Diagnosis of warm dense conditions in foil targets heated by intense femtosecond laser pulses using K α imaging spectroscopy

Warm dense conditions in titanium foils irradiated with intense femtosecond laser pulses are diagnosed using an x-ray imaging spectroscopy technique. The line shapes of radially resolved titanium Kα spectra are measured with a toroidally bent GaAs crystal and an x-ray charge-coupled device. Measured spectra are compared with the K-shell emissions modeled using an atomic kinetics – spectroscopy simulation code. Kα line shapes are strongly affected by warm (5-40 eV) bulk electron temperatures and imply multiple temperature distributions in the targets. The spatial distribution of temperature is dependent on the target thickness, and a thin target shows an advantage to generate uniform warm dense conditions in a large area. © 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement OCIS codes: (350.5400) Plasmas; (300.6560) Spectroscopy, x-ray; (320.7090) Ultrafast lasers References and links 1. R. W. Lee, H. A. Baldis, R. C. Cauble, O. L. Landen, J. S. 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Introduction
Investigation of states of matter between plasma and solid, so called warm dense matter (WDM) has attracted much interest recently [1][2][3][4].Materials with near the Fermi temperature and near solid density can be viewed as a high-density strongly coupled plasma or superheated liquid or solid.A proper description of such states of matter is of great importance for modeling many astrophysical objects [5], studying inertial confinement fusion [6], and understanding relativistic laser-matter interactions [7].
Intense short-pulse laser irradiation on solid density targets has been a unique platform to create and diagnosing various high energy density conditions.However, strongly coupled solid-density plasma formed by such interactions is a highly complicated issue.Within a small focal area (typically a few microns in diameter), fast and energetic electrons are generated [8][9][10].When the normalized vector potential of laser field is greater than the unity (a > 1), these electrons, mainly driven ponderomotively by j × B acceleration, could become relativistic and propagate through solid materials.They induce strong electric and magnetic fields, as well as currents [11].They also ionize materials and lead to various forms of radiation [12][13][14][15].Throughout these processes, the bulk solid target can be heated to several 10s eV on a picosecond time scale maintaining a relatively unchanged density, and WDM conditions could be created.
As fast electrons transverse through a target, they can produce vacancies in the K-shell of the target element and lead to characteristic K-shell emissions.Measurements of Kα x-rays have been widely used as reliable spectroscopic diagnostics for high-density plasmas [16][17][18][19].The atomic levels involved in K-shell radiation are sensitive to plasma conditions.In particular, M-shell vacancies are mainly created by collision of low temperature bulk electrons which have dominant numbers in the target.They can reduce the screening of the Lshell and induce blueshifts of Kα lines [20].Kα emission occurs within the lifetime of fast electrons, which is typically shorter than the hydrodynamic expansion time [21].Precedent works showed Kα line measurements could serve as a thermometer for the bulk of WDM samples created by high energy lasers [20,[22][23][24].
In this paper, we present the spatially resolved Kα doublet spectra from thin titanium foils irradiated by ultrashort multi-terawatt laser pulses.Using an atomic kinetics and spectral simulation, the spatially revolved multi-temperature distributions in warm dense slabs could be determined.The spectra were obtained by using a toroidally bent crystal spectrograph (providing one-dimensional energy dispersion and one-dimensional imaging) and an x-ray charge-coupled device (CCD) camera.Radially resolved spectra are determined via the discrete Abel-deconvolution method and are compared with the calculated Kα spectra using a spectroscopy simulation code including relativistic atomic configurations, SCFLY.The analysis implies that the existence of multiple electron temperatures of warm dense titanium ranges from 5 to 40 eV, and that the radial distribution of temperature is strongly dependent on target thickness.In particular, in a thin 1 μm target where hot electron refluxing plays a role in energy transport, a WDM condition with an average temperature of 20 eV could be achieved over 150 μm diameter, which is 10 times larger than the laser spot size.

