Much effort is being expended worldwide on the creation of huge laser installations such as the National Ignition Facility (NIF) in the USA,
Matter and Radiation at Extremes, Volume. 5, Issue 3, 035401(2020)
Self-focusing of UV radiation in 1 mm scale plasma in a deep ablative crater produced by 100 ns, 1 GW KrF laser pulse in the context of ICF
Experiments at the GARPUN KrF laser facility and 2D simulations using the NUTCY code were performed to study the irradiation of metal and polymethyl methacrylate (PMMA) targets by 100 ns UV pulses at intensities up to 5 × 1012 W cm-2. In both targets, a deep crater of length 1 mm was produced owing to the 2D geometry of the supersonic propagation of the ablation front in condensed matter that was pushed sideways by a conical shock wave. Small-scale filamentation of the laser beam caused by thermal self-focusing of radiation in the crater-confined plasma was evidenced by the presence of a microcrater relief on the bottom of the main crater. In translucent PMMA, with a penetration depth for UV light of several hundred micrometers, a long narrow channel of length 1 mm and diameter 30 μm was observed emerging from the crater vertex. Similar channels with a length-to-diameter aspect ratio of ~1000 were produced by a repeated-pulse KrF laser in PMMA and fused silica glass at an intensity of ~109 W cm-2. This channel formation is attributed to the effects of radiation self-focusing in the plasma and Kerr self-focusing in a partially transparent target material after shallow-angle reflection by the crater wall. Experimental modeling of the initial stage of inertial confinement fusion-scale direct-drive KrF laser interaction with subcritical coronal plasmas from spherical and cone-type targets using crater-confined plasmas seems to be feasible with increased laser intensity above 1014 W cm-2.
I. INTRODUCTION
Much effort is being expended worldwide on the creation of huge laser installations such as the National Ignition Facility (NIF) in the USA,
A drawback of the NIF ignition campaign is that underestimation of hydrodynamic instabilities during target implosion could result in mixing of fuel with shell material before collapse occurs. In addition, conversion of laser radiation into x-rays in a cylindrical hohlraum surrounding a target is excessively lossy.
However, in a subcritical coronal plasma with electron density ne/ncr < 1, in the vicinity of the critical electron density ncr (cm−3) ≈ 1.115 × 1021/λ2, where λ (μm) is the laser wavelength, there are three types of three-wave nonlinear processes that are collectively referred to as laser–plasma parametric instability (LPI).
The LPI convective gain in an inhomogeneous plasma,
The KrF laser fundamentally generates UV light at λ = 0.25 μm and possesses a number of attractive features. A wide bandwidth of ∼3 THz and a short gain recovery time of the gain medium of ∼2 ns allow temporal profiling of laser pulses with a powerful final spike, which is required for the most attractive shock-ignition (SI) ICF approach.
The typical plasma length of ∼1 mm that is characteristic of ICF-scale experiments is difficult to reproduce in LPI modeling experiments, since rather high laser energy is needed to irradiate planar targets in a large spot comparable to the plasma length. In early experiments on the 3ω Nd-glass Nova laser with an interaction energy of 1 kJ, exploding thin (∼3 μm) CH film targets were irradiated with 4 ns pulses at an intensity I ∼ 1013 W cm−2 on a 1 mm spot.
In the present paper, we consider the previously poorly studied interaction regime of 100 J, 100 ns KrF laser pulses with planar targets
II. EXPERIMENTS
A. Operating modes of GARPUN KrF laser
The main module of the large-aperture e-beam-pumped GARPUN KrF laser was constructed in 1991 and produced 100 J, 100 ns pulses in oscillator mode with optimal plane or unstable resonators. with injection of narrowband (or a broadband) radiation from a discharge-pumped KrF master oscillator into the unstable resonator of the main large-aperture GARPUN amplifier to control output beam divergence and spectral width, giving 100 J, 100 ns pulses of trapezoidal temporal shape (∼1 GW power); a subsequent double-pass amplification of 20 ns pulses of the master oscillator in the e-beam-pumped Berdysh and GARPUN amplifiers, giving 30 J, 20 ns pulses (∼1.5 GW peak power); amplification of subpicosecond pulses of a frequency-tripled Ti:sapphire front end in both amplifiers up to 0.6 J and ≤1 ps (∼1 TW); amplification of several multiplexed subpicosecond pulses, giving a short-pulse train separated by 3–5 ns time intervals, with output energy up to 2 J; simultaneous amplification of a subpicosecond pulse train up to 0.2–0.3 TW peak power in each pulse superimposed with a 30 J, 100 ns long pulse.
