Deep Penetration of UV Radiation into PMMA and Electron Acceleration in Long Plasma Channels Produced by 100 ns KrF Laser Pulses

Abstract

Long (~1 mm), narrow (30−40 μm in diameter) corrugated capillary-like channels were produced in the axially symmetric 2D interaction regime of 100 ns KrF laser pulses with polymethylmethacrylate (PMMA) at intensities of up to 5 × 10¹² W/cm². The channels extended from the top of a deep (~1 mm) conical ablative crater and terminated in a 0.5 mm size crown-like pattern. The modeling experiments with preliminary drilled capillaries in PMMA targets and Monte Carlo simulations evidenced that the crown origin might be caused by high-energy (0.1–0.25 MeV) electrons, which are much higher than the electron temperature of the plasma corona ~100 eV. This indicates the presence of an unusual direct electron acceleration regime. Firstly, fast electrons are generated due to laser plasma instabilities favored by a long-length interaction of a narrow-band radiation with plasma in the crater. Then, the electrons are accelerated by an axial component of the electrical field in a plasma-filled corrugated capillary waveguide enhanced by radiation self-focusing and specular reflection at the radial plasma gradient, while channel ripples serve the slowing down of the electromagnetic wave in the phase with electrons.

1. Introduction

Among the varieties of phenomena in the interaction between laser radiation and matter, the generation of high pressures and the acceleration of charged particles in laser plasma are of the greatest interest for a number of scientific and applied problems. These processes, which have different dependences on the intensity and wavelength of radiation, are directly related to the implementation of inertial confinement fusion (ICF) with laser heating, which was first suggested by N.G. Basov and O.N. Krokhin [1]. The ablation pressure increases with the intensity and decreases with the radiation wavelength as $p\propto I^{2/3}{\lambda }^{-2/3}$ in the assumption that the main part of the radiation energy is released near the critical plasma density and is transmitted to the ablation front due to electronic thermal conductivity, while Bremsstrahlung absorption in the plasma corona with subcritical density is small [2,3,4,5]. Other interaction models, where the main role, on the contrary, was assigned to reverse Bremsstrahlung absorption, give dependences of $p\propto I^{7/9}{\lambda }^{-2/9}$ [6] or $p\propto I^{7/9}{\lambda }^{-2/3}$ [7]. In the latter case, an increase in the absorption gradient for short-wavelength radiation is taken into account. Accounting for a radiative energy transfer in the theoretical model [8] does not change these scalings.

The efficiency of electron acceleration in a laser plasma, determined by the ponderomotive radiation pressure $p_r\propto I{\lambda }^2$, on the contrary, increases with the wavelength. This is why UV radiation is preferred in direct-drive ICF, based on the implosion of spherical shell capsules with deuterium-tritium (DT) fuel by the ablative pressure of plasma directly created by laser radiation [9]. Decreasing the wavelength reduces the risk of developing plasma instabilities and the associated generation of fast (“superheated”) electrons in a plasma corona at a typical radiation intensity of ~10¹⁴ W/cm² and pulse duration of ~20 ns [10]. Due to its large range, they warm up the fuel before the compressed stage, which prevents an achievement of the required highest density matter at the collapse of the capsule. On the contrary, in the ICF scheme with “fast ignition”, electrons with an energy of ~1 MeV were generated by an additional high-intensity short laser pulse (~10¹⁹ W/cm², ~20 ps). They play a crucial role in heating the pre-compressed fuel to a required high temperature [11]. In another promising ICF scheme with “shock ignition”, the additional heating of compressed DT fuel is provided by a strong shock wave (SW) converging to the center of the capsule, which is generated due to a sharp increase in radiation intensity up to ~10¹⁶ W/cm² in the rest 100–200 ps of the laser pulse [12]. High intensity at the final stage of the pulse significantly increases the generation of fast electrons with energies of ~100 keV in plasma, whose role is not yet completely clear at present. By warming up the fuel, they prevent compression: on the other hand, they transfer a part of energy to the SW and thereby provide higher pressure in the center of the capsule [13]. Note that very symmetrical laser irradiation is required to prevent the hydrodynamic instabilities development at the interfaces between an ablator, frozen and gaseous DT fuel and to avoid their mixing inside the spherical capsule [10].

