Abstract
1 Introduction
Laser–plasma interaction (LPI) at intensities
The interest in this interaction regime mainly concerns the physics of inertial confinement fusion (ICF), where the laser–plasma coupling and the generation of HE can considerably affect the implosion of the fuel pellet. In particular, accurate knowledge of parametric instabilities is crucial in the shock ignition (SI) concept[
Most of the experiments devoted to investigating LPI for ICF studies have been carried out at intensities of
Sign up for High Power Laser Science and Engineering TOC. Get the latest issue of High Power Laser Science and Engineering delivered right to you!Sign up now
A full numerical investigation of LPI in SI conditions is also impracticable because of the huge computational costs due to the large plasma size; therefore, 2D particle-in-cell simulations of LPI in this regime are presently limited to an interaction time of a few picoseconds (that is, a time much shorter than the duration of the shock ignition spike). It is worth remarking that 2D and 3D simulations are needed to model laser filamentation, spraying, cavitation and side scattering, which can be important in the SI regime. Advanced fully kinetic PIC simulations[
To date, only a few experiments on LPI at SI-relevant intensities have been carried out in moderate kilojoule-class laser facilities, as for example at OMEGA[
In recent years, we investigated LPI and shock generation at the Prague Asterix Laser System (PALS) facility by using a 300 ps laser pulse at
In this paper we investigate LPI and HE generation of the full energy (
2 Experimental setup
The laser pulse (300 ps), used in the fundamental mode (
Thin multilayer targets were used. The front layer, namely the interaction layer, with thickness ranging from 10 to
A scheme of the optical diagnostics used for investigating the parametric instabilities is reported in Figure
K
3 Interaction conditions
The plasma density where parametric instabilities are driven and their timing depend on local and instantaneous plasma conditions (temperature and density scalelength) and the laser intensity. Interaction conditions were modelled by radiative-hydrodynamic simulations carried out with the codes CHIC[
The resulting values of electron temperature and density scalelength
The plasma conditions, determined by plasma hydrodynamics, and the resulting interaction scenario depicted above, can be significantly modified by considering micrometre-scale variations of temperature and density, which are produced by the profile smoothing of the laser beam. The use of a random phase plate, in fact, limits the longitudinal and the transverse spatial coherence of the beam, subdividing the profile into small beamlets with random phases; according to simple calculations[
4 Reflectivity, backward- and side-stimulated Raman scattering
Light backscattered in the focusing cone was dominated by laser reflection and SBS light (
Typical time-integrated spectra of SRS scattered light up to
While the IR spectra acquired at
A deeper insight into the experimental data can be obtained by calculating the thresholds of BRS and SRSS at the densities of interest. According to Liu
5 Half-integer harmonic spectra
A valuable tool for investigating TPD and SRS is the observation of half-integer harmonic spectra, produced by the nonlinear coupling of laser light (
All the half-integer harmonic spectra exhibited several peaks, produced by different instabilities or by instabilities driven at different densities. In Figure
The blue-side feature in the
The spectrum of
6 Timing of TPD and SRS instabilities
Time-resolved spectroscopy of three-halves harmonics is here used for investigating the growth of TPD and BRS along the plasma density profile. Two distinct spectra are reported in Figure
The two peaks produced by EPWs at density close to
At times comparable to the disappearance of the TPD peaks, the peak produced by convective BRS becomes visible. In some shots, as shown in Figure
Another interesting piece of information is that BRS is initially driven as convective instability at a lower plasma density, corresponding to the lower wavelength edge of the BRS spectrum in Figure
Now that local conditions (density, time) where SRS and TPD are driven have been discussed, it is possible to inspect the relation between these instabilities and the experimental HE temperatures.