A short-pulse version of the installation upgraded in 2007 with a Ti: sapphire front-end was renamed GARPUN-MTW.
B. GARPUN KrF laser in injection-controlled operation
A large-aperture GARPUN amplifier with gain volume of 16 × 18 × 100 cm3 was transversely pumped by two counterpropagating e-beams with electron energy 350 keV, total e-beam current density 50 A cm−2, pulse length ∼100 ns, and specific pumping power Wb = 0.7–0.8 MW cm−3 of the working-gas mixture Ar/Kr/F2 at 1.4 atm pressure (for details, see Refs.
Figure 1.Injection-controlled GARPUN operation. (a) Input and output laser pulses (not to scale). (b)–(d) Streak camera images of far-field output radiation: (b) without injection; (c) with injection; (d) of the injected radiation passed through the resonator without amplification. (e) Near-field distribution of input energy. (f) Injection-controlled layout.
In the injection-controlled layout [
To obtain the time-integrated angular distribution over the laser pulse, a K8 glass plate (K8 is an analog of Schott Glass BK7), which absorbed 248 nm radiation, was placed in the focal plane of the F = 2 m lens. Fluorescence of the glass in the blue–green spectral region was imaged by an objective onto a Spiricon SP620U CCD beam profilometer (Ophir Photonics) [
Figure 2.Time-integrated far-field distribution of laser radiation in injection-controlled GARPUN operation: (a) K8 glass fluorescence under irradiation; (b) angular distribution together with energy fraction in a given angle.
To find out how much energy was contained in the central part of the angular distribution, the latter was measured within a dynamic range of ∼104 obtained by attenuating the incident radiation with a set of highly reflective mirrors with a residual transmittance of 1%–2%. A wedge formed by a pair of mirrors with transmittance 50% per round trip was set behind the attenuator and in front of the focusing lens. A sequence of N focal spots was imaged on a photographic film placed in the focal plane of the lens. The densitometric characteristics of the film were determined using a microdensitometer that measured the spot profiles for various exponentially decreasing energies EN = E1 × (0.5)N. The angular distributions in individual spots were then crosslinked to construct the full distribution shown in
C. Laser–target experiments
1. High-energy target irradiation conditions
The output laser beam was slightly prefocused by shifting the resonator mirrors from their normal positions. This reduced the beam cross-section so that it matched the aperture of the target chamber window and the focusing spherical mirror with F = 400 mm. The distribution of laser energy across the focal spot of the mirror was measured using calibrated photographic film. Since direct measurements were not possible, the laser beam was attenuated by a factor of ∼104 to the appropriate level. We assume that the same distribution was valid also in the case of full laser energy. For a given beam divergence and reduced beam cross section of 10 × 10 cm2, the central lobe of 150 μm diameter (at 0.1 of the maximum) was determined mostly by spherical mirror aberrations. It contained about 75% of the total laser energy, with the rest falling in the low-intensity wings of the angular distribution. For a trapezoidal laser pulse form and a steady angular distribution, the peak intensity in the middle of the spot could be expressed in terms of the laser energy falling on the target as I (W cm−2) = 1.14 × 1011EL (J). For the 50 J energy available on the target in the present experiments, the peak intensity reached I = 5 × 1012 W cm−2. The mean irradiance across the 150 µm diameter area was 2.3 times less than the peak value. For given focusing conditions, the length of the beam waist, ∼1 mm, was comparable to the ablation front propagation distance in an irradiated target, especially in the case of plastic material. At larger distances from the focus, the energy distribution gradually evolved into a ring-like structure like that of the near-field beam distribution with an unstable resonator. The focus position was optimized in the experiments to obtain the largest crater size, and it corresponded to the focus moving by ∼1 mm inside the target.