Experiment
The experiment was conducted using a Ti:sapphire laser system at the Matter in Extreme Conditions (MEC) instrument of the Linac Coherent Light Source (LCLS).The laser pulses delivered 700 mJ of energy of 50 fs in duration.They were focused by an off-axis parabola (F/#10) to a focal spot of 15 μm full-width-half-maximum (FWHM) diameter, and a peak intensity of (5 ± 1) × 10 18 W/cm 2 was obtained.The prepulse level was 10 −8 at a nanosecond prior to the main pulse.The laser pulses were p-polarized and the incidence angle was 10°.The targets were free-standing titanium foils of 1-10 μm in thickness.The target front surface (laser irradiated side) was coated with 100 nm of aluminum to prevent the direct interaction between the intense laser and bulk titanium and the generation of low-density hot Ti plasma emitting Kα radiation [20,22,25].After each laser shot, the target was translated to the fresh surface.
The spatio-spectral-resolved titanium Kα doublet was measured by using a toroidally bent GaAs (400) crystal (2d = 11.28Å) and an in-vacuum x-ray CCD detector.The toroid was 27 mm × 10 mm and had bending radii of 450 and 305.9 mm in the horizontal and vertical directions, respectively.The crystal was located 244 mm away from the target.For the central x-ray photon energy of E ph = 4511 eV, a Bragg angle of Θ = 77.06°was chosen.An x-ray CCD detector was placed on the Rowland circle, 439 mm away from the crystal.The x-ray optical depth of titanium in this energy range is 20 μm, larger than the target thicknesses, thus x-ray emissions from the whole bulk of foil could be detected.As shown in Fig. 1, simultaneous one-dimensional spatial imaging (Δx = 10 μm) in the vertical direction and onedimensional spectral dispersion (E/ΔE ~15,000) in the horizontal direction for the x-ray source were achieved [22].For the given size of the crystal, a spatial extent of ~1 mm and a spectral window of 4500-4540 eV were covered.
Figure 2(a) shows the x-ray CCD images for Kα emission from 10, 5, and 1 μm targets.For each case, 100 images were averaged.The vertical axis represents the spatial extent on the target surface (hereafter, referred to as the y position for convenience, with y = 0 being the position of laser focus), and the horizontal axis represents the spectral dispersion.The FWHM sizes of Kα 1 and Kα 2 were in the range of 85-100 μm, which were a factor of 5.5-6.5 greater than the size of the laser spot.These x-ray to laser spot size ratios are also consistent with earlier investigations under similar prepulse conditions [26,27].The horizontal lineout at a given y represented the emission from a sliced strip, y μm away from the laser focus [Fig.2(b)].For the 10 μm target, the emission profiles at y = 70-90 μm were close to the typical cold Kα line shape.As the center was approached (y = 0-23 μm), a smooth wing on the high-energy side of Kα 1 (~4515 eV) developed and the gap between the two peaks was filled.For thinner targets, these effects were more pronounced.In particular, for a 1 μm target, blue wings were observed in the y ~70 μm region and the emitted photon energy extended to ~4530 eV.
To obtain the radial distribution of the x-ray emission, the Abel deconvolution was applied to the spectra in Fig. 2(b) using the method described in the reference [23].We assumed that the hot-electron distribution as well as the x-ray emission were radially symmetric on the target plan.The emission zone was divided into concentric circles in increments of 22.5 μm in radius.The normalized Abel-inverted spectra are shown in Fig. 2(c).Vertical offsets are applied for clarity.
Overall, the radially resolved spectra display the effect of blue wings and more clearly exhibit the merging of the two peaks.It is noted that, from thick (5 and 10 μm) targets, the highest energy photons (4520 eV) are emitted from the central region (r ~0).However, from the thin 1 μm target, the highest energy photons (~4530 eV) are mainly emitted in the r = 23-45 um region, while being limited to ~4525 eV in the central region.Because higher energy Kα photons indicate more ionization of the M shell, these experimental results indicate a quite different bulk temperature distribution between thin (1 μm) and thick (5 and 10 μm) targets.

