ISSN 10637850, Technical Physics Letters, 2014, Vol. 40, No. 11, pp. 980–983. © Pleiades Publishing, Ltd., 2014. Original Russian Text © A.V. Garbaruk, M.S. Gritskevich, S.G. Kalmykov, A.M. Mozharov, M.V. Petrenko, M.E. Sasin, 2014, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2014, Vol. 40, No. 21, pp. 97–103.

Shock Waves in GasJet Target of a LaserProducedPlasma ShortWaveRadiation Source with TwoPulse Plasma Excitation A. V. Garbaruka, M. S. Gritskevicha, S. G. Kalmykovb*, A. M. Mozharovb, M. V. Petrenkob, and M. E. Sasinb a

b

St. Petersburg State Polytechnical University, St. Petersburg, 195251 Russia Ioffe Physical Technical Institute, Russian Academy of Sciences, St. Petersburg, 194021 Russia *email: [email protected] Received June 14, 2014

Abstract—Previous investigations of the laser plasma at twopulse mode of its generation revealed longliving perturbations of the gasjet target by the first pulse, leading to significant modulations of the plasma radiation. In the present paper, results of a numerical hydrodynamic simulation of the gasjet target are reported which provide explanation of the observed phenomena. An impact of the first pulse (prepulse) upon the target results in formation of a dense quasispherical layer in it, with a lowdensity area inside. This layer expands with the time and drifts downstream with the gas flow. Depending on the time interval between pulses, the second laser pulse can either intersect the dense layer or pass through the lowdensity gas, whereby the observed modula tions of the plasma emission can be explained. DOI: 10.1134/S1063785014110042

In experiments described in [1, 2], the laser plasma was induced in xenon (Xe) gas jet by successive impacts of two laser pulses. The first pulse (prepulse) of a KrF excimer laser with a wavelength of λ = 248 nm nm was followed after some delay time by the second (main) pulse of a Nd:YAG laser with λ = 1064 nm. Each pulse duration as measured at the base was about 30–35 ns. Resonant threephoton preion ization produced in Xe by the KrF laser prepulse was expected to increase the shortwave radiation output from plasma heated by the main IR laser pulse. How ever, in the experiment, significant variations of the plasma radiation intensity had been observed at very long delays of the main pulse–of order of several hun dreds of nanoseconds and even of microseconds– when the prepulseproduced plasma should already recombine. An assumption has been made that the UV laser prepulse excited density waves in plasma, with which the main IR laser pulse interacted later. Verifi cation of the assumption validity is the main objective of the present study. To realize this, a numerical hydro dynamic modeling of a perturbation produced by the prepulse in the gas jet has been undertaken, and its results are compared with experimental data. A supersonic Xe gas microjet flowing from a Laval nozzle (see [3], nozzle 1) was used as the target. Focused laser beams intersected at almost right angles so that their common focus was located on the jet axis directed along the third perpendicular. Measurements of the excimer laser beam geometry in the focal zone

[4] and photographs of the prepulseexcited plasma [1, 2] showed that the region of the UV laser beam interaction with the target had a nearly cylindrical shape with a diameter of 100–150 μm and length of 400–600 μm along the beam. The twodimensional axisymmetric approach has been chosen for the numerical simulation. The prepulse was supposed to generate instantly a spherical temperature perturbation with diameter Dper = 100– 200 μm in a quasistationary gas jet. In fact, the interaction of the prepulse with the gas jet target produces plasma consisting of ions and free electrons, rather than a neutral gas. However speeds of elastic density waves in the plasma (ion acoustic waves) and in the gas are the same, being determined by the thermal motion of heavy particles (ions and/or atoms). Another distinction between the plasma and the gas of neutral atoms is mechanism of temperature equalization behind the wave front. In the plasma, this mechanism is based on the electronic thermal con ductivity, the magnitude of which in the Xe plasma is significantly higher than the heat conductivity in the neutral gas. However, the temperature equalization rate is a rather secondary factor in the propagation of density perturbations in a gas, the role of which in the model under consideration is additionally masked by the value of initial perturbation temperature that is set on the basis of speculative assumptions. The lower limit of the temperature of medium in the region of interaction of the UV laser beam with the

