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Relativistic shock waves induced by ultra-high laser pressure

  • Shalom Eliezer (a1) (a2), Noaz Nissim (a2), Erez Raicher (a2) (a3) and José Maria Martínez-Val (a1)


This paper analyzes the one dimensional shock wave created in a planar target by the ponderomotive force induced by very high laser irradiance. The laser-induced relativistic shock wave parameters, such as compression, pressure, shock wave and particle flow velocities, sound velocity and temperature are calculated here for the first time in the context of relativistic hydrodynamics. For solid targets and laser irradiance of about 2 × 1024 W/cm2, the shock wave velocity is larger than 50% of the speed of light, the shock wave compression is larger than 4 (usually of the order of 10) and the targets have a pressure of the order of 1015 atmospheres. The estimated temperature can be larger than 1 MeV in energy units and therefore very excited physics (like electron positron formation) is expected in the shocked area. Although the next generation of lasers might allow obtaining relativistic shock waves in the laboratory this possibility is suggested in this paper for the first time.


Corresponding author

Address correspondence and reprint requests to: Shalom Eliezer, Soreq Research Center, Yavne, Israel. E-mail:


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Basov, N.G., Guskov, S.Y. & Feoktistov, L.P. (1992). Thermonuclear gain of ICF targets with direct heating of the ignitor. J. Soviet Laser Res. 13, 396399.
Betti, R., Zhou, C.D., Anderson, K.S., Perkins, L.J., Theobald, W. & Sokolov, A.A. (2007). Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001/14.
Cauble, R., Phillion, D.W., Hoover, T.J., Holmes, N.C., Kilkenny, J.D. & Lee, R.W. (1993). Demonstration of 0.75 Gbar planar shocks in X-ray driven colliding foils. Phys. Rev. Lett. 70, 2102–2015.
Eliezer, S. & Hora, H. (1989). Double layers in laser produced plasmas. Phys. Rept 172, 339410.
Eliezer, S. & Martinez Val, J.M. (2011). The comeback of shock waves in inertial fusion energy. Laser Part. Beams 29, 175181.
Eliezer, S. & Pinhasi, S.V. (2013). Laser induced fast ignition made realistic by relativistic velocities-dream or reality?
Eliezer, S. (2002). The Interaction of High-Power Lasers with Plasmas. Boca Raton: CRC press.
Eliezer, S. (2012). Relativistic acceleration of micro-foils with prospects for fast ignition. Laser Part. Beams 30, 225232.
Eliezer, S. (2013). Shock waves and Equations of state related to laser plasma interaction. Laser-Plasma Interactions and Applications, 68th Scottish Universities Summer School in Physics (McKenna, P., Neely, D., Bingham, R. & Jaroszynski, D.A., Eds.), pp. 4978. Heidelberg: Springer Publication.
Eliezer, S. & Ricci, R.A., eds. (1991). High Pressure Equation of State: Theory and Application. Enrico Fermi School CXIII 1989. Amsterdam: North Holland.
Eliezer, S., Ghatak, A., Hora, H. & Teller, E. (2002). Fundamental of Equation of State. Singapore: World Scientific.
Eliezer, S., Henis, Z., Martinez Val, J.M. & Vorobeichik, I. (2000). Effects of different nuclear reactions on internal tritium breeding in deuterium fusion. Nucl. Fusion 40, 195207.
Eliezer, S., Martinez Val, J.M. & Pinhasi, S.V. (2013). Relativistic shock waves in the laboratory. Laser Part. Beams 31, 113122.
Eliezer, S., Nissim, N., Martinez Val, J.M., Mima, K. & Hora, H. (2014). Double layer acceleration by laser radiation. Laser Part. Beams 32, ???.
Esirkepov, T., Borghesi, M., Bulanov, S.V., Mourou, G. & Tajima, T. (2004). Highly efficient relativistic ion generation in the laser piston regime. Phys. Rev. Lett. 92, 175003/14.
Fortov, V.E. & Lomonosov, I.V. (2010). Shock waves and equations of state of matter. Shock Waves 20, 5371.
Hoffmann, D.H.H., Blazevic, A., Ni, P., Rosmej, O., Roth, M., Tahir, N.A., Tauschwitz, A., Udrea, S., Varentsov, D., Weyrich, K. & Maron, Y. (2005). Present and future perspectives for high energy density physics with intense heavy ion and laser beams. Laser & Part.Beams 23, 4754.
Hora, H., Lalousis, P. & Eliezer, S. (1984). Analysis of the inverted double layers produced by nonlinear forces in laser produced plasmas. Phys. Rev Lett. 53, 16501653.
Hora, H. (1991). Plasmas of High Temperatures and Density. Heidelberg: Springer.
Jackel, S., Salzmann, D., Krumbein, A. & Eliezer, S. (1983). Multishock compression of solid planar targets using tailored laser pulses. Phys. Fluids 26, 31383147.
Lalousis, P., Foldes, I.B. & Hora, H. (2012). Ultrahigh acceleration of plasma by picosecond terawatt laser pulses for fast ignition of fusion. Laser Part. Beams 30, 233242.
Lalousis, P., Hora, H., Eliezer, S., Martinez Val, J.M., Moustaizis, S., Miley, G.H. & Mourou, G. (2013). Shock Mechanisms by ultrahigh laser accelerated plasma blocks in solid density targets for fusion. Phys. Lett. A 377, 885888.
Landau, L.D. & Lifshitz, E.M. (1987). Fluid Mechanics. Oxford: Pergamon Press.
McQueen, R.G. (1991). Shock waves in condensed media: their properties and the equation of state of materials derived from them. In High Pressure Equation of State: Theory and Application. Enrico Fermi School CXIII 1989 (Eliezer, S. & Ricci, R.A., Eds.), pp. 101216. Amsterdam: North Holland.
Naumova, N., Schlegel, T., Tikhonchuk, V.T., Labaune, C., Sokolov, I.V. & Mourou, G. (2009). Hole boring in a DT pellet and fast ion ignition with ultraintense laser pulses. Phys. Rev. Lett. 102, 025002/14.
Piazza, A.D., Muller, C., Hatsagortsyan, K.Z. & Keitel, C.H. (2012). Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Modern Phys. 84, 11771228.
Russo, G. (1988). Stability properties of relativistic shock waves: Applications. Astrophys. J. 334, 707721.
Taub, A.H. (1948). Relativistic Rankine-Hugoniot Equations. Phys. Rev. 74, 328334.
Tabak, M., Hammer, J., Glinsky, M.E., Kruer, W.L., Wilks, S.C., Woodworth, J., Campbell, E.M., Perry, M.D. & Mason, R.J. (1994). Ignition and high gain with ultra-powerful lasers, Phys. Plasmas 1, 16261634.
Vogler, Z. & Temple, B. (2012). Simulation of general relativistic shock wave interactions by a locally inertial Godunov method featuring dynamical time dilation. doi:10.1098/rspa.2011.0355.
Zeldovich, Y.B. & Raizer, Y.P. (1966). Physics of Shock Waves and High Temperature Hydrodynamic Phenomena. New York: Academic Press Publications.


Relativistic shock waves induced by ultra-high laser pressure

  • Shalom Eliezer (a1) (a2), Noaz Nissim (a2), Erez Raicher (a2) (a3) and José Maria Martínez-Val (a1)


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