The energy of HE generated by BRS can be calculated by considering the phase velocity
An estimate of the energy of HE generated by absolute TPD (or hybrid TPD/aSRS) is more tricky and less reliable. By considering the phase velocity of EPWs retrieved by the half-harmonic spectra, we obtain HE temperature values higher than
7 PIC simulations
Kinetic simulations of LPI have been performed with the relativistic electromagnetic PIC code EPOCH[
The simulation box has dimensions of
The first five picoseconds of the interaction is significantly influenced by a fast increase in the laser intensity, much faster than in the experiment. Thus we present here the results for the quasi-stationary stage of interaction, corresponding to the time from 5 to 9 ps. The longitudinal profile of the electron energy flux allows one to localize spatial zones where the laser absorption takes place. The electrons propagating into the target behind the critical density are responsible for a transport of about 10% of the incident laser energy flux, which gives the overall collisionless absorption. This electron energy flux is dominated by HE with a distribution which can be best fitted by the sum of two exponential functions with temperatures of 49 and 85 keV. The absorption process takes place in three spatially separated regions. About 1.3% of laser energy is absorbed in a low-density plasma in front of the quarter critical density surface, with the absorption rate being almost constant in this region. This region includes also the region where SRSS is observed in the experiment; however, since SRSS is driven more favourably in the s-polarization plane, the current simulation is not able to quantify this instability. About the same energy fraction (1.3%) is absorbed in a narrow region extending to about
Analysis of the simulation results shows that the overall interaction process is dominated by the laser beam filamentation, followed by SBS and SRS (see Figure
For the sake of clarity, a summary of the amount of laser energy spent in different channels, including both experimental and numerical data, is reported in Table
Coll. | SBS/laser | BRS | SRSS | HE | ||
---|---|---|---|---|---|---|
Abs. | Back | All | ||||
Experimental | – | 14%–20% | – | 0.6%–4% | * | 5.3% |
PIC | – | 30% | 3% | * | 10% | |
CHIC simul. | 9% | – | – | – | – |
Table 1. Energy spent in different energy channels during the interaction. The * symbol indicates mechanisms which have been observed but not quantified
Distribution of the electromagnetic field intensity in the simulation box averaged over 3 ps during the quasi-steady phase of the interaction is plotted in Figure
8 Conclusions
In the present experiment, LPI of an infrared laser pulse with a multilayer target at shock ignition intensity was characterized in detail. According to hydrodynamic simulations, the plasma temperature reaches values in excess of 4 keV during the interaction. The combination of laser intensity
On one hand, the value of plasma temperature determines the density range where convective BRS is driven. When temperature increases, Landau damping of BRS daughter plasma waves pushes the instability towards denser regions. On the other hand, plasma temperature is expected to rule the balance between TPD and SRS, because the threshold of TPD strongly increases in hot plasmas, leading to the damping of the instability. In our experiment, the presence of EPWs in the proximity of
We want also to emphasize that a joint observation of
A meaningful result of the present work is also the measurement of SRSS, which was rarely experimentally observed. This was measured at an angle of
The results of 2D PIC simulations performed in the relevant interaction conditions confirm the framework delineated by the measurements and contribute to shedding further light on LPI and collisionless absorption mechanisms. PIC results show that filamentation instability rules the transport and the absorption of the laser light, in agreement with thresholds of classical theory. Filamentation is driven in the underdense plasma, in front of and slightly beyond the
Finally, experimental data, CHIC hydrodynamic simulations and PIC kinetic simulations suggest the presence of two HE components: the lower energy one, with a temperature around 40 keV, generated by the damping of BRS waves, and the higher energy one, with a temperature of
References
[1] R. Betti, C. D. Zhou, K. S. Anderson, L. J. Perkins, W. Theobald, A. Solodov. Phys. Rev. Lett., 98(2007).
[2] R. Nora, W. Theobald, R. Betti, F. J. Marshall, D. T. Michel, W. Seka, B. Yaakobi, M. Lafon, C. Stoeckl, J. Delettrez, A. A. Solodov, A. Casner, C. Reverdin, X. Ribeyre, A. Vallet, J. Peebles, F. N. Beg, M. S. Wei. Phys. Rev. Lett., 114(2015).
[3] W. Theobald, R. Nora, W. Seka, M. Lafon, K. S. Anderson, M. Hohenberger, F. J. Marshall, D. T. Michel, A. A. Solodov, C. Stoeckl, D. H. Edgell, B. Yaakobi, A. Casner, C. Reverdin, X. Ribeyre, A. Shvydky, A. Vallet, J. Peebles, F. N. Beg, M. S. Wei, R. Betti. Phys. Plasmas, 22(2015).
