Theory of Thomson scattering in inhomogeneous media

Abstract

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.Fourth generation light sources hold the promise of improving our understanding of extreme states of matter by providing a probe which can penetrate through the enormous densities produced in inertial confinement fusion or laboratory astrophysics experiments. Thomson scattering by free electrons has emerged as a powerful diagnostic for such systems, through its extension from the optical through the x-ray regime, allowing it to take full advantage of the new capabilities provided by fourth generation light sources (e.g. LCLS, SACLA, European XFEL, SwissFEL) 1-3 . Thomson scattering allows for the measurement of density, temperature, and ionization state in plasmas, leading to an effective characterization of the plasma equilibrium state 1,4,5 , and progress in the understanding of the properties of high-energy-density matter has significantly relied upon this technique [6][7][8][9][10][11][12] . Thomson scattering has also been utilized for probing temperatures and magnetic fields in tokamaks 13,14 . Investigations using Thomson scattering to date have been based on the assumption of a homogenous or weakly inhomogeneous plasma. This limitation becomes particularly restrictive when considering the ultra-short x-ray pulses and near diffraction limited laser spot sizes of fourth generation light sources 15,16 . Under such conditions, large spatial and temporal gradients in the properties of matter are not negligible and are mainly determined by the extent of laser focus 17 . This situation is exemplified by inertial fusion experiments, where the capsule is compressed by a series of shocks 4,18 which introduce inhomogeneities on the scale of the particle mean free path (i.e., the shock width) and this significantly complicates the determination of the properties of the dense, compressed core in a scattering experiment 19 . Interpreting the scattering signals with models developed for homogenous equilibrium systems may thus lead to significant errors in the inferred properties of the matter.Here we dev...

Ab initiosimulations of the dynamic ion structure factor of warm dense lithium

“…In particular we find an ionization state of 1.0 in warm dense lithium which is lower than inferred in [27]. Finally, we check the effect of inhomogeneities [28] in the optically pumped, warm dense lithium target on the electron feature and calculate the ionization state based on the results of radiation-hydrodynamic simulations using a more realistic equation of state, where pressure ionization is considered. In addition, we propose to check the predicted dynamic properties of warm dense lithium in future high-resolution experiments at FELs.…”

“…The electron feature of each cell is calculated based on its local density and temperature; as inhomogeneity of the target affects the electron feature [28]. We are in this case neither on the stage of extracting all effects of density/temperature inhomogeneities for the available XRTS data nor diminish it from the noise.…”

Inverse problem instabilities in large-scale modeling of matter in extreme conditions

“…Because the data with the highest levels of uncertainty will be most affected, experimental results with large error bands should be treated with caution, especially if used as a benchmark for physical properties such as plasma correlations [14], or in determining the equation of state of extreme states of matter [20,22]. For the cases discussed here we deliberately used small uncertainties to constrain the parameters, and have neglected several additional sources of uncertainty For example, we have ignored the presence of gradients in the samples under investigation and the possibility that the measured outcome includes contributions from systems under very different conditions [48]. We have also ignored the effect of both model inaccuracy (e.g., in collision ionization models in atomic kinetics modelling [16]) and model inadequacy (e.g., breakdown of the Chihara decomposition in XRTS [49]).…”

Tracking the density evolution in counter-propagating shock waves using imaging X-ray scattering

“…1. Besides rigid graphite (RG), which is a porous polycrystalline system, we study pyrolytic graphite (PG) at a higher initial density of q 0 ¼ 2.2 g/cm 3 , which is non-porous and exhibits c-axis order along the surfacenormal.…”

“…One may avoid this dilemma by performing ultra-fast measurements on well-defined states, e.g., isochorically heated matter, 2 but this approach drastically reduces the phase space that can be probed. Alternatively, one needs to track carefully the evolution of the system, particularly its density and temperature, 3 to ensure probing of well-defined states or, at least, correctly averaging in time and space.…”