kinetics associated with cold-Kα lines.
SPECTRAL DEFORMATION OF Kα LINES WITH M-SHELL ELECTRONS
In the viewpoint of an average charge state, we can see a threshold temperature below which Kα lines with M-shell electrons are dominant. Figure 3 is the average charge state of chlorine in a polyvinyl-chloride (C2H3Cl) plasma irradiated by a C6+ beam, of which beam-current density and mean particle energy are, respectively, 3 kA/cm2 and 30 MeV, and the energy spread of the ion beam described by Maxwellian is 10% of the mean energy. The mean energy of 30 MeV is assumed so as to get enough cross-section of K-shell ionization (Kawamura et al., Reference Kawamura, Horioka and Koike2006), and the plasma ion density is assumed to be solid density (≈8.1 × 1022cm−3). The atomic population for Z total ≤ 7, which corresponds to Z 1s−vacant ≤ 8, is dominant in T e ≤ ~70 eV, and that for Z total ≤ 5, which is Z 1s−vacant ≤ 6 and main component of cold-Kα lines, is in T e ≤ ~30 eV. Therefore, the Kα lines from Cl+–Cl6+ are applicable in T e ≤ ~30 eV for plasma diagnostics.
Dependence of the average charge state of chlorine on electron temperature. Target material is C2H3Cl and the plasma ion density is solid density (≈8.1 × 1022cm−3). The incident beam is a C6+ beam, of which current density and mean energy, respectively are 3 kA/cm2 and 30 MeV. The energy spread of the ion beam described by Maxwellian is 10% of the mean energy.
The dependence of a spectral line-shape on the electron temperature is presented in Figure 4. Calculated spectra are convolved by Stark broadening with quasi-static electric-microfield, electron impact broadening using a semiclassical expression, natural and Doppler broadenings (Kawamura et al., Reference Kawamura, Mima and Koike2001, Reference Kawamura, Schlegel, Nishimura, Koike, Ochi, Matsui, Okihara, Sakabe, Johzaki, Nagatomo, Mima, Uschmann, Förster and Hoffmann2003). In the Doppler broadening calculation, the ion temperature is assumed to be equal to the electron temperature. At T e = 5 eV, the spectrum consists of mainly two Kα components of Cl+ and Cl2+. The 1s-vacant states of Cl+–Cl3+ contribute to the composite spectrum at T e = 10 eV. With increase in T e, the charge states of main cold-Kα components are Cl2+–Cl4+ in T e = 15–20 eV, and the Kα lines from Cl5+–Cl7+ have a large contribution to the spectra in T e ≥ 25 eV. Finally, the total blue-shift of the Kα lines from T e = 5 eV up to 30 eV is ~10 eV, and the clear spectral deformation can be observed.
Deformation of a spectral line-shape and blue-shift of cold Cl-Kα radiation from a polyvinyl-chloride (C2H3Cl) plasma. The plasma ion density is solid density. The incident beam parameters are same as in Figure 3.
Figure 5 also gives a time-evolution of Kα spectra for the demonstration of blue-shift with an assumption that population kinetics can be described by a collisional-radiative equilibrium (CRE) condition. The conditions of an incident ion beam are the same as the above calculation, and a flat-top pulse beam with a width of 100 ns is assumed. The energy deposition is approximated by a conventional Bethe's formula with some corrections for bound electrons (Mehlhorn, Reference Mehlhorn1981; Ziegler, Reference Ziegler1999), and a formula studied by Peter et al. (1991a, 1991b) for plasma free-electrons. An initial plasma ion density and electron temperature are, respectively, solid density and 10 eV. With the incident C6+ pulse beam, the electron temperature is raised from 10 eV up to about 15 eV assuming that created plasma is ideal, resulting in the spectral blue-shift of ~2.5 eV and sharpening. Such a time-evolution can be diagnosed using cold-Kα spectra with the spectral accuracy on the order of a 1 eV.
Demonstration of a time-evolution of Cl-Kα spectral deformation from a polyvinyl-chloride (C2H3Cl) plasma. The plasma ion density is solid density, and the electron temperature is raised from 10 up to ~15 eV heated by a C6+ beam, which is assumed to be flat-top with a width of 100 ns. The other beam parameters are same as in Figure 3.