In our previous burn-through experiments with thin targets,
Below, we analyze the structure of post-irradiated craters in Al and polymethyl methacrylate (PMMA). The former is an opaque material that absorbs incident UV radiation in a thin skin layer of thickness ∼10−2μm. The latter is a translucent material with a penetration depth for KrF laser light ranging from a few to several hundred micrometers,
2. High–energy interaction with Al targets
Top views of a crater in an aluminum target are shown in
Figure 3.Top views of a crater in an Al target with the image plane of the microscope adjusted to (a) the target surface, (b) two-thirds of the crater depth, and (c) the bottom of the crater.
3. High–energy interaction with PMMA targets
PMMA was chosen for irradiation since it is a plastic material with a low average atomic number that absorbs UV laser light well while being transparent in the visible spectrum and thus allowing optical diagnostics. The main features of the 2D ablation regime in PMMA are illustrated in
Figure 4.Side view of a crater produced in PMMA by a single laser pulse with
A cone-shaped crater of ∼1 mm length can be seen in
4. High-aspect-ratio channel formation in translucent materials by repeated low-energy UV pulses
To understand the mechanism of long channel creation in the experiments on high-intensity single-shot interaction with PMMA targets described above, we performed modeling experiments with translucent targets irradiated by repeated low-energy UV pulses. In earlier experiments, long narrow channels were drilled in highly transparent fused silica glass by a train of 30 ns UV laser pulses at a pulse repetition rate of 5 Hz.
In our study, we compared drilling of PMMA and fused silica glass (K8 glass, which, as already mentioned, is an analog of Schott Glass BK7). The penetration depth of KrF laser light at wavelength 248 nm in this glass was 30 μm, measured at intensities significantly lower than the ablation threshold. Experiments were performed with the discharge-pumped KrF laser described in Sec.
Figure 5.Distribution of a discharge-pumped KrF laser radiation in the focal spot.
A long narrow channel with a cone-shaped entrance crater was formed in the PMMA after irradiation for ∼100 s with a pulse repetition rate of 10 Hz, as shown in
Figure 6.Channels drilled by a train of 2 mJ, 20 ns KrF laser pulses in (a) PMMA at a repetition rate of 10 Hz and (b) K8 glass at 40 Hz, with irradiation times of ∼100 s and ∼300 s, respectively.
The K8 glass behaved similarly [
III. NUMERICAL SIMULATIONS
A. Problem description
Simulation of laser–target interaction was performed using the 2D Euler code NUTCY in cylindrical coordinates (z, r).
The calculations were performed in the region 0 < r < R0 and 0 < z < L. The radiation intensity was taken in the form
Figure 7.Input parameters for simulations: (a) laser pulse form; (b) target composition.
The target had two layers [
B. Simulation results
Figure 8.Axial positions of the SW front (1) and the AF (2) vs time in (a) 1D and (b) 2D simulations. The dashed line indicates the initial position of the vacuum–target boundary.
The distributions of plasma density and temperature along the z axis (r = 0) inside (z > 1 cm) and outside (z < 1 cm) the crater are presented in
Figure 9.(a) Simulated axial distributions (
IV. DISCUSSION AND FUTURE PLANS
The present experiments and 2D simulations confirmed that deep cone-shaped craters are formed by long pulses of UV radiation in both highly absorbing (metallic) and translucent (polymeric) materials owing to squeezing out of condensed matter by a conical SW rather than by the ablation itself. This increases the penetration depth of the radiation by several times and enlarges the plasma to millimeter scale lengths.
Small-scale self-focusing of radiation in such plasmas is evidenced by a microcrater relief on the bottom of the main crater. As the code used in the present simulations did not account for radiation refraction in an inhomogeneous plasma or for reflection by the crater wall, it could not describe radiation self-focusing in the crater. Nevertheless, the simulations did give crater and plasma parameters comparable to the experimental ones. We have used these parameters to estimate the laser threshold intensity required for the onset of beam self-focusing
Self-focusing and filamentation of laser radiation in plasmas have been investigated for many years (see, e.g., the review in Ref.
