X-Ray Thomson Scattering in High Energy Density Plasmas
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REVIEWS OF MODERN PHYSICS, VOLUME 81, OCTOBER–DECEMBER 2009 X-ray Thomson scattering in high energy density plasmas Siegfried H. Glenzer L-399, Lawrence Livermore National Laboratory, University of California, P.O. Box 808, Livermore, California 94551, USA Ronald Redmer Institut für Physik, Universität Rostock, Universitätsplatz 3, D-18051 Rostock, Germany ͑Published 1 December 2009͒ Accurate x-ray scattering techniques to measure the physical properties of dense plasmas have been developed for applications in high energy density physics. This class of experiments produces short-lived hot dense states of matter with electron densities in the range of solid density and higher where powerful penetrating x-ray sources have become available for probing. Experiments have employed laser-based x-ray sources that provide sufficient photon numbers in narrow bandwidth spectral lines, allowing spectrally resolved x-ray scattering measurements from these plasmas. The backscattering spectrum accesses the noncollective Compton scattering regime which provides accurate diagnostic information on the temperature, density, and ionization state. The forward scattering spectrum has been shown to measure the collective plasmon oscillations. Besides extracting the standard plasma parameters, density and temperature, forward scattering yields new observables such as a direct measure of collisions and quantum effects. Dense matter theory relates scattering spectra with the dielectric function and structure factors that determine the physical properties of matter. Applications to radiation-heated and shock-compressed matter have demonstrated accurate measurements of compression and heating with up to picosecond temporal resolution. The ongoing development of suitable x-ray sources and facilities will enable experiments in a wide range of research areas including inertial confinement fusion, radiation hydrodynamics, material science, or laboratory astrophysics. DOI: 10.1103/RevModPhys.81.1625 PACS number͑s͒: 52.25.Os, 52.35.Fp, 52.50.Jm CONTENTS D. Detectors 1650 E. Photometrics 1650 V. X-ray Thomson Scattering Experiments 1651 I. Introduction 1625 A. Isochorically heated matter 1651 A. Overview 1625 B. Matter heated by supersonic heat waves 1654 B. Historical development 1627 C. Shock-compressed matter 1655 C. Physical properties of dense plasmas 1628 D. Coalescing shocks 1657 D. X-ray scattering regimes 1629 VI. Summary and Outlook 1658 E. Sensitivity of scattering spectra to plasma List of Acronyms and Definitions 1659 parameters 1629 Acknowledgments 1659 II. Facilities for X-Ray Thomson Scattering Experiments 1632 References 1660 III. Theory of the Dynamic Structure Factor 1634 A. General expressions 1634 B. Application to Thomson scattering 1635 I. INTRODUCTION C. Elastic scattering feature 1637 A. Overview D. Free-electron feature 1637 1. Two-component screening 1637 Accurate measurements of the plasma conditions in- 2. Ionic correlations and electronic screening 1638 cluding temperature, density, and ionization state in E. Bound-free transitions 1638 dense plasmas are important for understanding and F. Numerical results 1639 modeling high energy density physics experiments. For 1. Collision frequency 1639 applications in this regime, new scattering techniques 2. Electron feature of the dynamic structure have been developed by Glenzer, Gregori, Lee, et al. factor 1639 ͑2003͒ and Glenzer, Landen, et al. ͑2007͒ that make use 3. Bound-free spectrum 1641 of x rays to penetrate dense or compressed matter. This 4. Ion feature 1641 capability is particularly important for laboratory astro- G. Theoretical spectra 1642 physics and inertial confinement fusion ͑ICF͒ experi- IV. Experimental Techniques 1643 ments ͑Lindl et al., 2004; Remington et al., 2006͒, and is A. Design of scattering experiments 1643 broadly applicable in the dense plasma community. Ex- B. X-ray probe requirements 1645 amples of important applications include the measure- C. Spectrometers 1648 ment of compression and heating of shock-compressed 0034-6861/2009/81͑4͒/1625͑39͒ 1625 ©2009 The American Physical Society 1626 Siegfried H. Glenzer and Ronald Redmer: X-ray Thomson scattering in high energy … matter and the fundamental characterization of thermo- tional to the number of tightly bound electrons as well dynamic properties including phase transitions ͑Beule et as the static structure factor. The latter takes into ac- al., 1999, 2001; Fortov et al., 2007͒ and new states of count the dependence on the ion-ion correlations. For matter ͑Bonev, Schwegler, et al., 2004͒. Specifically, x-ray the noncollective scattering conditions where the static scattering is applicable as a tool to resolve fundamental structure factor approaches 