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Plasma Physics and Controlled Fusion
Plasma Phys. Control. Fusion Plasma Phys. Control. Fusion 57 (2015) 075011 (7pp) doi:10.1088/0741-3335/57/7/075011
57 Enhancement of laser to x-ray conversion
2015 by a double-foil gold target
© 2015 IOP Publishing Ltd Z Y Ge1, R Ramis2, X H Yang1, T P Yu1, B B Xu1, Y Zhao1, H B Zhuo1, Y Y Ma1, W Yu3 and X J Peng4 ppcf
1 College of Science, National University of Defense Technology, Changsha 410073, People’s Republic of China 075011 2 E.T.S.I. Aeronáuticos, Universidad Politécnica de Madrid, Madrid 28040, Spain 3 Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai 201800, Z Y Ge et al People’s Republic of China 4 Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China Enhancement of laser to x-ray conversion by a double-foil gold target E-mail: [email protected] and [email protected]
Printed in the UK Received 30 January 2015, revised 10 May 2015 Accepted for publication 19 May 2015 Published 18 June 2015 PPCF Abstract A novel double-foil configuration is proposed to improve the laser to x-ray conversion 10.1088/0741-3335/57/7/075011 efficiency from laser irradiating a solid target. One-dimensional radiation hydrodynamic simulations show that the total x-ray conversion efficiency for the double-foil target is as high as 54.7%, which has a 10% improvement compared with the normal target. The improvement Papers is mainly due to the enhanced soft x-ray emissions. Influences of the target geometry parameters on the x-ray conversion efficiency are investigated. Detailed energy distributions 0741-3335 and the individual contributions of the two foils to the thermal and kinetic energy terms are presented. It is found that the main energy terms are mostly determined by the first foil, and the enhancement of radiation is attributed to the lower ion kinetic energy of the double-foil target. 7 Keywords: laser-plasma interaction, x-ray generation, radiation hydrodynamics (Some figures may appear in colour only in the online journal)
1. Introduction any kind of x-ray photons in the energy range of 0.1 keV to 10 keV can be obtained by changing the target materials. Laser-produced plasmas as intense x-ray sources have However, the CE of the x-ray generated by a solid target is attracted much interest in recent decades due to their wide limited due to the narrow emission region [21, 22]. Gas targets applications in many fields, such as advanced lithography [1], and doped low-density foam targets have been proposed as x-ray backlighter imaging [2], high energy density physics [3] more efficient x-ray sources owing to their very large emis- and inertial confinement fusion (ICF) [4–6]. One of the major sion region [23–29]. However, the gas targets are restricted goals in these applications is to enhance the x-ray conver- to a small range of photon energy, and the doped low-density sion efficiency (CE) and therefore the x-ray emission inten- foam targets are limited to very few materials because of the sity. Considerable work has been carried out by varying laser complex fabrication techniques. X-ray emissions can be also parameters such as wavelength, pulse profile, pulse duration enhanced by utilizing the vacuum hohlraum targets in ICF and intensity, or using various target materials and structures because the hot, underdense coronal plasma is confined by the in order to achieve higher x-ray radiation [7–17, 18]. hohlraum [30–32]. However, this type of target is not always The conventional method for generating x-rays is the nano- practical since the generated x-rays are also confined inside second laser irradiation of high-Z solid targets, because the the hohlraum. Pre-exploded thin foil can also provide an effi- fabrication of a solid target is very simple and high-Z mate- cient x-ray source that is very close to those obtained from rials exhibit a higher x-ray CE [19, 20]. Moreover, almost gas or doped low-density foam targets [33, 34]. However, the
0741-3335/15/075011+7$33.00 1 © 2015 IOP Publishing Ltd Printed in the UK Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al
Figure 1. Scheme of the double-foil target.