The laser light channeling observed in the PMMA target during its irradiation by a high-energy 100 ns laser pulse with an intensity of ∼5 × 1012 W cm−2 has a quite different origin. Based on its similarity to a high-aspect-ratio channel produced by a train of UV pulses with a low intensity of ∼109 W cm−2 in PMMA and to a filamented structure in K8 glass, we conclude that channel formation proceeded in two steps. First, a cone-shaped crater is produced and causes shallow-angle reflection of the incident radiation. Then, prefocused radiation undergoes self-focusing in the translucent target material owing to matter polarization in the laser field. This nonlinear optics effect, commonly known as Kerr self-focusing, occurs when the total power P of the laser pulse exceeds a critical power Pcr = 3.77λ2/8πn0n2, where n0 and n2 are the linear and nonlinear refractive indices (see, e.g., Ref.
Although the laser intensity and plasma temperature in the present work were somewhat lower than in the main ICF driving pulse, we believe that the effects of UV radiation self-focusing and filamentation in a 1-mm-scale plasma confined in a deep crater could be useful for experimental modeling of the initial “foot” stage of KrF laser–plasma interaction in the case of a prolonged direct-drive ICF plasma. A laser beam divergence of ∼5 × 10−5 rad allows a 50-fold increase in laser intensity to ∼1014 W cm−2 if an aberration-free F = 4 focusing mirror is used. Various types of LPI could then be investigated in a crater-confined plasma. Radiation channeling via Kerr self-focusing in translucent plastic ablators and D–T ice should also be anticipated in direct-drive ICF.
Owing to inhomogeneity of plasma heating, vortex formation in the plasma is possible near critical density. Such vortices would contribute to the emergence of crossed temperature and density gradients, which are responsible for the generation of strong spontaneous magnetic fields of order ∼10 MG (see, e.g., Ref.
One possible extension of this work at the GARPUN-MTW installation could be the interaction of short picosecond pulses with the 1-mm-length plasma produced in the conical crater by a 100 ns laser pulse. Such combined pulses have already been obtained,
V. CONCLUSION
Experiments at the GARPUN KrF laser facility and supporting 2D simulations with the 2D Euler code NUTCY were performed with opaque metal and translucent PMMA targets irradiated by 100 ns UV pulses at moderate intensities up to 5 × 1012 W cm−2. A deep crater of length 1 mm was produced through an essentially 2D effect of combined supersonic propagation of the ablation front and a conical shock wave. Small-scale filamentation of laser radiation in the crater-confined plasma caused by thermal self-focusing was evidenced by the formation of a microcrater relief. In PMMA, with a penetration depth for UV light of several hundred micrometers, a long narrow channel of length 1 mm and diameter 30 μm emerged from the crater apex. Similar channels with a length-to-diameter aspect ratio as high as 1000 were also produced in translucent PMMA and K8 fused silica glass by a train of UV pulses at a low intensity of ∼109 W cm−2. These channels were apparently formed via Kerr self-focusing and filamentation of the UV radiation in condensed matter, which had been prefocused in the growing crater.
In future experiments with increased intensities above 1014 W cm−2, it might be possible to investigate various types of laser–plasma instabilities in long crater-confined plasmas. Such experiments could serve for experimental modeling of the direct-drive ICF-scale interaction of high-energy KrF laser pulses with subcritical plasmas produced by irradiation of spherical and cone-type targets. Furthermore, the interaction of picosecond pulses with peak intensity above 1016 W cm−2 with the 1-mm-length plasma produced by 100 ns pulses in the conical crater could be investigated at the GARPUN-MTW facility through simultaneous amplification of both short (∼1 ps) and long (∼100 ns) pulses. To simulate thermal self-focusing in the laser plasma, work is underway to create a 2D numerical code for the joint solution of the gas dynamics and electrodynamics equations.
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V. D. Zvorykin, I. G. Lebo, A. V. Shutov, N. N. Ustinovskii. Self-focusing of UV radiation in 1 mm scale plasma in a deep ablative crater produced by 100 ns, 1 GW KrF laser pulse in the context of ICF[J]. Matter and Radiation at Extremes, 2020, 5(3): 035401
Category: Inertial Confinement Fusion Physics
Received: Dec. 13, 2019
Accepted: Mar. 20, 2020
Published Online: Nov. 25, 2020
The Author Email: Zvorykin V. D. (zvorykin@sci.lebedev.ru)