The above considerations in favor of UV laser radiation for generating higher ablative pressure were confirmed in many experiments [7,14,15,16,17,18,19] with plane targets performed at various laser radiation wavelengths in the intensity range of 10¹¹−10¹⁴ W/cm². It should be noted that in these experiments, during an exposure to nanosecond laser pulses, the ablation front passed a distance in the condensed matter less than the size of the irradiated spot, i.e., the one-dimensional (1D) plane geometry of the ablation front propagation and the SW generated by it was realized. In our previous experiments with Al, Pb, graphite and polyethylene (C₂H₄)_n targets at GARPUN KrF laser [20,21,22], pressures consistent with the above scaling were measured in the intensity range of 5 × 10¹¹–5 × 10¹² W/cm² for 100 ns pulses and a focal spot of ~150 μm. The largest pressure value at an intensity of 5 × 10¹² W/cm² reached 4 Mbar. For long pulse duration and axially symmetric two-dimensional (2D) interaction geometry, a new hydrodynamic regime with a 30-fold increase in the propagation velocity of the ablation front in targets was observed as caused by the radial squeezing out of the substance. As a result, a deep cone-shaped crater with a length of ~1 mm was formed in opaque graphite and aluminum targets which absorbed the UV light in a thin submicron layer.

In polymethylmethacrylate (PMMA), a range of KrF radiation is rather large, from tens to a hundred microns in dependence on manufacturing [23,24,25,26]. The ablation of PMMA proceeds via photochemical mechanisms with a low threshold for UV light; the lowest threshold of PMMA decomposition into a gaseous fraction is just 0.7 J/cm². Distinct features of the high-energy UV light interaction with PMMA observed in our experiments are: (i) a conical SW evidencing a 2D hydrodynamic regime; and (ii) a thin capillary-like channel with a diameter of 30‒40 μm extending deep into the target up to ~1 mm from the top of the ablative crater (Figure 1). The microscope images were obtained with sample illumination by an unpolarized incoherent light source and in a projection scheme in the polarized light of copper vapor laser [20,21,22]. The formation of the capillary channel is explained by the pre-focusing of incident radiation nearby the crater top due to specular reflection by the plasma density gradient near the conical surface and the self-focusing of radiation transmitted through plasma in the PMMA [27].

In this paper, we focus on the effect which has not been discussed yet. In Figure 1a, one can see a “crown” at the end of the capillary channel. Numerical simulations and novel experiments with preliminary drilled capillaries in PMMA targets evidence that this crown-like pattern is presumably associated with a deceleration of fast electrons which are generated and accelerated in extended laser plasma, filling a conical crater and a long “post-crater” capillary channel.

2. Performance of Experiments

The GARPUN KrF laser operated at a wavelength λ = 0.248 μm with an unstable telescopic resonator and a magnification parameter M = 6. A narrow-band (Δῡ ~ 0.1 cm⁻¹) radiation of discharge pumped master oscillator Lambda Physik EMG 150 TMSC (200 mJ and 20 ns) was injected into the cavity and provided a narrow-band output of up to 100 J in 100 ns trapezoidal pulses with a rise front of 20 ns (for details see [27]). A slightly convergent output laser beam with an initial cross-section of 14 × 18 cm² was directed into the vacuum chamber and focused by a spherical mirror with F = 400 mm in a spot of a 150 µm diameter (at the 0.1 level of the maximum), which contained 75% of the whole energy.

The layout of the laser-target experiments is shown in Figure 2a. PMMA targets were parallelepipeds in form with a thickness (along a laser beam) of 3–5 mm and side surfaces with optical quality, through which the plasma glow inside the laser crater was recorded (Figure 2b). A plasma plume was imaged with a long focus length objective lens F = 210 mm in the intermediate plane, where an optical slit was placed. It cut out a narrow strip displayed by the second objective lens on the streak cameras “Agat” or PS-1/S1 (General Physics Institute of Russian Academy of Sciences—GPI RAS). They scanned in time the visible plasma glow in the direction perpendicular to the slit orientation. To adjust an actual horizontal plasma propagation along the laser beam in the case of the PS-1/S1 camera (where the scanning direction is horizontal), additional mirror optics rotated the image plane (it is not shown in Figure 2). A point light source was used to preliminarily align the optical scheme. Its radiation was collimated to probe the interaction region and to obtain target images at streak cameras in “idle mode”, i.e., without scanning and in the absence of a laser shot. Precise target alignment was performed using a He–Ne laser, which illuminated the crater obtained in a previous laser shot. Images from an output screen of the Agat camera were registered with Spiricon SP620U profiler (Ophir Photonics). In the case of the PS-1/S1 camera, the images were registered with Anima-PX reader (Optronics Gmbh). Using the built-in software, the monochrome image on the screen was transformed into “pseudo-colors” corresponding to different intensity levels.