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Fig. 1. Gas density fields obtained with the numerical simulation of the shock wave excited by the UV laser prepulse in the Xe gas jet target (see the text for parameters). The jet axis coincides with the abscissa X axis and R is the radial coordinate. The nozzle outlet edge and plane of the output hole correspond to X = 13 mm. Jet density variations are shown with gray color gradations, see the scale in the top right corner. Solid lines originating from the focus point show contours of the beam of the main IR laser. The UV excimer laser beam is perpendicular to the figure plane, and its focus is also located at the point with X = 14 mm, R = 0. The uppermost fragment (t = 1 ns) indicates the initial conditions and shows the contour of the initial temperature perturbation (dotted curve).

target is determined by the energy of photoelectrons as Te, min ≈ hν = 5 eV, where hν is the KrF laser photon energy. The actual temperature can be somewhat higher due to the collisional heating of free elec trons in the laser radiation field, but the efficiency of this mechanism for the prepulse with its shorter wavelength (heating power is proportional to ~λ2) and lower energy is 40–50 times lower than the effi ciency of heating by the main IR laser. Since the absorption of laser radiation energy by plasma increases with the gasjet target density, the pertur bation temperature can be higher in jets of higher density. Absence of the prepulsegenerated plasma luminescence in the extreme UV (EUV) spectral range suggests that the plasma temperature in any case does not exceed Te, max ≤ 10–15 eV. TECHNICAL PHYSICS LETTERS

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The hydrodynamic modeling consists in numerical solving nonstationary Navier–Stokes equations for an axisymmetic compressible gas (Xe) jet flowing from a nozzle into the vacuum, on the axis of which a uniform spherical temperature perturbation is generated. Boundary conditions are set by specifying the stagna tion pressure and temperature at the input boundary of the computational region (nozzle inlet) and a certainly low static pressure (0.015 Pa) at the output one. Non slip adiabatic (zero heat flux) boundary conditions are imposed on impermeable solid walls. A stationary solution obtained in [3] is used as the initial field of flow parameters. The density distribution inside the area of the temperature perturbation is assumed to be unperturbed and the pressure is determined by the equation of state. The system of equations is solved 2014

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using the generalpurpose ANSYSFLUENT code [5, 6]. Figure 1 presents the simulated jet density fields calculated at the following parameters: stagnation pressure (total pressure in front of the nozzle inlet), P0 = 10 atm; temperature, T0 = 293 K; unperturbed gas density at the jet axis, njet axis ≈ 5.6 × 1018 cm–3; effective jet diameter (at halfheight of the radial den sity profile), Djet eff ≈ 700 μm. The spherical perturba tion with temperature Tper = 10 eV = 116000 K and diameter Dper = 150 μm is located on the jet axis at a distance of ΔX = 1 mm from the nozzle outlet edge. As it can be seen on Fig. 1, the temperature pertur bation generates a spherical shock wave in which the front expansion velocity is close to the speed of sound in the gas behind the front and at the initial time amounts approximately to ≈3.5 × 105 cm/s whereas the speed of sound in the unperturbed gas ahead of the front at the temperature about 20–50 K is 50– 75 times less. Immediately behind the front, a densi fied layer with an effective thickness of 20–30 μm is formed, in which the gas density is about three times higher than that before the front. Inside this dense spherical “shell,” an area is situated with density about ten times lesser than that of the unperturbed gas. The density of the spherical layer and its thickness remain almost unchanged, but its velocity drops as the front expands and the temperature of the gas inside decreases. This behavior agrees well with the solution of the classical problem of a strong point explosion [7]. By the time of t ≈ 500 ns, the shock wave front expan sion velocity becomes equal to the velocity of the gas outflow (VX ≈ 3 × 104 cm/s), so that the front segment

