Frequency-dependent reflectivity of shock-compressed xenon plasmas H. Reinholz* School of Physics, University of Western Australia, 35 Stirling Highway, Crawley, Western Australia 6009, Australia Yu. Zaporoghets, V. Mintsev, and V. Fortov Institute of Problems of Chemical Physics, Chernogolovka, Moscow Region 142432, Russia I. Morozov Institute for High Energy Densities of RAS, IHED-IVTAN, Izhorskaya 13/19, Moscow 127412, Russia G. Ro ¨ pke FB Physik, University of Rostock, Universita ¨tsplatz 3, D-18051 Rostock, Germany Received 23 February 2003; revised manuscript received 7 May 2003; published 26 September 2003 Results for the reflection coefficient of shock-compressed dense xenon plasmas at pressures of 1.6 –20 GPa and temperatures around 30 000 K using laser beams of wavelengths 1.06  m and 0.694  m are presented, which indicate metallic behavior at high densities. For the theoretical description of the experiments, a quan- tum statistical approach to the dielectric function is used. The comparison with molecular dynamics simula- tions is discussed. We conclude that reflectivity measurements at different wavelengths can provide informa- tion about the density profile of the shock wave front. DOI: 10.1103/PhysRevE.68.036403 PACS numbers: 52.25.Mq, 05.30.Fk, 71.45.Gm, 52.27.Gr I. INTRODUCTION Recently, dense plasmas showing the transition from di- electric to metallic behavior were investigated extensively 1–4. Highly compressed matter can be produced by shock waves from explosions or high-intense laser pulses. Heavy ion beams or z-pinch discharges are also used to create dense plasmas. For the diagnostics of properties in such highly compressed plasmas, optical measurements are most favor- able, e.g., the reflectivity is expected to give information on the free-charge carrier density. Reflectivity measurements under shock wave compres- sion have been performed for different materials. For in- stance, Basko and co-workers 3 discussed experiments on Al and Si. Whereas the electron density is estimated to change at the shock wave front within a small interval of several nanometers, the change in temperature occurs within a layer of about 0.3  m. Of high interest are recent experi- ments in liquid deuterium and water 4 which show a satu- ration of the reflectivity at values above 50%, indicating that a conducting state was attained. We will consider xenon plasmas. In addition to former measurements of the reflectivity at a wavelength of 1.06  m 1 results at the wavelength of 0.694  m 2 are reported. At pressures in the region of 1.6 –20 GPa and temperatures around 30 000 K a strong increase of the reflectivity has been observed indicating metallization. In papers by Kurilenko and Berkovsky 5,6, the first se- ries of experiments by Mintsev and Zaporoghets 1 was ana- lyzed. The dielectric function was calculated via a dynamical collision frequency. The Born approximation was improved by including structure factor and local field corrections, but no consistent description of the measured reflectivities has been achieved. A different approach to the reflectivity was taken by Norman and co-workers 7,8, who proposed that the assumption of nonequilibrium excitations of plasma waves might provide a reasonable agreement with the ex- perimental results. However, the structure of possible excita- tions of plasma waves in the shock wave front is an open question. The detailed discussion of the reflectivity experiments re- quires a consistent theory for the frequency- and wave- number-dependent dielectric function. The application of the Drude model for a step-like shock wave front, as performed in Ref. 1, does not lead to a satisfying explanation of the experimental data. Improvements in evaluating the dielectric function 9, such as the dynamical and nonlocal behavior of the collision frequency, shows only minor effects in the re- flectivity. In this paper, we will discuss a quantum statistical approach to the dielectric function as well as an alternative approach based on molecular dynamics MD simulations. An extended discussion of different effects, including the influence of the neutral particles, on the collision frequency will be presented. However, it will be shown that the use of the dielectric function in local thermodynamic equilibrium and the assumption of a sharp shock wave front are not ap- propriate to describe the experiments considered here. In contrast to a step-like profile of the shock wave front, a more general approach would take into account the variation of the plasma parameters in space and time. Because of ion- ization processes the plasma formation exhibits a relaxation time so that the density profile of the free-charge carriers is considered to be spatially extended across the propagating shock wave front. In a recent paper 9, it was argued that the reflectivity data at 1.06  m 1 can be interpreted assuming a finite width of the free-carrier density front profile. Having *Fax +49 0381-498 2857. Email address: heidi@physics.uwa.edu.au PHYSICAL REVIEW E 68, 036403 2003 1063-651X/2003/683/03640310/$20.00 ©2003 The American Physical Society 68 036403-1