laser parameters and foil thickness should be chosen carefully, those obtained from the normal solid targets [19, 20]. Very otherwise the x-ray emission can only be enhanced by a small long time plasma expansion and detailed non-local thermody- margin, since this scheme changes the target ablation process namic equilibrium (NLTE) atomic physics make a pure ana- from one-sided expansion (thick foil) to two-sided expansion lytical calculation and optimization of this configuration very (pre-exploded thin foil). Rarefaction waves coming from two difficult and not precise enough for designing experiments. sides of the thin foil will destroy the emission region quickly For that purpose, numerical simulations are performed with [35]. To depress the rarefaction wave of the hot coronal plasma the one-dimensional multi-group radiation hydrodynamics generated from the solid targets and enhance the laser to x-ray code Multi-1D [36, 37]. The hydrodynamic equations are CE, new approaches or solutions are required. solved in a Lagrangian formulation with coupled radia- In this paper, a novel double-foil gold target is proposed tion, electron thermal transport and laser energy deposition in order to enhance the laser to x-ray CE further. The double- mechanism of inverse bremsstrahlung. The electron thermal foil target consists of a thin foil and a thick foil as illustrated conduction is described by the interpolation between the in figure 1, which combines the one-sided (second thick foil) Spitzer’s regime and the flux limited regime. The flux limiter and two-sided (first thin foil) expansion together to a three- is set as f = 0.08, which is the same as that used for the anal- sided expansion. The presence of the first thin foil provides ysis of previous experiments [38]. MPQeos code provides the an additional two-sided expanding plasma x-ray source and data of equation of state (EOS) for Au in a tabular form [39]. avoids the direct irradiation of laser pulse on the second foil. Tabulated NLTE opacities divided into 100 energy groups in The second thick foil is mainly ablated by the x-ray radiation the range of 0.1–5 keV are calculated with the atomic physics generated at the rear side of the first thin foil. Collision of the code SNOP [40]. inner-expanding plasmas in the gap between the two foils In the simulations, 1 ns flat-top pulse, p-polarized lasers 14 2 will depress the rarefaction waves in the two foils. Ion kinetic with an intensity of 5 × 10 W cm are supposed to normally energy is then suppressed and converted to electron internal incident on the double-foil gold target from the left side as energy and radiation energy, thus the x-ray CE is enhanced shown in figure 1. The laser wavelength is 351 nm, which remarkably. Compared with the pre-exploded thin foil method, represents the typical frequency-tripled Nd:glass laser in the double-foil target exhibits a higher x-ray CE, and a prepulse experiments (short-wavelength laser always exhibits a higher is not needed anymore. One can also avoid the complex fab- laser to x-ray CE). The thickness of the first thin foil isd 1 = 0.3 rication technique for a gas or doped low-density foam target. μm, and the distance between the two foils is d2 = 400 μm. Au Furthermore, this double-foil target also offers the ability to is chosen as the target material for its high laser to x-ray CE generate a wide range of photon energies as the solid target. and wide applications, especially in ICF. Both the first thin This paper is structured as follows. In section 2, the detail foil and second thick foil (10 μm) have an initial density of 3 7 3 radiation hydrodynamics simulations are presented. Section 3 19.2 g cm− . A 1.92 × 10− g cm− low-density Au gas is filled deals with the influences of the target geometry parameters on in the gap between the two foils because vacuum is not per- the x-ray CE. Finally, we summarize the results and give the mitted in the simulation. For comparison, the laser irradiating conclusions in section 4. normal solid Au target is also simulated. Figure 2 shows the motion of the Lagrangian interfaces of 2. Numerical simulations the double-foil target. The red, blue and black lines represent the first thin foil, the second thick foil and the low-density The construction of a double-foil target can lead to under- Au gas, respectively. The laser pulse coming from the bottom dense plasma conditions that are much more complex than impinges on the target front side and deposits its energy in the
2 Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al
0.05 As shown in figure 3(a), for the normal solid target, after getting energy from the incident laser via the inverse 0.04 bremsstrahlung, electron internal energy increases very rap- idly. Then electrons convert their energies to ions primarily 0.03 through coulomb collision, atoms are thus ionized and excited, resulting in the generation of x-ray radiation. Meanwhile, due to the expansion of plasmas from the target surface, the ion 0.02 kinetic energy rises noticeably. At the end of laser irradiation (t = 1 ns), the electron internal energy reaches the maximum, 0.01 which is nearly 37.2%. Later on the laser pulse is turned off, the plasma will cool down, and the electron internal energy 0