[4] L. J. Perkins, R. Betti, K. N. LaFortune, W. H. Williams. Phys. Rev. Lett., 103(2009).
[5] A. R. Bell, M. Tzoufras. Plasma Phys. Control. Fusion, 53(2011).
[6] J. Trela, W. Theobald, K. S. Anderson, D. Batani, R. Betti, A. Casner, J. A. Delettrez, J. A. Frenje, V. Yu. Glebov, X. Ribeyre, A. A. Solodov, M. Stoeckl, C. Stoeckl. Phys. Plasmas, 25(2018).
[7] R. Yan, C. Ren, J. Li, A. V. Maximov, W. B. Mori, Z.-M. Sheng, F. S. Tsung. Phys. Rev. Lett., 108(2012).
[8] R. S. Craxton, K. S. Anderson, T. R. Boehly, V. N. Goncharov, D. R. Harding, J. P. Knauer, R. L. McCrory, P. W. McKenty, D. D. Meyerhofer, J. F. Myatt, A. J. Schmitt, J. D. Sethian, R. W. Short, S. Skupsky, W. Theobald, W. L. Kruer, K. Tanaka, R. Betti, T. J. B. Collins, J. A. Delettrez, S. X. Hu, J. A. Marozas, A. V. Maximov, D. T. Michel, P. B. Radha, S. P. Regan, T. C. Sangster, W. Seka, A. A. Solodov, J. M. Soures, C. Stoeckl, J. D. Zuegel. Phys. Plasmas, 22(2015).
[9] R. K. Kirkwood, J. D. Moody, J. Kline, E. Dewald, S. Glenzer, L. Divol, P. Michel, D. Hinkel, R. Berger, E. Williams, J. Milovich, L. Yin, H. Rose, B. MacGowan, O. Landen, M. Rosen, J. Lindl. Plasma Phys. Control. Fusion, 55(2013).
[10] E. I. Moses, R. N. Boyd, B. A. Remington, C. J. Keane, R. Al-Ayat. Phys. Plasmas, 16(2009).
[11] A. Casner, T. Caillaud, S. Darbon, A. Duval, I. Thfouin, J. P. Jadaud, J. P. LeBreton, C. Reverdin, B. Rosse, R. Rosch, N. Blanchot, B. Villette, R. Wrobel, J. L. Miquel. High Energy Density Phys., 17, 2(2015).
[12] O. Klimo, V. T. Tikhonchuk. Plasma Phys. Control. Fusion, 55(2013).
[13] O. Klimo, J. Psikal, V. T. Tikhonchuk, S. Weber. Plasma Phys. Control. Fusion, 56(2014).
[14] C. Riconda, S. Weber, V. T. Tikhonchuk, A. Hron. Phys. Plasmas, 18(2011).
[15] L. Yin, B. J. Albright, H. A. Rose, K. J. Bowers, B. Bergen, D. S. Montgomery, J. L. Kline, J. C. Fernandez. Phys. Plasmas, 16(2009).
[16] L. Yin, B. J. Albright, K. J. Bowers, W. Daughton, H. A. Rose. Phys. Rev. Lett., 99(2007).
[17] G. J. Morales, T. M. O’Neil. Phys. Rev. Lett., 28, 417(1972).
[18] C. Z. Xiao, Z. J. Liu, C. Y. Zheng, X. T. He. Phys. Plasmas, 23(2016).
[19] S. Weber, C. Riconda. High Power Laser Sci. Eng., 23, e6(2015).
[20] C. Z. Xiao, H. B. Zhuo, Y. Yin, Z. J. Liu, C. Y. Zheng, Y. Zhao, X. T. He. Plasma Phys. Control. Fusion, 60(2018).
[21] W. Theobald, R. Nora, M. Lafon, A. Casner, X. Ribeyre, K. S. Anderson, R. Betti, J. A. Delettrez, J. A. Frenje, V. Yu. Glebov, O. V. Gotchev, M. Hohenberger, S. X. Hu, F. J. Marshall, D. D. Meyerhofer, T. C. Sangster, G. Schurtz, W. Seka, V. A. Smalyuk, C. Stoeckl, B. Yaakobi. Phys. Plasmas, 19(2012).
