AbstractWe present a recent numerical analysis of impedance mismatch technique applied to carbon equation of state measurements. We consider high-power laser pulses with a Gaussian temporal profile of different durations. We show that for the laser intensity (${\approx }1{0}^{14} ~\mathrm{W} / {\mathrm{cm} }^{2} $) and the target design considered in this paper we need to have laser pulses with rise-time less than 150 ps

A. Aliverdiev

D. Batani

R. Dezulian

High Power Laser Science and Engineering

English

AbstractWe present a recent numerical analysis of impedance mismatch technique applied to carbon equation of state measurements. We consider high-power laser pulses with a Gaussian temporal profile of different durations. We show that for the laser intensity (${\approx }1{0}^{14} ~\mathrm{W} / {\mathrm{cm} }^{2} $) and the target design considered in this paper we need to have laser pulses with rise-time less than 150 ps.</jats:p

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Influence of a laser profile in impedance mismatch techniques applied to carbon EOS measurement

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High Power Laser Science and Engineering (2013), vol. 1(2), 102–104.c© Author(s) 2013. The online version of this article is published within an Open Access environment subject to the conditions of theCreative Commons Attribution licence <http://creativecommons.org/licenses/by/3.0/>.doi: 10.1017/hpl.2013.15Influence of a laser profile in impedance mismatchtechniques applied to carbon EOS measurementA. Aliverdiev1,2, D. Batani3, and R. Dezulian41Institute for Geothermal Researches DSC of Russian Academy of Sciences – Pr. Shamilya 39A, 367030, Makhachkala, Russia2Dagestan State University, Gadjieva Str. 43A, 367025, Makhachkala, Russia3University Bordeaux, CEA, CNRS, CELIA (Centre Laser Intense et Applications), UMR 5107, 33405 Talence, France4Dipartimento di Fisica ‘G. Occhialini’, Università di Milano-Bicocca, Milano, Italia(Received 15 April 2013; revised 30 May 2013; accepted 4 June 2013)AbstractWe present a recent numerical analysis of impedance mismatch technique applied to carbon equation of statemeasurements. We consider high-power laser pulses with a Gaussian temporal profile of different durations. We showthat for the laser intensity (≈1014 W/cm2) and the target design considered in this paper we need to have laser pulseswith rise-time less than 150 ps.Keywords: equation of state (EOS), high pressures, impedance mismatch technique1. IntroductionThe equation of state (EOS) of carbon at high pressures isa subject of interest for several branches of science, includ-ing astrophysics, material science, and applied engineering(first of all including fusion research). In particular, avery important point (in particular for the explanation oflarge magnetic fields of giant planets such as Uranus andNeptune) is the existence of a metallic phase of carbon[1–4].To reach it in laboratory conditions, it is possible to uselaser-driven shocks. The pressure (in Mbar) of such shockscan be estimated by P = 11.6 (I/1014)3/4 λ−1/4 (A/2Z)7/16(Z∗t/3.5)−1/8, where I is the laser intensity on the target inW/cm2, λ is the laser wavelength in µm, and A,Z, and Z∗,respectively, are the mass number, the atomic number, andthe effective ionization degree of the target, and the time tis in ns[5]. So intensities of the order of 1014 W/cm2, whichcan be obtained quite easily, allow getting pressures of theorder of 10 Mbar.A well-known experimental method to measure the EOSis based on the impedance mismatch technique and consistsin measuring the shock velocity of two different materials(test and reference) at the same time. The shock-wavemeasurements are realized by a streak camera recording theemission from the rear side of the shocked target. Usingtime-resolved imaging, we can experimentally determinethe times of the shock arrival for each part of targetCorrespondence to: A. Aliverdiev, Institute for Geothermal ResearchesDSC of Russian Academy of Sciences, Pr. Shamilya 39A, 367030,Makhachkala, Russia. Email: aliverdi@mail.ru(see Figure 1), and afterwards the velocity of the shockpropagating through the two steps, DAl and DC. Then ifthe EOS (and hence the shock adiabat) of the base material(aluminium) is known, we can calculate an EOS point forthe test material (carbon) as the intersection in the (P,U)plane of the line P = ρCDCU (momentum conservation law;ρC is the density of cold carbon) with the reflected isentropicrelease drawn from the intersection of P = ρAlDAlU (ρAlis the density of cold aluminium) with the aluminiumHugoniot adiabat (see Figure 2)[6,7].One of the critical points of this method is the effect ofthe temporal profile of the high-power pulse. Indeed, anideal shock can be produced only with a high-power flat-top laser pulse, and the analysis of the effect of the realtemporal profile of a high-power laser in experiments isimportant, because it can be a substantial contribution to thetotal experimental error. The aim of the present work was torealize a set of simulations for Gaussian pulses with differentdurations and to analyse the effect on the calculation ofshock velocities.2. SimulationsFor the realization of simulations we have used the hy-drocode MULTI (multigroup radiation transport in mul-tilayer foils)[8]. We have used the SESAME equationof state for aluminium[9] and porous carbon EOS cal-culated by MPQEOS[10] with a reduced initial density(1.6 g/cm3)[11,12], as presented in Ref. Ref. [13]. For each102Influence of a laser profile in impedance mismatch techniques applied to carbon EOS measurement 103Figure 1. Sketch of the configuration of EOS measurements using theimpedance