Position of interface (cm) starts to reduce. Furthermore, the electron internal energy will
Laser transfer into radiation energy and ion kinetic energy with time. −0.01 When t 3 ns, the fractions of the radiation energy, electron 0 0.5 1 1.5 2 2.5 3 = Time (ns) internal energy and ion kinetic energy become stable, which are 44.7%, 15.3% and 37.1%, respectively. Figure 2. Positions of cell interfaces as functions of time for the However, compared with the normal target, an obvi- double-foil target. The red, blue and black lines represent the ously different energy conversion process is observed for the first thin foil, the second thick foil and the low-density Au gas, double-foil target as shown in figure 3(b). At t 1 ns, there respectively. = is a much higher maximum electron thermal energy, almost first thin foil. Here, the electron temperature of the target is 46.5%. This is mainly caused by the more efficient laser heated up to 4 keV, generating a low-density blow-off plasma heating of the underdense expanding plasma generating from expanding into the vacuum. As a consequence of the front- the first thin foil. Besides, differing from the monotonically side plasma expansion and the associated repulsion, the whole increasing trend for the normal target, the ion kinetic energy thin foil is accelerated in the laser direction with an average of the double-foil target presents a more complex temporal 7 1 velocity of 3.5 × 10 cm s− . Meanwhile, the bulk of the target evolution. During the laser pulse injection, the ion kinetic is heated by the x-rays generated at the front side of first thin energy increase continuously with time until t = 0.75 ns. foil. The radiation penetrates the entire thin foil, ablating both After that, it turns to decrease because of the collision of the the rear side of the first foil and the front side of the second inner-expanding plasmas between the two foils as described foil. This is the typical three-sided expansion process for the in figure 2. At t = 1.2 ns, the ion kinetic energy is minimum double-foil target. At 0.75 ns the inner-expanding plasmas (18.3%), which reflects the maximum compression of the from the two foils begin to collide with each other, and the target, as shown in figure 2. Then it increase again with the whole thin foil starts to decelerate. After 1 ns, the pulse is recoil of the thin foil, and approaches 25.0% at t = 3 ns. switched off, the ablation scheme will change from the three- Finally, although the fraction of the electron internal energy sided expansion to the two-sided expansion, and the target for the two types of targets are almost the same, the fraction temperature decreases consequently since there is no more of the radiation energy for the double-foil target is as high heating by the laser. At nearly 1.2 ns, the expanding double- as 54.7%, which has a 10% improvement compared with the foil target is maximally compressed by the impact of the inner- normal target. The enhancement of the radiation emission is moving thin foil. After that, the out-flowing plasma produced mainly attributed to the lower ion kinetic energy. This proves by the second thick foil will push the thin foil and turn over its that the double-foil target can effectively minimize the hydro- direction to move outward. Thus the ion kinetic energy starts dynamic losses and increase the laser to x-ray CE remarkably. to increase again, and the whole target temperature cools X-ray emission spectra integrated over 3 ns in time for the down further. The flow diagram displays the hydrodynamics two types of targets are presented in figure 4. It’s well known process and reveals the scheme of x-ray enhancement for the that the radiation from the high temperature gold plasmas con- double-foil target clearly. sists of three major x-ray emission bands due to the transitions Conservation of the total energy yields that almost all the from upper electronic excited states to the M-shell, N-shell and absorbed laser energy is divided into three leading partitions [41]: O-shell states of Au [43]. There are valleys of weak emission between these emission bands. Clear M-band, N-band and η EELrad EEie ki, α =++ (1) O-band emissions from Au plasmas are observed in figure 4,
where EL and ηα are the incident laser energy and laser which proves the efficiency of the Multi code. Generally, the absorption rate. Erad, Eie, and Eki represent the total radia- double-foil target exhibits a similar emission spectra distri- tion energy, electron internal energy, and ion kinetic energy, bution and the same range of photon energies (0.1–5 keV) respectively. Ion internal energy and electron kinetic energy as the normal target. This demonstrates that the double-foil are always neglected [42]. The laser to x-ray CE is defined as target can also generate a wide range of photon energies just ηrad = EEradL/ . In order to investigate the underlying physics like the normal solid target. Compared with the normal target, of the x-ray conversion enhancement, the incident laser the soft x-ray emissions in the spectral region 0.1–1 keV are energy transformations are demonstrated in figure 3 for both significantly enhanced by almost 21%, while only 6% in the the double-foil gold target and the normal solid target. region 1.6–5 keV (M-band) by using the double-foil target.