[22] C. Goyon, S. Depierreux, V. Yahia, G. Loisel, C. Baccou, C. Courvoisier, N. G. Borisenko, A. Orekhov, O. Rosmej, C. Labaune. Phys. Rev. Lett., 111(2013).
[23] S. Depierreux, P. Loiseau, D. T. Michel, V. Tassin, C. Stenz, P. E. Masson-Laborde, C. Goyon, V. Yahia, C. Labaune. Phys. Plasmas, 19(2012).
[24] P. Koester, L. Antonelli, S. Atzeni, J. Badziak, F. Baffigi, D. Batani, C. A. Cecchetti, T. Chodukowski, F. Consoli, G. Cristoforetti, R. De Angelis, G. Folpini, L. A. Gizzi, Z. Kalinowska, E. Krousky, M. Kucharik, L. Labate, T. Levato, R. Liska, G. Malka, Y. Maheut, A. Marocchino, P. Nicolai, T. O’Dell, P. Parys, T. Pisarczyk, P. Raczka, O. Renner, Y. J. Rhee, X. Ribeyre, M. Richetta, M. Rosinski, L. Ryc, J. Skala, A. Schiavi, G. Schurtz, M. Smid, C. Spindloe, J. Ullschmied, J. Wolowski, A. Zaras. Plasma Phys. Control. Fusion, 55(2013).
[25] D. Batani, L. Antonelli, S. Atzeni, J. Badziak, F. Baffigi, T. Chodukowski, F. Consoli, G. Cristoforetti, R. De Angelis, R. Dudzak, G. Folpini, L. Giuffrida, L. A. Gizzi, Z. Kalinowska, P. Koester, E. Krousky, M. Krus, L. Labate, T. Levato, Y. Maheut, G. Malka, D. Margarone, A. Marocchino, J. Nejdl, Ph. Nicolai, T. O’Dell, T. Pisarczyk, O. Renner, Y. J. Rhee, X. Ribeyre, M. Richetta, M. Rosinski, M. Sawicka, A. Schiavi, J. Skala, M. Smid, Ch. Spindloe, J. Ullschmied, A. Velyhan, T. Vinci. Phys. Plasmas, 21(2014).
[26] D. Batani, L. Antonelli, F. Barbato, G. Boutoux, A. Colatis, J. L. Feugeas, G. Folpini, D. Mancelli, Ph. Nicolai, J. Santos, J. Trela, V. Tikhonchuk, J. Badziak, T. Chodukowski, K. Jakubowska, Z. Kalinowska, T. Pisarczyk, M. Rosinski, M. Sawicka, F. Baffigi, G. Cristoforetti, F. DAmato, P. Koester, L. A. Gizzi, S. Viciani, S. Atzeni, A. Schiavi, M. Skoric, S. Guskov, J. Honrubia, J. Limpouch, O. Klimo, J. Skala, Y. J. Gu, E. Krousky, O. Renner, M. Smid, S. Weber, R. Dudzak, M. Krus, J. Ullschmied. Nucl. Fusion, 59(2019).
[27] D. Baton, M. Koenig, E. Brambrink, H. P. Schlenvoigt, C. Rousseaux, G. Debras, S. Laffite, P. Loiseau, F. Philippe, X. Rybeyre, G. Schurtz. Phys. Rev. Lett., 108(2012).
[28] M. Hohenberger, W. Theobald, S. X. Hu, K. S. Anderson, R. Betti, T. R. Boehly, A. Casner, D. E. Fratanduono, M. Lafon, D. D. Meyerhofer, R. Nora, X. Ribeyre, T. C. Sangster, G. Schurtz, W. Seka, C. Stoeckl, B. Yaakobi. Phys. Plasmas, 21(2014).
[29] G. Cristoforetti, A. Colatis, L. Antonelli, S. Atzeni, F. Baffigi, D. Batani, F. Barbato, G. Boutoux, R. Dudzak, P. Koester, E. Krousky, L. Labate, Ph. Nicolai, O. Renner, M. Skoric, V. Tikhonchuk, L. A. Gizzi. Europhys. Lett., 117, 35001(2017).