3. Plasma Hydrodynamics for PMMA Targets

2D hydrodynamic interaction regime is clearly seen for the PMMA target irradiation image in Figure 3 obtained with a PS-1/S1 streak camera. When a 100 ns laser pulse with a peak intensity of 10¹² W/cm² and a rise time of ~20 ns (see [27]) exposed a PMMA target, the maximum speed of plasma expansion into a residual gas of 100–150 km/s was achieved at the pulse plateau. By the end of the laser pulse, the propagation velocity of the plasma glow slowed down, which is obviously due to a rapid decrease in the density and temperature in the plasma corona as it expanded away from the target. An intense glow was also observed deep in the target propagating up to ~1 mm depth for 10–20 ns from the beginning of the laser pulse. It is much bigger than the focal spot diameter of 150 μm. This evidences a valumetric absorption of the UV laser light in a translucent PMMA material and very fast 2D ablation front propagation into the target. Over time, this inside glow gradually shifted to the target surface due to the increased absorption of the incident radiation in a plasma corona.

A crater with a depth of up to 1 mm remained in the PMMA target after a laser pulse (Figure 1). When the next laser pulse struck the same crater produced by a previous pulse, radiation was absorbed in the target depth, and plasma glow moved deeper inside the target. This is clearly seen in the time-integrated (static) images of the PMMA glow obtained by displaying the target luminescence onto the profiler (Figure 4 on the left) and also on the space–time scans obtained with Agat streak camera (Figure 4 on the right).

4. An Origin of the Crown Ending the Capillary Channel in PMMA

We believe that the crown-like pattern ending the 1 mm capillary channel in PMMA might be a multitude of deceleration tracks of an electron beam. Fast electrons could be generated as a result of a self-focusing of incident radiation in the deep ablative crater [27,28] and the development of laser plasma instabilities (LPI) favored by a long interaction length of a narrow-band laser radiation with underdense plasma [10,13]. Electrons could then be captured in the adjacent narrow capillary filled with plasma (Figure 5a). At an increased scale with an adjusted image intensity/contrast profile, the capillary in Figure 5b reveals a quasi-periodic structure with an axial period comparable with its diameter of 30–40 μm. The capillary channel resembles a corrugated plasma waveguide first considered by T. Tajima for a laser-driven plasma electron accelerator [29]. While hollow dielectric capillaries with a smooth wall or straight plasma-filled capillaries were shown to guide high-intensity laser radiation (see, e.g., [30,31]), the corrugated plasma capillary retarding the propagation of an electromagnetic laser field in phase with electrons effectively increases the acceleration length [32]. In our case, an interplay of laser radiation self-focusing in the plasma and specular reflection at a radial density gradient near the capillary wall creates a corrugated waveguide with an enhanced on-axis intensity profile and an electric field axial component which accelerates electrons along the capillary.

Note that a quite different direct electron acceleration mechanism controls the acceleration process in a self-produced corrugated capillary channel at rather low laser intensity I ≤ 5 × 10¹² W/cm² in a long 100 ns UV laser pulse (λ = 0.248 μm) with a laser field parameter $a_0=8.5\times {10}^{-10}{[I(\mathrm{W}/{\mathrm{cm}}^2){\lambda }^2({\mathsf{\mu }\mathrm{m}}^2)]}^{1/2}\ll 1$ compared with well-known laser-driven plasma-based acceleration regimes at relativistic intensities I ≥ 10¹⁸ W/cm² in femtosecond IR pulses (λ ≈ 1 μm) with $a_0\ge 1$ [33].

