Abstract
1 Introduction
In direct-drive inertial confinement fusion (ICF)[1,2] a millimetre-sized spherical capsule containing a cryogenic mixture of deuterium and tritium is irradiated by multiple laser beams, that ablate the external plastic shell, driving the compression and the heating of the fuel up to its ignition. The efficiency of the compression can be however reduced by the onset of laser–plasma instabilities, such as stimulated Brillouin scattering (SBS)[3,4] and cross-beam energy transfer (CBET)[5], that can produce a loss of laser energy and an imbalance of laser beam coupling. Moreover, compression can be deteriorated by suprathermal hot electrons (HEs) with energy of approximately more than 50 keV, generated during laser–plasma interaction (LPI), that can be absorbed by the cold fuel, enhancing its entropy and preventing ignition. It was estimated that a tolerable level of HE energy coupled to the cold fuel, that is, not so large to prevent the fuel ignition, is of the order of
Many experiments were carried out at the OMEGA laser facility[8–11] on this issue, both in planar and spherical irradiation geometry, producing an extensive knowledge of LPI at laser intensity
LPI studies in conditions relevant for direct-drive ignition (
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In the present work we report the results of an experiment carried out at the GEKKO XII laser facility in planar target multibeam irradiation geometry, which is able to explore the transition region between TPD- and SRS-dominated regimes, where both parametric instabilities and HE generation are characterized in detail. In agreement with the framework depicted by previous experiments, the results here show that TPD is driven in a saturated regime while SRS steeply grows in near-threshold conditions with modest values of light reflectivity of approximately
2 Experimental setup
The laser beam arrangement and the setup of diagnostics available at the GEKKO XII laser facility are sketched in Figure 1(a). The facility, located at the Institute of Laser Energy (ILE) of Osaka University, consists of 12 beams, bundled in an overall
Figure 1.(a) Scheme of the experimental setup. For the sake of simplicity, here the diagnostics are plotted in a plane, conserving the angles from the normal direction to the target. In the real setup, diagnostics are arranged at ports located in a spherical chamber. Below each diagnostic, polar () and azimuthal () angles of the corresponding port are reported. (b) Target multilayer structure, consisting of an Al flash coating, a polystyrene layer (CH), a Cu tracer layer and a polyethylene layer (CH), starting from the laser irradiation side. (c) Laser beam configuration in the bundle. Green and blue numbers refer to driver and interaction beams, respectively. Behind the turning mirrors at Ports 1, 3 and 6, the time-integrated optical spectrometer, the optical streak camera and the SRS calorimeter are located, respectively.
The focal spot size of the driver and interaction beams could be inferred by an X-ray pinhole camera, acquiring an X-ray image of the plasma with a 15 μm aluminium filter at a spatial resolution of 30 μm. As visible in Figure 2(a), the profiles obtained in both the irradiation configurations show in fact an inner peak with FWHM of approximately 280 μm due to the interaction beams, while the profile obtained in the shots with the driver beams shows a larger base with FWHM of approximately 850 μm.
Figure 2.(a) Pinhole camera profiles of the laser spot obtained in shots with (red line) and without (black line) the driver beams. (b) Values of density scalelength
The targets consisted of thin multilayer flat foils, as shown in Figure 1(b), including (i) a 10–50 μm-thick polystyrene ablation layer, (ii) a 5 μm-thick copper layer, used as a tracer of HEs via Kα line emission, and in a few shots (iii) a 20 μm-thick polyethylene back layer, aimed at reducing the effect of HEs refluxing on the Cu Kα emission. Different values of the ablator layer thickness were here used with the aim of estimating the temperature of HEs through the consequent variation of the Cu Kα emission.
The experiment made use of several diagnostics, which are described in detail in a separate publication[17]. Here, we describe only the subset of diagnostics that is devoted to characterizing the LPI, the generation of HEs and their propagation into the target.
The backscattered light, showing signatures of SRS and TPD, was collected behind the last turning mirrors of two different interaction laser beams, namely beams
The amount of light backscattered by SRS in the laser focusing cone was measured by a calorimeter located behind the last mirror of an interaction laser beam, namely beam
Energy and number of HEs were investigated by using a Cu Kα spectrometer, two electron magnetic spectrometers (EMSs) and a Bremsstrahlung cannon (BSC). The Kα fluorescence emission of copper (
The Bremsstrahlung cannon, a high-energy X-ray spectrometer (HEXS) at the GEKKO XII facility, was located behind the target at 70° from the normal (
Finally, two EMSs were located inside the interaction chamber, looking at the target from the rear side at 30° and 50° from its normal direction (EMS 1,
Fujifilm BAS-MS IPs were used for EMS, HEXS and Cu Kα diagnostics; they were scanned by using a Typhoon FLA 7000 scanner at a delay from the exposure time going from 30 to 50 minutes, depending on the diagnostics.