1, the intensity of the elastic physics questions such as the equation of state of dense scattering feature provides an accurate measure of the matter ͑Collins et al., 1988; Young and Corey, 1995͒, ionization state. Absolute calibration is provided by structure factors in two-component plasmas ͑Hansen comparing with the inelastic scattering component and McDonald, 2006͒, limits of the validity of the ran- whose intensity is well known from the sum rules ͑Kohn dom phase approximation ͑RPA͒͑Pines and Bohm, and Sham, 1965͒. For isochorically heated matter where 1952; Bohm and Pines, 1953͒, and the role of collisions the ion density is known a priori, the ionization state ͑Reinholz et al., 2000; Redmer et al., 2005͒. inferred from the ratio of the inelastic Compton to the The spectrally resolving x-ray scattering technique is elastic Rayleigh scattering components yields the elec- now widely applied in many large ͑Gregori et al., 2004; tron density. Gregori, Glenzer, Chung, et al., 2006; Sawada et al., The collective properties of the dense plasmas can be 2007͒ and medium-size laboratories ͑Ravasio et al., 2007; accessed by the proper choice of the scattering angle and Kritcher, Neumayer, Castor, et al., 2008; Garcia Saiz, x-ray probe energy. In the forward scattering regime, Gregori, Gericke, et al., 2008͒ to study dense plasma collective plasmon ͑Langmuir͒ oscillations ͑Tonks and properties. Accurate and precise data are obtained simi- Langmuir, 1929͒ have been observed by Glenzer, lar to data from low density plasmas when optical Th- Landen, et al. ͑2007͒. The plasmon frequency shift from omson scattering was first introduced to study plasmas the incident x-ray probe energy directly provides the lo- in the 1960s. Powerful x-ray sources ͑Landen, Farley, et cal electron density via the Bohm-Gross ͑Bohm and al., 2001; Lee et al., 2003͒ take the place of optical lasers Gross, 1949͒ dispersion relation. Besides well-known to penetrate through dense or compressed matter and to thermal corrections, the dispersion relation in dense access the dense plasma physics regime with electron plasmas includes additional terms for degeneracy and densities of solid and above. These x-ray sources must quantum diffraction. Experiments in isochorically fulfill the stringent requirements ͑Urry et al., 2006͒ on heated solid-density plasmas show that the density from photon numbers and bandwidth for spectrally resolved downshifted plasmons agrees with the values inferred x-ray Thomson scattering measurements in single-shot from noncollective scattering. In addition, forward scat- experiments ͑Landen, Glenzer, et al., 2001͒. tering on plasmons is not dependent on knowledge of X-ray Thomson scattering was first demonstrated em- the ion density and is thus directly applicable to charac- ploying laser-produced He-␣ x-ray sources to perform terize compressed matter and to determine the optical scattering measurements in isochorically heated solid- properties. density matter ͑Glenzer, Gregori, Lee, et al., 2003; Glen- Plasmons are affected by Landau damping as well as zer, Gregori, Rogers, 2003͒. Measurements in backscat- electron-ion collisions. Thus, a consistent description of ter geometry have accessed the Compton scattering the plasmon spectrum describing both the frequency regime where the scattering process is noncollective and shift and the spectral shape requires a theory beyond the the spectrum shows the Compton downshifted line that RPA. Experiments have been successfully described is broadened by the thermal motion of the electrons. with the Mermin approach ͑Mermin, 1970; Höll et al., Thus, the inelastic scattering spectrum reflects the elec- 2004; and Thiele et al., 2006͒ that takes into account the tron velocity distribution function, and for a Maxwell- dynamic collision frequency for calculating damping. In Boltzmann distribution function, yields the electron cases where collisional damping is not the dominant temperature with high accuracy. For Fermi-degenerate mechanism, the Born approximation has been shown to states of matter, on the other hand, the Compton scat- be sufficient. In future studies of cold plasmas with small tering spectrum provides the Fermi energy and thus the Landau damping, plasmon measurements will provide electron density. Experiments observing these distribu- an experimental test on the theory of collisions yielding tions have been interpreted employing first-principles conductivity ͑Röpke, 1998; Redmer et al., 2003; Kuhl- methods ͑Pines and Bohm, 1952; Gregori, Glenzer, Roz- brodt et al., 2005; Höll et al., 2007͒, which is an important mus, et al., 2003; Redmer et al., 2005͒ that includes de- dense plasma property for radiation-hydrodynamic generacy effects and provide the plasma conditions with modeling of high energy density physics experiments. high accuracy.