Simulation
To gain deeper physical insight, Ti Kα emissions are modeled using the atomic kinetics and spectroscopy code, SCFLY [28].The spectral module of SCFLY includes the relativistic configuration of atoms, and can provide the detailed emission structures from the various charge states configurations in the complex environment.In the simulation, we include two electron populations.The first is the fast electrons directly accelerated by the intense laser pulse.They represent a small fraction of total electrons (<1% of valence electrons), but they are energetic enough to knock off K electrons by collision, which leads to Kα emission.The hot-electron temperature of T hot = 0.5 MeV is estimated by using the Wilks formula  Though the hot electron temperature and fraction affect the number of Kα photons emitted, the line shape shows very little dependency.In contrast, the line shape shows a strong dependency on the bulk electron temperature.In Fig. 3, the calculated Kα line shapes at different T bulk values are shown.When T bulk < 5 eV, no significant effect is observed.The blue wing around 4515 eV starts to develop when T bulk > 5 eV.As T bulk increases beyond 10 eV, the wing extends to higher energy.Kα 2 gets weaker and the gap between the two peaks fills up.At > 20 eV, the Kα 1 peak begins to shift to higher energy, and structures near the Kα 2 peak are smeared out.In the experiment, similar trends were observed as it approaches to the laser focus or the thinner target was shot.
We applied the calculated results to the Abel-inverted spectra.But most of experimental spectra have both high and low temperature features together, and were hardly reproduced with single T bulk calculations.For example, a spectrum from a 10 μm target [Fig.4(a)] has both a sharp slope beyond 4511 eV and a tail beyond 4520 eV.A spectrum from 1 μm target [Fig.4(b)] has a large blue wing as well as a significant emission at cold Kα 1 (4511 eV).This comparison led us to consider the T bulk distribution [18,24,29].Mixed spectra with two different T bulk values, 5 eV + 15 eV in a 5:5 ratio, and 13 eV + 34 eV in 5:5 provide better agreements with the experimental data in Fig. 4(a) and (b).The ratios are arbitrarily chosen.The reason for choosing such a temperature distribution is to account for gradients in the plasma parameters.Not only are there gradients in the radial direction, but there are also gradients between the target front and back sides that can contribute.The temporal evolution of plasma temperature over the duration of Kα emission is also a factor.).For the thick (5 and 10 μm) foils, the average temperature decreases linearly as a radius increases and near r ~100 μm, it is about 50% of the hottest region near the laser focus.The high and low temperatures contributions are nearly the same in the whole range.It should be noted that because the calculated spectra do not exhibit much difference at low-temperature regime and the temperature below 5 eV could not be well-determined Therefore, low bulk T at r > 40 μm of 10 μm foil, r > 80 μm of 5 μm foil are set to be 2.5 eV, which is the half of 5 eV.For the thin (1 μm) foil, overall higher temperatures across a large radius is found.The highest high bulk T , 40 eV is found at r ~40 μm.Although it might be yet premature to conclude the highest temperature regime is located away from the laser focus in consideration of a large uncertainty at the center of symmetry caused by Abel transformation, the off-center regime in a thin target could be heated effectively compared to thicker targets.Hot electron refluxing could be a possible mechanism of the lateral energy transport [30,31].As a result, the relatively uniform average temperatures ( avg bulk T ~20 eV) can be achieved in a large regime, which is about 10 times of the laser spot.
. The second population comprises most of the valence electrons (or bulk electrons).They have a low temperature, T bulk = 0-50 eV, but affect the ionization states, in particular the degree of M-shell ionization.The effects of each temperature and their population ratio on the Kα doublet are tested.

Fig. 3 .
Fig. 3.The Ti Kα spectra at different bulk electron temperatures.Bulk temperature in eV are indexed to each curve.The spectra are peak-normalized.

Fig. 4 .
Fig. 4. Experimental data (red solid line) for (a) 10 μm and (b) 1 μm targets compared with simulations.Single temperature spectra (black dash lines), and best-fits by mixing two spectra (black solid line).

Fig. 5 .
Fig. 5. Electron temperature distributions for three targets of different thicknesses.The average bulk temperatures (square -solid line) were determined with two different values of T bulk (grey shade).The 5 eV lines shows the low-limit of Kα diagnostics as a temperature sensor, and temperatures below this line are not shown.Finally, the bulk temperature distributions for three different targets are compared as shown in Fig.5.At each radius, a weighted average of two bulk temperatures is determined based on the previous bi-temperature analysis ((1 )avg high low bulk bulk bulk T a T a T = + −).For the thick (5 and 10 μm) foils, the average temperature decreases linearly as a radius increases and near r ~100 μm, it is about 50% of the hottest region near the laser focus.The high and low temperatures contributions are nearly the same in the whole range.It should be noted that because the calculated spectra do not exhibit much difference at low-temperature regime and the temperature below 5 eV could not be well-determined Therefore, low