3 Interaction conditions
The processes at play in LPI depend on the local conditions of interaction, such as local values of the laser intensity, electron temperature, plasma expansion velocity and electron density, as well as their spatial gradients. These conditions are here modelled by 2D radiative-hydrodynamic simulations carried out with the DUED code[20] for both the shots with and without the driver beams. The values of plasma temperature and density scalelengths, calculated at densities in the range of 0.1nc–0.25nc, are reported in Figure 2(b) for different times. Hydrodynamic simulations show that plasma conditions are dominated by the interaction beams, with coronal temperatures in the underdense plasma in excess of 2 keV in the proximity of the laser peak in both irradiation configurations. The density scalelength of the plasma increases with time, with values of approximately 80 μm and 120 μm at the laser peak time and after 200 ps, respectively, in the case of interaction beam only; the use of the driver beams leads to a modest rise of these values of approximately 15% (
Local conditions of interaction are here also determined by the partial overlap of the single-beam focal spots on the target surface. As discussed in the literature and observed in previous experiments, this condition can drive collective SRS and TPD[21], where common daughter waves are driven by different beams. This leads to a decrease of the threshold of the instabilities, as discussed below.
Finally, the local conditions of interaction are here modified by the formation of laser speckles, produced by the RPP. Here, the spatial manipulation of the laser coherence operated by the RPP splits a single beam into approximately 2000 speckles of size
4 Experimental results
4.1 Two plasmon decay
The onset of TPD is usually investigated by the observation of the half-integer harmonics of laser light in the plasma emission spectrum[24], which are produced by the nonlinear coupling of plasma waves driven by TPD with laser light. Here, both time-resolved and time-integrated spectra showed evidence of half-harmonic
Typical
Figure 3.Comparison of time-integrated backscattered light spectra measured in shots with (red lines) and without (black lines) the driver beams: (a) /2 emission peaks and (b) SRS spectra.
The narrowest red-shifted peak at
Two other features are visible in the spectra, a large blue-shifted peak at approximately 680–688 nm and a symmetrical less intense red-shifted peak at approximately 720–723 nm, which are signatures of convective TPD driven at densities lower than
4.2 Stimulated Raman scattering
SRS spectra obtained in shots with and without the driver beams, measured by the time-integrated spectrometer, are reported in Figure 3(b). They show a broadband emission in the range of
4.3 SRS and TPD timing
The timing of TPD and SRS could be measured by time-resolved backscattered spectra acquired by the streak camera at port
Figure 4.Time-resolved spectra obtained for a shot where driver beams were used. (a) Time-integrated spectrum, obtained by vertical binning of the streaked spectrum shown in (b). (c) Time profile of the various spectral components observed in the spectrum. (d) Time profile of the driver and interaction beam. The horizontal white and vertical black dotted lines, in (b) and (c) respectively, indicate the times of driver and interaction beam peaks.
4.4 Multibeam LPI
In a few shots, some beams (
Figure 5.Comparison of SRS spectra obtained in shots with a variable number of interaction beams. No driver beams were used in these shots. The time-integrated spectrometer was located behind port . (a) Shots with (black line) and without (red line) the beam . (b) Shots with all the beams (blue lines) compared with shots where beams and (green lines) and , and (magenta lines) were switched off.
Additional information is provided by the time-integrated intensities of SRS and
Figure 6.(a) SRS and /2 intensities normalized by the number of beams versus the total laser energy. Measurements here refer to shots without the driver beams. Labels 6, 7 and 9 indicate the number of laser beams switched on in the shots. (b) Growth of /2 intensity versus the parameter .
This result is strengthened by the scaling of
In collective processes, parametric instabilities driven by different laser beams share a daughter wave; considering the processes with the lowest thresholds[21,30], it is expected that TPD and SRS here share scattered EPW and electromagnetic waves, respectively. This hypothesis could explain why SRS light is not scattered in the back direction.
4.5 Hot electrons
The energy of the HEs propagating into the target was estimated by different diagnostics and compared. The spectra measured by the two EMSs extended up to energies in excess of 400 keV, showing an exponential decay for energies higher than approximately
Figure 7.(a) Typical HE spectrum obtained by the EMSs, where the red rectangle shows the fitting region and the black dashed line is the background level. (b) Values of HE temperature obtained by the EMSs at 50° (black squares) and at 30° (red circles) and by the HEXS (blue triangles) versus the parameter. Solid and empty symbols indicate the shots without and with the driver beams, respectively. The relative uncertainty is 20 for all datasets, indicated as an example by the error bar on the left. The dashed lines represent the linear fitting for the complete sets of EMSs at 30°, EMSs at 50° and HEXS data.