3 Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al
Figure 3. Temporal evolution of the energy fractions of the incident laser energy EL, radiation energy Erad, electron internal energy Eie, and ion kinetic energy Eki for the normal target (a) and the double-foil target (b). All the energies are normalized to the total incident laser energy.
1.2 Double−foil target 1 Normal target
0.8
0.6
0.4 Emission intensity 0.2
0 0 1 2 3 4 5 Photon energy (KeV) Figure 5. Target thickness dependences of the conversion Figure 4. Normalized time-integrated x-ray emission spectra for efficiencies of radiation energyE rad, electron internal energy Eie, the double-foil target and the normal target. and ion kinetic energy Eki for the normal target.
Thus the emission improvement is mainly from the increased While the second foil is a pedestal which absorbs the trans- soft x-ray emissions, whereas the M-band emissions almost mitted laser light from the first thin foil and transforms it into have no increase. This is particularly exciting in the applica- radiation further. In this section, more detailed discussions tion of ICF since the enhanced soft x-ray emissions are desir- are given to understand the influences of the target geometry able for higher energy coupling efficiency in the hohlraum [4]. parameters on the x-ray CE. Actually, both the thickness of the Furthermore, a practical backlight of Au in the energy range first thin foil and the distance between the two foils can affect 1–2 keV for opacity measurement is expected from figure 4. the x-ray emission significantly. For simplicity, the thickness This kind of spectral enhancement is important to provide of the second thick foil is fixed as 10 μm, which can avoid available backlights with higher luminous intensity for var- the penetration of the radiation. Considering the characteristic ious applications. three-sided expansion of the double-foil target, the individual contribution of the two foils to the radiation enhancement will 3. Influences of target geometry parameters on be studied separately. x-ray CE In order to investigate the influence of the first foil’s thick- ness on the x-ray CE, we firstly focus on the single normal The former section presents the basic simulation results of target case. Because it’s necessary to know how the energy the energy distributions and x-ray emission spectrum for partitions of the first thin foil couple with the second foil, the double-foil target. It has been shown that the x-ray CE especially for the radiation. The total and rear-side x-ray increases mainly in the soft x-ray emission, which is caused energy normalized to the incident laser energy as a function by the reduction of the ion kinetic energy. Generally, the of the target thickness for the normal target are displayed first thin foil acts as a converter that produces the two-sided in figure 5. The general trend for the total x-ray emission is expanding low-density, high-temperature plasma, in which monotonically increasing with the target thickness up to the the laser light is mainly absorbed and converted into x-rays. massive target value (44.7%). However, for the rear-side x-ray
4 Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al
Figure 6. (a) Total conversion efficiencies of the radiation energyE rad, electron internal energy Eie, and ion kinetic energy Eki versus the first foil thicknessd 1. (b) Individual conversion efficiencies of the electron internal energy and ion kinetic energy of the two foils versusd 1 for the double-foil target. The other parameters are the same as that in figure 2.