[30] G. Cristoforetti, L. Antonelli, S. Atzeni, F. Baffigi, F. Barbato, D. Batani, G. Boutoux, A. Colaitis, J. Dostal, R. Dudzak, L. Juha, P. Koester, A. Marocchino, D. Mancelli, Ph. Nicolai, O. Renner, J. J. Santos, A. Schiavi, M. M. Skoric, M. Smid, P. Straka, L. A. Gizzi. Phys. Plasmas, 25(2018).
[31] S. Atzeni, A. Marocchino, A. Schiavi. Phys. Plasmas, 19(2012).
[32] L. Antonelli, J. Trela, F. Barbato, G. Boutoux, P. Nicolai, D. Batani, V. Tikhonchuk, D. Mancelli, S. Atzeni, A. Schiavi, F. Baffigi, G. Cristoforetti, S. Viciani, L. A. Gizzi, M. Smid, O. Renner, J. Dostal, R. Dudzak, L. Juha, M. Krus. submitted to Phys. Plasmas(2019).
[33] A. Visco, R. P. Drake, D. H. Froula, S. H. Glenzer, B. B. Pollock. Rev. Sci. Instrum., 79(2008).
[34] J. Breil, S. Galera, P. H. Maire. Comput. Fluids, 46, 161(2011).
[35] S. Atzeni, A. Schiavi, F. Califano, F. Cattani, F. Cornolti, D. Del Sarto, T. Liseykina, A. Macchi, F. Pegoraro. Comput. Phys. Commun., 169, 153(2005).
[36] A. Colaitis, G. Duchateau, X. Ribeyre, Y. Maheut, G. Boutoux, L. Antonelli, Ph. Nicolai, D. Batani, V. Tikhonchuk. Phys. Rev. E, 92(2015).
[37] D. Batani, C. Bleu, Th. Lower. Eur. Phys. J. D, 19, 231(2002).
[38] H. A. Rose, D. F. Dubois. Phys. Fluids B, 5, 590(1993).
[39] D. Pesme, S. Huller, J. Myatt, C. Riconda, A. Maximov, V. T. Tikhonchuk, C. Labaune, J. Fuchs, S. Depierreux, H. A. Baldis. Plasma Phys. Control. Fusion, 44, B53(2002).
[40] C. S. Liu, M. N. Rosenbluth, R. B. White. Phys. Fluids, 17, 1211(1974).
[41] B. B. Afeyan, E. A. Williams. Phys. Rev. Lett., 75, 4218(1995).
[42] W. Seka, B. B. Afeyan, R. Boni, L. M. Goldman, R. W. Short, K. Tanaka, T. W. Johnston. Phys. Fluids, 28, 2570(1985).
[43] F. Baffigi, G. Cristoforetti, L. Fulgentini, A. Giulietti, P. Koester, L. Labate, L. A. Gizzi. Phys. Plasmas, 21(2014).
[44] L. A. Gizzi, D. Giulietti, A. Giulietti, P. Audebert, S. Bastiani, J. P. Geindre, A. Mysyrowicz. Phys. Rev. Lett., 76, 2278(1996).
[45] T. D. Arber, K. Bennett, C. S. Brady, A. Lawrence-Douglas, M. G. Ramsay, N. J. Sircombe, P. Gillies, R. G. Evans, H. Schmitz, A. R. Bell. Plasma. Phys. Control. Fusion, 57(2015).
[46] G. Q. Liao, Y. T. Li, C. Li, L. N. Su, Y. Zheng, M. Liu, W. M. Wang, Z. D. Hu, W. C. Yan, J. Dunn, J. Nilsen, J. Hunter, Y. Liu, X. Wang, L. M. Chen, J. L. Ma, X. Lu, Z. Jin, R. Kodama, Z. M. Sheng, J. Zhang. Phys. Rev. Lett., 114(2015).
[47] Y. J. Gu, O. Klimo, Ph. Nicolai, S. Shekhanov, S. Weber, V. T. Tikhonchuk. High Power Laser Sci. Eng., 7(2019).
Set citation alerts for the article
Please enter your email address