According to the study by Kauffman et al. (Reference Kauffman, Wooods, Jamison and Richard1975), the contribution of the multiple ionization KL n (n stands for a number of L-shell vacancies.) of neon was discussed. In their study, colliding particles come from an incident ion beam. On the other hand, in our study, even if the multiple ionization associated with M-shell KM n is occurred to chlorine by an incident ion beam, because of high density plasma free-electrons up to ~1023cm−3, the M-shell ionization is governed by the surrounding plasma free-electrons. The particle density of an incident ion beam is at most 1013–14cm−3 and the difference of the colliding particle densities between free-electrons and incident ions is up to 9–10 digits. The contribution of the multiple ionization KM n can be neglected. Concerning the multiple ionization associated with the L-shell of chlorine, the binding energies of the L-shell electrons of each low charge state are about 10 times those of the M-shell electrons. Those are about 200–300 eV. Therefore, the contribution of the multiple ionization KL n by an incident ion beam is much less than that of KM n, and the well-defined spectra for temperature diagnostics without any consideration of the multiple ionization may work well.
CONTRIBUTION OF SATELLITE LINES AND OPACITY EFFECT TO Kα LINES WITH M-SHELL ELECTRONS
Concerning satellite lines, atomic states with an excited electron in the outer-shell (Cln+:1s2s 22p 63s 23p (5−n)nl) may have a contribution to the composite spectra. In Figure 6, the Kα lines from the excited states 1s2s 22p 63s 23p (5−n)3d strongly overlap with those from Cln+: 1s2s 22p 63s 23p (6−n) and Cln+1: 1s2s 22p 63s 23p (5−n). However, due to a large contribution of continuum lowering at solid density, an ionization energy of bound electrons is reduced and population of atomic states with a shallow ionization potential is estimated to be small. In Figure 7, the dependence of average continuum lowering ΔE (Stewart & Pyatt, Reference Stewart and Pyatt1966) on the electron temperature T e is given, and a comparison with the average ionization energies I p of Cln+: 1s2s 22p 63s 23p (6−n), which are the ground-states of 1s-vacant states, is made. I p is shown on the average with respect to a total quantum number J associated with a nl-electronic-configuration. With increase in T e up to 30 eV, ΔE can be raised to ~60 eV, which is near the average ionization energy of Cl3+. Since an ionization degree is affected not only by local electron-temperature but also by continuum lowering, (T e + ΔE) is a good index to predict the degree. From Figures 4 and 7, the spectral deformation can be seen with increase in the index, and such atomic excited states as Cln+: 1s2s 22p 63s 23p (5−n)nl may be neglected at solid density.
Radiative decay rates and transition energies of the satellite lines of Cl cold-Kα lines, which are also calculated by GRSP92 and RATIP codes.
Comparison between the average continuum lowering and the ionization energies of 1s-vacant Cln+: 1s2s 22p 63s 23p (6−n).
To utilize the cold-Kα lines for cold dense plasma diagnostics, opacity effect is also one of the critical properties. In one of our past studies (Kawamura et al., Reference Kawamura, Schlegel, Nishimura, Koike, Ochi, Matsui, Okihara, Sakabe, Johzaki, Nagatomo, Mima, Uschmann, Förster and Hoffmann2003), highly charged major Cl-Kα lines at a certain electron temperature are saturated at the plasma thickness of a few microns, and those minor ones at a few tens microns. This is because the final atomic states associated with the Kα lines belong to bulk ions. However, the final atomic states of the Kα lines with M-shell electrons discussed here are Cln+: 1s 22s 22p 53l (8−n)(1 ≤ n ≤ 6). As discussed above, the binding energies of the L-shell electrons are about 200–300 eV in accordance with M-shell ionization, and the temperature of bulk-electrons is too low to ionize the electrons. Therefore, those states have a small contribution to determine overall population kinetics, resulting in small opacity for the cold-Kα lines. This is a qualitative suggestion at the moment, and quantitative consideration will be done in near future.
CONCLUSIONS
The plasma diagnostics with cold-Kα radiation is proposed. To utilize the radiation, clear blue-shift of cold-Kα lines has to be examined, and the lines show the shifts of about 10 eV in accordance with M-shell ionization. From the spectral calculation, the clear deformation of the spectral shape is found in the electron temperatures of ≤30 eV. Concerning the Kα lines from the 1s-vacant states with an exited electron in the outer-shell, it may be expected that they have a small contribution to the composite spectra due to a large continuum lowering at solid density. Opacity effect on the cold-Kα radiation is briefly discussed, and give a suggestion qualitatively. Finally, cold-Kα lines are one of promising tools for cold dense plasma diagnostics. The opacity effect will be quantitatively studied, and reported somewhere.