5. Monte Carlo Simulation of e-Beam Degradation in PMMA Targets

To validate the suggested model, numerical simulations were performed with the Monte Carlo code described elsewhere [34]. The code was further elaborated to simulate the coupled electron and bremsstrahlung X-ray transport through matter in the energy range from 0 to 1 MeV [35]. In this range, scattering cross-sections of the electrons and photons have a complex dependence on energy and cannot be described by analytical expressions. At the same time, for low-energy particles, the detailed structure of atomic shells becomes significant which requires the use of direct cross-section data. For this reason, the evaluated data library of Lawrence Livermore National Laboratory EPICS2014 distributed by the International Atomic Energy Agency (IAEA) [36] was chosen, which allowed better calculations of multiple electron trajectories and integrated energy deposition in PMMA samples. Approximately 50,000 histories were traced in simulations and the obtained trajectories of individual electrons are shown by various colors in Figure 6. The e-beam with an initial diameter of 30 μm was assumed, and began its interaction with PMMA at a 0.5 mm distance from the target front surface. Monoenergetic electron energy was varied in the range of 150–500 keV. Distributions of energy deposition in dependence of depth were obtained by integrating the energy losses of electrons over the radial coordinate and for the whole ensemble of particles (Figure 7).

The comparison of the simulated results of e-beam scattering and absorption with the experimental pattern in Figure 5 shows that qualitative agreement with the crown form and size is achieved for the initial electron energy of approximately 200–250 keV.

6. The Modeling Experiments on Electron Acceleration in the PMMA Target with Preliminary Drilled Capillary

In this section, we describe the modeling experiments on electron acceleration in the PMMA target with a preliminary drilled capillary first reported at the LPpM3-2019 Conference [37]. The layout of these experiments is shown in Figure 8a. A high-aspect-ratio capillary was drilled in a PMMA sample by a discharge-pumped master oscillator EMG 150 TMSC operating with 1−2 mJ energy in 20 ns pulses at a 10 Hz repetition rate. Thus, PMMA targets with channels of 3 mm length and 30−40 μm diameter were produced (for details see [27]). Note an important distinction of these channels with a smooth wall from the above-discussed self-produced corrugated capillaries. A high-energy 100 ns UV pulse of GARPUN KrF laser was focused on the capillary inlet comparable in size with a spherical mirror focal spot and with an intensity of I ≈ 10¹² W/cm². A stack of GAFCHROMIC radiochromic films set close to a capillary outlet served as an electron detector. To prevent film exposure by UV laser light, the stack was covered by 10 μm Al foil. The microscopic image of the PMMA sample after a laser shot (Figure 8b) shows a damaged area of approximately 2 mm in depth, formed by an SW energy load, and also the remainder of the capillary with a length of 1 mm.

Although the protective Al foil survived after the laser shot, the emulsion layer was detached on the first and second films in the stack (Figure 8c). Assuming that the film destruction was caused exactly by electrons, their initial energy can be estimated from several tens to a hundred keV in a comparison of the tabulated data for the electron range [32] with the present attenuation in the combined thickness of the Al foil (10 μm) and radiochromic films (~300 μm). These evidence a slightly lower accelerated electron energy than in the case of the self-produced corrugated capillaries. Although these are rather rough estimates, they nevertheless may confirm the importance of a corrugated capillary structure for more efficient electron accelerator.

7. Conclusions

The formation of a long (~1 mm) and a narrow (30−40 μm in diameter) capillary-like corrugated channel finished by a post-channel crown was observed in an axially symmetric 2D hydrodynamic regime, which is typical for the interaction of 100 ns UV laser pulses with a translucent PMMA targets at GARPUN KrF laser facility at intensities up to 5 × 10¹² W/cm². A deep penetration of the UV radiation in PMMA and high ablation front velocities were confirmed by a spatial-temporal evolution of the visible plasma glow. The modeling experiments with a preliminary drilled capillary channel and Monte Carlo simulations evidence that the crown origin might be caused by an electron beam acceleration of up to a few hundred keV energies, which is much higher than the electron temperature of the plasma corona ~100 eV [21,22]. This indicates the presence of an unusual direct electron acceleration regime. It is supposed that electrons are firstly generated due to laser plasma instabilities favored by a long-length interaction of a narrow-band radiation with ablative plasma in a deep (~1 mm) crater. Electrons injected into a high-aspect-ratio self-produced corrugated plasma capillary are further accelerated by an axial component of the electrical field enhanced in a plasma-filled waveguide due to radiation self-focusing and specular reflection at radial density gradient, while channel ripples serve for slowing down the electromagnetic wave in phase with the electrons. Further experiments are underway to prove the alleged model.