moving upstream stops. Somewhat earlier, at the moment of t ≈ 400 ns, the front diameter becomes close to diameter of the jet, the jet breaks, and its part downstream from the break location leaves the region under consideration. At t ≈ 1.5–2 μs, the remaining, upstream part of the front comes on the run with the jet and after some time the jet recovers. According to the above scenario, the development of the plasma generated by the IR laser pulse must sub stantially depend on the moment of time at which this pulse arrives. As it can be seen on Fig. 1, in the case of delays within 100 ns ≤ Δt ≤ 500 ns, the IR laser beam crosses the dense gas layer in two places symmetric rel ative to the focus and spaced by a distance of several hundred microns, so that the plasma cloud should split into two separate fragments. In case of Δt ≥ 600 ns, plasma will not at all be formed because the laser beam passes through a space where the gas is almost absent. At still longer delays, the beam hits on the unperturbed jet. Figure 2 shows experimentally observed variations of the plasma EUV emission as a function of the delay time between the pulses under conditions close to those used in the present numerical simulation: P0 = 13 atm; distance from the nozzle outlet edge, ΔX = 1 mm; unperturbed gas density at the jet axis, njet axis ≈ 7 × 1018 cm–3. One can see that the EUV emission, in fact, disappears at Δt ≈ 550 ns and reappears again only at Δt ≥ 2–3 μs. Displayed in [1] photographs of the plasma taken in the experiment under discussion also correspond to the calculated scenario: (i) at Δt = 234 ns, the luminous cloud of the plasma induced by the main IR laser pulse consists of two fragments; (ii) at Δt = 624 ns, the plasma light is not observed at all and only a residual mark of the UV prepulse is seen; and (iii) at Δt = 8 μs, the plasma light reappears. It should also be noted that photographs in [1] qualitatively confirm the results of our previous numerical simulations of the unperturbed jet [3]: the extension of the plasma along the laser beam in exper iments with ΔX = 1 and 4 mm corresponds to the cal culated effective jet diameters. The described shock wave structure can be applied in practice to enhance the observable EUV output. To raise the plasma emissivity, the main IR laser pulse should be switched on at the moment of time when the laser beam focus is located in the dense gas layer. To reduce the selfabsorption of the EUV radiation in the surrounding lowionized and neutral gas, the observa tion geometry has to be organized so that observer’s line of sight passed through the low density area nearly at right angle to the shock front. In conclusion, note that the idea to induce a shock wave in the gasjet target by means of the prepulse and then to use its dense front for enhancement of the laser plasma emissivity had been proposed and experimen tally tested earlier in [8, 9].

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REFERENCES 1. A. Garbaruk et al., Proceedings of the Int. Workshop on EUV and Soft XRay Sources (November 3–7, 2013, Workshop Proc. S12; Dublin, Ireland), http://www.euvlitho.com/2013/S12.pdf. 2. V. V. Zabrodskii, Yu. M. Zadiranov, S. G. Kalmykov, A. M. Mozharov, M. V. Petrenko, M. E. Sasin, and R. P. Seisyan, Tech. Phys. Lett. 40 (8), 668 (2014). 3. A. V. Garbaruk, D. A. Demidov, S. G. Kalmykov, and M. E. Sasin, Tech. Phys. 56 (6), 766 (2011). 4. Yu. M. Zadiranov, S. G. Kalmykov, M. E. Sasin, and P. Yu. Serdobintsev, Tech. Phys. 57 (12), 1681 (2012). 5. J. Murthy, W. Minkowycz, E. Sparrow, and S. Mathur, in Handbook of Numerical Heat Transfer, 2nd. ed., Ed.

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by W. Minkowycz, E. Sparrow, and J. Murthy (J. Wiley & Sons, Hoboken, NJ, 2006). S. R. Mathur and J. Y. Murthy, Numer. Heat Transf. B: Fundam. 32 (2), 195 (1997). Ya. B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and HighTemperature Hydrodynamic Phe nomena (Fizmatlit, Moscow, 2008), pp. 82–87 [in Russian]. R. de Bruijn et al., J. Phys. D: Appl. Phys. 36, L88 (2003). R. de Bruijn et al., Phys. Plasmas 12, 042701 (2005).

Translated by P. Pozdeev

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