mismatch technique. A streak camera measures the times ofthe shock arrival; the shock velocities DAl and DC are calculated from thedifference of these times.Figure 2. Calculation of the (P,U) EOS point for carbon from measuredDAl,DC and Al Hugoniot adiabat using the impedance mismatch method.case we have realized three different 1D ‘sub-simulations’for the three parts of the target: (i) Al 8 µm, (ii) Al 16.5 µm,and (iii) Al–C 11.5 µm + 9.5 µm corresponding to Al base,Al step, and carbon step (see Figure 1), and have determinedthe shock arrival times to the rear target surface, as in the realexperiment[13].We have tested four Gaussian laser profiles with the samepeak intensity (Imax = 2.05 × 1014 W/cm2) and full widthat half maximum (FWHM) durations τ = 200, 300, 450,and 600 ps. Gaussian profiles were calculated by I =Imax exp(−2.77 ( t−ττ )2) (see Figure 3). So the initial inten-sity at zero time was 6.3% of the maximum. Also we used anideal flat-top pulse of the same intensity and 450 ps durationfor reference.3. Results and discussionFigure 4 presents the dependence of the difference betweenshock arrivals for Gaussian pulses and the reference one (flattop) as a function of duration τ for the three parts of thetarget.If the rise-time of the Gaussian pulse is small (τ 6 300 psfrom Figure 4), the difference is the same for the base andboth steps. This implies that the shock velocity calculationsare not affected. Physically this means that for τ 6 300 psthe shock becomes stationary both in the base (8 µm thick)and in the steps. In this case the effect of the Gaussian pulsesis just to shift all breakout times by the same amount. WeFigure 3. Laser pulse profiles used in the simulations.Figure 4. The dependences of the difference between shock arrivals forGaussian pulses and the reference one (flat top) from τ for all threeparts of the target: (i) base (Al: 8 µm); (ii) Al step (Al: 16.5 µm);and (iii) carbon step (Al–C: 11.5 µm + 9.5 µm) – 1base,1Al and1C, correspondingly. All dependences are very close to each other forτ 6 300 ps.notice that these spatial profiles are not exactly the same(see Figure 5), but the same time differences for the shockbreakouts are enough for a correct calculation of shockvelocities.Simulations done for τ > 300 ps show that instead theshock has the time to become stationary in the steps (thedifference is indeed the same for the two steps) but notfor base. In this case the shock velocity cannot simply becalculated as D= thickness/(tstep − tbase).4. ConclusionOn the basis of hydro simulations, we can conclude that,with the considered laser intensity (≈1014 W/cm2) andtarget design, it is necessary to have the duration of theGaussian pulse not longer 300 ps. In the opposite case,the shock does not have the time to become stationarybefore the shock breaks out of the base. These results canbe extrapolated to pulses with any shape by saying thatthe pulse rise-time should be less than 150 ps. Dependingon target thickness, the pulse rise-time required will bedifferent; however, the method described here is general.104 A. Aliverdiev et al.Figure 5. Comparison of spatial profiles for the shocks initiated by flat-top and Gaussian (FWHM duration 300 ps) pulses. Lines 1 and 2 (dashed)are shock profiles for a flat-top laser pulse at 200 and 500 ps (close tothe shock breakout on the base and the carbon step). Lines 3 and 4 (solid)are shock profiles for a Gaussian laser pulse at 314 and 614 ps. We noticethat both profiles have the same time shift 1= 114 ps. Despite the profiledifferences the fronts for both shocks are very close to each other. Thelaser strikes from the right. Zero on x corresponds to the target front. Thevertical line at −11.5 µm is the initial Al–C interface. Ablation surfacesand Al–C interfaces for flat-top profiles at 200 and 500 ps are indicated(for 200 ps, the Al–C interface is the initial one).AcknowledgementsThe work was partially supported by ESF (SILMI, 3964),EU COST program, and RFBR (12-01-96500, 11-01-00707).References1. F. P. Bundy, Physica A 156, 169 (1989).2. M. P. Grumbach, and R. M. Martin, Phys. Rev. B 54, 15730(1996).3. M. Van Thiel, and F. H. Ree, Phys. Rev. B 48, 3519 (1993).4. A. A. Correa, S. A. Bonev, and G. Galli, PNAS 103, 1204(2006).5. D. Batani, A. Balducci, W. Nazarov, T. Lower, T. Hall,M. Koenig, B. Faral, A. Benuzzi, and M. Temporal, Phys.Rev. E. 63, 046410 (2001).6. Ya. B. Zel’dovich, and Yu. P. Raizer, Physics of Shock Wavesand High-Temperature Hydrodynamical Phenomena (Dover,New York, 2002).7. P. M. Celliers, G. W. Collins, D. G. Hicks, and J. H. Eggert,J. Appl. Phys. 98, 113529 (2005).8. R. Ramis, R. Schmalz, and J. Meyer-ter-Vehn, Comput. Phys.Commun. 49, 475 (1988).9. K. S. Holian ed. T-4 Handbook of Material Properties DataBases, Vol. 1C: Equations of State, LANL Report No. LA-10160-MS UC-34 (1984).10. A. Kemp, and J. Meyer-ter-Vehn, Nucl. Instrum. MethodsPhys. Res. A. 415, 674 (1998).11. A. Aliverdiev, D. Batani, R Dezulian, and T. Vinci, Radiat.Eff. Defects Solids 165, 566 (2010).12. A. Aliverdiev, D. Batani, R Dezulian, and T. Vinci,Nukleonika 56, 165 (2011).13. D. Batani, F. Strati, H. Stabile, M. Tomasini, G. Lucchini,A. Ravasio, M. Koenig, A. Benuzzi-Mounaix, H. Nishimura,Y. Ochi, J. Ullschmied, J. Skala, B. Kralikova, M. Pfeifer,Ch. Kadlec, T. Mocek, A. Prag, T. Hall, P. Milani, E. Bar-borini, and P. Piseri, Phys. Rev. Lett. 62, 065503 (2004).

influence of a laser profile in impedance mismatch techniques applied to carbon eos measurement

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influence of a laser profile in impedance mismatch techniques applied to carbon eos measurement

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