emission, it firstly increases with the target thickness, and then To promote the understanding of the individual contribu- reaches the maximal CE of 7.8% as the target is 0.3 μm thick. tion of the two foils to the total thermal and kinetic energy With thicker targets, the CE of rear-side x-ray will decrease terms, the influences of the first foil thicknessd 1 on the con- dramatically. This is because for a very thin target, it burns version efficiencies of Eie and Eki for the two foils are respec- through very quickly and part of the laser energy goes through tively provided in figure 6(b). Apparently, the total thermal the plasma without absorption, so that the x-ray radiation is and kinetic energy are mainly determined by the first foil, small. With the increasing of the target thickness, the total especially for the thicker first foil cases d( 1 > 0.1 μm). For the x-ray emission during the burn-through time is enhanced, second foil, with the increase of d1, both energy terms reduce whereas the rear-side emission decreases since more radia- markedly. This is because the second foil is mostly heated tion has been absorbed by the thicker targets. The conver- by the transmitted laser and the x-rays generated at the rear sion efficiencies of electron internal energy and ion kinetic side of the first thin foil. With a thicker first foil, both heating energy versus the target thickness are also depicted in figure 5. sources decrease rapidly, resulting in the reductions of the It is shown that the conversion fractions of these two energy thermal and kinetic energy of the second foil. When d1 > 2 μ terms both increase with the target thickness. At 0.25 μm, they m, the contributions of the second foil to the two energy terms approach the maximums, which are 43.4% and 19.3% for Eki are negligible (<1%). Whereas, for the first foil, when the foil and Eie, respectively. If the target thickness increases further, is very thin (e.g. d1 = 0.01 μm), the fractions of the thermal both energy terms will decrease. When the thickness is beyond and kinetic energy of the first foil are small since the laser 0.5 μm, the CEs of the ion kinetic energy and electron internal transmits through the thin foil without efficient absorption. energy tend to be constants (37.1% and 15.3%, respectively). Then both energy terms rise quickly with the foil thickness The essential feature of the first foil as a converter is that it until d1 = 0.2 μm, which exhibits a very similar trend like should not only be thick enough to absorb most of the incident the single normal target case, as shown in figure 5. However, laser energy to produce the x-ray emission, but also be thin during 0.2 μm0< 5 Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al Figure 7. (a) Total conversion efficiencies of the radiation energyE rad, electron internal energy Eie, and ion kinetic energy Eki versus the distance between the two foils d2. (b) Individual conversion efficiencies of the electron internal energy and ion kinetic energy of the two foils versus d2 for the double-foil target. The other parameters are the same as that in figure 2. first foil will change from the two-sided expansion to the one- We also compare the individual contribution of the two foils sided expansion, so that both the thermal and kinetic energy to the total Eie, Eki energy partitions in figure 7(b). As discussed increase again and approach the thick normal target values. above, the total thermal and kinetic energy of the double-foil Although the second foil is a pedestal and its thickness is target are mostly determined by the first foil, especially for fixed in our discussion, the distance between two foils also the ion kinetic energy. The percent of the first foil in the total play a key role in the distribution of incident laser energy. The ion kinetic energy is nearly 95%, whereas the second foil’s is dependences of the total x-ray energy, electron internal energy, below 5%, which can be neglected. For the electron internal and ion kinetic energy CEs on the distance between the two energy, in a large distance range (0.1 μm < 6 Plasma Phys. Control. Fusion 57 (2015) 075011 Z Y Ge et al attenuation of the heating radiation source causes the reduction 11475259, and 11175253), the National High-Tech 863 of the electron internal energy for the second foil. Project, the Research Project of NUDT and the National Basic Research Program of China (Grants No. 2013CBA01504 and 2011CB808100). 4. Summary and conclusions A new double-foil configuration is proposed to improve the References x-ray conversion efficiency from laser irradiating solid target. 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