Relativistic shock waves induced by ultra-high laser pressure SHALOM ELIEZER, 1,2 NOAZ NISSIM, 2 EREZ RAICHER, 2,3 AND JOSÉ MARIA MARTÍNEZ-VAL 1 1 Institute of Nuclear Fusion, Polytechnic University of Madrid, Madrid, Spain 2 Soreq Research Center, Yavne, Israel 3 Hebrew University of Jerusalem, Jerusalem, Israel (RECEIVED 17 November 2013; ACCEPTED 7 January 2014) Abstract 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 velocityand temperature are calculated here for the first time in the context of relativistic hydrodynamics. For solid targets and laser irradiance of about 2 × 10 24 W/cm 2 , 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 10 15 atmospheres. The estimated temperature can be larger than 1 MeV in energy units and therefore veryexcited 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. Keywords: Equation of state; Laser; Plasma; Relativistic shock wave; Ultra-high power 1. INTRODUCTION The modern science of high pressure started with the pio- neering work of William Percy Bridgman who received the Physics Nobel prize in 1946 for this research. This is studied experimentally in the laboratory by using static and dynamic techniques. In static experiments, the sample is squeezed between pistons or anvils. In the dynamic experiments shock waves are created. Since the passage time of the shock wave is short in comparison with the dis- assembly time of the shocked sample, one can do shock wave research for any pressure that can be supplied by a driver. The shock wave science in the laboratory is the driver for creating high energy density physics (Eliezer & Ricci, 1991; Eliezer et al., 2002; Hora, 1991; Hoffmann et al., 2005). It is well known that the interaction of a high power laser with a planar target creates a one dimensional (1D) shock wave (Fortov & Lomonosov, 2010; Eliezer, 2013). The theoretical basis for laser induced shock waves analyzed and measured experimentally so far is based on plasma abla- tion. For laser intensities 10 12 W/cm 2 < I L < 10 16 W/cm 2 and nanoseconds pulse duration hot plasma is created. This plasma exerts a high pressure on the surrounding material, leading to the formation of an intense shock wave moving into the interior of the target. The momentum of the out- flowing plasma balances the momentum imparted to the compressed medium behind the shock front similar to a rocket effect. The highest pressures so far of about 1 Gbar in the lab- oratory have been achieved with high power lasers (Eliezer, 2002; Cauble et al., 1993). For I L < 10 16 W/cm 2 , the ab- lation pressure is dominant. For I L ≫ 10 16 W/cm 2 , the radiation pressure is the dominant pressure at the solid- vacuum interface and the ablation pressure is negligible. In this last case, the ponderomotive force drives the shock wave. In this paper, we are interested in laser irradiances I L > 10 21 W/cm 2 in order to get a relativistic laser induced shock wave. The theoretical foundation of relativistic shock waves is based on relativistic hydrodynamics (Landau & Lifshitz, 1987) and was first analyzed by Taub (1948). Relativistic shock waves may be of importance in intense stellar explosions or in col- lisions of extremely high energy nuclear particles. Further- more, relativistic shock waves may be a new route for fast ignition nuclear fusion (Eliezer & Martinez Val, 2011; Eliezer, 2012). Furthermore, relativistic acceleration of micro-foil has been suggested with the very high laser irradiances (Esirkepov et al., 2004; Eliezer et al., 2013). 243 Address correspondence and reprint requests to: Shalom Eliezer, Soreq Research Center, Yavne, Israel. E-mail: shalom.eliezer@gmail.com Laser and Particle Beams (2014), 32, 243–251. © Cambridge University Press, 2014 0263-0346/14 $20.00 doi:10.1017/S0263034614000056