The Bremsstrahlung cannon HEXS measurements showed a detectable signal up to the sixth or seventh IP layer, depending on the shot. The detailed procedure followed to analyse the data is described in Ref. [31]; in short, it was performed in two steps by means of GEANT4 simulations. In the first stage, photons incident on the HEXS were assumed to have an energy distribution given by
Figure 8.(a) Signal obtained in different IP in the HEXS and calculated deposited energy calculated by GEANT4 simulations using an exponential function with photon temperature of 24.5 keV. (b) The intensity measured by using targets with different plastic thickness and calculated values by using , keV.
The conversion efficiency of laser energy to HEs estimated by the HEXS analysis was in the range of
A confirmation of the
4.6 Discussion
It was previously shown that TPD scales with the parameter
At times before the laser peak, TPD begins to damp and finally turns off. Possible mechanisms could be the steepening of the density profile at the quarter critical density or the ion fluctuations produced by ponderomotive effects[37], as shown by particle in cell simulations[36].
SRS reaches its maximum growth after the peak of TPD, where the delay between the two instabilities is due to the higher threshold of SRS, which therefore needs higher values of laser intensity and density scalelength to be driven. Calorimetric measurements in shots without the driver beams show a very low value of SRS reflectivity of
In Figure 9, the measured values of SRS reflectivity (marked as stars) are compared with the classical model of convective gain in a linear density profile (red curve), given by Rosenbluth[38], where
Figure 9.Curves of the growth of SRS reflectivity obtained from a multispeckle model (black) and a non-smoothed beam (red) as a function of the Rosenbluth gain calculated for the nominal laser intensity. Magenta and blue stars represent experimental results in shots without and with the driver beams, respectively, where the gain has been calculated considering the single-beam intensity. Empty stars represent shots with a smaller number of beams, as indicated by numbers 6, 7 and 9. The relative uncertainty of the reflectivity values due to the calibration procedure is around 30, which is as large as the star size.
As shown in Figure 9, the experimental conditions are located in a region of the curve where the growth is significantly steep, far from the saturation. This explains the considerable enhancement observed for SRS in shots with the driver beams, although they provide an increase of density scalelength of only 10
It is also interesting to observe that the SRS reflectivity gets closer to the multispeckle model when the number of beams is progressively reduced (empty stars in Figure 9). This can be explained by recalling that the experimental gain is here calculated by considering the single-beam laser intensity. The above observation therefore suggests that collective processes result in a reduction of the SRS threshold with respect to single-beam laser intensity, or seen in a different way, an effective value of laser intensity given by the overlapped fields should be considered for computing the SRS gain, implying that a larger number of speckles are able to drive SRS. In this context, the speckle distribution given by the coherent overlapping of single-beam speckles should also be considered, suggesting a larger number of speckles and therefore also of high-intensity ones.
As suggested by the experimental results, the multibeam irradiation produced SRS light scattering in directions other than the backscattering. Analytical models suggest that multibeam SRS, where multiple laser beams couple to a common scattered electromagnetic wave, could occur in ICF conditions[21,30]. However, while multibeam TPD was extensively characterized in OMEGA experiments, multibeam SRS, which is expected to be dominant in long-scale NIF direct-drive experiments, still needs an accurate investigation. The first clear indication of sidescattered common-wave SRS was obtained by Depierreux et al.[41]; the results obtained in the present experiment provide further evidence of the importance of collective SRS processes in determining the instability threshold and extent.
The conversion efficiency of HEs
5 Conclusions
In the present experiment, LPI is investigated by using a bundle of nine partially overlapped laser beams in an irradiation regime of interest for direct-drive ICF. Laser intensities are here intermediate between those envisaged for the classical direct-drive scheme, massively explored at the OMEGA laser facility, and those expected in the shock ignition scheme. Experimental data show that TPD develops in a strongly saturated regime and turns off before the laser peak, while SRS steeply grows in a linear convective regime in near-threshold conditions, therefore resulting in modest values of scattered light reflectivity. SRS reflectivity is well reproduced by considering the convective growth in independent speckles, where local laser intensities are distributed according to an exponential function and saturation of the SRS growth into the most intense speckles is taken into account. Despite the uncertainties about the distribution of local intensities into the speckles and about the noise level in the plasma, our basic model[23] satisfactorily reproduces the measured SRS reflectivity and confirms that SRS growth is in a regime far from saturation. Both SRS and TPD are shown to depend on the overlapped laser intensity rather than on single-beam intensity, suggesting that both the instabilities are collectively driven by multiple beams, therefore sharing common daughter waves. In the case of SRS, this hypothesis is corroborated by the observation that light is predominantly scattered out of the lens cone.
Results also show that in the explored irradiation conditions, consisting of a transition region between the domain of TPD and SRS, the generation of HEs is still dominated by TPD, giving rise to electrons with temperatures around 20–50 keV and conversion efficiencies below 1
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